Chapter 29. Optics and Quantum Electronics

Optics and Quantum Electronics

Academic Staff Prof. James G. Fujimoto, Prof. Erich P. Ippen, Professor Franz X. Kärtner

Research Staff, Visiting Scientists and Affiliates Dr. Cristian Antonelli, Dr. Yu Chen, Dr. Richard Ell, Dr. Ariel Gordon, Dr. Katherine Hall, Dr. Robert Huber, Dr. Faith Omer Ilday, Dr. Christian Jirauschek, Dr. David Kielpinski, Dr. Frank Ludwig, Dr. Oliver Muecke, Dr. Norihiko Nishizawa, Dr. Lelia A. Paunescu, Dr. Marco Presi, Dr. Luciano Socci, Dr. Hideyuki Sotobayoshi, Dr. Kenya Suzuki, Dr. Kenji Taira, Dr. Maciej Wojtkowski

Graduate Students Aaron Aguirre, Mohammed Araghchini, Andrew Benedick, Jonathan Birge, Hyunil Byun, David Chao, Jeff Chen, Marcus Dahlem, Mingyan Fan, Fuwan Gan, Blaise Gassend, Felix Grawert, Paul Herz, Aristidis Karalis, Jung-Won Kim, Tony Ko, Andrew Kowalevicz, Jonathan Morse, Ali Motamedi, Milos Popovic, Peter Rakich, Michelle Sander, Hanfei Shen, Jason Sickler, Aleem Siddiqui, Vivek Srinivasan, Axel Winter

Technical and Support Staff Dorothy Fleischer, Donna Gale

Research Areas and Projects

Ultrashort Pulse Laser Technology

Phase-Coherent Spectrum from the Visible to the Infrared by Combining Ultrabroadband Ti:sapphire and Cr:forsterite Lasers Two-Dimensional Spectral Shearing Interferometry for Ultrashort Pulse Characterization Resonant Silicon-Germanium Saturable Bragg Reflectors Cavity-Enhanced Optical Parametric Chirped-Pulse Amplification Soliton self-frequency shift from 1.03 µm to 1.55 µm and Related Timing Jitter Synchronously pumped few-cycle Titanium-Sapphire Laser Multipass Cavity Femtosecond Laser Development

Femtosecond Frequency Combs and Phase Control

Carrier-Envelope Phase Dynamics and Noise Analysis in Octave-Spanning Ti:Sapphire Lasers High Repetition Rate, Broadband, Mode-Locked Ti:Sapphire Laser Composite Plate for Carrier-Envelope Phase Control Balanced Optical-RF Phase Detector Passively Modelocked High-Repetition Rate Erbium-doped Bismuth Oxide Glass Waveguide Laser Broadband Frequency Comb Generation at 1 µm with a Passively Modelocked High-Repetition Rate Bulk Ytterbium-glass Laser Development of Stable Frequency Combs at High Repetition Rates Using Fiber Lasers and Supercontinuum Generation

Ultrafast Phenomena and Quantum Electronics

Multimode Phenomena in Quantum Cascade Lasers Characterization of Optical Switches and Wavelength Converters Using Two-Color Heterodyne Pump-Probe Nonlinear Effects in Photonic Crystal Fibers – Nd:Glass Femtosecond Laser

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Frequency Swept Lasers and Fourier Domain Mode Locking (FDML)

Physics and Technology of Ultrafast X-ray Sources

The Ehrenfest Theorem and the Single Atom HHG Spectrum Role of Many Electron Effects in High Harmonic Generation Femtosecond Timing Distribution in X-ray Free Electron Lasers

Photonics and Devices

Design of High-Index-Contrast Microring-Resonator Add-Drop Filters Polarization Insensitive Microphotonics: A Key Milestone for High Index Contrast Integrated Photonics Hitless Filter Tuning and Universally Balanced Interferometers Global Design Rules for Silicon Waveguides and Resonators Optimizing Design of High-Index-Contrast Adiabatic Structures Efficient, Out-of-plane Fiber-to-chip Coupler Designs Fiber to Chip Couplers Silicon Electronic Photonic Integrated Circuits for High Speed Analog to Digital Conversion Silicon Electro-Optic Modulator Unpolarized Supercontinuum Sources for Broadband Studies of 1D and 3D Photonic Crystals Ultra-wide Tuning of Photonic Microcavities via Evanescent Field Perturbation Propagation without Diffraction in a 2D Photonic Crystal for Optical Interconnects

Laser Micro-Machining of Photonic Devices

Publications, Presentations, Thesis and Books

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Ultrashort Pulse Laser Technology

Phase-Coherent Spectrum from the Visible to the Infrared by Combining Ultrabroadband Ti:sapphire and Cr:forsterite Lasers

Sponsors Office of Naval Research (ONR) N00014-02-1-0717 Air Force Office of Scientific Research (AFOSR) FA9550-04-1-0011

Project Staff Jung-Won Kim and Professor Franz X. Kärtner

Coherent superposition of multiple mode-locked lasers has been recognized as one of the most promising techniques to generate well-isolated, highly-stable single-cycle optical pulses beyond the bandwidth limitations of gain media and laser mirrors. To synthesize single-cycle optical pulses, we have worked on the synthesis of optical combs spanning from the visible to the infrared range from mode-locked Ti:sapphire and Cr:forsterite lasers.

As one step closer toward the single-cycle pulse synthesis, we present the generation of a phase- coherent spectrum [1] spanning from 600 nm to 1500 nm from a long-term stable Ti:sapphire and Cr:forsterite laser system with residual timing and phase rms-jitters of 375 as and 570 as, respectively.

Figure 1 shows the schematic of the synchronization set-up. Ultrabroadband Ti:sapphire (600- 1200nm) and Cr:forsterite (1100-1500nm) lasers are combined at the broadband 50:50 beam splitter [2]. For timing synchronization, a balanced cross-correlator [3] is used. Once tight synchronization between the two laser pulses is obtained, a heterodyne beat signal between the two lasers in the spectral overlap region is obtained. This beat signal is locked to a local oscillator (fLO in Fig. 1) by modulating the pump power of the Ti:sapphire laser with an AOM.

Figure 1: Schematic outline of the synchronization set-up. AOM, acousto-optic modulator; APD, Avalanche photodiode; BPF, band-pass filter; Cr:fo, Cr:forsterite laser oscillator; GD, group delay element; GDD, group delay dispersion; LF, loop filter; PD, digital phase detector; SFG, sum frequency generation; Ti:sa, Ti:sapphire laser oscillator.

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To lock the difference in carrier-envelope offset frequency, ∆fceo, between the two lasers, we filter out a 15 nm wide part of the spectrum in the overlap spectral range at 1120 nm and detect it with a high-speed InGaAs Avalanche photodetector. Fig. 2 (a) shows the RF spectrum of the output from the photodetector. Heterodyne beatnotes (mfR±∆fceo, m=integer) show ~30 dB SNR measured with a 30 kHz resolution bandwidth. The beatnote at 215 MHz is bandpass filtered, amplified, and frequency divided by a factor of 16 to increase the locking range. This beatnote is locked to an RF synthesizer, fLO, at ~13.43 MHz via modulating intra-cavity energy of the Ti:sapphire laser with an AOM (see Fig. 1).

(a) (b) Figure 2: (a) RF spectrum (RBW 30 kHz) of the beat signals from the InGaAs APD output in Fig. 1. Red shadowed region indicates the bandpass filter centered at 215 MHz that selects the beat signal used for phase-locking. (b) In-loop phase error signal from the digital phase detector (PD in Fig. 1). Red line shows the free-running phase error signal over 300 µsec time scale. Blue line shows the residual in-loop phase error for 1 second when it is locked. The residual phase jitter from 1 Hz to 1 MHz is 0.38π rad (570 as). Note that the phase errors shown here are already scaled to the full range, i.e., [-16π, +16π] range.

Figure 2 (b) shows the output from the digital phase detector for the free-running and locked states with two different time scales (300 µs and 1 s respectively). When it is locked, the in-loop integrated rms phase noise is 0.38π radians measured from 1 Hz to 1 MHz. This is equivalent to 570 as rms phase jitter from 1 Hz to 1 MHz. To our knowledge this is the lowest reported phase jitter between two independent mode-locked lasers [4]. The main reason for this improvement is due to the very low timing jitter between the two lasers achieved by the balanced cross-correlator. Further improvements are clearly possible by optimization of the phase-locked loop and noise reduction in the Cr:forsterite laser which seems to be the main reason for the large remaining carrier-envelope phase noise. This large noise currently prevents us from locking the difference carrier-envelope frequency to zero by homodyne detection and synthesizing a single-cycle pulse. Note, this cannot be achieved with conventional offset locking in a long-term stable way because offset locking introduces an uncontrolled path difference between the two laser outputs. In conclusion, we have presented a phase-coherent ultrabroadband optical spectrum ranging from the visible to the infrared by timing synchronization and phase-locking of mode-locked Ti:sapphire and Cr:forsterite lasers. In addition to the low sub-femtosecond timing jitter demonstrated previously [3], a sub-femtoseond rms phase jitter between the two lasers of 0.38π rad (570 as) measured from 1Hz to 1MHz is demonstrated. It is expected that further noise reduction enables a phase jitter much less than 2π which opens up the possibility to generate single-cycle pulses at 1 µm from a long-term stable setup.

References: [1] J. Kim, T. R. Schibli, L. Matos, H. Byun and F. X. Kaertner, “Phase-coherent spectrum from ultrabroadband Ti:sapphire and Cr:forsterite lasers covering the visible to the infrared”, Proceedings of Ultrafast Optics Conference 2005, Paper M3-5, Nara, Japan, Sep 2005.

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[2] J. Kim, J. R. Birge, V. Sharma, J. G. Fujimoto, F. X. Kaertner, V. Scheuer, G. Angelow, “Ultrabroadband beam splitter with matched group delay dispersion”, Opt. Lett. 30, 1569 (2005).

[3] T.R. Schibli, J. Kim, O. Kuzucu, J. Gopinath, S.N. Tandon, G.S. Petrich, L.A. Kolodziejski, J.G. Fujimoto, E.P. Ippen, and F.X. Kaertner, Opt. Lett. 28, 947 (2003).

[4] A. Bartels, N. R. Newbury, I. Thomann, L. Hollberg, and S. A. Diddams, Opt. Lett. 29, 403 (2004).

Two-dimensional spectral shearing interferometry for ultrashort pulse characterization

Sponsors Office of Naval Research (ONR) N00014-02-1-0717 National Science Foundation ECS-0501478 Air Force Office of Scientific Research (AFOSR) FA9550-04-1-0011

Project Staff Jonathan R. Birge, Richard Ell, and Professor Franz X. Kärtner

As few-cycle pulses have become common, spectral shearing interferometry (SPIDER [1]) has become a proven method for measuring the spectral phase of such pulses [2, 3]. Here, we present a two-dimensional spectral shearing (2DSI) technique which, in contrast to SPIDER, requires only the non-critical calibration of the shear frequency and does not perturb the pulse before up-conversion. Rather than encode phase as a sensitively calibrated fringe in the spectral domain, this method robustly encodes phase along a separate dimension, greatly reducing demands on the spectrometer and allowing for complex phase spectra to be measured with high accuracy over extremely large bandwidths, potentially exceeding an octave.

In the present scheme, the pulse under test is up-converted with two chirped pulse copies. The two chirped quasi-CW signals are created in an interferometer and mixed with the short pulse in a Type-II crystal (see Fig. 1). The two up-converted copies are sheared spectrally, but are collinear and temporally identical (they essentially form a single pulse). The delay of one of the chirped pulses is scanned over a few optical cycles by vibrating the corresponding mirror in the interferometer. This is tantamount to scanning the zeroth-order phase of one of the pulse copies. The spectrum of the output pulse is recorded as a function of this phase delay, yielding a 2-D intensity spectrum that is given by ωτ=−Ω+−−Ω+ ω ω ω τ φ ω φ ω IAA( ,φφ ) 2 ( ) ( )cos[cw  ( ) ( )] D.C. (1) 2 τωg()Ω+O ( Ω ) where τφ and ωCW are the delay and local frequency, respectively, of the quasi-CW signal being scanned, A(ω) is the magnitude of the up-converted pulse spectrum, and φ(ω) is the spectral phase. The under-bracketed term is the first-order finite difference of the spectral group delay multiplied by the shear frequency.

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Fig. 1. Schematic of 2DSI optical setup.

A simple two-dimensional raster plot of the raw spectra (see Fig. 2) reveals the shifted pulse λ spectrum along the -axis, with fringes along the τφ-axis that are shifted by an amount proportional to the group delay at the corresponding wavelength. The user can thus immediately ascertain the salient properties of the complex spectrum simply by looking at the raw output of the measurement: each spectral component is vertically shifted in proportion to its actual shift in time. Precise quantitative determination of the fringe phase (and thereby group delay spectrum) can be directly obtained from the output with FFTs taken along the phase axis, with no iterative processing or filtering required.

Fig. 2. Raw output of 2DSI for: (a) 5 fs pulse and (b) the same pulse dispersed by 1 mm of fused silica.

The only calibration needed is for the shear, Ω. This calibration can be done very accurately and easily by measuring the pulse before and after transmission through a known dispersive element. Multiple shears can be used to measure a given pulse as a self-consistent verification that no spurious absolute phase errors have occurred. This ability also allows for a wide range of pulse widths to be measured by the same setup.

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It is not necessary to know the length or rate of the scan, so long as it is relatively linear over the measurement and long enough to determine a phase. Only the relative phase of the fringes matters in (1) and so the technique is robust to experimental noise. This fact also greatly simplifies the implementation and analysis of 2DSI.

Fig. 3. Group delay measurement of 1 mm of fused silica.

To gauge the relative accuracy of the method, we measured a few-cycle (~5 fs FWHM) pulse from a prismless Ti:sa laser [4]. We then introduced a 1 mm fused silica plate and measured the dispersed pulse. Raw output of the scans is shown in Fig. 2. The resulting group delay, obtained by directly subtracting the computed group delays from two measurements, matches the theoretical value well (Fig. 3). The difference curve is smooth despite significant group delay ripple in the individual pulses (caused by the chirped mirrors in the laser) evidenced in Fig. 2. The fused silica plate was not used to calibrate the shear for this experiment.

Fig. 4. Predicted interferometric autocorrelation for 5 fs pulse.

To demonstrate the absolute accuracy of the system, we performed an interferometric autocorrelation (IAC) on the same 5 fs pulse and compared it to that predicted by the spectral phase obtained from our 2DSI measurement and a separately measured spectrum. The predicted and experimental IAC traces are shown in Fig. 4. They conform well, though with slight deviations that we attribute largely to limitations in the IAC technique for few-cycle pulses (note, for example, that the IAC is not absolutely symmetric, as it ideally should be).

In summary, 2DSI does not require the dispersive splitting of the measured pulse that is characteristic of SPIDER, nor the associated highly sensitive calibration of pulse delay. This, together with the significant relaxation on spectrometer resolution, renders 2DSI extremely well

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suited for the measurement of wide-bandwidth pulses, including those with potentially complicated spectral phase. Further work is underway to optimize the sensitivity and to increase the scanning frequency to video rates to enable online laser optimization. We are also investigating the possibility of single-shot 2DSI using tilted wavefronts and a 2-D CCD sensor.

References [1] C. Iaconis and I. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort pulses,” IEEE JQE 35, 501–509 (1999).

[2] L. Gallmann, D. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10-fs optical pulses: a comparison,” Appl. Phys. B 70, S67–S75 (2000).

[3] K. Yamane, Z. Zhang, K. Oka, R. Morita and M. Yamashita, “Optical pulse compression to 3.4 fs in the monocycle region by feedback phase compensation,” Optics Letters 28, 2258–2260 (2003).

[4] Venteon UltraBroad, NanoLayers GmbH, www.nanolayers.de.

Resonant Silicon-Germanium Saturable Bragg Reflectors

Sponsors National Science Foundation (NSF) ECS-0322740 Defense Advanced Research Agency (DARPA) W911NF-04-1-10431 Air Force Office of Scientific Research (AFOSR) FA9550-04-1-0011

Project Staff Hyunil Byun, Felix Grawert, Ali Motamedi, Professor Erich Ippen, Professor Franz X. Kärtner

We demonstrate that resonant coatings on a Saturable Bragg Reflector (SBR) can lower the saturation fluence and increase the modulation depth by enhancing the field intensity inside the absorber layer. In this report, we show a resonant silicon-germanium SBRs that has a four times lower saturation fluence and a four times increased modulation depth.

An SBR can be used to passively mode-lock a laser by its intrinsic property of an intensity- dependent reflectivity. An SBR is composed of an absorber layer on the dielectric mirror stack. In earlier work, III-V compound semiconductor materials have been used for SBR’s. However, for on-chip integrated lasers on the silicon platform group-IV semiconductors such as silicon or germanium can be much more easily integrated in a CMOS compatible process. Using such absorbers we have demonstrated previously 220fs pulses from a bulk Er/Yb-glass laser at 167MHz repetition rate [1,2].

As we aim for higher repetition rates for a mode-locked laser, the fluence on the saturable absorber needs to decrease. Because, at higher repetition rates the intracavity pulse energy is reduced. In order to overcome this problem, the necessary fluence for a saturable absorber used for CW mode-locking is lowered by putting a additional coating on top of a standard SBR which enhances the field intensity inside the absorber layer. Therefore, the resonantly-coated SBR has effectively a lower saturation fluence and bigger modulation depth than a standard SBR without resonant coating since the fluence at the absorber layer is increased at a given incident fluence.

Three-layer top and five-layer top coatings have been designed. As more layers are deposited for resonance enhancement, the reflectivity of the coatings increase and the field in the absorber layer is more enhanced. The target field intensity for the resonant coatings is shown in Table 1. The resulting absorption and enhancement of the peak fluence are given in Table 2.

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Table 1. Layer thickness for resonant coatings. Table 2. Absorption and peak field intensity depending on the number of layers of resonant coatings. The intensity of 3-layers 5-layers incident beam is set to 100% for a relative comparison. Original SBR - - Peak field Absorption SiO2 534nm 560nm intensity in Ge at 1550nm Ta2O5 181nm 190nm layer SiO2 267nm 280nm No Ta2O5 0nm 190nm resonant 0.75% 32% SiO2 0nm 280nm coating Air - - 3-layers 1.6% 67% 5-layers 3.0% 130%

In order to achieve the field enhancement in Table 1, resonant coatings were deposited on the original SBR structure (Figure 5). The thickness of each coating is specified in Table . The low- index material closer to the original structure starts with a half wavelength thickness and the subsequent layers are quarter wavelength thick to function as a reflector. Resonant coatings 4.0 Germanium 6 pairs 3.5 5 2 O 2 2

3.0 SiO Ta SiO 2.5 Silicon active Index r

Ref 2.0 Si substrate 1.5

1.0 0.0 1.5 2.0 2.5 3.0 3.5 4.0

z(µm) four times larger field enhanced by resonant coatings original field without resonant coatings Figure 5. Structure of SiGe-SBR with five layers of resonant coatings

(b) (a)

Figure 6. (a) Pump-probe traces of the previous SiGe-SBR without resonant coatings. (b) Pump-probe traces of the resonantly-coated SiGe-SBR taken at various fluence values.

The nonlinear response of the device was characterized by degenerate pump-probe measurements with 150fs pulses from an OPO centered at 1540nm (Figure 6). At a pulse energy fluence of 9.2 µJ/cm2 a maximum modulation depth of 0.52% was reached. This modulation depth is four times larger than that of the previous SBR and the corresponding fluence is four times smaller [2]. This measurement results agree with the simulation which showed a field intensity enhancement by factor of four.

Although resonant coatings can provide enhanced absorption and modulation depth, they can bring unwanted side effects. With those resonant coatings, the field intensity increases not only in

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the absorber layer but also in the back mirror. Thus eventual losses in the back mirror are also enhanced.

In conclusion, we developed resonant silicon germanium SBRs which have smaller saturation fluence and higher modulation depth by a factor of four when compared to standard SBRs. These SBRs will be applied to passively mode-locked lasers with higher repetition rates where the pulse energy is reduced.

References

1. Felix J. Grawert. PhD Thesis, MIT, 2005

2. F. J. Grawert, S. Akiyama, J. T. Gopinath, F. O. Ilday, J. Liu, H. Shen, K. Wada, L. C. Kimerling, E. P. Ippen and F. X. Kärtner, Appl. Phys. Lett. 74, 3927~3929 (1999)

Cavity-Enhanced Optical Parametric Chirped-Pulse Amplification

Sponsors National Science Foundation (NSF) ECS-0501478 Air Force Office of Scientific Research (AFOSR) FA9550-04-1-0011

Project Staff Prof. F. Ömer Ilday, Aleem Siddiqui, Dr. Oliver D. Muecke, and Prof. Franz. X. Kärtner

Development of robust and inexpensive techniques for the amplification of few-cycle pulses will have tremendous impact in diverse fields, including high-harmonic generation. Recently, coherent addition of pulses in an enhancement cavity has been proposed and demonstrated as a method of short-pulse amplification [1]. However, this method gets increasingly difficult for short pulses due to intra-cavity dispersion and self-phase modulation. Lately, there is much interest in optical parametric chirped-pulse amplification (OPCPA) [2]. Utilizing virtual energy states, there is no storage of the pump light in parametric amplification, necessitating synchronous pumping with comparable pump and signal pulse durations. Thus, a high-energy pump source with picosecond pulses and excellent beam quality is required.

Here, we report a novel scheme, which conceptually combines the OPCPA and enhancement cavity techniques (Fig. 1): The pump beam is coherently enhanced in an external cavity, which contains a nonlinear crystal phase-matched for parametric amplification of a signal pulse. The cavity is transparent at the signal wavelength. The stretched signal pulses are synchronized and time-gated to overlap spatially and temporally with the pump beam and undergo parametric amplification once the cavity is loaded. This way, signal pulses with a bandwidth supporting few- cycle pulses can be amplified without the limitations set by the cavity. Cavity-enhanced OPCPA extends the analogy of parametric amplification to regular amplification one step further; the cavity assumes the role of pump light storage with the product of the cavity roundtrip time and the finesse corresponding to the gain relaxation time.

Several major advantages can be identified. The pump light itself can be in the picosecond range or longer, thus dispersion ceases to be a limitation to the enhancement cavity. With increasing finesse of the cavity, the pump source has only to provide lower peak powers, opening up the use of laser sources which excel in high average power, but are limited in peak power, such as fiber amplifiers. The high-finesse cavity will act as an excellent spatial filter for the pump beam, ensuring a high beam quality for the amplified pulse.

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Fig. 1. Schematic of the cavity-enhanced OPCPA. Nonlinear crystal 1 and (optional) nonlinear crystal 2 are for parametric amplification and nonlinearity management, respectively.

The dynamics of the cavity-enhanced OPCPA can be understood in two independent steps, which can be analyzed separately. During the loading phase, the nonlinear crystal is a passive element. Once the cavity is fully loaded, the signal pulse is triggered and makes a single pass through the cavity. Thus, parametric amplification is not influenced by the enhancement cavity. Then, the entire sequence is repeated.

Pump enhancement factors approaching 50 and parametric gain larger than 20 dB can be realized with 1.0µm pump and 1.55 µm signal, using periodically poled lithium niobate (PPLN), which already represents a significant advance. Gain is given by G=0.25(1+ exp(gl)), where for PPLN, g = 5.2 (Ip/GW/cm2)0.5/mm. Thus, for an intensity of about 0.5 GW/cm2 in a 2 mm-long crystal, input to output gain of about 26dB is achieved. The peak phase shift due to the Kerr nonlinearity per roundtrip in the crystal is 5.6 x 10-3, which allows for an addition of about 50 pulses.

At higher peak powers, Kerr nonlinearity will eventually pose a limitation by causing the cavity modes to shift dynamically. We show that this can be overcome by nonlinearity management utilizing cascaded quadratic processes [3]. These processes provide self-defocusing Kerr nonlinearity, permitting temporal and spatial compensation of n2 to first order [4]. We numerically simulated the loading of a cavity with a pulse train from a high-power laser at 1064 nm. The cavity comprises a 2 mm-long BBO crystal for parametric amplification and dispersion-compensating mirrors. A spot size of r=60 µm in a 2 mm-long crystal results in a nonlinear phase shift per roundtrip of 3.6 x10-2rad/MW. For nonlinearity compensation with the cascade process, another BBO crystal of equal length is added. The benefits of nonlinearity management are illustrated in Fig. 2(a). The cavity finesse is 100π. Without compensation, about 50 pump pulses can be added up to reach an intra-cavity pulse power of 0.5 MW. Due to the less favorable χ(2) / χ(3) ratio of BBO, this leads to a maximum parametric gain of only 7.6 dB. Using nonlinearity compensation, pump pulses with even 100 times higher peak power can attain the theoretical limit of 100 times enhancement. At a peak power of 5 MW, small-signal parametric gain of 37 dB is expected. In these calculations, the pulse duration is fixed at 10 ps. For shorter pulses, the buildup process becomes complicated due to the interplay of nonlinearity and dispersion (Fig. 2(b)). Nonlinearity management becomes even more crucial in experiments utilizing nonlinear crystals with less favorable ratios of gain to self-phase modulation.

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Fig. 2. Results of numerical simulations: (a) Loading of the cavity with and without nonlinearity compensation. Solid (dashed) lines depict intra-cavity energy (peak power) enhancement. (b) Intra-cavity buildup factor as a function of the peak power of the pump pulses with and without compensation of the nonlinearity. The lines connecting the dots are only a guide to the eye.

In conclusion, we propose a new technique, cavity-enhanced OPCPA as a practical route to high average and peak power sources of few-cycle optical pulses. The role of the cavity is analogous to the storage of pump light in an excited atomic state in regular amplification. In order to reach even higher energies, nonlinearity management can be utilized. Practical implementation of this scheme using fiber lasers is underway. Thus far, we have obtained single-pass OPCPA using an Er-fiber laser, synchronized with a Yb-fiber laser, which seeds a solid-state amplifier. The enhancement cavity is currently under construction.

References [1] E. O. Potma, C. Evans, X. S. Xie, R. J. Jones, and J. Ye, “Picosecond-pulse amplification with an external passive optical cavity,” Opt. Lett. 28, 1835-1837 (2003).

[2] A. Dubietis, G. Jonusauskas, A. Piskarskas, “Powerful femtosecond pulse generation by chirped and stretched pulse parametric amplification in BBO crystal,” Opt. Commun. 88, 433-440 (1992).

[3] F. Ö. Ilday, and F. W. Wise, “Nonlinearity management: a route to high-energy soliton fiber lasers,” J. Opt. Soc. Am. B 19, 470-476 (2002).

[4] F. Wise, L. Qian, X. Liu, “Applications of cascaded quadratic nonlinearities to femtosecond pulse generation,” J. Nonlin. Opt. Phys. Mat. 11, 317-338 (2002), and references therein.

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Soliton Self Frequency Shift from 1.03 µm to 1.55 µm and Related Timing Jitter

Sponsors Office of Naval Research - N00014-02-1-0717

Project Staff Jeff Chen, Dr. Omer Ilday, and Professor Franz X. Kärtner

The soliton self-frequency shift (SSFS) in optical fibers is a well-known phenomenon and applications such as widely tunable sources have been demonstrated in the past [1, 2]. In this paper, we present one of the longest SSFS to our knowledge, comparable to [3], connecting the wavelengths of 1.03 µm and 1.55 µm where powerful rare earth doped fiber amplifiers are available. This experiment opens up opportunities for applications such as seeding of parametric amplifiers or the pursuit of carrier-envelope phase independent clockworks, since the difference frequency between 1.04 µm and 1.5 µm is at 3.39 µm, where a transportable frequency standard exists [4]. Frequency metrology applications are critically dependent on the coherence properties of the frequency-shifted pulse. We measure the timing jitter of the output with respect to the input pulse and trace its origin back to laser intensity noise.

Numerical simulations guided us to use NL-3.0-975 photonic crystal fiber (PCF) from Crystal- -1 -1 2 2 Fibre with a nonlinear coefficient γ= 25 W Km and β2= -8 ps /km at 1.03 µm and -33 ps /km at 1.55 µm. The experimental setup is shown in figure 1(a). Pulses at 1.03 µm with energy of 0.24 nJ are generated from an ytterbium doped fiber laser with a repetition rate of 33 MHz. An ytterbium-doped fiber amplifier followed by a grating pair compressor produces nearly transform- limited pulses with 78 fs duration and 3.8 nJ of energy. These pulses are coupled into a 1.5 m- long PCF via an objective lens. The pulse energy in the PCF is 1.5 nJ. The output from the PCF is connected to an erbium doped fiber amplifier (EDFA), which boosts the energy of the frequency-shifted pulse at 1.55 µm to 1.2 nJ. The pulse width of the shifted pulse at 1.55 µm is measured to be 714 fs without dispersion compensation.

(a) Er Fiber Amplifier 1.0 1.55µm PCF 0.8 Unabsorbed 980nm 0.6 Yb Fiber pump light Objective Laser Lens 0.4 Intensity (A.U)

1.03µm 0.2

0.0 600 800 1000 1200 1400 1600 Yb Fiber Grating Pair Isolator Amplifier wavelength (nm) Compressor Fig. 1. (a) Experiment setup to generate 1.55 µm pulse from a 1.03 µm source. (b) Normalized pulse spectrum measured by an optical spectrum analyzer before (dashed line) and after the PCF (solid line).

Normalized pulse spectra before and after the frequency shift are shown in figure 1(b). We are able to control the amount of the frequency shift across the entire spectral range by adjusting the launched pulse energy into the PCF, while the spectrum of the red-shifted pulse keeps a soliton- like shape. Even longer self-frequency shifts are possible with a longer PCF and/or higher pulse energy.

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A simplified model for the timing jitter between the Raman shifted pulse and the original pulse entering the PCF can be derived from the well-known formula for frequency shift of a first order soliton undergoing SSFS [5]: 1 γ 4 E 4 ∆ω (z) =− 0 T z, (1) R β 3 R 30 | 2 | where β2 is the GVD of the fiber, TR is the Raman response time, z is the incremental fiber length, E0 is the pulse energy, γ is the nonlinear coefficient of the fiber. The timing shift is simply: L ∆t(L) = β ∆ω (z')dz'= β ∆ω (L)L / 2 (2) 2 ∫ R 2 R 0 where L is the total fiber length. The relative intensity noise (RIN) of the laser, characterized by its normalized power spectral density SRIN, causes therefore a timing jitter with spectral density St, which scales as: = ∆ 2 (3) St ( f ) 16 t (L)SRIN ( f ) Experimentally, the shifted component is spectrally filtered and photo detected to generate harmonics of the repetition rate. Figure 2(a) shows that the measured timing jitter spectrum obtained by electronically mixing the harmonics at 1.3 GHz of the frequency-shifted component and the direct output of the Yb amplifier. The timing jitter calculated using Eq. (3) is in good agreement with the measured jitter as shown in Figure 2(b). The integrated measured timing jitter are 47 fs, 60 fs, and 140 fs for the pulses shifted to 1250 nm, 1350 nm, and 1450 nm respectively, where the majority of the noise contributions arise from 1 kHz to 1 MHz frequency range. This large timing jitter is clearly an obstacle for the intended frequency metrology applications. However, it should be possible to suppress the RIN by using a noise eater.

-28 -28 10 10 -4 10 S Density RINSpectra -29 Measured Jitter Shifted to 1250nm 10 /Hz)

/Hz) -29 2 2 10 Shifted to 1350nm RIN Before PCF -30 -6 Shifted to 1450nm 10 Calculated Jitter 10 (S (S t

t -30 10 -31 10 10-8 10-31 10-32 -10 -33 10 -32 10 10 RIN -34 -12

10 (1/Hz) -33 10 10 10-35 -34 -14 10 -36 10 10 Jitter DensitySpectra S Jitter Spectra Density S Density Jitter Spectra 10-35 10-37 101 102 103 104 105 106 101 102 103 104 105 106 Frequency (Hz) Frequency (Hz) 2(a) 2(b) Fig. 2. (a) Measured timing jitter spectral density. (b) Calculated timing jitter spectral density at 1350nm with an integrated timing jitter of 57 fs, compared to measured timing jitter spectral density at 1350nm, with an integrated value of 60fs.

In summary, we have achieved SSFS over 520 nm, from 1.03 µm to 1.55 µm, connecting the two wavelength ranges, where powerful fiber amplifiers are available. The timing jitter added by the SSFS process was studied theoretically and experimentally. We expect this source to find applications in seeding of parametric amplifiers and assuming successful use of noise suppression techniques, as clock works for frequency metrology systems.

Reference [1] K. S. Abedin and F. Kubota, IEEE J. Sel. Topics in Quant. Electron. 10, 1203 (2004). [2] H. Lim, F. Ö. Ilday, and F. W. Wise, Conference on Lasers and Electro-Optics, 1701 – 1702, 2003 [3] D. T. Reid, I.G. Cormack, W.J. Wadsworth, et al., J. Modern Optics 49 (5-6): 757-767, 2002 [4] O. D. Mücke et al., Opt. Lett. 29, 2806 (2004). [5] G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001), Chap. 5.

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Synchronously pumped few-cycle Titanium-Sapphire Laser

Sponsors Air Force Office of Scientific Research (AFOSR) FA9550-04-1-0011

Project Staff Dr. Richard Ell, and Professor Franz X. Kärtner

Kerr-lens mode-locked Titanium-Sapphire (Ti:sapphire) laser oscillators are the dominant work horses in the field of ultrafast spectroscopy, optical frequency metrology, amplified systems, and many other research fields where pulse durations in the range from 5-100 fs and several hundred mW of output power are required [1]. Kerr-lens mode locking is generally not self-starting and particularly few-cycle, high-repetition rate oscillators suffer from poor starting behavior and require fast mechanical perturbations to initiate mode locking. We overcome this limitation by experimentally investigating the possibility of employing a mode locked pump source.

Pumping Ti:sapphire lasers with a mode-locked pump laser has many advantages. First of all, the Kerr-lens mode locking becomes self-starting and does not require active starting mechanisms [2]. Especially, high repetition rate systems with repetition frequencies up to 1 GHz benefit from this approach. Far more general, it is very interesting to study the behavior of few-cycle Ti:sapphire lasers when using mode-locked pump sources instead of the widely used continuous wave (CW) sources. From earlier publications [2] it was a priori not clear if for few-cycle pulses <10 fs self-starting is still possible since timing is much more critical than for the demonstrated 30 fs [2]. It is of scientific interest to study how the laser dynamics is influenced by pulsed excitation if the lasers are free running or actively synchronized. Also, mode-locked pump lasers are far easier to frequency double via second-harmonic generation thereby enlarging the range of possible pump lasers to for example mode-locked, frequency-doubled solid-state or fiber lasers.

In the experiments, we used a commercial, frequency-doubled picosecond Nd:YVO4 laser as a pump source. The laser emits a maximum of 6.5 W of green (532nm) pump light with pulse durations on the order of 7ps. The Ti:sapphire laser was a home-built, broadband, octave- spanning oscillator [1] that could also be modified to emit longer, tunable pulses around 100 fs. One end mirror of the Ti:sapphire laser was mounted on a translation stage to adapt the cavity length to the repetition rate of the pump laser.

(a) (b) ~ 5-10ms average power power level mode-locked

power level SHG detector signal (a.u.) CW power

0.0 0.4 0.8 1.2 1.6 2.0 1.050 1.060 1.070 1.080 1.090 time (s) time (s)

Figure 1. (a): Fundamental and second harmonic average power of the self-starting modelocked Ti:sapphire laser with a chopper wheel in the intracavity beam illustrating the fast and reliable self-starting behavior. (b): Magnification of the temporal evolution of the fundamental average power. The transient from CW operation towards modelocked operation typically lasts 5-10 ms.

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For approximately equal repetition frequencies (100 MHz), the Ti:sapphire laser becomes self- starting [3]. This is very reliable for a wide range of pulse durations (6-100 fs) and within a detuning range of roughly +/-5 µm. In terms of oscillator alignment and optimization of the Kerr- lensing process, and the overall behavior of the laser, there is no difference to the case of CW pumping. To analyze the self-starting behavior in more detail, we introduced a chopper wheel into the intracavity beam of the Ti:sapphire laser and detected the emitted fundamental and second- harmonic light. Figure 1 (a) displays the periodic and reliable self-starting by showing the fundamental and second-harmonic power. In Figure 1(b), a close look reveals the complex dynamics observed during the build-up of the modelocked pulses inside the cavity. The build-up time is on the order of 5-10ms. This is about one to two orders of magnitude slower than typical build-up times for standard KLM lasers [4]. When the two laser cavities are not actively synchronized, it is interesting to examine the residual modulation of the emitted laser pulses. Figure 2 shows the RF spectrum of the Ti:sapphire pulses that exhibit a sideband modulation of – 60 dBc. In the optical domain this corresponds to only 0.1% intensity modulation.

0 ) RBW=10Hz

-20

-40

-60

-80

RF-spectral power density (dBc)

99.890 99.900 99.910 99.920 99.930 RF-frequency (MHz)

Figure. 2. Radio-frequency spectrum of the quasi-synchronously pumped Ti:sapphire. The repetition frequency of the ps-pump laser is detuned by about 5 kHz and matches the gray dotted line. The output power of the Ti:sapphire laser is modulated by only –30 dBc, corresponding to a 60 dB suppression in the radio-frequency power spectrum.

In conclusion, synchronous pumping of few-cycle Ti:sapphire lasers is a very attractive alternative to traditional CW pumping and has many advantages. The Kerr-lens mode locking becomes self- starting and the spurious output power modulation for free running oscillators is negligible for most applications and disappears for actively synchronized resonators. This opens up the route to a more general use of mode-locked lasers for Ti:sapphire pumping like for example fiber lasers.

References: 1. Oliver D. Muecke, Richard Ell, Axel Winter, Jung-Won Kim, Jonathan R. Birge, Lia Matos, and Franz X. Kaertner, Optics Express 13, 5163 (2005). 2. Craig W. Siders, Erhard W. Gaul, Michael C. Downer, Alexei Babine and Andrey Stepanov, Rev. Sci. Instrum. 65, 3140 (1994). 3. Richard Ell, Gregor Angelow, Wolfgang Seitz, Max J. Lederer, Heinz Huber, Daniel Kopf, Jonathan R. Birge, and Franz X. Kaertner, Optics Express 13, 9292 (2005) 4. G. Cerullo, S. De Silvestri, and V. Magni, Opt. Lett. 19, 1040 (1994).

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Multipass Cavity Femtosecond Laser Development

Sponsors National Science Foundation – ECS-01-19452, BES-01-19494, ECS-0501478 Air Force Office of Scientific Research – FA9550-040-1-0046, FA9550-040-1-0011

Project Staff Dr. Andrew M. Kowalevicz, Dr. Alphan Sennaroglu, Aurea T. Zare, Professor James G. Fujimoto

1. Introduction to Multipass Cavity Lasers

The standard cavity in Kerr-Lens Mode-locked (KLM) lasers consists of two curved focusing mirrors, a flat end mirror, and a flat output coupler, arranged in an X or Z configuration, although other designs have been analyzed [1, 2]. This four-mirror resonator design has been extensively studied not only to characterize sensitivity to misalignment and stability but also to optimize performance [3-5]. Basically, there has been no significant change in cavity architecture since the first KLM laser in 1991. In our project, we introduced the multipass cavity (MPC) in KLM lasers to increase pulse energies as well as to develop more compact lasers. By extending the cavity length of a Mode-locked laser resonator, the pulse repetition rate can be reduced. Thus, for a given average power (determined by the available pump power), a higher pulse energy can be achieved. Furthermore, use of these extended cavities enables the direct generation of high- energy femtosecond pulses without the need for cavity dumping or regenerative amplification.

In a practical laser system, it is important to maintain compactness as the cavity length is extended. Previously we have shown that this can be achieved by using Herriott-type MPCs [6, 7]. An MPC, in its simplest form, consists of a stable two-mirror resonator and a mechanism for injecting and extracting light beams, as shown in Fig. 1. When an off-axis optical beam is injected into the MPC, it undergoes multiple bounces before it exits. Hence, the effective optical path length is increased by using a compact arrangement of mirrors. To date, MPCs have been widely used in many applications such as accurate optical loss measurements [8], stimulated Raman scattering [9, 10], long-path absorption spectroscopy [11], high-speed path-length scanning [12], and construction of compact solid-state lasers [13, 14].

Figure 1. MPC consisting of two mirrors [15].

The concept of cavity length extension can be applied to achieve enhanced performance in a variety of situations. One application is to increase the pulse energy available from laser sources that have low average output powers, such as diode-pumped lasers or low-pump-power lasers. Novel resonator designs, which can be operated with low pump powers, have been proposed and demonstrated [16, 17]. Because the cost of the pump laser can be dramatically reduced, these low-threshold lasers provide a more economical alternative to standard lasers. In these cases, however, average output powers are reduced and pulse energies can be low. MPC designs can enable these lasers to generate higher pulse energies, while still retaining low-pump-power operation, thus enabling lower-cost lasers that achieve comparable pulse energies as with more expensive systems.

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MPC lasers can also be used to obtain high energy femtosecond pulses from a laser operated at standard power levels. Traditionally, high-energy femtosecond pulses were achieved by using amplified laser systems. As a simple and cost-effective alternative, several groups have used telescopes and similar relay imaging methods to extend laser cavities and reduce repetition rates from 100 MHz to several tens of megahertz [18, 19]. By using a MPC design, however, pulse repetition rates can be reduced even further to the few-megahertz regime to yield higher energy femtosecond pulses [7]. This allows for high pulse energies to be generated directly from laser oscillators, without the need for complicated and costly amplification systems.

Finally, in a practical laser system, it is important to maintain compactness as the cavity length is extended. Because the distance between the two MPC mirrors is traversed a large number of times in a nearly collinear fashion, MPCs make efficient use of space. Extremely long laser cavities can be compressed into sizes used for standard cavities, while standard cavities can be made to fit in compact footprints.

Since they can generate higher-energy femtosecond pulses in the few-megahertz regime, MPC lasers are extremely good sources for nonlinear material processing, especially for fabricating glass materials with microsecond-order thermal relaxation times. For this application, we constructed a MPC KLM Ti:Sapphire laser that generated energies as high as 150 nJ with 43 fs pulse duration, corresponding to 3.5 MW peak power. The cavity length is increased to approximately 20 times the length of a standard Ti:Sapphire laser. The total path length in air is 51 m and the repetition rate is reduced to 5.85 MHz. Fig. 2 shows a schematic of this extended cavity Ti:Sapphire laser.

Figure 2. Schematic layout of the MPC KLM Ti:Sapphire laser. The pump source was a frequency-doubled Nd:Vanadate laser operating at 532 nm. The short cavity extends from the output coupler (OC) to M6, with arms 45 cm and 95 cm long. The MPC is inside the dotted box. L: lens, M: mirror [20].

2. Design Principles of Q-Preserving MPC lasers

In this section, we present general design principles for MPCs for applications in KLM femtosecond lasers. The MPC is designed to leave invariant the spot-size distribution of the standard, unextended laser cavity. This design will be referred to as a q-preserving configuration. We will discuss an analytic condition for q-preserving MPCs, various design considerations, categorization of all possible two-mirror configurations, and results of three MPC experiments.

We utilize the analysis of the q-parameter transformation to design the MPC. The transformation of the q parameter is governed by the ABCD matrix, where q’ = (Aq+B)/(Cq+D), with A, B, C, and D representing the elements of the final transformation matrix. Then, we define a ray transfer matrix MT, to represent a single round trip through the optical system of lenses and displacements. For example, in a two-curved-mirror MPC with mirrors having identical radii of

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curvature R, as shown in Fig. 3, we take MT to be the round-trip ray transfer matrix describing propagation from reference plane ZR1 to the reference plane ZR2. The final MPC transformation n matrix can be written as MT , where n is the number of round trips, as a function of the angular advance, θ, between two consecutive beam positions and the ABCD matrix elements of MT. In Fig. 3, the two-mirror MPC is unfolded for the ease of analysis, represented using a periodic equivalent lens system composed of lenses having focal lengths f = R/2. In order to preserve the n q parameter, we desire the transfer matrix to be equal to plus or minus the identity matrix, or MT = (-1) m I. This results in the condition of nθ = mπ (1) with m being an integer. This condition is satisfied when the bouncing beam traces out an integer number of full circular trajectories before coming back to its initial entry position, for the case when m is even. If m is odd, the beam traverses an integer number of half circles around the edges of the end mirrors.

Figure 3. Unfolded representation of an MPC. The round trip is composed of the unit cell from ZR1 to O and the unit cell from O to ZR2 [21].

Because most designs use MPCs consisting of two mirrors, we focus on the characteristics of two-mirror MPCs designs, where the resonator consists of either a flat and curved mirror (FC) or two curved mirrors (CC). By inducing the relation between the angular advance and the cavity parameters using the formulas in [21], we can infer that θ ≤ π for the FC case and θ ≤ 2π for the CC case. These results, together with Eq. (1), constrains the values of m and n such that m ≤ n (FC) and m ≤ 2n (CC). By determining the reference planes where the rays connecting the spots on the end mirrors intersect, we can obtain a full description of the ray paths within the MPC. The beam must return to its entry position only after completing the correct number of round trips. It should not only return to the same position in space with the same beam parameters, but also be collinear with the input beam. The number of spots is determined by the number of round trips, and spot separation determines the ease of using a pickoff mirror or notched mirror to insert or extract the beam.

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Figure 4. Spot patterns at M1 and M2 for n = 7 and increasing m for the FC case. The relative ratio of the spot pattern radii decreases with an increase in angular advance until it reaches zero when m = n [21].

The initial ray offset and tilt can be adjusted so that the spots yield a circular pattern with a radius of r1 at M1 (See Fig. 3). Then, the rays will intersect a reference plane at position z to form a circular pattern with radius rz and we can obtain solutions for radii at the second mirror M2, and midway between the mirrors [9]. With Eq. (1), we can simplify the solutions for the FC and CC cases. Fig. 4 represents the spot patterns at the mirrors for n = 7 and different values of m for the FC case.

The unit cell concept provides a useful qualitative description of a MPC. To construct a practical q-preserving MPC, one requires the mirror separation and the location of the initial and final reference planes. Use of unit cells easily establishes the proper location of these reference planes. Unit cells also help identify errors in q-preserving performance and effects on the resonator stability map. In the two-mirror configuration shown in Fig. 3, any position within the lens array can be chosen as the initial reference plane. Let us use L to represent a lens and D to represent a displacement. Depending on the initial plane, special unit cells that are either antisymmetric (DL, LD) or symmetric (LDL, DLD) arise. While there is no fundamental symmetry that separates MPC configurations into different categories, it is pedagogically useful to divide the possible choices into classes based on design attributes, including the beam injection and extraction scheme, the position of the initial reference plane, and the choice of m (even or odd). Figures 5 and 6 illustrate cavity choices with notched mirrors and pickoff mirrors, respectively, for injection and extraction. Shaded mirrors have the same radius of curvature, with solid mirrors having one half the radius of shaded ones. Unfilled mirrors are flat. Dotted lines indicate the beginning and end reference planes for a single transit. The solid line with an arrow represents a complete unit cell.

Figure 5. Possible notched-mirror q-preserving MPC designs [21].

Based on different injection and extraction techniques, there are 32 possibilities for the two-mirror MPC design, each with advantages and disadvantages based on the particular application. In determining the best cavity design, we must consider factors, such as (1) the ease and flexibility

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of implementation, (2) extraction and injection of the beam, (3) q-preserving error, and (4) the accessibility of the final reference plane for placement of other components. Notched mirror designs have the advantage of having simple implementation and being useful for large n values since there are no mirrors obstructing the paths in the cavity. Pickoff-mirror cavities require specialized optics and mounting but give the freedom to independently inject and extract the beam.

In practical applications, we must consider MPC alignment and dispersion compensation. The most expedient method for MPC alignment is to first construct and optimize the short, unextended laser cavity and then introduce the MPC. The high reflector can then be replace by a plane-plane substrate or interferometer flat, with a low-transmission coating functioning as an output coupler. Then the laser output can be used to align the MPC. The partial reflector should be positioned close to the first reference plane of the MPC. If the cavity is properly aligned, the extended MPC cavity will have the same stability operating point as the short cavity.

MPC femtosecond lasers can have significantly large dispersion due to the increased air travel length, so MPC resonators require the components for dispersion compensation. One way to compensate dispersion is to use double-chirped mirrors (DCMs). It is desirable to use DCMs instead of prisms because DCMs allow for the setting of the operating point by mode-locking the short laser cavity and for the dispersion in the multipass components to be managed separately. The dispersion in the long cavity can be adjusted by tuning the dispersion or changing the number of DCMs.

Figure 6. Possible pickoff-mirror q-preserving MPC designs [21].

We review the results of three experiments that used flat-curved MPCs to achieve pulse energy amplification and cavity compactness. The first experiment is an application where a MPC was used to increase the pulse energy of a Cr:LiSAF laser [22]. An astigmatically compensated x- folded cavity was pumped with three single-mode diodes providing up to 120 mW of power. The original cavity had a repetition rate of 115 MHz and the maximum pulse energy was 0.14 nJ [23]. The cavity was extended by using a flat-curved MPC with pickoff mirrors. The extended cavity repetition rate was 8.6 MHz and the output power was 6.5 mW, corresponding to 0.75 nJ, a factor of 5 increase in pulse energy [24]. The second experiment was a demonstration where we developed a compact Ti:sapphire femtosecond laser [25]. The short cavity, with a repetition rate of 250 MHz, was extended with an FC MPC using notched mirrors. For n = 9 and m = 2, the

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mirror separation of 23.4 cm provided an extension of the cavity length by 8.4 m and reduces the repetition rate to 8-31 MHz. In the third experiment, we obtained a 20-fold increase in pulse energy, as mentioned in the previous section [20].

In this section we have presented a general theory that governs the operation of MPCs and examined practical design issues related to femtosecond pulse generation. We reviewed the condition that must be satisfied for the MPC to be q-preserving. The ability of a MPC to reproduce the stability operating point of the standard cavity, while extending the resonator length, allows for a wide variety of applications for improved laser performance and design. The spot pattern and ray intersections within q-preserving cavities were determined based on the cavity parameters m and n. This information is especially important for beam injection and extraction. Beyond the theoretical analysis, we have presented a complete list of all possible q-preserving configurations for two-mirror MPCs when pickoff or notched mirrors are used. The unit cell concept was further introduced to aid in cavity design. We then discussed the trade-offs among different types of MPC cavities. Finally, we presented the results of several experiments that elucidate use of different MPC designs in femtosecond pulse amplification. The versatility of laser designs based on MPCs promises to improve the performance of femtosecond lasers as well as to enable new applications of this technology.

References

[1] H. A. Haus, J. G. Fujimoto, and E. P. Ippen, "Analytic Theory of Additive Pulse and Kerr Lens Mode Locking," IEEE J. Quantum Electron. 282086-96 (1992). [2] V. L. Kalashnikov, V. P. Kalosha, I. G. Poloyko, and V. P. Mikhailov, "Optimal resonators for self-mode locking of continuous-wave solid-state lasers," Journal of the Optical Society of America B-Optical Physics 14(4): 964-69 (1997). [3] T. Brabec, C. Spielmann, P. F. Curley, and F. Krausz, "Kerr lens modelocking," Optics Lett. 171292-94 (1992). [4] V. Magni, G. Cerullo, and S. De Silvestri, "ABCD matrix analysis of propagation of gaussian beams through Kerr media," Optics Communications 96348-55 (1993). [5] V. Magni, G. Cerullo, S. D. Silvestri, and A. Monguzzi, "Astigmatism in Gaussian--beam self--focusing and in resonators for Kerr--lens mode locking," J. Opt. Soc. Am. B 12476- 85 (1995). [6] S. H. Cho, B. E. Bouma, E. P. Ippen, and J. G. Fujimoto, "Low-repetition-rate high-peak power Kerr-lens mode-locked Ti:Al2O3 laser with a multiple-pass cavity," Optics Letters 24417-19 (1999). [7] S. H. Cho, F. X. Kartner, U. Morgner, E. P. Ippen, J. G. Fujimoto, J. E. Cunningham, and W. H. Knox, "Generation of 90-nJ pulses with a 4-MHz repetition-rate Kerr-lens mode- locked Ti : Al2O3 laser operating with net positive and negative intracavity dispersion," Optics Letters 26(8): 560-62 (2001). [8] R. Herriott and H. J. Schulte, "Folded optical delay lines," Applied Optics 4883-89 (1965). [9] W. R. Trutna and R. L. Byer, "Multiple-Pass Raman Gain Cell," Applied Optics 19(2): 301-12 (1980). [10] B. Perry, R. O. Brickman, A. Stein, E. B. Treacy, and P. Rabinowitz, "Controllable Pulse- Compression in a Multiple-Pass-Cell Raman Laser," Optics Letters 5(7): 288-90 (1980). [11] J. B. McManus, P. L. Kebabian, and W. S. Zahniser, "Astigmatic Mirror Multipass Absorption Cells for Long-Path-Length Spectroscopy," Applied Optics 34(18): 3336-48 (1995). [12] P. L. Hsiung, X. D. Li, C. Chudoba, I. Hartl, T. H. Ko, and J. G. Fujimoto, "High-speed path-length scanning with a multiple-pass cavity delay line," Applied Optics 42(4): 640-48 (2003). [13] H. Z. Cheng, P. L. Huang, S. L. Huang, and F. J. Kao, "Reentrant two-mirror ring resonator for generation of a single-frequency green laser," Optics Letters 25(8): 542-44 (2000).

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[14] S. L. Huang, Y. W. Chen, P. L. Huang, J. Y. Yi, and H. Z. Cheng, "Multi-reentrant nonplanar ring laser cavity," Ieee Journal of Quantum Electronics 38(10): 1301-08 (2002). [15] A. Sennaroglu, A. M. Kowalevicz, Jr., E. P. Ippen, and J. G. Fujimoto, "Compact femtosecond lasers based on novel multipass cavities," IEEE Journal of Quantum Electronics 40(5): 519-28 (2004). [16] K. Read, F. Blonigen, N. Riccelli, M. Murnane, and H. Kapteyn, "Low-threshold operation of an ultrashort-pulse mode-locked Ti:sapphire laser," Optics Letters 21(7): 489-91 (1996). [17] A. M. Kowalevicz, T. R. Schibli, R. P. Prasankumar, F. X. Kaertner, and J. G. Fujimoto, "Ultra-low-threshold, Low Cost, Kerr Lens Modelocked Ti:Al2O3 Laser," Opt. Lett. 271-3 (2002). [18] A. R. Libertun, R. Shelton, H. C. Kapteyn, and M. M. Murnane, "A 36 nJ-15.5 MHz extended-cavity Ti:sapphire oscillator," Conference on Lasers and Electro-Optics, Baltimore, MD, 1999. [19] A. Poppe, M. Lenzner, F. Krausz, and C. Spielmann, Utrafast Phenomena1999. [20] A. M. Kowalevicz, A. T. Zare, F. X. Kartner, J. G. Fujimoto, S. Dewald, U. Morgner, V. Scheuer, and G. Angelow, "Generation of 150-nJ pulses from a multiple-pass cavity Kerr- lens mode-locked Ti:Al2O3 oscillator," Optics Letters 28(17): 1597-9 (2003). [21] A. M. Kowalevicz, A. Sennaroglu, A. T. Zare, and J. G. Fujimoto, "Design principles of q- preserving multipass-cavity femtosecond lasers," Journal of the Optical Society of America B (Optical Physics) 23(4): 760-70 (2006). [22] L. K. Smith, S. A. Payne, W. L. Kway, L. L. Chase, and B. H. T. Chai, "Investigation of the Laser Properties of Cr3+:LiSrGaF6," IEEE J. Quantum Electron. 282612-18 (1992). [23] B. Agate, B. Stormont, A. J. Kemp, C. T. A. Brown, U. Keller, and W. Sibbett, "Simplified cavity designs for efficient and compact femtosecond Cr:LiSAF lasers," Optics Communications 205(1-3): 207-13 (2002). [24] R. P. Prasankumar, Y. Hirakawa, A. M. Kowalevicz, Jr., F. X. Kaertner, J. G. Fujimoto, and W. H. Knox, "An extended cavity femtosecond Cr:LiSAF laser pumped by low cost diode lasers," Optics Express 11(11): (2003). [25] A. Sennaroglu, A. M. Kowalevicz, F. X. Kartner, and J. G. Fujimoto, "High-performance, compact, prismless, low-threshold 30-MHz Ti:Al2O3 laser," Optics Letters 28(18): 1674- 76 (2003).

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Femtosecond Frequency Combs and Phase Control

Carrier-Envelope Phase Dynamics and Noise Analysis in Octave-Spanning Ti:Sapphire Lasers

Sponsors Defense Advanced Research Projects Agency(DARPA)-HR 0011-05-C-0155 Office of Naval Research - N00014-02-1-0717

Project Staff Lia Matos, Dr. Oliver D. Mücke, Jeff Chen, and Professor Franz X. Kärtner

Carrier-envelope (CE) phase stabilized octave-spanning Ti:sapphire laser oscillators [1,2] have numerous intriguing applications as ultraprecise clockworks in optical clocks and in attosecond time-domain spectroscopy. In this project, we have performed a detailed study of the intensity- related CE-phase dynamics in octave-spanning frequency combs (OSFCs) and a complete noise analysis of the CE phase-lock loop (PLL) dynamics which revealed the current limitations to achieve minimum CE phase noise for the above-mentioned applications [3].

Figure 1: (a) Carrier-envelope frequency shift (black curve) and relative change in intracavity power (grey curve) as function of pump power. Above 6.3 W, a cw component appears in the spectrum (not shown). (b) Block diagram of the phase-lock loop composed of the carrier-envelope frequency stabilized laser. The voltage-controlled oscillator (VCO) is depicted in the dashed box.

In Fig. 1(a), the measured shift of the CE frequency fCE and the relative change in intracavity power versus pump power are depicted for a 200 MHz OSFC [2]. A simple linear behavior (∆fCE =11 MHz/W×∆Ppump) is found, provided the correct pump power level is used to prevent the appearance of pulse instabilities such as a continuous-wave (cw) breakthrough, which occurs above 6.3 W of pump power in the laser system used. In the range where single pulse operation occurs, these data are in excellent agreement with theoretical predictions by Haus and Ippen [4] based on soliton-like pulse propagation in Kerr media. It turns out that the intensity dependence of the CE-phase dynamics in OSFCs is significantly simpler than in systems which employ external spectral broadening to achieve the required octave, where the effect of intensity- dependent spectral shifts of the comb was found to be of importance [5]. In OSFCs, in contrast, the center frequency of the pulse has no observable variation with pump power, because the pulse spectrum completely fills up the available bandwidth and is in fact limited by the bandwidth of the output couplers available.

We also performed a complete noise analysis and modeling of CE-phase stabilized OSFCs (see Fig. 1(b)). We found that the inclusion of the pump power to intracavity pulse energy transfer

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function of the Ti:sapphire laser, i.e., the Ti:sapphire gain dynamics, is essential to obtain correct predictions for the CE-phase noise behavior. Fig. 2 shows as an example a comparison of the measured and modeled transfer function from pump power to intracavity pulse energy. Fig. 3(a) shows the measured and computed CE phase noise accounting for the most important noise sources in the system, that are the pump laser noise, the phase detector noise, and the

Figure 2: Measured (red and blue) and modelled (green and orange) amplitude and phase response of OSFC laser, in cw and mode-locked operation.

transfer functions of feedback-loop elements as shown in Fig. 1(b). Improved noise performance could be obtained by increasing the closed-loop bandwidth, which is currently about 100 kHz. This bandwidth is dictated by the phase margin of the feedback loop, which is necessary for stability. Note that the VCO shown in Fig. 1(b) integrates a frequency deviation into a phase deviation causing the feedback loop to start off with a –90° phase (see Fig. 3(b)). When the bandwidth of the gain medium is approached, additional phase accumulates from the gain dynamics and the time delay from the acousto-optic modulator (AOM, see Fig. 1(b)), which renders the system unstable if the gain setting is not properly reduced. This imposes a limitation to the maximum loop gain since the jointly added phase from the AOM and the laser dynamics reduces the phase margin.

In the future, different strategies for further reduction of the CE phase noise will be pursued, such as replacing the AOM by an electro-optic modulator and the use of lead-lag circuits.

Figure 3: (a) Measured carrier-envelope phase noise of a self-referenced 200 MHz Ti:sapphire frequency comb pumped by a Spectra-Physics Millennia Xs (blue curve) and computed carrier-envelope phase noise spectrum (red curve). (b) Phase response of open-loop transfer function of the carrier-envelope phase-lock loop (red). The contributions from the loop filter (green), AOM (blue), and laser dynamics (orange) to the open-loop phase are shown for comparison.

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References: 5. L. Matos, D. Kleppner, O. Kuzucu, T. R. Schibli, J. Kim, E. P. Ippen, and F. X. Kaertner, Opt. Lett. 29, 1683 (2004).

6. O. D. Mücke, R. Ell, A. Winter, J. Kim, J. R. Birge, L. Matos, and F. X. Kärtner, Opt. Express 13, 5163 (2005).

7. L. Matos, O. D. Mücke, J. Chen, and F. X. Kärtner, Opt. Express 14, 2497 (2006).

8. H. A. Haus and E. P. Ippen, Opt. Lett. 26, 1654 (2001).

9. K. W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, IEEE J. Sel. Top. Quantum Electron. 9, 1018 (2003).

High Repetition Rate, Broadband, Mode-Locked Ti:Sapphire Laser

Sponsers Defense Advanced Research Projects Agency(DARPA)-HR 0011-05-C-0155

Project Staff Andrew Benedick, Mohammad Araghchini, Jonathan Birge , Michelle Sander, Dr. Oliver D. Mücke, Dr. Richard Ell, Professor Franz X. Kärtner

One approach towards arbitrary optical waveform generation is based on a carrier envelope phase controlled laser operating at high repetition rates. Such a system has a well controlled optical comb of frequencies as an output. Eventually, each comb line can be resolved and arbitrarly modulated to create and arbitrary output electric field waveform. At the heart of such a system is a high repetition rate laser, such that the comb spacing is as large as possible. One approach towards such a system is based on a Ti:sapphire laser based frequency comb at a repetition rate of 1 GHz. Later this source will be scaled in various approaches to 10 GHz. The challenge in construction of high repetition rate lasers is, that as the repetition rate is scaled up, the high pulse energy necessary to take advantage of the Kerr effect decreases requiring a corresponding increase in intracavity field intensity within the Kerr media.

The laser constructed in this project is shown schematically in Fig. 1. A ring resonator was selected for this stage of the project since it simplifies dispersion and astigmatism compensation. In a linear resonator, both dispersion and astigmatism must be balanced on either side of the gain medium while in the ring resonator both effects are additive allowing greater freedom in component placement, an important factor in a resonator of this size.

The four mirror ring resonator uses (2) 30mm ROC focusing mirrors and 2 plane mirrors, all four of which are double chirped mirror pairs. The double chirped mirrors provide negative dispersion compensation while the BaF2 plate and wedge, .5mm of which has the same dispersion as ~1m of air, provide positive dispersion to allow fine tuning of the overall cavity dispersion. The BaF2 wedge also serves as the output coupler for the laser. Because of the relatively flat dispersion of BaF2 over the gain bandwidth of Ti:Sapphire, the current output coupling of the laser is a constant 1.25%.

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Pump Laser

2mm Ti:Al2O3 30mm DCM (typ. 2) 8cm

DCM BaF2 BaF2/OC (typ. 2) PZT

15cm

Fig.1. 1GHz Repetition Rate Ti:Sapphire Mode-Locked Laser

In this arrangement the laser provides two output beams of approximately equal power, one from each side of the wedge. Work is in progress to design a dielectric reflecting output coupler for one side of the wedge which will allow the uncoated side of the wedge to be put at Brewster’s angle, consolidating the output power to one beam without affecting the overall dispersion characteristics of the cavity. Unidirectional operation of the laser is ensured by the fifth silver mirror placed opposite to the desired output beam[1,2].

With 6W from the 532nm pump laser the total output power from the Ti:sapphire laser is 315mW, or an average pulse energy of 0.3nJ. Overlapped with the output spectrum of this laser in Fig 2. is the spectrum of a 200MHz Ti:Sapphire octave spanning laser [4] that had an optimized output coupler to enhance the wings of the pulse. These spectra show, that pulse spectra comparable to the 200MHz laser (~5fs) are expected upon implementation of an optimized output coupler in the 1GHz ring laser. The broad spectrum also allows us to utilize the standard 1f-2f self referencing scheme to stabilize the carrier-envelope frequency directly with the output from the laser.

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-20 -30 -40 200MHz -50 -60 1GHz

10*Log(PSD) W/nm 10*Log(PSD) -70 -80 550 650 750 850 950 1050 1150 1250 Wavelength(nm)

Fig. 2. Absolute output spectrum of an octave spanning 200 MHz Ti:Sapphire laser and a 1GHz Ti:Sapphire laser. The spectral wings of the 200MHz laser is enhanced by the output coupler.

Stabilization of the laser’s repetition rate will be achieved by referencing to a methane stabilized He-Ne laser at 3.39um, which was recently installed in the laboratory. Difference Frequency generation in a periodically poled Lithium Niobate crystal will use the 670nm and 830nm components of the Ti:Sapphire laser output to create 3.39um which will be heterodyned with the He-Ne reference. Together with the 1f-2f carrier-envelope offset control the optical output of the Ti:sapphire laser is absolutely controlled.

References 1. W.S. Pelouch, P.E. Powers, and C.L. Tang “Self-Starting mode-locked ring-cavity Ti:Sapphire laser,” Optics Letters 17 (22): 1581-1583 NOV 15 1992 2. A. Bartels, T. Dekorsy, and H. Kurz “Femtosecond Ti:Sapphire ring laser with a 2-GHz repetition rate and its application in time-resolved spectroscopy,” Optics Letters 24 (14): 996- 998 JUL 15 1999 3. O. D. Mücke, O. Kuzucu, F. N. C. Wong, E. P. Ippen, and F. X. Kärtner, S. M. Foreman, D. J. Jones, L.S. Ma, J. L. Hall, and J. Ye “Experimental implementation of optical clockwork without carrier-envelope phase control,” Optics Letters 29 (23): 2806-2808 DEC 1 2004 4. O. D. Mücke, R. Ell, A. Winter, J. Kim, J. R. Birge, L. Matos, and F.X. Kärtner, “Self- Referenced 200 MHz Octave-Spanning Ti:Sapphire Laser with 45 Attosecond Carrier- Envelope Phase Jitter,” Optics Express 13 (13): 5163-5169 JUN 27 2005

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Composite Plate for Carrier-Envelope Phase Control

Sponsors Defense Advanced Research Projects Agency(DARPA)-HR 0011-05-C-0155 Office of Naval Research - N00014-02-1-0717

Project Staff Dr. Richard Ell, Jonathan R. Birge, Mohammad Araghchini, and Professor Franz X. Kärtner

Controlling the carrier-envelope phase (CEP) of Titanium-Sapphire (Ti:sapphire) lasers enables complete control of the temporal evolution of the electric field of the emitted few-cycle pulses [1]. Electric-field sensitive highly nonlinear experiments as well as optical frequency metrology both benefit significantly from this unprecedented level of control. An established way to change the value for the CEP and its temporal evolution, the carrier-envelope frequency fCE, is to change the amount of dispersive material experienced by the laser pulses. While this easily changes the ratio of group- and phase velocity and hence the CEP or fCE , it unavoidably also modifies the second- and higher order dispersion and thereby spreads the pulse in time and changes its pulse parameters. This is harmful for electric field sensitive experiments [2] as well as for intracavity tuning of fCE. To avoid this problem, we invented a composite material plate allowing for a change of the CEP (fCE) with negligible impact on the pulse dispersion and hence pulse parameters like pulse duration and energy [3].

In the approach chosen here, we change the composition of the material inserted in the beam path. By doing so, we change the CEP (fCE) but keep second- and higher order dispersion nearly constant. Figure 1(a) shows a schematic drawing of the composite plate made up of BaF2 and a thinner fused silica part oppositely wedged and glued together. The beam passes the plate in the plane of the drawing under Brewster’s angle. Figure 1 (b) on the right hand side displays the measured dispersion together with a fit. When moving the plate along the wedge direction, we continuously replace BaF2 by fused silica which changes the ratio of group- and phase velocity but keeps dispersion unaltered. To illustrate this, it is interesting to know the alteration in group delay, when tuning the CEP by 2π by pure material in comparison to material exchange.

Removing (or inserting) 80 µm of BaF2 or 60 µm of fused silica changes the CEP by 2π but also alters the group delay by roughly 2.5-3.5 fs. For the few-cycle pulses that are relevant for our discussion (5-8fs) this is already quite high. In comparison, when exchanging 200 µm of BaF2 by 200 µm of fused silica, the group delay only varies by 0.5 fs – much less impact on the dispersive properties than for the former case, with the same variation in CEP.

(a) (b 90 measurement fit: 1.16mm BaF + 0.42mm FS 80 2

)

) 2 BaF 70 m 2

m

5 60

2 GDD (fs 50

40

SiO2 600 700 800 900 1000 1100 wavelength (nm) d

ForFigure a proof-of-principle2. (a) Sketch of the compositexperimente plate we made inco of rporateda thick BaF the2 wedge composite and a thinner glass fused plate silica into wedge. an Shown interferometricis a top view wi autocorrelatorth the thickness usedd of the for plate time exaggerated domain characterization relative to the length of few-cycle of roughly pulses. 25 mm. We The were plate is 10 ablemm toin continuouslyheight and the tune laser the beam relative passes phase through of the both el ectricmaterials fields in thein the plane two of interferometer the drawing under arms Brewster’s – a ancleargle. (bproof): Measured that the avera platege second works order according dispersion to andour fitdesign revealin [3].g a totalFinally, thickness we incorporatedof 1.58 mm. the

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composite plate into an octave-spanning 200MHz laser with CEP control. The plate is part of the intracavity dispersion management and by translating the plate, we were able to continuously tune fCE over half the repetition frequency with negligible impact on pulse duration and energy. This is shown in Figure 2 where fCE is initially close to half the repetition rate and is then tuned towards zero by moving the plate accordingly.

Figure 2. Sequence of measurements illustrating the arbitrary choice of the carrier- envelope frequency fCE by varying the position of the plate inside the laser cavity of an octave-spanning 200 MHz laser. In the graph shown, f is varied over half the repetition CE rate frep/2.

In conclusion, dispersion neutral control of the carrier-envelope phase over a wide tuning range is desirable not only for intracacity control of few-cycle lasers but also in electric field sensitive experiments were a significant degradation of any observable signal is to be avoided. Our composite glass plate accomplishes this very well and is the first implementation of such an idea.

References: 10. L. Matos, D. Kleppner, O. Kuzucu, T.R. Schibli, J. Kim, E.P. Ippen, and Franz X. Kaertner, Opt. Lett. 29, 1683 (2004). 11. A. Apolonski, P. Dombi, G.G. Paulus, M. Kakehata, R. Holzwarth, Th. Udem, Ch. Lemell, K. Torizuka, J. Burgdörfer, T.W. Hänsch, and F. Krausz, Phys. Rev. Lett. 92, 073902-1 (2004). 12. Richard Ell, Jonathan R. Birge, Mohammad Araghchini, and Franz X. Kaertner, Optics Express, in press (2006).

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Balanced Optical-RF Phase Detector

Sponsors EU Commission in the Sixth Framework Program, 011935 EUROFEL. Office of Naval Research (ONR) N00014-02-1-0717

Project Staff Jung-Won Kim, Dr. Frank Ludwig and Professor Franz X. Kärtner

It has been recognized that mode-locked lasers have a great potential for generating ultra low- jitter RF-signals [1]. Recently, it has been shown that the extraction of an RF-signal from an optical pulse train emitted by a mode-locked laser using direct photo detection is limited in precision by excess phase noise [2]. The major contribution to this excess noise has been identified to be the amplitude-to-phase (AM-to-PM) conversion in the photo detector. In Ref. [3], we measured the AM-to-PM conversion factor, and it typically ranges from 1 to 10 ps/mW depending on the bias voltage and diode types. The intensity noise of the laser can be converted into a significant amount of phase noise by this process. Previously, we demonstrated a scheme to avoid this conversion by transfer of timing information in the optical domain based on a free- space Sagnac interferometer [4]. However, due to acoustic vibrations and poor phase noise properties of the free-running voltage-controlled oscillator (VCO), the relative jitter between the extracted RF-signal and the mode-locked laser was limited to 60 fs from 100 Hz to 10 MHz bandwidth.

In this report, a balanced optical-RF phase detector for the extraction of low-jitter RF-signals from optical pulse trains is presented. It is based on precise phase detection by use of a differentially- biased Sagnac fiber-loop and synchronous detection, which is similar to Sagnac-loop based gyroscopes [5] and clock recovery systems [6]. We used the phase error signal from this balanced optical-RF phase detector, which is robust against drifts and photo detector nonlinearities, to regenerate low-jitter RF-signals from optical pulse trains. As a first experimental demonstration based on this balanced optical-RF phase detector, 3-fs relative timing jitter between the extracted RF-signal and the optical pulse train is demonstrated.

Figure 1: Schematic outline of the balanced optical-RF phase detector.

Figure 1 shows the schematic setup of the balanced optical-RF phase detector. The solid and dotted lines indicate optical and electrical signal paths respectively. The optical signal path can be

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implemented either by an optical fiber or a high-index contrast waveguide. Part of the input pulse train is tapped to the Photodiode #1. This photodiode is used to generate a synchronous detection signal with half the repetition rate (fR/2) of the optical pulse source. This signal is applied to both the phase modulator and the mixer. The rest of the input pulse train is sent to the Sagnac-loop. By the phase modulation at the frequency of fR/2, the output pulse train from the Sagnac-loop has an amplitude modulation. The amplitude of this signal is proportional to the phase error between the input optical pulse train and the input RF-signal. Therefore, we need to detect the amplitude of this modulated signal. After bandpass-filtered at fR/2, this signal is mixed with the synchronous detection signal at the mixer. By this down-conversion to the baseband, we can extract the phase error signal.

For the demonstration experiment [7], a stretched-pulse Er-doped fiber laser (repetition rate fR = 44.26 MHz) is used as the optical pulse source. By closing the loop with a 10.225-GHz (231st harmonic of the fundamental repetition rate) VCO (PSI DRO-10.225), we could get a long-term stable locking between the laser and the VCO over several hours.

Figure 2: In-loop residual phase noise spectra. When it is locked, the integrated timing jitter between pulse trains and RF-signals is 3 fs (1 Hz-10MHz).

Figure 2 shows the measured in-loop phase error. The voltage signal from the phase detector was measured with a low-noise vector signal analyzer (VSA), and converted into single-sideband (SSB) phase noise at 10.225 GHz. The red dashed line shows the phase noise of the free running VCO (taken from the datasheet), and the blue line shows the measured in-loop phase noise when it is locked. The black line is the noise floor from the VSA. This measurement shows that the integrated in-loop jitter is 3.0 fs ± 0.2 fs from 1 Hz to 10 MHz.

In summary, we have demonstrated a balanced optical-RF phase detector for extracting low jitter RF-signals from optical pulse trains. A residual timing jitter of less than 3-fs is measured from 1 Hz to 10 MHz between the RF-signal and the optical pulse train. This scheme is further scalable to suppress the relative timing jitter between optical pulse train and extracted RF-signal to the sub-femtosecond regime. It is also insensitive to the amplitude noise of both the optical pulse source as well as the RF-source.

References [1] S. Namiki and H. A. Haus, IEEE. J. Quantum Electron. 33, 649 (1997).

[2] E.N. Ivanov, S.A. Diddams and L. Hollberg, IEEE J. Sel. Top. Quant. Elec. 9, 1059 (2003).

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[3] J. Kim, F.O. Ilday, A. Winter and F.X. Kärtner, “Timing Distribution and RF-Synchronization of Mode-Locked Lasers,” in 2005 Digest of the LEOS Summer Topical Meetings, pp. 149-150.

[4] J. Kim, F.X. Kärtner and M.H. Perrott, Opt. Lett. 29, 2076 (2004).

[5] K. Böhm, P. Russer, E. Weidel, and R. Ulrich, Opt. Lett. 6, 64 (1981).

[6] L.K. Oxenlowe et al., “Optical clock recovery employing an optical PLL using cross-phase modulation in a Sagnac-interferometer,” Proceedings of CLEO 2001, pp. 525-526.

[7] J. Kim et al., “A Balanced Optical-RF Phase Detector”, Proceedings of CLEO 2006.

Passively Modelocked High-Repetition Rate Erbium-doped Bismuth Oxide Glass Waveguide Laser

Sponsors Office of Naval Research – MURI N0004-02-1-0717 DARPA – HR0011-05-C-0155 Air Force Office of Scientific Research – F49550-04-01-0011

Project Staff Hanfei Shen, Jonathan Morse, Hyunil Byun, Professor Franz Kärtner, Professor Erich Ippen

The development of novel broadband light sources at 1.5 µm is strongly motivated by the widespread application of WDM technology and is key to expanding the usable bandwidth of optical transmission systems. In addition, in combination with external supercontinuum generation, these sources have the potential to be compact, stable, high-bandwidth optical oscillators, with applications in optical metrology, ultra-wideband optical communications, sub- diffraction-limit imaging, and optical arbitrary waveform generation.

Rare-earth doped glass amplifiers are particularly promising. Thulium-doped glass amplifiers can provide gain in the 1480-1510 nm wavelength range. Erbium-doped tellurite glass have a gain bandwidth of 70 nm centered around 1530 nm that covers the conventional gain bandwidth of silica-based erbium-doped glasses as well as somewhat longer wavelengths. The widest emission band from erbium-doped glasses in the 1.5 µm wavelength range have been reported in a Bi2O3-B2O3-SiO2 system [1], making it an attractive alternative and a strong candidate for use in a modelocked laser. In addition to the broad bandwidth, the erbium doping can be much higher in a bismuth-oxide glass host than in conventional silica, offering the possibility of a significant reduction in the device length needed for laser gain. This makes the material attractive for short- cavity high-repetition-rate systems.

Both cw signal amplification [2] and picosecond pulse amplification [3] over the wavelength range of 1520-1600 nm using a bismuth oxide-based erbium-doped fiber amplifier have been observed. In addition, wavelength-tunable passive modelocking from 1570 nm to 1600 nm was demonstrated with a bismuth oxide-based erbium-doped fiber laser [4]. We look to extend this work with a bismuth oxide-based erbium-doped waveguide laser, whose short cavity length would enable us to achieve GHz repetition rates.

Our collaborators at Asahi Glass Company (Japan) have provided us with sample waveguides in 2 cm and 6 cm lengths. Several waveguides of height 3.5 µm and widths ranging from 3-7 µm are written on each sample chip. Figure 1(a) below is a picture of one of these waveguides being diode pumped at 977 nm through a tapered lensed fiber. Figure 1(b) shows the spectral gain profile of a sample waveguide.

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Gain (dB)

1.510 1.520 1.530 1.540 1.550 1.560 1.570 1.580 Wavelength (µm)

Figure 1. (a) Bismuth oxide-based erbium-doped waveguide being pumped at 977 nm through a tapered lensed fiber. (b) Spectral gain profile of a sample waveguide.

We are currently working towards demonstrating cw lasing in the waveguide laser. Once completed, we plan to modelock the waveguide laser using an ultra-broadband silicon/germanium saturable Bragg reflector (SBR) designed for high repetition rates [5]. The proposed cavity layout is shown in Figure 2. With this setup, we hope to achieve shorter pulses and higher repetition rates than previously demonstrated erbium-doped waveguide systems. In addition, together with extra-cavity amplification and smooth broadband supercontinuum generation with highly nonlinear bismuth-oxide fiber [6], we hope to demonstrate a stable frequency comb spanning the 1-2 µm wavelength range.

980 nm Er-doped Bismuth Glass Pump Waveguide Lensed Fiber SBR 1550 nm Laser Out WDM Output Lens Collimator Coupler

Figure 2. Planned cavity layout for the erbium-doped bismuth-oxide waveguide laser.

References: 1. S. Tanabe, N. Sugimoto, S. Ito, and T. Hanada, “Broad-band 1.5 m emission of Er3+ ions in bismuth-based oxide glasses for potential WDM amplifier,” Journal of Luminescence 87-89, 670 (2000). 2. N. Sugimoto, “Ultrafast optical switches and wavelength division multiplexing amplifiers based on bismuth oxide glasses,” Journal of the American Ceramic Society 85, 1083 (2002). 3. H. Sotobayashi, J.T. Gopinath, and E.P. Ippen, "23 cm long Bi2O3-based EDFA for picosecond pulse amplification with 80 nm gain bandwidth," IEEE Electronics Letters 39, 1374 (2003). 4. H. Sotobayashi, J.T. Gopinath, E.M. Koontz, L.A. Kolodziejski, and E.P. Ippen, "Wavelength tunable passively modelocked bismuth oxide-based erbium-doped fiber laser," Optics Communications 237, 399 (2004). 5. F.J. Grawert, J.T. Gopinath, F.O. Ilday, H.M. Shen, E.P. Ippen, F.X. Kärtner, S. Akiyama, J. Liu, K. Wada, and L.C. Kimmerling, “220-fs erbium-ytterbium:glass laser mode locked by a broadband low-loss silicon/germanium saturable absorber,” Optics Letters 30, 329 (2005).

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6. J.T. Gopinath, H.M. Shen, H. Sotobayashi, E.P. Ippen, T. Hasegawa, T. Nagashima, and N. Sugimoto, "Highly nonlinear bismuth oxide fiber for supercontinuum generation and femtoseconds pulse compression," Journal of Lightwave Technology 23, 3591 (2006).

Broadband Frequency Comb Generation at 1 µm with a Passively Modelocked High-Repetition Rate Bulk Ytterbium-glass Laser

Sponsors Office of Naval Research – MURI N0004-02-1-0717 DARPA – HR0011-05-C-0155 Air Force Office of Scientific Research – F49550-04-01-0011

Project Staff Hanfei Shen, Jonathan Morse, Hyunil Byun, Dr. Gale Petrich, Professor Leslie Kolodziejski, Professor Franz Kärtner, Professor Erich Ippen

As discussed in other sections, stable, robust, broadband frequency combs are useful in a number of applications, including frequency metrology and optical arbitrary waveform generation. Ti:sapphire-generated frequency combs range from 600 nm to over 1 µm, and combs seeded by Er-based lasers are centered at 1.5 µm. It would be advantageous to have an additional frequency comb source centered at 1 µm, bridging these two wavelength spans. We plan to build a high-repetition-rate modelocked bulk Yb:glass laser as this source. Then, with this source, we plan to amplify and then generate a frequency comb through supercontinuum generation with highly nonlinear fiber.

Ytterbium-doped materials are attractive as diode-pumped, tunable ultrafast laser sources for a number of reasons, including their broad absorption and emission bandwidths, their low thermal loading, and the long fluorescence lifetime (1-2 ms). In addition, the Yb3+ avoids loss processes such as excited-state absorption, upconversion, and concentration quenching prevalent in other ultrafast gain media [1]. Yb:glass materials are appealing because they are significantly cheaper than crystals and have a smooth fluorescence spectrum, making them particularly suitable for ultrashort pulse generation. Compared with Nd:glass, another source at 1 µm, Yb:glass has the advantage of a wider gain bandwidth, and has 2-3 times less quantum defects, favorable for more efficient lasing. However, Yb:glass is not without problems. It has a low emission cross section (~10–21–10-20 cm2), and its quasi-three-level nature requires a relatively high pump intensity for efficient laser operation. An additional complication of the latter feature is that, in contrast to four- level lasers like Ti:sapphire, the peak wavelength and the gain bandwidth depend on the excitation level, which in turn depends on the doping level of the glass gain media and on the amount of loss in the cavity. A plot of this behavior is shown in Figure 1(a); and the emission and absorption cross sections from which the calculation was made are shown in Figure 1(b) [2]. Both figures are for Yb-doped phosphate glass grown by Kigre, labeled QX/Yb, which we will use in our experiments. From the figures, one can see that the gain bandwidth of Yb:phosphate glass is fairly broad; and also that the absorption band is fairly large, which makes pumping with commercially available diodes possible.

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a)

Figure 1. (a) Quasi-three level behavior of spectral gain curve of QX/Yb phosphate glass. (b) Emission and absorption bands of Kigre QX/Yb phosphate glass [2].

Honninger et al. have demonstrated passive modelocking of diode-pumped Yb:phophate and Yb:silicate glass lasers, achieving self-starting modelocking with intracavity semiconductor saturable-absorber mirrors and soliton modelocking [2]. Pulses as short as 58 fs from Yb:phosphate and 61 fs from Yb:silicate have been generated.

For our work, we plan to implement a short cavity design to achieve high repetition rates. To passively modelock our Yb:phosphate glass laser, we will apply oxidized SBR technology we have developed for lasers at other wavelengths [3]. The designs will be adjusted for high repetition rate operation and suppression of Q-switched modelocking. Once modelocked, we will expand the frequency comb by passing the laser output through highly nonlinear bismuth-oxide fiber to generate supercontinuum [4].

Finally, we will also investigate the possibility of Kerr lens modelocking the Yb:glass laser. 3+ Among Yb -doped gain media, we have only found Yb:YVO4 to have achieved KLM in the -13 literature [5]. Though Yb:phosphate glass has a lower nonlinear refractive index n2 (1.22 × 10 esu) than Ti:sapphire (2.2 × 10-13 esu) or Cr:YAG (2.9 × 10-13 esu), there may still be sufficient intracavity power to initialize KLM.

References: 1. W. Krupke, “Ytterbium solid-state lasers – the first decade,” IEEE Journal of Selected Topics in Quantum Electronics 6, 1287 (2000).

2. C. Honninger, R. Paschotta, M. Graf, F. Morier-Genoud, G. Zhang, M. Moser, S. Biswal, J. Nees, A. Braun, G.A. Mourou, I. Johannsen, A. Giesen, W. Seeber, and U. Keller, “Ultrafast ytterbium-doped bulk lasers and laser amplifiers,” Applied Physics B 69, 3 (1999).

3. S.N. Tandon, J.T. Gopinath, H.M. Shen, G.S. Petrich, L.A. Kolodziejski, F.X. Kartner, and E.P Ippen, "Large-area broadband saturable Bragg reflectors by use of oxidized AlAs," Optics Letters 29, 2551 (2004).

4. J.T. Gopinath, H.M. Shen, H. Sotobayashi, E.P. Ippen, T. Hasegawa, T. Nagashima, and N. Sugimoto, "Highly nonlinear bismuth oxide fiber for supercontinuum generation and femtoseconds pulse compression," Journal of Lightwave Technology 23, 3591 (2006).

3+ 5. A.A. Lagatsky, A.R. Sarmani, C.T.A. Brown, and W. Sibbett, et al., "Yb -doped YVO4 crystal for efficient Kerr-lens mode locking in solid-state lasers," Optics Letters 30, 3234 (2005).

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Development of Stable Frequency Combs at High Repetition Rates Using Fiber Lasers and Supercontinuum Generation

Sponsors DARPA – HR0011-05-C-0155 Air Force Office of Scientific Research – F49550-04-01-0011

Project Staff Jason W. Sickler, David Chao, Professor Erich P. Ippen

The development of stable optical frequency combs based on mode-locked lasers has advance rapidly over the past decade [1-4]. These stable combs are proving useful in a number of applications, most notably in frequency metrology [2] where the comb is locked to a stable frequency reference (such as an atomic transition) and thus serves as a frequency “ruler”.

Another application of stable frequency combs is in optical arbitrary waveform generation. In this application, each frequency component’s amplitude and phase is independently controlled, and the resulting frequency components are superposed. In this way the Fourier construction of an arbitrary optical waveform is accomplished.

In order to generate a stable frequency comb, two parameters must be controlled. First, the spacing of the comb frequencies must be stabilized. This corresponds to stabilizing the repetition rate of the laser and can be achieved by a number of locking techniques [5]. Second, the carrier- envelope offset (CEO) frequency must be locked. In the frequency domain, this corresponds to a shift of the frequency comb from zero frequency. In the time domain, this corresponds to a changing delay between the carrier and the pulse envelope and results from a difference in the group and phase velocities.

One technique for locking the carrier-envelope phase involves generating an octave-spanning comb from the laser source, and then frequency doubling the low-frequency portion of the comb to overlap with the high-frequency portion. The difference frequency is detected to measure the CEO frequency [1]. The following equation describes the beat signal that is created:

f =+−+⎡⎤22()()fNff Nf ceo⎣⎦ ceo rep ceo rep

Our work seeks to develop a stabilized frequency comb source in the 1550 nm wavelength range using mode-locked fiber lasers in the context of developing an optical arbitrary waveform generator. Because the spectra from such lasers are generally not octave-spanning, the output of these lasers will be coupled into nonlinear fibers to generate octave-spanning supercontinuum spectra, which may then be used to stabilize the mode-locked fiber laser frequency comb [3, 4]. Initial efforts seek to accomplish this at 1 GHz repetition rates, with plans to later develop 10 GHz and 40 GHz systems.

Previous work on regeneratively-synchronized, harmonically mode-locked, fiber lasers demonstrated 1 GHz repetition rate from a soliton fiber laser [6]. Because the mode-locking mechanism is passive, no external oscillator is required, leading to a more simple locking system and, in most cases, lower noise. Figure 7 shows the layout of this system, including the regenerative synchronization loop used for harmonic mode-locking. The intra-cavity etalon will suppress amplitude and timing noise, particularly noise corresponding to the occurrence of pulse dropouts/pairs. The laser repetition rate will be locked to the etalon; the required locking electronics for this are still in development, and are not shown.

The required octave-spanning supercontinuum spectrum will be generated with highly nonlinear fibers (HNLFs). The 1 GHz laser output will first be amplified, and then coupled into an HNLF to

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generate the supercontinuum spectra. Figure 8 illustrates the envisioned final state of the system, with estimates of the powers and pulse durations occurring at various points. Efforts to carefully prepare the optical pulse train and to find the appropriate HNLF are currently in progress.

The current state of the supercontinuum generation system is simpler than that shown in Figure 8. It consists of a pre-amplifier, a pulse shortening fiber, and HNLF, in that order. Figure 9 shows results from this system. With improved pulse powers, broader octave-spanning supercontinuum spectra should be achievable.

Figure 7. The harmonically mode-locked, regeneratively synchronized fiber laser. The intracavity etalon will filter amplitude and phase noise, and serve as the reference cavity for repetition rate stabilization. Stabilization electronics that lock the laser to the etalon are not shown.

Figure 8. The envisioned supercontinuum generation system.

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Figure 9. The power spectra densities for the amplified laser output before the HNLF (gray), and the resulting supercontinuum spectrum (black).

References: 1. Jones, D.J., et al., Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis. Science, 2000. 288(5466): p. 635-639.

2. Diddams, S.A., et al., Direct Link between Microwave and Optical Frequencies with a 300 THz Femtosecond Laser Comb. Physical Review Letters, 2000. 84(22): p. 5102-5105.

3. Tauser, F., A. Leitenstorfer, and W. Zinth, Amplified femtosecond pulses from an Er:fiber system: Nonlinear pulse shortening and self-referencing detection of the carrier-envelope phase evolution. Optics Express, 2003. 11(6).

4. Hong, F.-L., et al., Broad-spectrum frequency comb generation and carrier-envelope offset frequency measurement by second-harmonic generation of a mode-locked fiber laser. Optics Letters, 2003. 28(17): p. 1516-1518.

5. Drever, R.W.P., et al., Laser phase and frequency stabilization using an optical resonator. Applied Physics B (Photophysics and Laser Chemistry), 1983. B31(2): p. 97-105.

6. Yu, C.X., et al., Gigahertz-repetition-rate mode-locked fiber laser for continuum generation. Optics Letters, 2000. 25(19): p. 1418-1420.

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Ultrafast Phenomena and Quantum Electronics

Multimode phenomena in quantum cascade lasers

Sponsors Army Research Office (ARO) W911NF-04-1-0253

Project Staff Dr. Ariel Gordon, Christine Wang (Harvard), Dr. Laurent Diehl (Harvard), Professor Alexey Belyanin (Texas A&M), Professor Federico Capasso, (Harvard), J. Faist (Univ. Neuchatel) and Professor Franz X. Kärtner

In 2000, R. Paiella et al. reported strong evidence of self-pulsations at the cavity roundtrip frequency in electrically pumped quantum cascade lasers (QCLs) [1]. The emission of 3-5 picoseconds-long pulses was indirectly inferred from the data. No detailed pulse characterization was however available at that time, because of the lack of suitable mid-infrared autocorrelation techniques. Several questions regarding the nature of the mode locking mechanism remained open.

Nonlinear interferometric autocorrelation measurements have led to the conclusion that the mode-locked regime of the QCLs is not characterized simply by a train of isolated pulses separated by the cavity roundtrip time but rather by a rich multimode dynamics. In addition, given that the gain recovery time of QCLs is in general extremely short compared to the cavity round- trip time, stable mode locking is not expected according to conventional theories [2,3]. The aim of the project reported here is to understand the different multimode regimes that can occur in QCLs, and more generally, in lasers with fast gain recovery.

We have identified two mechanisms that play a key role in the multimode dynamics of lasers: A coherent multimode instability and spatial hole burning. The coherent multimode instability is related to the so-called Risken-Nummedal-Graham-Haken (RNGH) instability [4,5]. The latter was theoretically predicted as early as in 1968: the CW solution loses its stability when the pumping level exceeds the lasing threshold by typically 9-10 times. Its observation remains controversial [6,7,8]. In our experiments, the multimode instability occurs at much lower pumping rates than 9- 10 times above threshold. However, we have shown that the presence of a saturable absorber, provided e.g. by a Kerr-lensing mechanism lowers the threshold for the instability considerably. A typical signature of this type of mechanism is a spitting in the laser spectrum of the order of the Rabi frequency. The second mechanism is spatial hole burning.

The lasers studied can be divided into two categories. In the first category, the sidewalls of the laser ridge are covered by a lossy metal contact, which acts as a Kerr-lens type saturable absorber [1]; the latter is weaker in the second category, as the gold contacts and the waveguide core are separated by a thick insulating InP layer. The above differences are clearly visible in Fig. 1.a & b. The optical spectra measured in continuous mode with devices belonging to each of the two categories show obvious signs of instability, as illustrated in Fig. 1.c & d. In type 1 devices (Fig. 1.c), the spectra are single mode and become clearly multimode with two pronounced sidebands separated around the cw solution by the Rabi frequency. This is a typical signature of the RNGH instability. In type 2 devices (Fig. 1.d), the envelope of the spectra show continuous multiple peaks, whose separation is independent of the pumping level.

We have developed a model of the instability using the Maxwell-Bloch equations. Both a saturable absorber and spatial-hole burning were incorporated into the calculations. When a saturable absorber is present, the spectra obtained numerically show clearly the growth of mode sidebands around the original CW frequency separated by the Rabi frequency, and thus have the same characteristic as the type 1 spectra. When spatial hole burning is dominant, the simulated spectra show the growth of the instability at very low pump ratios above the lasing threshold.

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In summary, we have observed wideband multimode operation in QCLs with spectral signatures that can be traced back to spatial-hole burning and the RNGH instability. Furthermore it will be shown in detail that the characteristics of the measured spectra are in good agreement with spectra computed from a model based on the Maxwell-Bloch equations.

a b Plated Au n+ InGaAs Gold InP Gold Gold re-grown re-grown Active Material Active InP cladding

+ n InP substrate 2

12 220 mA c d 12 47 mA 250 mA 50 mA 255 mA 55 mA 260 mA 60 mA 8 280 mA 0.15 THz 8 70 mA 300 mA Ω ≈ 0.4 THz 80 mA 400 mA 0.8 THz R 100 mA 500 mA 120 mA 600 mA 4 4 700 mA 140 mA Spectral Intensity(a.u.)

800 mA 160 mA

900 mA 180 mA

1000 mA 200 mA 0 0 1280 1300 1320 1340 1360 1380 1925 1950 1975 2000

Wavenumber (cm-1) Wavenumber (cm-1)

e f

Fig. 1. a SEM image of type 1 laser. b. SEM image of type 2 laser. c. Spectra of type 1 laser. d. spectra of type 2 laser. e. Simulated spectrum with a saturable absorber. f. Simulated spectrum without a saturable absorber.

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References

[1] R. Paiella, et al., Science 290, 1739 (2000)

[2] H. A. Haus, IEEE J. Quantum Electron., 11, 736 (1975)

[3] H. A. Haus, J. Appl. Phys., 46, 3049 (1975)

[4] H. Risken and K. Nummedal, J. Appl. Phys., 39, 4662 (1968)

[5] P. Graham and H. Haken, Z. phys. 213, 420 (1968)

[6] E. Pessina, G. Bonfrate, F. Fontana and L. A. Lugiato, Phys. Rev. A, 56, 4086 (1997)

[7] E. Roldan, G. J de Valcarcel, J. F. Urchueguia and J. M. Guerra, JOSA B, 20, 816 (2003)

[8] L. W. Hillman, J. Krasinski, R. W. Boyd and C. R. Stround, Phys. Rev Lett., 52, 1605 (1984).

Characterization of optical switches and wavelength converters using two-color heterodyne pump-probe

Sponsors: DARPA – DAAD19-03-1-0090 Air Force Office of Scientific Research – FA9550-04-01-0011

Project Staff: Ali Motamedi, Jade P. Wang, Ryan D. Williams, Prof. Erich P. Ippen, Prof. Rajeev Ram, Prof. Leslie Kolodziejski, Dr. Scott Hamilton

To accommodate the increasing demand for higher bit rate optical communication, a new generation of optical communication networks is being developed in which optical-to-electrical conversion bottlenecks will be minimized by keeping the data in the optical domain. Such all- optical networks require advanced photonic technologies for a variety of ultrafast all-optical signal processing functions including optical logic and wavelength conversion. An important focus of our research is to study the ultrafast dynamics of active and nonlinear semiconductor devices for potential application to such processing.

A device that can be used as both a wavelength converter and an ultrafast optical logic gate is the integrated SOA-based Mach-Zehnder (MZ) interferometer [1,2]. This device takes advantage of nonlinear cross-phase modulation between optical signals in the semiconductor amplifier (SOA) segments. The differential phase between the two SOA arms of the interferometer can be optically controlled via input optical (control) signals entering the two arms. A schematic of such a device, being designed and fabricated in Prof. Kolodziejski’s group, is shown in Figure 1. The designs of individual component structures in this integrated active-passive device are also shown as insets in Figure 1. Signals entering ports A and A’ control the transmission of signals entering the B port.

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Figure 1: Schematic of an integrated SOA-based nonlinear Mach-Zehnder interferometer. Insets show designs and optical mode simulations of the individual components.

For operation at data bit rates greater than 100 Gb/s the ultrafast carrier dynamics of the SOA’s play a crucial role. Patterning effects due to carrier population dynamics with recovery times on the order of 100ps need to be minimized or compensated for. Ultrafast nonequilibrium dynamics that take place on a sub-picosecond timescale begin to play a role [3]. To analyze these effects and optimize the design and functionality of these devices, we need to study both the index of refraction changes and gain/loss changes that occur in various materials and device structures with femtosecond time resolution and with a variety of wavelength combinations [4]. To that end we have developed a two-color heterodyne [5] pump-probe approach for femtosecond studies in the 1.5µm wavelength regime. Figure 2 shows the experimental setup for this approach.

In this schematic, the150-fs pulse optical signal centered at 1.53µm from the output of a synchronously pumped optical parametric oscillator (OPO) is divided into two paths, the pump and the probe. The probe beam passed through a highly nonlinear bismuth-oxide fiber [6]. The output signal from this fiber consists of a broad chirped optical-spectrum centered at 1.53µm in frequency domain, while in the time domain, the pulsewidth is larger than the initial 150fs at the output of the OPO. This signal is then passed through a bandpass filter (BPF) centered at 1560nm, and passed through a grating pair to remove the chirp and shorten the pulsewidth back to 150fs. This signal is divided once again into two paths, one of which (probe) is frequency shifted by 40 MHz with an acousto-optic modulator (AOM) and is incident upon the device under test (DUT), while the other (ref) is frequency shifted by 39 MHz and is passed around the DUT.

In the pump path, the original signal is passed through a translation stage which is controlled by a computer to change the time delay between the pump and the probe, and is then subsequently chopped and directed to the DUT. The output signal from the DUT consisting of the both the pump and the probe signals at two different wavelengths is passed through a BPF centered at 1560 nm to remove the pump signal. The probe signal and the reference signal are then combined and detected using a photodiode. The output of the photodiode consists of the beat signal between the probe and Ref signals at 1MHz frequency which in turn is detected by the receiver and its amplitude and phase is measured using a lock-in amplifier. Using this method we can study both gain and index of refraction changes as a function of time.

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Figure 2: Schematic of heterodyne, two-color femtosecond pump-probe apparatus

In addition to the above studies, we are also employing a two-color pump probe at 800nm pump and 1550nm probe for investigations of ultrafast dynamics in SiGe saturable absorber mirrors and ion implanted Si devices.

References: 1. R. P. Schreieck, M. H. Kwakernaak, H. Jackel, and Hans Melchior, “All-optical switching at Multi-100Gb/s data rates with Mach-Zehnder interferometer switches”, IEEE J. Quant. Electron., 38, 1053-1061, 2002.

2. K. E. Stubkjaer, “Semiconductor optical amplifier-based all-optical gates for high-speed optical processing,” IEEE J. Sel. Top. In Quant. Electron., 6, 1428-1435, 2000. 3. K.L. Hall, E.R. Thoen and E.P. Ippen,, “Nonlinearities in Active Media, Semiconductors and Semimetals,” Chapter 2, Vol 59, Eds. E. Garmire and A. Kost, Academic Press, 1998.

4. T. Katayama, H. Kawaguchi, “Measurement of self- and cross-gain saturation dynamics using two-color heterodyne pump-probe technique”, IEEE Photonics Tech. Lett., 17, 1244-1246, 2005.

5. K.L. Hall, G. Lenz, E.P. Ippen, and G. Raybon, “Heterodyne Pump-Probe Technique for Time- Domain Studies of Optical Nonlinearities in Waveguides,” Optics Lett. 17, pp. 874-876, 1992

6. J. T. Gopinath, H. M. Shen, H. Sotobayashi, E. P. Ippen, T. Hasegawa, T. Nagashima, N. Sugimoto, “Highly Nonlinear Bismuth-Oxide Fiber for Smooth Supercontinuum Generation at 1.5 µm,” Opt. Express,12, p.5697-5702, 2004.

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Nonlinear Effects in Photonic Crystal Fibers – Nd:Glass Femtosecond Laser

Sponsors National Institutes of Health – R01-CA75289-07, R01-EY11289-20 National Science Foundation – ECS-01-19452, BES-0522845 Air Force Office of Scientific Research – F49620-01-1-0186, F49620-01-01-0084 The Telecommunications Advancement Foundation The Whitaker Foundation The Poduska Family Foundation

Project Staff Aaron D. Aguirre, Dr. Norihiko Nishizawa, Professor James G. Fujimoto, Wolfgang Seitz (High Q Laser Production, GmbH, Austria), Max Lederer (High Q Laser Production, GmbH, Austria), Daniel Kopf (High Q Laser Production, GmbH, Austria)

The high cost and complexity of femtosecond laser sources has driven the development of lower cost alternatives for ultrahigh resolution optical coherent tomography (OCT) imaging [1-8]. Among them, continuum generation in highly nonlinear fibers is one of the promising techniques. Photonic crystal fiber (PCF) technology is extremely powerful because it enables customization of the fiber dispersion profile, which can be used to control the nonlinear processes responsible for continuum generation. The realization of supercontinuum generation in PCF [9] has enabled ultrahigh resolution OCT at wavelengths throughout the visible and near infrared [10-12].

We have developed a novel PCF design concept for a broadband, stable continuum light source for ultrahigh resolution OCT imaging [13]. By injecting pulses at 1064 nm from a Nd:Glass laser into a commercially available photonic crystal fiber with a parabolic dispersion profiles and two closely spaced zero dispersion points centered around 1050 nm, we numerically and experimentally demonstrate that a stable continuum can be generated with high brightness double peaks centered at 800 nm and 1300 nm, two primary wavelengths of interest to the OCT imaging community.

Figure 1. Simulated fiber length dependence of the continuum spectrum generated by 85 fs, 18 kW peak power pulses at 1060 nm. Nearly complete depletion of the pump wavelength is observed along with creation of two high brightness main peaks centered near 800 nm and 1300 nm.

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Fig. 1 presents numerical results for the length dependence of the continuum, with spectra displayed on a linear scale. The fact that the continuum rapidly evolves into a double peak structure with nearly complete depletion of the pump wavelength predicts that the main spectral peaks can be localized to the important OCT imaging wavelength regions near 800 nm and 1300 nm. The input spectrum is rapidly broadened within 10 cm to a full spectral width of more than one octave between 700 nm and 1500 nm. Additional propagation in the fiber leads to further depletion of the region between the two spectral peaks as well as filling in and smoothing of the main peaks.

Figure 2. Simulated pump wavelength dependence for optimal continuum generation. Input pulses of 85 fs, 18 kW peak power illustrate differences in continuum as a function of pump wavelength.

Fig. 2 presents spectra resulting from simulations of 85 fs, 18 kW peak power pulses propagated through a 2 m length of the photonic crystal fiber at various center wavelengths around the depletion region. For OCT imaging, spectral shape is a critical determinant of image quality since non-Gaussian spectra with large modulation can lead to large coherence wings on the interference point spread function [14]. The simulations indicate that smooth, twin peak spectra can be achieved when the wavelength of the pump pulse is located between the two zero dispersion wavelengths. Since choosing the optimal pump wavelength is largely equivalent to optimizing the fiber dispersion profile for a fixed pump wavelength, custom photonic crystal design and fabrication should enable ultrahigh resolution OCT with several commercially available femtosecond oscillators.

The measured continuum spectrum (the solid line) and the pump spectrum (the dashed line) are presented in Fig. 3. The continuum spectrum shown is a concatenation of spectra measured separately with 0.5 nm resolution, a method which enables more precise representation of spectral shape and relative amplitude. The spectrum agrees reasonably well with previously presented simulation results. As predicted in the simulation, energy is efficiently depleted from the pump wavelength and transferred to the two spectral bands around 800 nm and 1300 nm.

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Bandwidths of 156 nm and 116 nm are achieved at 1300 nm and 800 nm, respectively. However, the modulation seen on the spectrum is greater than expected based on numerical simulations for an injected pulse at 1064 nm. Error in the approximation of the higher order dispersion terms for the fiber, the change in the fiber’s dispersion profile over the length and coupling effect may be the causes for the spectral modulation.

Figure 3. Experimental measurement of continuum spectrum on (a) linear and (b) log scales. The pump laser spectrum is also shown in (a). These spectra are created from concatenation of individually measured spectra in the 800 nm and 1300 nm wavelength regions.

Figure 4 shows the recorded RF noise spectra acquired using a fast photodiode. The measurements were made at the first harmonic of the laser repetition rate and normalized to the carrier power. Detected first harmonic carrier power was 1.13 dBm for the oscillator alone and - 22.97 dBm and -17.0 dBm for the wavelength regions of 800 nm and 1300 nm, respectively. The noise spectra largely tracks that of the oscillator alone implying that OCT imaging can be performed with high sensitivity due to the lack of excess amplitude noise.

Figure 4. Experimental measurement of RF noise spectra for the filtered wavelength regions around (a) 800 nm and (b) 1300 nm. The noise spectra are compared to the RF spectrum for the Nd:Glass oscillator alone.

The continuum spectrum was used with time-domain, ultrahigh resolution OCT systems to demonstrate imaging in biological tissue. It should be noted that, while these sources were demonstrated for time-domain ultrahigh resolution OCT imaging, they can also be implemented

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with spectrometer based spectral domain OCT systems for high speed, ultrahigh resolution OCT at 800 nm and 1300 nm [15-18]. System performance characterization is presented for both 800 nm and 1300 nm in Fig. 5. Figures 5(a) and (b) compares the point spread function on a linear scale for both wavelengths while (c) and (d) presents the same data on a logarithmic scale. At 800 nm, 3.0 µm full width at half maximum (FWHM) is achieved, which for index of refraction in tissue of 1.38 will provide ~ 2.2 µm in tissue. At 1300 nm, 6.5 µm FWHM provides ~ 4.7 µm in tissue. The sidelobe coherence artifacts on the point spread functions at both wavelengths are present at ~ 25-30 dB, indicating further work to investigate spectral smoothing in the PCF will be important for performance improvement since sidelobe levels of 40-50 dB are desirable for OCT imaging. Sensitivity was measured to be ~ -103 dB for 1.0 mW sample exposure at 800 nm and ~ -107 dB for 3.0 mW sample exposure at 1300 nm.

(a) (b)

3.0 um 6.5 um

(c) (d)

Figure 5. Ultrahigh resolution OCT performance evaluation. Linear (a,b) and logarithmic (c,d) point spread functions are shown for both 800 nm (a,c) and 1300 nm (b,d).

Fig. 6 presents representative OCT imaging results in formalin fixed hamster cheek pouch at 800 nm and 1300 nm. Fine features such as the epithelium (e), connective tissue (c), and muscular layers (m) in the fixed tissue specimen can be visualized with high resolution and high contrast. Some blurring of the images results from the sidelobe coherence artifact, but this can be improved with further optimization of the continuum light source.

While it is unlikely that continuum generation sources will find widespread use for ultrahigh resolution retinal imaging at 800 nm due to the availability of broadband superluminescent diode (SLD) sources [8], they offer a very promising alternative to SLD’s for ultrahigh resolution imaging in other applications where more power and/or longer wavelengths are required. The novel PCF design with two closely spaced zero dispersion wavelengths offers a solution to the problems of excess noise and low power efficiency that have hindered the use of supercontinuum generation for ultrahigh resolution OCT in the 1300 nm wavelength range. The work also suggests that a

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single commercially available oscillator combined with various highly nonlinear fibers can be used to generate stable, high brightness spectra for ultrahigh resolution OCT imaging throughout the near infrared wavelength region.

Figure 6. Ultrahigh resolution OCT images of formalin fixed hamster cheek pouch at (a) 800 nm and (b) 1300 nm. Enhanced image penetration is noticeable at 1300 nm and important features such as the epithelium (e), connective tissue bands (c), and muscular layers (m) can be distinguished.

References

[1] A. M. Kowalevicz, T. R. Schibli, F. X. Kartner, and J. G. Fujimoto, "Ultralow-threshold Kerr-lens mode-locked Ti:Al2O3 laser," Optics Letters 27(22): 2037-39 (2002). [2] A. Unterhuber, B. Povazay, B. Hermann, H. Sattmann, W. Drexler, V. Yakovlev, G. Tempea, C. Schubert, E. M. Anger, P. K. Ahnelt, M. Stur, J. E. Morgan, A. Cowey, G. Jung, T. Le, and A. Stingl, "Compact, low-cost Ti:Al2O3 laser for in vivo ultrahigh- resolution optical coherence tomography," Optics letters 28(11): 905-7 (2003). [3] D. L. Marks, A. L. Oldenburg, J. J. Reynolds, and S. A. Boppart, "Study of an ultrahigh- numerical-aperture fiber continuum generation source for optical coherence tomography," Optics Letters 27(22): 2010-12 (2002). [4] P. C. Wagenblast, T. H. Ko, J. G. Fujimoto, F. X. Kaertner, and U. Morgner, "Ultrahigh- resolution optical coherence tomography with a diode-pumped broadband Cr3+: LiCAF laser," Optics Express 12(14): 3257-63 (2004). [5] L. Vabre, A. Dubois, and A. C. Boccara, "Thermal-light full-field optical coherence tomography," Optics Letters 27(7): 530-2 (2002). [6] A. M. Kowalevicz, T. Ko, I. Hartl, J. G. Fujimoto, M. Pollnau, and R. P. Salathe, "Ultrahigh resolution optical coherence tomography using a superluminescent light source," Optics Express 10(7): (2002). [7] C. Grivas, T. C. May-Smith, D. P. Shepherd, R. W. Eason, M. Pollnau, and M. Jelinek, "Broadband single-transverse-mode fluorescence sources based on ribs fabricated in pulsed laser deposited Ti : sapphire waveguides," Applied Physics a-Materials Science & Processing 79(4-6): 1195-98 (2004).

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[8] T. H. Ko, D. C. Adler, J. G. Fujimoto, D. Mamedov, V. Prokhorov, V. Shidlovski, and S. Yakubovich, "Ultrahigh resolution optical coherence tomography imaging with a broadband superluminescent diode light source," Optics Express 12(10): 2112-19 (2004). [9] J. K. Ranka, R. S. Windeler, and A. J. Stentz, "Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm," Optics Letters 25(1): 25-27 (2000). [10] I. Hartl, X. D. Li, C. Chudoba, R. K. Hganta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, "Ultrahigh-resolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber," Optics Letters 26(9): 608-10 (2001). [11] B. Povazay, K. Bizheva, A. Unterhuber, B. Hermann, H. Sattmann, A. F. Fercher, W. Drexler, A. Apolonski, W. J. Wadsworth, J. C. Knight, P. S. J. Russell, M. Vetterlein, and E. Scherzer, "Submicrometer axial resolution optical coherence tomography," Optics Letters 27(20): 1800-2 (2002). [12] W. Drexler, "Ultrahigh-resolution optical coherence tomography," Journal of Biomedical Optics 9(1): 47-74 (2004). [13] A. D. Aguirre, N. Nishizawa, J. G. Fujimoto, W. Seitz, M. Lederer, and D. Kopf, "Continuum generation in a novel photonic crystal fiber for ultrahigh resolution optical coherence tomography at 800 nm and 1300 nm," Optics Express 14(3): 1145-60 (2006). [14] S. R. Chinn and E. A. Swanson, "Blindness Limitations in Optical Coherence Domain Reflectometry," Electronics Letters 29(23): 2025-27 (1993). [15] M. Wojtkowski, T. Bajraszewski, P. Targowski, and A. Kowalczyk, "Real-time in vivo imaging by high-speed spectral optical coherence tomography," Optics Letters 28(19): 1745-47 (2003). [16] M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, "Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation," Optics Express 12(11): 2404-22 (2004). [17] N. Nassif, B. Cense, B. H. Park, S. H. Yun, T. C. Chen, B. E. Bouma, G. J. Tearney, and J. F. de Boer, "In vivo human retinal imaging by ultrahigh-speed spectral domain optical coherence tomography," Opt Lett 29(5): 480-2 (2004). [18] S. H. Yun, G. J. Tearney, B. E. Bouma, B. H. Park, and J. F. de Boer, "High-speed spectral-domain optical coherence tomography at 1.3 mu m wavelength," Optics Express 11(26): 3598-604 (2003).

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Frequency swept lasers and Fourier Domain Mode Locking (FDML)

Sponsors National Institutes of Health – R01-CA75289-06, R01-EY11289-18 National Science Foundation – ECS-01-19452, BES-0119494 Air Force Office of Scientific Research – F49620-01-1-0186, F49620-01-01-0084 German Research Foundation (DFG) - HU 1006/1-1 The Whitaker Foundation

Project Staff Dr. Robert Huber, Desmond C. Adler, Dr. Maciej Wojtkowski, Dr. Kenji Taira, Professor James G. Fujimoto, J. Y. Jiang (Thorlabs, Inc.), A. E. Cable (Thorlabs, Inc.)

Femtosecond lasers have found various applications as high performance light sources for biomedical imaging. Besides the use of their high pulse powers for non-linear imaging, their broad spectrum and short coherence length served as enabling tools for ultrahigh resolution optical coherence tomography (OCT - see the chapter for Laser Medicine and Biomedical Imaging) [1-3]. Recently, efforts have been made to apply narrowband, rapidly tunable narrowband continuous wave lasers for OCT imaging to achieve higher acquisition speeds and sensitivity [4-15]. This concept is called “swept source OCT,” or sometimes “optical frequency domain imaging (OFDI).” The measurement concept is similar to optical frequency domain reflectometry (OFDR), although the requirements for the laser are very different in OCT applications. The concept of swept source OCT imaging and the experimental imaging setup are described in the foretold chapter in detail. In this section, we will discuss the progress in laser development for swept source OCT.

1. Standard frequency swept lasers

Since the invention of the laser, many different concepts and designs of narrowband tunable or swept laser sources have been investigated for numerous applications. However, none of these designs could provide sufficient performance to meet the demands for swept source OCT. To be suitable for OCT imaging, a laser at 1300 nm wavelength, with 100 nm or more tuning range, 0.1 nm or less instantaneous linewidth and 50,000 – 500,000 sweeps per second is desired [14]. The resulting frequency sweep rates are up to 1019 Hz/s, and the required average output power is >10 mW.

1.1 Design and scaling principles

In order to understand the operation, describe the dynamics, and investigate limitations of such rapidly tuned lasers, a high speed, frequency swept laser light source at 1300 nm was developed. The laser uses a fiber ring design with an additional booster amplifier. Details of the setup are described in ref. [12]. To assist in optimization of the swept laser performance, a theoretical model was developed for the dynamic operation of swept laser sources [12]. The following discussion addresses the fundamental limitation of standard cavity-tuned lasers. In cavity-tuning, the maximum tuning speed is usually limited by the time-constant of the laser to build up lasing from the amplified stimulated emission (ASE) background. This time constant is dependent on the filter function, the ASE intensity, the saturation power, the laser gain and the cavity roundtrip time. In the following analysis we consider two distinct limits, which characterize the frequency tuning behavior of the frequency swept laser source: (i) the saturation limit and (ii) the single roundtrip limit.

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Figure 1. Left: Schematic of the amplified frequency swept laser source. The laser uses a fiber coupled semiconductor amplifier and a tunable fiber Fabry-Perot-filter. An extracavity semiconductor amplifier boosts the laser output. Right: Concept of cavity tuning: build up of laser activity from ASE background.

(i) Saturation limit The first limit or characteristic frequency at which a change in the laser dynamics can be expected is the “saturation limit”. This limit represents the maximum frequency tuning speed which still allows for full build-up of lasing activity from the ASE background. Fig. 1 (right) shows the concept for estimating this characteristic frequency. We assume a background intensity of ASE from the laser medium. The broad green curve shows the ASE spectrum of the laser gain medium, with a characteristic mode structure inside a cavity (narrow green curves). When the filter window is tuned in wavelength, the ASE background is amplified up to the saturation power limit of the gain medium, provided that the time the filter transmits the given wavelength is enough for this build up. The maximum frequency tuning speed which allows the build up of saturated lasing from ASE can be estimated to be:

v ⋅η log ()Gc⋅⋅∆⋅⋅ρλη f ≈≈tuning sweep ∆λ ⎛⎞P ⋅∆λ tuningrange sat tuningrange ⋅⋅ ⋅∆λ log ⎜⎟Lnref tuningrange ∆⋅λ P ⎝⎠ASEtotal

With the physical cavity length L, the mean refractive index of the cavity nref, the gain factor of the laser medium G, the bandwidth of the optical passband of the tunable filter ∆λ, the total wavelength range over which the filter is tuned ∆λtuningrange, the speed of light c, the saturation power of the gain medium Psat, a factor η accounting for a non-linear sweep and the tuning rate in nm/s νtuning. This “saturation build up limit” represents the maximum sweep frequency for which the filter is tuned over its full width half maximum in a time that is sufficient to build up saturated lasing from ASE. Although this is only a rough estimate, it can give design rules for high speed frequency swept laser sources. It is expected that this value gives the order of magnitude of the frequency sweep above which a decrease in output power will occur.

Using the experimental parameters of ∆λ= 0.135 nm, ∆λtuningrange = 120 nm, PASEtotal = 1 mW, Psat = 10 mW, η = 1/π (accounting for the higher sweep speed in a nonlinear sinusoidal sweep), G = 158 (22 dB), ρ = 0.2, L = 2.4 m, and nref =1.46, the estimated sweep speed is ~11,600 Hz for the presented ring laser. This value represents a rough estimate of how fast the laser can be tuned while preserving the maximum power output. Shorter cavities, long duty cycles and linear scans will enable higher speeds. Experimentally it was observed that tuning from shorter to

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longer wavelengths (i.e. to lower energy or frequency) is favored compared to tuning in the opposite direction. This effect can be related to nonlinear effects and carrier dynamics in the semiconductor gain medium. This assists the tuning process because the lasing does not have be build up solely from ASE.

(ii) Single roundtrip – post filtering limit For frequency sweep speeds higher than the “saturation limit”, the output power will decrease until it reaches the “single roundtrip limit”, the frequency tuning speed above which the light on the average makes only one pass from the gain medium to the filter and is coupled out. The filter has tuned so rapidly that during the next roundtrip it already blocks the wavelength. The output light shows the characteristics of ASE which is spectrally filtered and amplified once (on the average). An expression for the sweep frequency for the single roundtrip limit is given by

∆⋅⋅ληc f = sin gle ∆⋅⋅λ Ln tuningrange ref

Using the parameters of the experimental setup, the sweep frequency for the single round trip limit is fsingle is 30,700 Hz. This limit represents an estimate of the maximum frequency for which laser feedback can occur. When the laser is frequency swept above this speed, it operates like a post-filtered broadband light source rather than a tuned cavity.

Fig. 2 (left) shows the output power of the laser for different drive frequencies of the filter. The plots give the power values for the forward sweeps (blue) and the backward sweeps (green). The values are normalized to the output power in non-swept operation. The rectangle marks the region between saturation limit and single roundtrip limit. It can be seen that up to the saturation limit, the power stays almost constant and begins to drop when tuning frequencies exceed the saturation limit. The power falls off completely when the single roundtrip limit is approached. No laser operation is possible above the single roundtrip limit. Due to the saturation limit and the single roundtrip limit, high quality imaging was restricted to drive frequencies of 20 kHz (with a unidirectional filter sweep) or 10 kHz (with a bidirectional filter sweep). In both cases the resulting line rate in OCT applications is limited to about 20 kHz for high quality images. These effects represent a fundamental limit in standard tunable lasers. Concepts for shifting the optical frequency inside the laser cavity, such as the use of acousto-optic or electro-optic frequency shifters, during the roundtrip can usually not provide sufficient shifting to support the desired tuning rates because these devices typically do not generate shifts larger than a few GHz.

The only solution to increase the tuning speed in standard tunable lasers is to decrease the cavity length and build a shorter resonator, as described in subsection 1.2. A completely different and more elegant solution that entirely overcomes the previously-described speed limitations and simultaneously improves many other performance aspects of the swept source is the concept of Fourier Domain Mode Locking (FDML), described in section 2.

1.2 Short Bulk cavity lasers

Short laser cavities can improve the performance and maximum sweep rate of tunable lasers [12], as described in subsection 1.1. A free space bulk cavity design with a standing wave linear geometry appears most promising to reduce the total optical path length inside the cavity. The following subsection describes the setup and performance of such a design [14].

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Figure 2. Left: Output power vs. sweep frequency. Right: Imaging examples.

Fig. 3 shows a schematic representation of the frequency swept, external cavity laser system. Starting from the left side of the figure: The semiconductor gain element (1) is approximately 1 mm in length, with an estimated index of refraction of 3.5 at 1300 nm. The left facet serves as the output coupler for the laser and the output facet reflectivity is estimated to be 15 %. The semiconductor gain element is bonded to a TE cooler and is maintained at 22° C. The intra-cavity side of the semiconductor gain element utilizes a curved waveguide and an anti-reflection (AR) coated facet with an estimated effective intra-cavity facet reflectivity of approximately 10-4, which suppresses self-lasing and allows the semiconductor element to serve as an effective gain medium for the external cavity. The collimating lens is an AR coated aspheric lens (2) with a 2 mm focal length. A free space region of 370 mm between the collimating aspheric lens and the grating is used to adjust the overall length of the cavity. The diffraction grating (3) has 1017 lines/mm and is mounted on a resonant galvanometer scanner (Electro-Optical Products Corp.) that provides a total optical angular displacement of 14 degrees at 8 kHz. After the grating there is a 45 mm focal length achromatic doublet lens (4) which was optimized for 1.0 µm, 1.3 µm and 1.5 µm wavelengths. The lens focuses different spectral components onto a high reflecting end mirror (5). A slit with 10 µm width (6), bonded directly onto the reflective surface of a broadband dielectric mirror (5) provides active wavelength selection. Only light within a certain wavelength band, such that it is focused on the slit, will be reflected by the end mirror. The end mirror is placed at the back focal plane of the doublet lens and has a reflectivity of greater than 98.5 %. The end mirror and slit assembly act as the back-reflector of the laser resonator. Light output from the laser is collimated by an AR coated aspheric lens with a focal length of 0.7 mm (not shown in Fig. 1) and directed through a -55 dB optical isolator that prevents feedback into the laser cavity. An AR coated, 4 mm focal length aspheric lens is then used to couple the light into an AR coated, single mode fiber.

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Figure 3. Schematic diagram of the high speed, frequency swept laser system.

In addition to providing a constant cavity length during tuning, this design also provides robustness to misalignment because it uses a cat’s eye configuration at the end mirror. This configuration can provide superior stability over designs with a quasi-collimated beam on the end mirror, enabling better long term stability [16]. A further advantage of the design is the ability to change the filter function using different slit widths. Spatial filtering is performed by the slit in the Fourier-plane, analogous to a spectrometer so that cavity alignment is preserved. In addition to a fixed slit, it is also possible to use an adjustable slit.

In OCT applications, the described laser enabled bidirectional, high quality imaging at a line rate of 16 kHz. The axial resolution was slightly better than the SOA-based fiber laser described in section 1 due to a full-width tuning range of 133 nm. Fig. 4 shows in vivo imaging examples of a human finger and a xenopus laevis tadpole in an OCT microscopy application.

Figure 4. Left: Images of a human finger in vivo (3 mm x 1.5 mm) using forward sweeps only (top) and backward sweeps only (bottom). Right: 3D rendering of a volumetric OCT data set (tadpole in vivo), acquired with the swept laser source.

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2 Fourier Domain Mode Locking (FDML)

Rapidly tunable narrowband continuous wave lasers offer the possibility to dramatically increase the imaging speed in optical coherence tomography (OCT) [4-15]. However, fundamental physical limitations impede the utilization of the full potential of swept source OCT as discussed in the prior sections [12]. In standard tunable lasers the performance decreases with increasing tuning rate [12], so satisfactory imaging quality in swept source OCT with these lasers is restricted to several tens of kHz. Sophisticated optical frequency shifting spectrometers, multi- detector balancing setups, or opto-electronic self referencing must be applied to reduce the problems with standard tunable lasers at higher sweep rates [17, 18]. It has been shown in section 1 that a reduction in the cavity length can help to increase the possible tuning speed [12, 14]. However, a reduced cavity length leads to a wider frequency spacing of the laser modes, resulting in fewer active modes within the filter bandwidth. There are strong indications that the reduced number of modes leads to more pronounced beat noise in the output signal and degrades dynamic range and imaging performance. A new concept is therefore introduced to entirely overcome the speed limitations in swept laser sources: Fourier Domain Mode Locking (FDML) [19-22].

2.1 Concept of Fourier Domain Mode Locking (FDML)

Fourier Domain Mode Locking is a new technique to overcome limitations in the maximum tuning speed of swept laser sources and to generate a spectrally very clean frequency sweep – equivalent to train of highly chirped laser pulses [19-22].

Fig. 5 is a schematic showing the concept of an FDML laser compared to a standard frequency- swept laser. In a standard frequency-swept laser, light from a broadband gain medium is spectrally filtered by a narrowband optical bandpass filter within the cavity and fed back to the gain medium.

Figure 5. Left: Standard tunable laser. Right: Fourier domain mode locking (FDML). The tunable optical bandpass filter is periodically driven with a period matched to the round-trip time of the cavity or a harmonic.

In the standard swept laser, only longitudinal modes with frequencies that are transmitted through the narrowband optical filter can lase. When the center frequency of the narrowband optical filter is tuned during a frequency sweep, lasing must build up from spontaneous emission at each new frequency position of the filter. This significantly limits the performance of high-speed, frequency- swept lasers, imposing a trade-off between the speed of the frequency sweep versus linewidth, output power, and tuning range [12].

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In FDML lasers, a dispersion managed delay line is incorporated into the laser cavity and the narrowband optical filter is tuned periodically at the cavity round-trip time, or a harmonic of the round-trip time (Fig. 5 (right)). This produces a quasi-stationary mode of operation. Light from one frequency sweep propagates through the cavity and returns to the filter at the exact time when the transmission window of the optical bandpass filter is tuned to the same optical frequency. Therefore, light from the previous round-trip is coupled back to the gain medium and lasing does not have to build up from spontaneous emission. In other words, an entire frequency sweep is optically stored within the dispersion managed delay line in the laser cavity. Under ideal operation, sequential frequency sweeps have the same phase evolution and are mutually coherent. The narrowband optical bandpass filter dissipates almost no energy because the backcoupled light contains only frequencies that are matched to the transmission window filter at each moment. In the frequency domain, this requires destructive interference of all longitudinal modes that are not transmitted through the narrowband filter at a given time. Thus, the phases of the longitudinal modes must be locked. Standard mode-locked lasers have longitudinal modes locked with constant phase, which corresponds to the generation of a train of short pulses at a repetition rate equal to the cavity round-trip time. Fourier domain mode-locked lasers have modes locked with a different phase relationship. The laser output is not a train of short pulses; instead, it is a train of frequency sweeps or highly chirped, very long pulses. The tunable narrowband filtering is equivalent to an infinite number of narrowband amplitude modulators that are slightly out of phase. Fourier domain mode locking is performed by periodic spectral modulation, rather than amplitude modulation. This can be viewed as the Fourier domain analog of mode locking for short-pulse generation.

2.2 Design and operation of the FDML laser

Fig. 6 is a schematic diagram of the FDML laser. The laser is based on a fiber-ring geometry with a semiconductor optical amplifier (SOA from InPhenix, Inc.) as a gain medium and a fiber Fabry- Perot filter (FFP-TF, Micron Optics, Inc.) as the tunable, narrowband optical bandpass filter. The SOA is polarization insensitive with a polarization dependent gain of ~0.5 dB. The fiber Fabry-

Figure 6. Schematic diagram of the Fourier domain mode-locked (FDML), high-speed, frequency-swept laser.

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Perot tunable filter has a free spectral range of ~200 nm at a center wavelength of 1300 nm and a finesse of ~800. The waveform driver for the fiber Fabry-Perot consists of a digital function generator and an electric power amplifier for driving the low-impedance ~2.2 µF capacitive load of the fiber Fabry-Perot lead zirconate titanate (PZT) actuator. With respect to thermal stability, the drift of the resonance frequency caused by temperature variations as well as drift in the PZT bias offset were minimal and a manual adjustment after about 15 minutes warm up time ensured stable operation for many hours. The optical isolators eliminate extraneous intracavity reflections and ensure unidirectional lasing of the ring cavity. A 30% fiber splitter acts as the output coupler. After isolation, the laser output is amplified with a second fiber-coupled semiconductor amplifier (SOA from InPhenix, Inc.), which functions as a booster amplifier. The booster SOA is also polarization insensitive, with a polarization dependent gain of about 0.5 dB. The physics of post- amplification are discussed in detail in ref. [22]. The losses throughout the cavity are typically 0.35 dB for each isolator, <2 dB for the fiber Fabry-Perot filter, 1.8 dB for the 30 % output coupler and 2.2 dB, 1.5 dB and 1 dB for 7 km, 4.8 km and 3.3 km lengths of fiber, respectively. Between -5 dB and -7 dB of the output of the SOA are coupled back into the SOA. The fiber-to-fiber small signal gain of the SOA is 20 dB.

2.3 Performance of the FDML laser

Fig. 7 shows the transient intensity profiles of the frequency-swept laser for forward (shorter to longer wavelengths) and backward (longer to shorter wavelengths) frequency sweeps at different effective sweep rates. The data is shown for the direct laser output without post-amplification in order to ensure that the transient intensity profiles are not obscured or shaped by saturation effects (see ref. [12]). The physical cavity length was 7 km, which corresponds to a 10-km optical path length. Resonances in the tunable filter drive frequency were observed at 29 kHz and at the higher harmonics. Because two frequency sweeps, one forward and one backward, were generated for each sinusoidal drive cycle, a 29 kHz filter drive frequency corresponds to an effective sweep rate of 58 kHz. In contrast to other high-speed, frequency-swept lasers, in FDML lasers, the forward and backward frequency sweeps have the same intensity profile and the same maximum power.

Figure 7. Transient intensity profiles of the FDML laser for different effective sweep rates. The traces always show the transient intensity for one forward and one backward frequency sweep.

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Figure 8. Integrated spectra of the FDML source for different effective sweep rates.

Fig. 7 shows that neither the shape, nor the amplitude of the transient intensity profiles changes as the filter drive frequency is increased. The maximum filter drive frequency and frequency sweep rate (change of the optical frequency per time) are only limited by the mechanical response of the tunable narrowband optical filter. This enables very high-speed OCT imaging, as demonstrated in the following subsections. Fig. 8 shows the integrated spectral output of the source and again no sweep frequency dependence can be observed. Fig. 9 (top) shows the RF fringe signals from a Michelson interferometer for the case of an FDML and a standard swept laser. As expected, the mutual coherent sweeps in the FDML case provide superior phase stability. The roll off characteristic of the point spread functions in OCT application (Fig. 9 (bottom) reflects the instantaneous linewidth or coherence length. Again the superior performance of FDML lasers is evident, up to 7 mm ranging is possible whereas in the comparable standard lasers a considerable decrease over 3 mm can be observed. From the coherence length a linewidth of 0.06nm can be calculated, which is much narrower than the filter width of about 0.25 nm. This important result underlines the fact that in FDML the linewidth is decoupled from the filter width, similar to non-swept lasers. Much broader spectral filters can therefore be applied, reducing component costs and reducing losses in the cavity.

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Figure 9. Superior performance of a FDML laser compared to a non-FDML laser. Top: FDML lasers show much higher phase stability of the RF fringe signals in OCT applications. Bottom: The instantaneous linewidth of FDML lasers is much narrower and the instantaneous coherence length much longer than that of a comparable standard swept laser. The result is a much slower roll off in the point spread functions in OCT application for the case of a FDML laser.

2.4 OCT imaging with FDML laser

The application of the frequency-swept FDML laser for high-speed, swept-source OCT imaging is shown in the images of Fig. 10. The images of a human finger in vivo are acquired at a sweep rate of 40 kHz. Compared to the images acquired with a non FDML laser (see section 1) these images exhibit superior background levels, contrast, and noise performance. No artifacts in the form of stripe like structures can be seen, the images have an extremely clean appearance, and penetration well into the dermis is apparent.

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Figure 10. OCT images acquired with FDML laser; images of human finger in vivo.

2.5 “Buffered FDML”: The second generation of Fourier Domain Mode Locking

FDML removes the fundamental limitations of the maximum achievable sweep speed in swept laser sources. To take full benefit of this concept, the component choices and the laser cavity design have been optimized to achieve record effective sweep rates of 370 kHz. Fig. 11 (left) shows the optimized setup of a classic FDML laser with an optical roundtrip frequency of ~185 kHz. The layout is similar to the FDML laser demonstrated in ref. [22]. The laser resonator is a 2 km long fiber ring cavity with a semiconductor optical amplifier (SOA - InPhenix, Inc.) as the gain medium, two isolators (ISO) to provide unidirectional lasing, and a fiber Fabry Perot tunable filter (FFP-TF - LambdaQuest, Inc.) with a high resonance frequency as the optical bandpass filter. The filter is driven with a sinusoidal waveform at 184.841 kHz, synchronous to the optical roundtrip time of the light. Because two optical frequency sweeps are generated for each period of the sinusoidal drive wave (bidirectional sweeps), the resulting effective sweep rate is 369.682 kHz. 70% of the intra-cavity power is coupled out and, after optical isolation, amplified by a booster SOA (Covega, Inc.). An average output power of 36 mW was achieved with a total tuning range of 100 nm and an instantaneous linewidth of approximately <0.1 nm, at a center wavelength of 1300 nm. Fig.11 (right) shows the transient intensity profiles. In the center of the plot, one forward sweep (-1.5 to 1.2 µs) and one backward sweep (1.2 to 3.9 µs) can be seen. A maximum instantaneous power of ~70 mW is achieved.

Figure 11. Left: Setup of high speed and high power FDML laser with 370,000 optical frequency sweeps per second. Right: transient output power.

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Figure 12. Left: Dynamic range of classic FDML in OCT application for forward and backward sweeps. Right: Dynamic range of buffered FDML in OCT application for forward and backward sweeps.

In OCT systems, the values for sensitivity and axial resolution are typically emphasized as performance metrics. However, especially in highly scattering tissue, the dynamic range of the system is also important. Fig. 12 (left) shows the measured dynamic range of the OCT signal for various imaging depths at 370,000 sweeps/s using an FDML laser. Note that the backward sweeps exhibit a far superior roll-off characteristic with increasing imaging depth compared to the forwards sweeps. Starting at 62 dB for short delays, the dynamic range for the backward sweeps remain above 40 dB over a depth range of 4 mm. In contrast, the forward sweeps roll off to <15 dB at a 4 mm depth range. For imaging applications in highly scattering tissue, the limited dynamic range of the forward sweeps results in poor detail visualization and causes weak reflections to be obscured by the contributions from stronger reflections. For optimum imaging performance at high speeds, only the backward sweeps should be used. In previous FDML lasers such a unidirectional sweep operation would result in an axial scan rate equal to the filter drive frequency, which is only half the frequency achieved by bidirectional sweep operation.

To overcome this problem, we introduced the concept of “buffered FDML” as depicted in Fig. 13 (left). The upper part of the figure shows the fringe signal from an isolated reflection using a classic FDML laser. Each symmetric pair of fringes represents a forward and a backward scan. In buffered FDML system, the laser gain is turned off during the time normally occupied by the forward scan and the resulting time gap is filled with a delayed copy of the backward sweep. The experimental setup for buffered FDML is shown in Fig. 13 (right). The SOA current is modulated such that optical amplification only occurs during the backward sweep. The 2 km fiber delay line of the FDML laser has an additional ouput coupler placed at the 1 km midpoint of the cavity. The fiber delay acts as an optical memory and buffers the backward sweep for half of the drive period. The second output coupler generates the desired time-shifted copy of the backward sweep. The output coupling ratios for the first and the second couplers are 30% and 50% respectively, which approximately equalizes the output power in both copies of the sweep. The outputs are combined in a 50/50 fiber coupler and post-amplified. The resulting fringe signal in buffered FDML operation is shown in Fig. 13 (bottom-left). Only backward sweeps are generated, yet the sweep frequency is maintained at two times the drive frequency. Both sweeps generated during one drive cycle exhibit almost identical properties with respect to their dynamic range (Fig. 12 (right)) and high-quality OCT imaging can be performed at a line rate equal to two times the drive frequency over large depth ranges.

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Figure 13. Left: RF fringe signals for a FDML laser (bidirectional - top) and a buffered FDML laser (unidirectional – bottom); the modulation, copy and delay concept of buffered FDML is sketched by the circles and arrows. Right: Experimental setup of buffered FDML.

Fig. 14 shows examples of images obtained with the buffered FDML laser operating at 370,000 sweeps per second. The images show renderings of a 3D-OCT volumetric data set acquired with a 14-bit A/D system. The 3D reconstructions exhibit low background, no artifacts, high signal to noise a good contrast and deep penetration. The high detail visualization can be seen in the clear definition of the fine spiral structures of the sweat ducts. The overall appearance of the images is very clean, indicating low sidelobes in the point spread function. Imaging at 370,000 sweeps per seconds is an important step towards real time 3-dimensional imaging.

Figure 14. 3-dimensional rendered data sets of human finger in vivo acquired at a laser sweep rate of 370,000 lines/s.

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References

[1] D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254(5035): 1178-81 (1991). [2] W. Drexler, U. Morgner, R. K. Ghanta, F. X. Kärtner, J. S. Schuman, and J. G. Fujimoto, "Ultrahigh-resolution ophthalmic optical coherence tomography," Nature Medicine 7(4): 502-07 (2001). [3] W. Drexler, U. Morgner, F. X. Kartner, C. Pitris, S. A. Boppart, X. D. Li, E. P. Ippen, and J. G. Fujimoto, "In vivo ultrahigh-resolution optical coherence tomography," Optics Letters 24(17): 1221-23 (1999). [4] A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. Elzaiat, "Measurement of Intraocular Distances by Backscattering Spectral Interferometry," Optics Communications 117(1-2): 43-48 (1995). [5] F. Lexer, C. K. Hitzenberger, A. F. Fercher, and M. Kulhavy, "Wavelength-tuning interferometry of intraocular distances," Applied Optics 36(25): 6548-53 (1997). [6] B. Golubovic, B. E. Bouma, G. J. Tearney, and J. G. Fujimoto, "Optical frequency-domain reflectometry using rapid wavelength tuning of a Cr4+:forsterite laser," Optics Letters 22(22): 1704-06 (1997). [7] S. R. Chinn, E. A. Swanson, and J. G. Fujimoto, "Optical coherence tomography using a frequency-tunable optical source," Optics Letters 22(5): 340-2 (1997). [8] S. H. Yun, C. Boudoux, G. J. Tearney, and B. E. Bouma, "High-speed wavelength-swept semiconductor laser with a polygon-scanner-based wavelength filter," Optics Letters 28(20): 1981-83 (2003). [9] M. A. Choma, M. V. Sarunic, C. H. Yang, and J. A. Izatt, "Sensitivity advantage of swept source and Fourier domain optical coherence tomography," Optics Express 11(18): 2183- 89 (2003). [10] S. H. Yun, G. J. Tearney, J. F. de Boer, N. Iftimia, and B. E. Bouma, "High-speed optical frequency-domain imaging," Optics Express 11(22): 2953-63 (2003). [11] M. A. Choma, K. Hsu, and J. Izatt, "Swept source optical coherence tomography using an all-fiber 1300-nm ring laser source," Journal of Biomedical Optics 10(4): #044009 (2005). [12] R. Huber, M. Wojtkowski, K. Taira, J. G. Fujimoto, and K. Hsu, "Amplified, frequency swept lasers for frequency domain reflectometry and OCT imaging: design and scaling principles," Optics Express 13(9): 3513-28 (2005). [13] J. Zhang and Z. P. Chen, "In vivo blood flow imaging by a swept laser source based Fourier domain optical Doppler tomography," Optics Express 13(19): 7449-57 (2005). [14] R. Huber, M. Wojtkowski, J. G. Fujimoto, J. Y. Jiang, and A. E. Cable, "Three- dimensional and C-mode OCT imaging with a compact, frequency swept laser source at 1300 nm," Optics Express 13(26): 10523-38 (2005). [15] Y. Yasuno, V. D. Madjarova, S. Makita, M. Akiba, A. Morosawa, C. Chong, T. Sakai, K. P. Chan, M. Itoh, and T. Yatagai, "Three-dimensional and high-speed swept-source optical coherence tomography for in vivo investigation of human anterior eye segments," Optics Express 13(26): 10652-64 (2005). [16] J. J. Snyder, "Paraxial Ray Analysis of a Cats-Eye Retroreflector," Applied Optics 14(8): 1825-28 (1975). [17] M. A. Choma, C. H. Yang, and J. A. Izatt, "Instantaneous quadrature low-coherence interferometry with 3 x 3 fiber-optic couplers," Optics Letters 28(22): 2162-64 (2003). [18] W. Y. Oh, S. H. Yun, B. J. Vakoc, G. J. Tearney, and B. E. Bouma, "Ultrahigh-speed optical frequency domain imaging and application to laser ablation monitoring," Applied Physics Letters 88(10): no.103902 (2006). [19] R. Huber, K. Taira, and J. G. Fujimoto, "Fourier Domain Mode Locking: Overcoming limitations of frequency swept light sources and pulsed lasers," paper presented at Conference on Lasers and Electro-Optics Europe/ European Quantum Electronics Conference (CLEO/Europe - EQEC 2005), Munich, Germany, 2005.

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[20] R. Huber, K. Taira, M. Wojtkowski, and J. G. Fujimoto, "Fourier Domain Mode Locked Lasers for OCT imaging at up to 290kHz sweep rates," Optical Coherence Tomography and Coherence Techniques II, Munich, Germany, 2005. [21] R. Huber, K. Taira, M. Wojtkowski, and J. G. Fujimoto, "Fourier domain mode-locked lasers for swept source OCT imaging at up to 290 kHz scan rates," Coherence Domain Optical Methods and Optical Coherence Tomography in Biomedicine X, San Jose, CA, 2006. [22] R. Huber, M. Wojtkowski, and J. G. Fujimoto, "Fourier Domain Mode Locking (FDML): A new laser operating regime and applications for optical coherence tomography," Optics Express 14(8): 3225-37 (2006).

Physics and Technology of Ultrafast X-ray Sources

The Ehrenfest Theorem and the Single Atom HHG Spectrum

Sponsors Air Force Office of Scientific Research (AFOSR), FA9550-04-1-0011

Project Staff Dr. Ariel Gordon, Dr. Robin Santra (Argonne), Prof. Franz X. Kärtner

In spite of the existing extensive body of knowledge about high harmonic generation (HHG), the existing theoretical literature offers almost no absolute quantitative data for the expected EUV and x-ray intensities in HHG experiments. The importance of such a prediction cannot be overestimated: It will show whether current experiments are extracting the entire potential in terms of efficiency and performance, it will guide experiments to possibly better setups, and it will show what is the best performance one can ever expect from a HHG based device.

The vast majority of the existing HHG calculations give a qualitative rather than a quantitative picture, and the yields are most often given in arbitrary units. The apparent reason is the lack of a description of the single-atom response that would be both quantitatively accurate and fast to evaluate. Some studies [1-2] solve simultaneously the Maxwell equations and the time dependent Schrödinger equation (TDSE). However quantitative results are still not obtained, presumably because of insufficient numerical accuracy or reduced dimensionality. Others solve the three- dimensional Maxwell equations with the three step model (TSM) describing the medium response [3]. This approach also does not provide quantitative results, because the usually employed version of the TSM overestimates the HHG photon yield by orders of magnitude [4].

We have developed an excellent analytic approximation for the HHG single atom response spectrum based on an improved formulation of the TSM. The approximation relates to the effective potential picture, where the atom is assumed to be described by a single electron moving in an effective potential: 1 H =− ∇2 +VxEt()r − (). (1) 2 eff H is the Hamiltonian, Veff is the effective potential, and E(t) is the laser field. Atomic units are used. The model in Eq. (1) is commonly used in the combined Maxwell-Schrödinger codes [1] and elsewhere in HHG. The accuracy of the analytic approximation is typically better than a couple of tens of percents, as found by comparison to a numerical integration of the TDSE.

The proposed analytic approximation for the high frequency part of the HHG spectrum is based on the TSM. One should distinguish between two cases: Whether the electron is initially in the ground state of Veff or in an excited state. The latter case is especially important if Veff describes a many-electron atom, because then the highest occupied orbital of the ground state is

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technically an excited state of Veff. In argon, for example, it would be a 3p state. In addition, one can be simply interested in modeling an experiment where the initial state is an excited atomic state.

If the electron is initially in the ground state of Veff , the standard TSM can be considerably improved if the dipole moment of the electron is computed in the acceleration form (employing Ehrenfest's theorem). This essentially amounts to the replacement of the TSM recombination amplitude by the expression [5] ()=− ∂ () aVrec vrv0 xeff (2) 0 and v are the ground state and a momentum eigenstate respectively.

When the initial state is an excited state, it can be shown [6] that the TDSE keeps the population of the lower-lying states very small. Projecting the latter out of the momentum eigenstate, the recombination amplitude takes the form [6] n−1 ()=− ∂ () + ∂ () anVnVjjrec vrvrvxeff∑ xeff . (3) j=1 n is the initial excited eigenstate of Veff and j are all the eigenstates with lower energies.

Figure 1 compares our analytic approximation for the HHG spectrum to numerical solutions of the TDSE. Figure 1a shows the comparison for atomic hydrogen. The low frequency part of the spectrum was computed employing the plasma approximation (see e. g. Eq. (44) in Ref. [4]). To our knowledge, this approximation has not been previously tested in the context of HHG by comparison to the TDSE. Quantitative agreement is demonstrated. Figure 1b demonstrates good agreement for argon, where the Veff we used is the Hartree-Slater potential, similarly to Ref. [1]. Including the last term of Eq. (3) is shown to be crucial.

a b

Harmonic energy (eV) Harmonic energy

Fig. 1. HHG spectra of a hydrogen (a) and an argon (b) atom in a single cycle 800nm pulse with the amplitudes of 0.14 (a) and 0.12 (b) a.u. Numerical TDSE calculations (black) are compared to analytic approximations (blue). In (a) the plasma approximation was added to the TSM for describing the low frequency part of the spectrum. The red line in the inset shows the spectrum of the error (numerical TDSE minus analytic approximation) at low energies. The dashed line in (b) was calculated omitting the last term in Eq. (3), demonstrating the importance of the latter.

The improved version of the TSM we suggest here, along with the plasma approximation, combine to a simple analytic formula which reproduces almost the entire HHG spectrum to excellent precision. At least in the context of many applications, such as modeling HHG

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experiments including optical propagation effects, the problem defined by Eq. (1) can be considered solved analytically to the required precision. This work opens the way to upgrading the existing HHG modeling from the qualitative to the quantitative level.

References [1] N. H. Shon, A. Suda, and K. Midorikawa, Phys. Rev. A 62, 023801 (2000). [2] M. B. Graade and K. J. Schafer, Phys. Rev. Lett. 89, 213901 (2002). [3] E. Priori, G. Cerullo, M. Nisoli, S. Stagira, S. De Silvestri, P. Villoresi, L. Poletto, P. Ceccherini, C. Altucci, R. Bruzzese, and C. de Lisio, Phys. Rev. A 61, 063801 (2000). [4] T. Brabec and F. Krausz, Rev. Mod. Phys. 72, 545 (2000). [5] A. Gordon and F. X. Kärtner, Phys. Rev. Lett. 95, 223901 (2005). [6] R. Santra and A. Gordon, Phys. Rev. Lett. 96, 073906 (2006).

Role of many electron effects in high harmonic generation

Sponsors Air Force Office of Scientific Research (AFOSR), FA9550-04-1-0011

Project Staff Dr. Ariel Gordon, Dr. Robin Santra (Argonne National Laboratory), Prof. Franz X. Kärtner

The three step model [1] provides a simple picture of the high harmonic generation (HHG) process in intense laser fields: An electron is ionized and accelerated by the laser field, and then recollides with the parent ion. The vast majority of the models associate the emitted radiation with this one “active” electron alone: The radiation amplitude is typically obtained from the oscillating dipole moment that this one electron creates.

However it is obvious that the bound electrons are disturbed by the electron-ion recollision. The electrostatic field of the recolliding electron must, to some extent, set them into motion. These electrons begin to oscillate, and the oscillation can result in the emission of radiation. Since all noble gases apart from helium have many bound electrons, the contribution of this radiation can be significant. In other words, much of the HHG radiation in heavy noble gases should be emitted by the "inactive" electrons.

We propose [2] this mechanism, which has been termed polarizational recombination in the electron-ion collision literature [3], as the source of the enhanced HHG radiation in heavier noble gases compared to lighter ones. In order to compute the radiation emitted by all electrons to first approximation, one can compute the acceleration of the active electron in the unscreened Coulomb potential. That is, to compute the acceleration of the recolliding electron as if it recollided with a bare nucleus. The factor of Z, the atomic number, which arises from this descreening, is actually due to the Z-1 bound electrons and one free electron which radiate.

A cartoon illustrating the idea is shown in Fig. 1. Consider an electron that is about to recollide with its parent ion. The electron experiences some force that is exerted on it by the nucleus and the bound electrons. Then if F is the force exerted by a bound electron on the free electron, the total force exerted on the free electron is also F - F: An attractive force of F - F - ZF and a repulsive force Z×F (Z- +Z - - of (Z-1)F. The radiation F - F emitted by the free - electron is proportional F - F to F, and all Z-1 electrons emit additional Fig. 1: Illustration of the calculation of the radiation emitted by the radiation proportional to

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(Z-1)F. The total emitted radiation is therefore proportional to ZF, as if the nucleus were unscreened.

References

[1] M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L’Huillier, and P. B. Corkum, Phys. Rev. A, vol. 49, pp. 2117-2132, 1994. [2] A. Gordon, F. X. Kärtner, N. Rohringer, and R. Santra, Phys. Rev. Lett., 96, 223902 (2006). [3] A. V. Korol, F. J. Currell, and G. F. Gribakin, J. Phys. B, vol. 37, pp. 2411-2428, 2004.

Femtosecond Timing Distribution in X-ray Free Electron Lasers

Sponsors EU Commission in the Sixth Framework Program, 011935 EUROFEL. Office of Naval Research (ONR) N00014-02-1-0717

Project Staff Jung-Won Kim, Jeff Chen, Dr. F. Ömer Ilday, Axel Winter (DESY), Dr. Frank Ludwig (DESY) and Professor Franz X. Kärtner

Seeding of free electron lasers operating in the EUV and soft X-ray regime with radiation generated via high harmonics from noble gases may result in a fully coherent X-ray laser. For seeding of such large-scale facilities spanning over several hundreds meters to a few kilometers scale, it is critical to synchronize low-level RF-systems, photo-injector lasers, seed radiation and potential probe lasers with low timing jitter in a long-term stable arrangement [1-4]. Figure 1 shows the schematic outline of the timing distribution and synchronization system for such a facility. The pulse repetition rate of an optical master oscillator implemented as a mode-locked laser is stabilized to a frequency standard or a low noise microwave oscillator. The pulse train is distributed to all critical sub-systems by use of timing stabilized fiber links. Finally, a low-jitter, drift-free synchronization between the optical pulse trains and RF-signals will result in a fully synchronized timing system over the large-scale accelerator facility.

Figure 1: Schematic outline of timing distribution and synchronization for an XFEL facility [1,2].

Optical Master Oscillator – Low-jitter Mode-locked Laser It has been long recognized that mode-locked lasers have an enormous potential for generating and transmitting ultra low-jitter RF-signals [5]. Currently the most promising candidates for ultra- low jitter optical master oscillators are Er/Yb-glass lasers [6], passively mode-locked Er-doped fiber lasers [7] and Yb-doped fiber lasers [8]. The crucial performance indicator for such a source is the phase noise or timing jitter integrated from c/2L, where c is the speed of light in the fiber

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and L is the fiber length, to the Nyquist frequency, i.e. half of the lasers repetition rate. Since this noise cannot be taken out by a timing-stabilized fiber link, the high-frequency jitter will set an inherent limitation to the precision in timing achievable with a given distribution system.

Figure 2 (a) shows the measurement result of the stretched-pulse Er-fiber laser [7], compared with the commercial microwave signal generator performance. The integrated timing jitter from 1 kHz to 22 MHz (Nyquist bandwidth) is 10 fs, which is already better than a high-quality microwave signal generator. Note, that the measurement was limited in precision by the direct photo detection, and, in theory, it can reach down to sub-fs jitter levels.

Timing Distribution Precise transfer of RF-signals through fiber links for timing information dissemination has been demonstrated recently [9,10]. For timing distribution over a large-scale free electron laser facility, timing stabilized fiber links are used. If the fiber length is L, we assume that no length fluctuations are faster than 2L/c, where c is the speed of light in the fiber. Relative fiber expansion by temperature change is typically on the order of 10-7/K, which can be compensated for by a fiber length control loop by referencing the back reflected pulse from the fiber end with a later pulse from the mode-locked laser.

Recently, we have demonstrated a timing distribution in a 500-meter long accelerator environment (more detailed information on experiments and results can be found in Refs. [3] and [4]). Figure 2 (b) shows the in-loop phase noise measurement results for fiber link stabilization. When the loop is open, the jitter integrated from 0.1 Hz to 5 kHz is 66 fs; when the loop is closed, the jitter is suppressed down to 12 fs. Thus, a fiber link of 500 meters scale in the accelerator environment can be readily stabilized to 10-fs level using pure RF-techniques. Note, that by use of optical cross-correlation techniques [11], long-term stable sub-fs level stabilization will be feasible in the near future.

(a) (b) Figure 2: (a) Phase noise spectra of Marconi 2041 signal generator and free-running Er-doped fiber laser [3]. (b) In-loop measurement result of the timing stabilized fiber link [3,4].

Optical-to-RF Synchronization Once precise timing information encoded as an optical pulse train arrives at each remote location where we aim to synchronize, it is crucial to convert this optical signal into low-jitter and drift-free RF-signal in a long-term stable way. Recently, it has been shown that the extraction of an RF- signal from an optical pulse train using direct photodetection is limited in precision by excess phase noise [12]. The major contribution to this excess noise was identified to be the amplitude- to-phase (AM-to-PM) conversion in the photodetector. The intensity noise of the laser can be converted into a significant amount of phase noise and drift by this process.

A balanced optical-RF phase detector for the extraction of low-jitter, high-power, and drift-free RF-signals from optical pulse trains is proposed and demonstrated. It is based on precise phase

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detection by use of a differentially-biased Sagnac fiber-loop and synchronous detection. We used the phase error signal from this balanced optical-RF phase detector, which is robust against drifts and photodetector nonlinearities, to regenerate low-jitter RF-signals from optical pulse trains. Detailed operation principle can be found in “A Balanced Optical-RF Phase Detector” chapter of this Progress Report. Figure 3 (a) shows the measured in-loop phase noise spectra. The voltage signal from the phase detector was measured with a low-noise vector signal analyzer (VSA), and converted into single-sideband (SSB) phase noise at 10.225 GHz. This measurement shows that the integrated in-loop jitter is 3.0 fs ± 0.2 fs from 1 Hz to 10 MHz when it is locked. We are currently pursuing sub-fs jitter level by scaling up the optical and RF power, and will perform a long-term out-of-loop measurement in the near future.

Optical-to-Optical Synchronization Synchronization is necessary not only between optical and RF-subsystems but also between different optical systems, for example, between the photo-injector laser and the master oscillator. For the optical-to-optical synchronization, we can use a balanced optical cross-correlator [11]. The technique uses nonlinear optical processes as an extremely sensitive way to detect a timing difference between optical pulses (a detailed description of operation can be found in Ref. [11]). Figure 3 (b) shows the long-term timing jitter measurement between Ti:sa and Cr:fo lasers. The pulses from two lasers are locked with 380 as jitter over 12 hours without thermal drift.

(a) (b) Figure 3: (a) SSB in-loop phase noise spectra at 10.225 GHz. The integrated timing jitter from 1 Hz to 10 MHz is 3 fs when it is locked. (b) Long-term out-of-loop cross-correlation trace. A 380-as timing jitter between two mode-locked lasers is demonstrated over 12 hours.

Outlook In summary, we introduced a scalable, integrated timing distribution and synchronization system for future accelerator and seeded XFEL facilities. The key components and technologies, i.e., low-jitter optical master oscillator, timing distribution by stabilized fiber links, and long-term stable optical-to-RF and optical-to-optical synchronization, are demonstrated. Today, 30-fs jitter level synchronization over several hundreds meters is possible; it is clearly scalable to sub-10-fs by further optimization in the near future.

References [1] J. Kim et al., “Large-scale timing distribution and RF-synchronization for FEL facilities”, FEL 2004. [2] F. X. Kärtner et al, “Progress in Large-Scale Femtosecond Timing Distribution and RF- Synchronization”, PAC 2005. [3] A. Winter et al., “High-Precision Optical Synchronization Systems for X-Ray Free Electron Lasers”, FEL 2005. [4] F. Ö. Ilday et al., “Long-Distance Optical Synchronization System for X-ray Free Electron Lasers” CLEO 2006.

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[5] S. Namiki and H. A. Haus, IEEE J. Quantum Electron. 33, 660 (1997). [6] J. B. Schlager, B. E. Callicoatt, R. P. Mirin, N. A. Sanford, and D. J. Jones, J. Ye, Opt. Lett. 28, 2411 (2003). [7] G. Lenz, K. Tamura, H. A. Haus, and E. P. Ippen, Opt. Lett. 20, 1289 (1995). [8] F. Ö. Ilday, J. R. Buckley, H. Lim, F. W. Wise, and W. G. Clark, Opt. Lett. 28, 1365 (2003). [9] J. Ye et al., J. Opt. Soc. Am. B 20, 1459 (2003). [10] K. W. Holman, D. J. Jones, D. D. Hudson, and J. Ye, Opt. Lett. 29, 1554 (2004). [11] T. R. Schibli et al., Opt. Lett. 28, 947 (2003). [12] E. N. Ivanov, S. A. Diddams and L. Hollberg, IEEE J. Sel. Top. Quant. Elec. 9, 1059 (2003).

Photonics and Devices

Design of High-Index-Contrast Microring-Resonator Add-Drop Filters

Sponsor Pirelli Labs S.p.A., Milan, Italy

Project Staff Miloš A. Popović, Michael R. Watts, Tymon Barwicz, Peter T. Rakich, Luciano Socci, Prof. Erich P. Ippen, Prof. Franz X. Kärtner, Prof. Henry I. Smith

Reconfigurable optical add/drop multiplexers (R-OADMs) enable dynamic reconfiguration of wavelength-division multiplexing (WDM) optical networks. Microphotonic filters based upon microring resonators [1] promise to enable complex, densely integrated chip R-OADMs capable of processing large aggregate data rates. In particular, strongly confining optical structures based on high index contrast (HIC) are a promising solution because they permit small resonators with high Q and a large free spectral range (FSR) needed to span a typical WDM spectrum of ~30 nm [2,5]. However, HIC structures pose severe fabrication challenges in terms of critical dimension size and dimensional sensitivity of resonances, polarization states, etc. Even their theoretical design has not been adequately explored, due to the breakdown of simple analytic approximations in the HIC limit, and the need for computationally intensive, rigorous, 3D vector- field simulations. In addition, bandstop spectral responses in the through port with high in-band extinction ratios, on the order of 40 dB, are required for WDM applications. Yet, no high-order microring filters have been reported to our knowledge providing more than a few dB of through- port extinction, due to the high sensitivity of this response function to parameter variations.

We have identified and resolved two critical theoretical design issues in HIC filters, previously unaddressed in literature – coupling-induced resonance frequency shifts (CIFS) [4] and coupler mode-scattering losses [2,3,5] – that have enabled the demonstration of high-efficiency filters in high index contrast >50% [2,3,5]. The former effect, CIFS, amounts to the shifting of resonance frequencies of individual cavities in a multi-cavity filter, due to the electromagnetic interaction with

Figure 1. Coupling-induced resonance frequency shifts (CIFS) [4]: (a) Field snapshot of rigorous FDTD simulation of third-order filter design with identical rings; (b) the resulting response has an undesired asymmetry in the response reducing through-port extinction to 3dB. Matching of full FDTD simulation and CIFS theory with a transfer matrix model confirms CIFS origin of impairment. Non-identical rings must be used, each with dimensions or index corrected for CIFS to recover the ideal response. In practice, other fabrication-caused asymmetries must also be compensated [6].

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(a) (b) (c)

Figure 2. Coupler loss [2,3,5]: (a) Ring-bus coupler using two 900 nm-wide single-mode waveguides reconfines and excites higher-order mode in coupling region, resulting in filter loss; (b) narrowing bus waveguide to 700 nm suppresses coupler-region parasitic mode without compromising ring resonator bend loss Q, leading to low loss coupler, and filter.

(a)

(b)

Figure 3. High through port extinction from multistage filters [5]: (a) Scanning electron micrograph of three- stage filter with resonance frequency compensation applied to middle ring of each stage; multistage geometry has high (b) measured filter response shows first demonstrated microring-resonator filters with a through-port extinction usable to telecom applications. The over 50 dB extinction is beyond needs of telecom applications. Flat-top, drop roll-off by 30 dB at 80 GHz from channel center and 20 nm FSR allow add-drop applications.

adjacent cavities, a higher-order effect than the energy coupling that produces the filter response. Fig. 1 shows that CIFS can be of the order of the filter bandwidth, severely distorting the res- ponse and causing virtually the disappearance of a through-port stopband. Proper compensation of CIFS and additional fabrication related frequency mismatch [6] enabled frequency-matched filters to be demonstrated [2]. The latter effect, mode scattering in couplers, resulted from the appearance of parasitic higher-order, transient leaky modes in HIC coupler regions even where the individual waveguides are single mode. Fig. 2(a) shows the excitation of such a parasitic mode, evidenced by the field modulation in the bus waveguide. Coupler mode scattering was found to be able to contribute considerable filter losses, comparable to microring bending loss, and material and sidewall roughness losses in ring filters [2,3,5]. By appropriately narrowing the bus waveguide, spurious modes could be eliminated (Fig. 2(b)), while preserving a wide (low bend loss and dimensionally tolerant) ring waveguide (Fig. 2(c)).

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In addition, to demonstrate high through port extinction, we have proposed a multistage filter design comprising reduced-order stages (Fig. 3(a)) to significantly reduce sensitivity [4]. As a result, the first microring-resonator filters were demonstrated having high in-band extinction, greater than 50 dB (Fig. 3(b)). They also showed 20 nm FSR, >30 dB adjacent channel rejection (drop port), and 2 dB drop loss. Future work will address hitless wavelength tuning of the filters.

References 1. B.E. Little, “Advances in microring resonators,” in Proc. IPR Conference, 2003, pp. 165-167.

2. M.A. Popović, M.R. Watts, T. Barwicz, P.T. Rakich, L. Socci, E.P. Ippen, F.X. Kärtner and H.I. Smith, in Optical Fiber Comm. Conference 2005, vol. 5, pp. 213-215, paper OFK1.

3. M.R. Watts, Ph.D. thesis (2005).

4. M.A. Popović, C. Manolatou and M.R. Watts, Opt. Express 14, 1208 (2006).

5. M.A. Popović, T. Barwicz, M.R. Watts, P.T. Rakich, L. Socci, E.P. Ippen, F.X. Kärtner and H.I. Smith, Opt. Lett. 31, no. 17, Sep 1, 2006 (to appear).

6. T. Barwicz, M.A. Popović, M.R. Watts, P.T. Rakich, E.P. Ippen and H.I. Smith, J. Lightwave Technol. 24, 2207 (2006).

Polarization Insensitive Microphotonics: A Key Milestone for High Index Contrast Integrated Photonics

Sponsor Pirelli Research Labs, Milan Italy

Project Staff Peter T. Rakich, Dr. Tymon Barwicz, Miloš A. Popović, Dr. Michael R. Watts, Professor Franz X. Kärtner, Professor Henry I. Smith and Professor Erich P. Ippen

Microphotonics promise to revolutionize optics through the miniaturization of optical elements and dense integration on planar surfaces to achieve complex optical functionality crucial for future telecommunications networks, and for applications ranging from sensing to spectroscopy. For all of these applications, microring cavities have been identified as crucial building blocks. Such cavities are necessary for the construction of on-chip filters and resonators, and have been the subject of intense study over the past decade. Recent progress in design and lithographic techniques have given rise to the first telecom-grade add-drop microring based filters [1-3] in high-index contrast (HIC) SiN (1:2.2) materials systems. Despite the remarkable performance achieved by these filters, they exhibit severe polarization sensitivities, rendering them useless when interfaced with fiber optics, which scramble the polarization of light transmitted within. To address this issue we have demonstrated the first polarization insensitive HIC microphotonic device through polarization diversity scheme.

The polarization diversity concept we explore is simple; it requires that the TE and TM polarizations of light entering the chip be split into separate ports on-chip. If the TM polarization is rotated to become TE polarization as well, both ports can be passed through identical (TE polarization) filters before they are recombined in an analogous fashion. Proper implementation of this scheme results in the optical circuits seen in Fig. 1, necessarily adding a significant degree of complexity.

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Figure 1: (a) Diagram of HIC optical circuit used to implement the polarization diversity scheme. Several new components required for proper implementation, including a coupler, polarization splitter, polarization rotator, and waveguide crossings. (b) Optical micrograph of fabricated optical circuit.

Optical studies of this integrated optical circuit were carried out with use of a tunable laser source and an electronic polarization controller enabling arbitrary polarization synthesis at the input of the device. Light is coupled into and collected from the device with lensed fibers before it is passed through a monochromator. The monochromator acts as a tunable bandpass filter, enabling improved rejection of the ASE pedestal necessary for high-contrast thru-port measurements. The monochromator and the laser are synchronously tuned while the power transmission is collected at the output of the monochromator. The TE and TM eigenstates of the circuit could be identified through the transmission characteristics of individual microring resonators, and a large sample of other polarization states could be made by randomly sweeping the Poincaré sphere with the polarization controller.

Despite the complexity and large number of components used in the fabricated optical circuit seen in Fig 1b, careful optical studies revealed truly remarkable optical performance. The drop- port and thru-port response of cascaded 3rd order microring filters used in this polarization diversity scheme can be seen in Fig 2 for numerous input polarization states. The thru-port response exhibits greater than 35dB in-band extinction over a 25GHz bandwidth, while the Drop- port demonstrates a 2dB insertion loss and a 52GHz bandwidth. Through optical studies of the circuit, excitation of TE and TM polarizations can be seen, as well as 100 randomly chosen polarization states For both the thru and the drop ports the polarization dependent loss (PDL) of the entire circuit does not exceed 2.2dB. Such low filter PDL would not be achievable without good frequency alignment between the two fabricated filters, and outstanding performance from the polarization splitters, rotator and waveguide crossings [4-5]. It should be emphasized that no post-fabrication trimming or tuning was performed to achieve these results.

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Figure 2: Transmission characteristics of cascaded 3rd order microring filter incorporating polarization diversity scheme. TE and TM eigenstates of the drop-port and thru-port are shown in solid, while 100 randomly chosen states are displayed in grey. Circuit exhibits less than 2.2dB PDL over entire C-band.

In conclusion, integrated polarization diversity was demonstrated as a means of constructing polarization-transparent microphotonic circuits from arbitrary polarization-sensitive microphotonic devices. A rigorous test case was created by realizing a polarization-transparent optical add-drop filter from polarization-sensitive microring resonators. The resulting microphotonic circuit is, to our knowledge, the most complex successfully realized. It demonstrated almost complete elimination of polarization sensitivity while maintaining impressive filter performance. Polarization transparency is a key milestone for microphotonics. In this paper, we have shown that with the proposed approach and high-fidelity nanofabrication, HIC microphotonics, such as photonic crystal structures and microring resonators, can be used in real world applications today.

References 1. Popovic, M.A., Barwicz, T., Watts, M.R., Rakich, P. T., Socci, L., Ippen, E.P., Kärtner, F.X.& Smith, H.I., Multistage high-order microring-resonator filters with relaxed tolerances for high through-port extinction, presented at the Conference on Lasers and Electro-Optics CLEO/QELS’05, Baltimore MD, 2005, Paper CMP2.

2. Barwicz, T., Popovic, M.A., Watts, M.R., Rakich, P.T., Ippen, E.P. & Smith, H.I, Fabrication of add-drop filters based on frequency-matched microring resonators, accepted for publication in the J. Lightwave Technol. (2006).

3. Popovic, M.A., Barwicz, T., Watts, M.R.,Rakich, P.T., Socci, L., Ippen, E.P., Kärtner, F.X. and Smith, H.I., Multistage high-order microring-resonator add-drop filters, Optics Letters 31 (17), (2006)

4. Watts, M.R., Haus, H.A. & Ippen, E.P., Integrated mode-evolution-based polarization splitter, Optics Letters 30 (9), 967-969 (2005).

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5. Watts, M.R., Haus, H.A., Integrated mode-evolution-based polarization rotators, Optics Letters 30 (2), 138-140 (2005).

Hitless Filter Tuning and Universally Balanced Interferometers

Sponsor Pirelli Labs S.p.A., Milan, Italy

Project Staff Miloš A. Popović, Michael R. Watts, Prof. Erich P. Ippen, Prof. Franz X. Kärtner

We describe hitless tuning mechanisms for microphotonic filters [1], and a proposed new class of optical interferometers that emerged from this work [2]. Microphotonic filters based on high- index-contrast microring resonators, described in another section in this report, hold out considerable promise to enable chip-scale reconfigurable optical add-drop multiplexers (R- OADMs). For the wavelength channel that these filters operate on to be reconfigurable, the filters must not only be wavelength tunable, but also undergo the reconfiguration operation in a “hitless” manner. This means that express channels in the wavelength-division-multiplexed (WDM) spectrum that are passing through the filter must not be disturbed during the reconfiguration of the filter from the current channel to a new target channel.

A bypass interferometer is one way to achieve such “hitless tuning” functionality in a general way, by placing the filter in one arm of the interferometer. To tune the filter, first the interferometer is made to continuously transfer the entire WDM spectrum from the filter arm to the bypass arm, all the while maintaining all express wavelengths unattenuated in the output port. Once the signal is in the bypass arm, the filter may be tuned to any wavelength. An implementation of such an interferometer, referred to as a hitless switch, based on antisymmetrically cascaded ∆β switches and an intermediate π differential phase shift was proposed by Prof. H.A. Haus in a memo in 2003. This work was presented with additions in [1]. It was shown that the device enabled hitless tuning of higher-order filters without substantial impairments. Demonstration of such a hitless tunable filter based on microring resonators is in progress.

As a follow-up to this work, we proposed a new general class of optical interferometers that are a generalization of this hitless switch, and of which it is a member [2]. They are illustrated in Fig. 1, and have the property that, in the absence of embedded filter F, all signal entering one input port (a1) exits one output port (b2’) at all wavelengths and at all times. Only a few constraints are required: A and A’ are 4 ports with 2 input and 2 output ports, A and A’ must be identical devices (except if non-reciprocal, magnetooptic devices, in which case A’ has a reversed bias field with respect to A in addition), they are substantially lossless and reflectionless, and are connected as shown in Fig. 1, with a π differential phase shift in the interferometer arms. The generalization is made possible by the understanding that from a physical standpoint the recombining property

Figure 1. General schematic of a universally balanced interferometer (UBI), with a filter inserted in one arm [3]. Based on only a few constraints, the interferometer recombines all input entering a1 into b1’, regardless of the details of A and A’.

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Figure 2. Non-dispersive FSR multiplier (×3) for an add-drop filter [2]: (a) UBI with lattice-filter splitter/combiner and microring filter in one arm; (b),(c) splitter A and output port amplitude and group delay responses without ring filter show dispersionless broadband UBI; (d),(e) drop and output port responses with filter show small group delay at suppressed resonances. relies only on time reversibility of Maxwell’s equations and a unitary phase condition that holds for lossless, reflectionless 4-ports. This also leads to the required orientation of A’ with respect to A. Since the recombining property does not depend on the details of the device contained in A and A’, the devices are referred to as universally balanced interferometers (UBIs). For example, they describe the general class of switches and their configurations that may be used for hitless tuning as described in [1]. However, the devices A and A’ need not be switches and may contain resonators, circulators, etc.

Another important application of a UBI proposed in [2] is for multiplication of the effective free spectral range (FSR) and wavelength tuning range of microphotonic resonator-based filters, with virtually no excess dispersion. While Vernier-type schemes have previously been employed to multiply the FSR of resonators, such schemes either do not preserve through-port channels [3], or else introduce excessive group delay and dispersion into through-port express channels due to the narrowband nature of the filters [4,5]. Because UBIs are coherent interferometers, they permit express channels to be arbitrarily split between the filter and the bypass arm in any ratio, and still recombine all those channels at the output. Therefore, one may employ slowly- wavelength-varying, lattice-type filters (cascaded Mach-Zehnder interferometers) as splitter A and combiner A’, as illustrated in Fig. 2(a). They have minimal dispersion. Their amplitude response (Fig. 2(b)) is designed to pass input signals with maximum efficiency to the UBI arm with the ring filter at one ring resonance, but to the bypass arm for the adjacent two resonances, thereby tripling the effective FSR (Fig. 2(d)). Due to the low dispersion of A and A’, the complete filter sees no significant group delay, or group delay variation (dispersion) at suppressed resonances (Fig. 2(e)). In fact, if splitter A is a lattice filter, it can be proved that the small dispersion they do exhibit is exactly canceled by the combiner A’ leading to identically zero excess dispersion contributed by the UBI (with the exception of waveguide dispersion itself that is always present).

Other kinds of UBIs using splitters A and combiners A’ formed of resonant elements, as well as folded implementations have been also been investigated, and this new class of interferometers is expected to enable new device designs for multiple other applications.

References 1. H.A. Haus, M.A. Popović and M.R. Watts, IEEE Photon. Technol. Lett. 18, 1137 (2006). 2. M.A. Popović, E.P. Ippen and F.X. Kärtner, Opt. Lett. 31, no. 18, Sep 15, 2006 (to appear).

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3. S.T. Chu, B. Little, V. Van, J. Hryniewicz, P. Absil, F. Johnson, D. Gill, O. King, F. Seiferth, M. Trakalo and J. Shanton, in Opt. Fiber Comm. Conf. 2, PDP9 (2004). 4. Y. Yanagase, S. Suzuki, Y. Kokobun and S.T. Chu, J. Lightwave Technol. 20, 1525 (2002). 5. M. Margalit, U.S. Pat. No. 6,839,482 B2 (2005).

Global Design Rules for Silicon Microphotonic Waveguides and Resonators

Sponsor Pirelli Labs S.p.A., Milan, Italy

Project Staff Miloš A. Popović, Tymon Barwicz, Prof. Erich P. Ippen, Prof. Franz X. Kärtner

Silicon microphotonics, based on waveguides with strong optical confinement that results from high index contrast (HIC), has been gaining ground as new applications emerge for densely integrated photonic circuits and the integration of electronics and photonics [1,2]. Yet, the majority of work with Si waveguides [3,4] has relied on ad-hoc waveguide designs, typically with square or 2:1 aspect ratio cross section (~450x200nm), and a rigorous theoretical consideration of optimal designs has been lacking. On the other hand, it is important to understand the theoretical design tradeoffs of HIC waveguides, because HIC photonic circuits have extremely small critical dimensions and high sensitivities to dimensional error and sidewall roughness.

In [5], we undertook a systematic, rigorous design study of silicon-in-silica waveguides and resonators with strong optical confinement (allowing high-Q, high FSR resonators), and while addressing critical parameters for tunable filters, sought optimal silicon waveguide cross-section designs. Contrary to presently used 2:1 aspect ratio TE designs, we found that 6:1 aspect-ratio TE and 2:1 TM waveguide designs optimize resonance-frequency dimensional tolerances, optical metal-electrode loss and a number of other constraints in typical filters. We investigated optimal waveguide designs in terms of cross-section and field polarization, with respect to an extensive set of practically relevant criteria: sufficiently large feature sizes; low sensitivity of resonance frequencies and waveguide-cavity couplings to dimensional variations; high Q and large FSR; small propagation loss due to waveguide roughness; and efficient thermo-optic tuning. With a view toward thermally tunable high-order microring resonators, we found that dimensional sensitivity of the resonance frequency, and proximity of metallic heaters (causing optical absorption) ultimately determine the choice of design.

Fig. 1(a) maps the set of largest single-TE-mode (SM-TE) and single-TM-mode (SM-TM)

(a) (b)

Figure 1. Single-TE-mode (TE21 cutoff, 2 modes) and single-TM-mode (TM21 cutoff, 3 modes) rectangular Si waveguide dimensions of all aspect ratios; (b) TM waveguide effective and group indices for all 3 modes vs. aspect ratio [5].

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(a) (b)

Figure 2. (a) Resonant frequency sensitivity to microring waveguide width for TE and TM designs (for thickness sensitivity AR → 1/AR, TE ↔ TM); (b) ring loss Q due to 100nm Chromium metallic slab (heater) at displacements above ring [5]. rectangular Si waveguides for all waveguide cross-section aspect ratios, AR. Larger cross- section increases confinement and achievable FSR, for a given bending loss, while for microring resonators excited by evanescent side-coupling single-mode waveguides are suited. That is, only one resonator mode must be excited to avoid spurious spectral resonances and to prevent coupler loss due to low-Q spurious modes [2]. Mode effective indices specify confinement (bend loss) while in HIC guides mode group indices enter into the tunability, FSR, and cavity loss Q due to propagation losses, Fig. 1(b) shows effective and group indices of SM-TM designs. Three modes are allowed in this case – TE11, the used TM11, and TE21 – because, by symmetry, TE and TM modes will not couple. This unconventional “overmoded” SM-TM design, where the employed TM mode is not the fundamental (best confined) mode, is justified by the analysis of propagation loss [6] that shows that TM modes in wide, thin waveguides can radiate less than TE.

Where active tuning and stabilization of individual cavities is undesirable, sensitivity of resonance frequencies to dimensional errors is critical. It impacts the feasibility of producing multiple resonators with the same, or prescribed relative, resonance frequencies. Fig. 2(a) shows that near-square waveguides that might offer polarization-independent operation (without a diversity approach) have ~200GHz/nm sensitivity to width (and thickness) error making polarization insensitive operation very difficult to achieve, since subatomic dimensional control would be called for in filters of a few to 10’s of GHz bandwidth. Typical TE guides with AR = 2 show ~100GHz/nm and require dimensional control to picometers. Recent frequency-matched HIC filters showed that a sensitivity of 40GHz/nm is manageable with high-fidelity nanofabrication [7]. Fig. 2(a) shows that TE guides with AR>6 and TM guides with AR>1.8 have less than 40GHz/nm sensitivity. Larger AR choices further reduce sensitivity. On the other hand, upper bounds on the aspect ratio are imposed by confinement related issues, such as bend loss (Q), FSR, coupling to the Si substrate, and thermal tunability. For thermally tunable Si add-drop filters optical loss due to optical field overlap with metallic heaters is the most critical parameter. Fig. 2(b) shows that for TM guides with AR>2, a 100nm Cr slab placed above the waveguides must be displaced over 1µm above a ring resonator to avoid spoiling a loss Q of 250k, suitable for a 40GHz-wide filter [8]. TE waveguides are better confined, so AR<7 can be used with a 1µm waveguide-to-heater gap.

A rigorous, global optimization study of Si waveguides was undertaken with critical parameters relevant for resonator-based filters. We have found that Si microring resonator waveguide designs are constrained primarily by dimensional sensitivity and tuning requirements, giving two designs: TE-excited waveguides of AR=6, and TM-excited (“oversized”) waveguides of AR=2.

References 1. B.E. Little, “Advances in microring resonators,” in Proc. IPR Conference, 2003, pp. 165-167. 2. F.X. Kärtner et al., Invited Paper, Photonics West 2006. 3. V.R. Almeida, C.A. Barrios, R.R. Panepucci and M. Lipson, Nature 431, 1081 (28 Oct 2004). 4. J. Niehusmann et al., Opt. Lett. 29, 2861 (2004).

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5. M.A. Popović, T. Barwicz, E.P. Ippen and F.X. Kärtner, in Conference on Lasers and Electro- Optics (CLEO), Long Beach, California, May 21-26, 2006, paper CTuCC1. 6. T. Barwicz and H.A. Haus, J. Lightwave Technol. 23, 2719-2732 (2005). 7. T. Barwicz et al., J. Lightwave Technol. 24, 2207 (2006). 8. M.A. Popović, M.R. Watts, T. Barwicz, P.T. Rakich, L. Socci, E.P. Ippen, F.X. Kärtner and H.I. Smith, in Proc. Optical Fiber Comm. Conf., 2005, OFK1.

Optimizing Design of High-Index-Contrast Adiabatic Structures

Sponsor Pirelli Labs S.p.A., Milan, Italy

Project Staff Miloš A. Popović, Charles Holzwarth, Tymon Barwicz, Marcus Dahlem, Peter Rakich, Prof. Erich P. Ippen, Prof. Franz X. Kärtner, Prof. Henry I. Smith

Silicon microphotonic waveguides with strong optical confinement that results from using high index contrast (HIC) are enabling high-Q, large-FSR resonators and densely integrated photonic circuits [1-3]. However, strongly confined structures generally have extremely high dimensional [4] and substantial wavelength sensitivity. Yet, the design of broadband devices that are tolerant to dimensional errors is important in HIC silicon photonic circuits for integrated power splitters (directional couplers), waveguide crossings, polarization beam splitters, switches, etc.

Integrated optical devices based on the adiabatic evolution of modes have been used successfully for some time to achieve broadband, tolerant operation [5-8]. Typically, the considered designs have relied on low-index contrast devices whose main drawback is that they require large lengths (order of magnitude larger) in comparison to devices based on direct or evanescent coupling mechanisms, but they are well suited to approximate design by coupled- mode theory. In strong-confinement-based devices, i.e. high-index-contrast, adiabatic structures are of greater practical interest because they can be very compact, in spite of the inherently required slow variation. For a given device shape, crosstalk power to the nearest undesired mode falls off as 1/(δβ L)2, with δβ the effective index spacing of the mode of interest and the undesired mode, and L is the device length. In other words, the required device length scales inversely with: δβ, and the root of the tolerable crosstalk power. Recently, HIC polarization splitters and rotators were proposed that are only a few tens to hundreds of microns in length [8].

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In this work [9], we have investigated the design of optimum shapes for HIC adiabatic structures, where analytical approximations are not suitable for estimating the coupling among the structure modes along the length of the structure, because HIC structures support vector mode fields with significant discontinuities. A design algorithm was found that allows optimal design of a HIC adiabatic structure in terms of certain criteria, based on a single rigorous numerical simulation, without iteration. For a two-mode structure, it consists of rigorously computing the coupling strength along a linear-taper structure length by using a numerical mode solver and appropriate mode overlaps. Then, a coordinate stretching function is computed that will warp the lengthwise coordinate of the structure in order to transform its linear-taper coupling distribution into a desired optimal coupling distribution. A simple, closed-form nonlinear inversion formula was found that provides this transformation, based on given simulated and desired coupling distributions.

The second part of the design problem is the choice of coupling distribution that minimizes length or crosstalk. Since in the relevant operating regime of weak coupling the crosstalk vs. length is approximately the Fourier transform of the coupling distribution with device position [7], the choice of coupling distributions is known to be in some ways analogous to the choice of window functions in digital filters [6]. The best choice has not been clarified. Although in digital filters certain window shapes are known to provide the best tradeoffs allowing narrow spectra with minimum sidelobe levels, we found that different window functions are optimal for optical devices. This is because digital filters typically consider window functions with unity amplitude. On the other hand, it turns out that for a tapered structure of given length, the integrated coupling along length is constant independent of the coordinate warping of the structure in between. This means that the area of the window function, rather than its maximum amplitude, is conserved. Under this constraint, typically window functions resembling a rectangular coupling distribution provide the shortest structures, with smoothing applied near the edges to suppress sidelobes. This leads to designs resembling the so-called Tukey window with parameters adjusted to be find a near rectangular window. Several other aspects including contributions of evanescent modes provide additional design modifications in high-index-contrast. Further work will describe extension of the approach to multiple and leaky modes, i.e. the case of loss, in HIC.

cross

cross ~20dB

bar

bar

(a) (c) (e)

(b) (d) (f)

Figure 1. Optimized design of SiN adiabatic HIC “waveguide crossing” (100%) coupler [9]: (a) schematic of SiN structure, (b,d) mode coupling and eff. indices along device length, (c) predicted crosstalk is <20 dB for devices only 20 µm long, (f) scanning electron micrograph of fabricated device, (e) measured spectra of 100 µm long device shows 20dB extinction.

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Figure 2. Adiabatic Si-core structures [9]: (a) adiabatic 3dB coupler design and (b) Mach-Zehnder interferometer using adiabatic 3dB couplers, (c) measured MZI spectra show >27dB nulls over 60nm, indicating better than 55:45% splitting.

Designs in Si-rich SiN and in silicon wire waveguides were produced and experimentally realized. Fig. 1 shows a broadband “waveguide crossing” or 100% coupler in HIC SiN, showing proper operation over 1500-1600nm and 20dB measured extinction between the cross-port and bar-port. Fig. 2 shows a silicon Mach-Zehnder interferometer, showing 27dB extinction over 60nm in both ports. This corresponds to better than 55:45% splitting ratio over that wavelength range. Work is under way to combine these structures with resonators in more complex photonic circuits.

References 1. B.E. Little, “Advances in microring resonators,” in Proc. IPR Conference, 2003, pp. 165-167. 2. F.X. Kärtner et al., Invited Paper, Photonics West 2006. 3. V.R. Almeida, C.A. Barrios, R.R. Panepucci and M. Lipson, Nature 431, 1081 (28 Oct 2004). 4. M.A. Popović, T. Barwicz, M.R. Watts, P.T. Rakich, L. Socci et al., Opt. Lett. 31, 2571 (2006). 5. Y. Shani, C.H. Henry, R.C. Kistler, et al., IEEE J. Quantum Electron. 27, 556 (1991). 6. A. Syahriar, V.M. Schneider and S. Al-Bader, J. Lightwave Technol. 16, 1907 (1998). 7. G.H. Song and W.J. Tomlinson, J. Opt. Soc. Am. A 9, 1289 (1992). 8. M.R. Watts, H.A. Haus and E.P. Ippen, Opt. Lett. 30, 967 (2005). 9. M.A. Popovic, Ph.D. Thesis, MIT, to be published.

Efficient Out-of-Plane Microphotonic Fiber-to-Chip Coupler Designs

Sponsor Air Force Office of Scientific Research (AFOSR), FA9550-04-1-0011

Project Staff Mingyan Fan, Miloš Popović, Maxime Defosseux, Tymon Barwicz, Prof. Franz X. Kärtner

In optical networks, optical-electrical-optical (OEO) conversions at the nodes constitute bottlenecks in network performance. Due to the ever-increasing demand for speed and performance, an important research area in optical communications is to eliminate the need for optical-electrical conversions through the development of all-optical signal processing units for switching, wavelength routing, dispersion compensation, etc. These optical signal processing devices are well suited to implementation in nanophotonic waveguides, and thus a problem of fiber to chip connection emerges, wherein a means is required to efficiently couple light from the large-area mode of an optical fiber into the submicron mode of a nanophotonic waveguide.

We present a novel grating-based fiber-to-chip coupler design, with grating teeth engineered to provide high directionality while requiring a minimum of lithographic layers and fabrication complexity [1]. The idea of using periodic structures such as gratings to couple out-of-plane light into waveguides has been around since the 60s/70s [2]. The concept has seen a revived interest recently for high index-contrast (HIC) microphotonics due to the strong HIC scattering that

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enables all input light to be coupled out vertically over a 10µm grating length, which is the width of a fiber mode, and thus necessary for efficiently coupling to it. The goal of this project is to contribute to the understanding and resolution of this out-of-plane coupler problem through the design of a grating-based out-of-plane coupler for connection between fiber and nanophotonic waveguides, and in particular through the proposal of a simple and efficient solution to a standing problem of radiation directionality in gratings.

One of the major challenges in designing such a coupler is achieving high directionality in the transfer of light from the waveguide to the fiber. In order to do so, the designed grating needs to be highly asymmetric. The coupler device consists of an etched grating on top of a nanophotonic waveguide. The optical fiber that couples light into and out of the waveguide is placed vertically above the coupler grating. Due to the almost symmetric layering of the waveguide and under the assumption of a weak grating, half of the radiated power travels upwards toward the fiber and half propagates downwards into the substrate. In order for the power incident from the left side of the waveguide to be fully coupled to the fiber placed above, without loss of radiation into the substrate, vertical symmetry in a simple uniform grating needs to be broken. In recent work [3], a gold metallic reflector layer was deposited on one side of a grating coupler to increase directionality into a single (upward) radiation direction. However, this approach is highly complicated, requiring wafer bonding, back-thinning, and metallic layers.

In addition, diffracted power from the waveguide needs to couple to a fiber, which can be accurately modeled as having a Gaussian field distribution. Thus the distribution in the beam cross-section of diffracted power from the grating must also be approximately Gaussian to give the best coupling. Light from the fiber placed directly above the waveguide is diffracted by the grating structure and couples into the underlying waveguide. Due to the inherent horizontal symmetry of the uniform grating, light captured into the waveguide is divided equally and transmitted and propagated towards either the left or right end of the waveguide. By the reciprocity theorem, efficiency for coupling in one and the other direction is the same (e.g. from a fiber above to the left waveguide port, and the reverse), so a vertically and horizontally symmetric grating promises no better than 25% coupling efficiency in principle.

We have taken a design approach based on antenna theory, decomposing the grating coupler radiation into contributions due to an element pattern (tooth design) and array pattern (grating periodicity). To resolve the vertical symmetry issue, we break the symmetry by design of the geometry of a single grating tooth, i.e. the element pattern. By applying concepts of antenna theory to achieve total destructive interference for the downward radiation and constructive interference of radiation upwards, the single grating tooth can radiate asymmetrically and achieve high directionality. For the horizontal symmetry, the uniformity of grating tooth sizes may be apodized in order to break up the symmetry lengthwise along the grating. In fact, a radiation distribution profile of the grating that closely resembles that of a Gaussian field distribution yields highest coupling efficiencies.

Following the proposed approaches, we are able to demonstrate high upward vs. downward radiation directionality ratios of 10-20:1 (Figure 1) with designs that only require a two-level etch fabrication process, as predicted by finite-difference time-domain (FDTD) simulation. Efficient coupler designs are in both SiN and SOI core waveguides, with extensibility to other high-index- contrast waveguides. Due to limited index contrast in the SiN with HSQ overcladding design, the efficiency coupling to a standard 10um fiber is 45% (Figure 2a), but in the SOI design, the coupling efficiency is improved to 73.9% (Figure 2b).

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To further assess the validity of the design, an experimental demonstration of a design to be fabricated in SiN is forthcoming.

References 1. M. Fan, Efficient Out-of-Plane Microphotonic Fiber-to-Chip Coupler Designs, M. Eng. Thesis, Department of Electrical Engineering and Computer Science, MIT, 2006. 2. F. Van Laere, G. Roelkens, J. Schrauwen, D. Taillaert, P. Dumon, W. Bogaerts, D. Van Thourhout and R. Baets, in Optical Fiber Comm. Conf., 2006, post-deadline paper PDP15. 3. A. Ashkin and E.P. Ippen, Light Wave Coupling into Thin Film Light Guides. U.S. Patent 3,674,335 (1972).

Fiber to Chip Couplers

SOI Design (td1=240nm, td2=60nm) SiN Design (td1=480nm, td2=120nm) 1 1

0.9 0.9

0.8 0.8 X: 1550 Y: 0.8325 X: 1550 0.7 0.7 Y: 0.7565 up 0.6 up radiation 0.6 down radiation down R R 0.5 0.5 T T total radiation Power Ratio Power

0.4 Power Ratio 0.4 radiated

0.3 0.3

0.2 0.2 X: 1550 0.1 0.1 Y: 0.06054

0 X: 1550 0 1480 1500 1520 Y: 0.041221540 1560 1580 1600 1620 1640 1450 1500 1550 1600 1650 Wavelength (nm) Wavelength (nm)

Figure 1. Coupler design directionality results (a) SiN with HSQ overcladding showing up/down ratio of 18:1 or 94.83%, and (b) SOI with HSQ overcladding showing up/down ratio of 14:1 or 93% directionality.

(a) (b)

Figure 2. Coupler efficiencies: (a) SiN with HSQ overcladding with efficiency coupling to a fiber of 45%; (b) SOI with HSQ overcladding with adjusted efficiency coupling to a fiber of 73.9%

Sponsors Pirelli Labs S.p.A., Milan, Italy

Project Staff Anatoly Khilo, Raul Barreto, Milos Popovic, Tymon Barwicz, Professor HenryI. Smith, Professor Franz X. Kärtner

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High index contrast waveguides offer such benefits as miniaturization of optical integrated circuits, increased FSR Single mode of ring filters, etc. However, it is more difficult to couple light fiber core from a standard single mode fiber to waveguides with a small cross-section. We are developing horizontal fiber-to- chip couplers to couple light from standard single mode fiber to a high-index contrast silicon waveguide, which has Si waveguide a mode field cross section about 500-1000 times smaller than the fiber. The coupling problem is illustrated in Figure 1. As a first step, we are solving the problem of coupling (drawn to scale) from a high-index contrast (small-core) fiber with mode field diameter of about 4 microns instead of a standard single Figure 1. Problem of coupling of mode fiber with mode field diameter of about 9 microns. single mode fiber to Si waveguide. Starting from the silicon waveguide in Fig. 2 we open up the very small field diameter of about 0.5 micron in the silicon waveguide by overcladding the waveguide with a polymer and tapering the silicon waveguide to a few 10’s of a nanometer tip over a length of a few hundred microns. This presses adiabatically the mode out of the silicon waveguide and matches it to the polymer waveguide with a mode field diameter of about 4 micron. Fig. 3 shows the intensity distribution of TE modes in the taper for several widths of the Si waveguide. For widths less than 80 nm, the mode is well matched to the polymer waveguide mode. The dimensions of the polymer waveguide are matched to the mode of the fiber so that the coupling loss at the input interface does not exceed 0.2 dB. We envision that based on this concept couplers with less than 1 dB overall losses can be fabricated.

Figure 2. Coupler from a small core fiber to high- Figure 3. TE mode at several positions along index contrast Si waveguide. the taper; w is the Si waveguide width.

References [1] T. Shoji, T. Tsuchizawa et. al., Electr. Lett. 38, 1669-1670 (2002). [2] S. McNab, N. Moll, Y. Vlasov, Opt. Expr. 11, 2927 (2003).

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Silicon Electronic Photonic Integrated Circuits for High Speed Analog to Digital Conversion

Sponsors Defense Advanced Research Projects Agency (DARPA) under Grant W911NF-04-1-0431

Project Staff Reja Amataya, Tymon Barwicz, Hyunil Byun, Fuwan Gan, Charles. W. Holzwarth, Oluwamuyiwa O. Olubuyide, Jason S. Orcutt, Min Park, Milos. A. Popović, Peter. T. Rakich, Professors George Barbastathis, Erich. P. Ippen, Judy L. Hoyt, Franz X. Kaertner, Michael Perrott, Rajeev J. Ram, and Hank I. Smith and Dr. Michael Geis, Matthew Grein, Ted Lyszczarz, Steven Spector, and Jung U. Yoon from MIT Lincoln Laboratory

The goal of this program is to leverage the low jitter properties of mode-locked lasers to achieved an electronic-photonic integrated circuit (EPIC) that facilitates high speed analog-to-digital conversion (ADC) beyond the bottleneck set by electronic jitter. Several photonic ADC techniques have been investigated in recent years [1,2]. The photonic ADC architecture pursued here in the form of an EPIC is known as time-interleaved optical sampling using wavelength-division multiplexing (WDM) [2] techniques. The envisioned EPIC is shown in Figure 1. A chirped optical clock signal from a mode-locked laser is channelized in time using precisely-tuned WDM filters to create time-interleaved optical sampling signals, each

Figure 1: Schematic layout of EPIC for high-speed ADC. operating at the rate of the mode-locked laser. The total sampling rate is then the optical clock rate times the number of WDM channels. However, in order to realize the high resolution, the sampling times of the interleaved channels must be uniform, the converter gains from each channel must be closely matched, and the sample memory effects must be minimal. These characteristics require monitoring and very tight feedback control of the WDM filters which is most

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easily possible with an EPIC. The ADC chip requires the development of a number of devices: WDM filter banks with large FSR and precise control of relative resonance frequencies, wideband optical modulators, Ge- photodetectors, and low jitter femtosecond lasers, potentially also integrated. These devices are pursued in a close collaboration between research groups at MIT Campus and MIT Lincoln Laboratory in various technologies. All these devices and techniques must be integrated on a CMOS compatible technology platform. As an example the proposed ADC chip requires filters with large free spectral range (FSR) and low loss. These two key requirements call for microring filters fabricated in a high-index contrast (HIC) material system.

The microring resonator filter designs used for fabrication of the filter banks presented here are based on to the design described in [3]. By utilizing this design with the HIC materials of silicon- rich silicon nitride (n =2.2 @ 1550 nm) forming the core, and silicon dioxide (n =1.455 @ 1550nm) or air cladding a very wide FSR of 20 nm is realized. The filter design was fine tuned to achieve the objective of a 3 dB bandwidth of 50 GHz and less than 30 dB adjacent channel crosstalk for 150 GHz spaced channels. The critical feature size of the gap between the bus and ring waveguides is 160 nm for these filters (Figure 2a). 8-Channel Second Order Filter Bank -0.5% Dose 0.0 -5.0 -6.0 B) -7.2 d

in thru

~702n ransmission ( m T 400nm SiNx Power 16µm -36.0 -37.2 210nm SiO2 drop -45.0 -535.38 -217.07 95.55 419.57 -375.90 -54.79 253.20 579.63 (a) (b) Relative Frequency (GHz)

Figure 2: (a) Top view of second order microring resonator filter. (b) Cross-section view of bus waveguide showing smooth vertical sidewalls. (c) Through- and drop-port characteristics of filter bank with second order single stage filters and 159 GHz channel spacing. Frequencies are all relative to 1540 nm.

Direct-write scanning electron beam lithography (SEBL) was used due to its combination of high resolution and high level of dimensional control. The basic fabrication process used is similar to that described in [4]. Controlling the resonant frequency of HIC microring resonator filters requires an extremely high level of dimensional control. To overcome the discretization in e-beam step size, e-beam dose modulation is used. The filter showed channel spacings of about 159±6 GHz, a channel bandwidth of 46.5GHz, a drop loss averaged over 40 filters of 1.5±0.5 dB and a adjacent channel crosstalk of less than -30 dB,.(Figure 2(b)). Fine tuning of filters to an exact frequency grid by thermal means (heaters) is in progress. Description of the other devices necessary for the EPIC ADC-chip can be found in various summaries of the participating groups throughout this progress report.

References: P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J.L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically sampled analog-to-digital converters,” IEEE Trans. Microwave Theory Tech. 49(10), 1840 (2001). M. Y. Frankel, J. U. Kang, and R. D. Esman, “High-performance photonic analogue-to-digital converter,” Electron. Lett. 33(25), 2096 (1997). M.A. Popović, T. Barwicz, M.R. Watts, P.T. Rakich, L. Socci, E.P. Ippen, F.X. Kärtner and H.I. Smith, “Multistage high-order microring-resonator add-drop filters,” Opt. Lett., vol. 31, no. 17, September 1, 2006 (to appear). 4. T. Barwicz, M.A. Popović, M.R. Watts, P.T. Rakich, E.P. Ippen and H.I. Smith, “Fabrication of Add-Drop Filters Based on Frequency-Matched Microring Resonators,” J. Lightwave Technol., vol. 24, no. 5, May 2006, pp. 2207-2218.

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Silicon Electro-Optic Modulator

Sponsors National Science Foundation (NSF) under Grant ECS-0322740 Defense Advanced Research Projects Agency (DARPA) under Grant W911NF-04-1-0431

Project Staff Fuwan Gan, Dr. Steven Spector and Dr. Ted Lyszczarz (MIT-Lincoln Laboratory), and Professor Franz X. Kärtner

One of the most important electro-optic devices for future electronic-photonic integrated circuits (EPIC’s) based on silicon technology is a CMOS-compatible high-speed optical modulator that converts electronic signals into optical signals. The plasma and thermal effects in silicon have long been known as efficient means to achieve such modulation [1]. Early on p+in+-structures based on the plasma effect have been proposed and realized for silicon-based optoelectronic phase and amplitude modulators with switching speeds up to 10MHz [2]. The speed of these devices was limited by carrier recombination. Very recently a modulator based on a MOS structure has been reported operating at 10GHz speed [3]. However, this device needs an applied voltage of 5 to 10V with a figure of merite VπL>1V cm which are both rather large for EPIC applications. In this project, we investigate high-speed electro-optic modulators based on high-index-contrast silicon strip waveguides that minimize optical loss, power consumption and voltage-length products while increasing the modulation bandwidth.

λ (a)

(b) w wd wr P+ h N+ hs WG doping2 doping1 Fig. 1. Mach-Zehnder modulator with coplanar RF-feeder shown in top view (a) and cross section (b).

Aluminum oxide silicon

oxide 200 nm 2 µm

Fig. 2. SEM images of the cross-section of the modulator waveguide.

A schematic layout of the modulator is shown in Fig.1(a) which depicts a conventional Mach- Zehnder arrangement and Fig.1(b) which shows a schematic cross-section through one of the electrically driven phase modulator sections. The light intensity is modulated by the phase shift induced in each arm of the interferometer due to carrier injection. Fig. 2 shows SEM images of the modulator waveguide cross-section. The diode was fabricated with a standard CMOS compatible lithography process. The fabricated waveguide dimensions are wxh=520nmx220nm. Aluminum is used as electrical contact on top of the highly doped contact regions to minimize the

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contact resistance. The waveguide sidewalls are lightly doped to reduce resistance without incurring excessive optical loss. If the intrinsic region of the modulator is doped, it can also be used in reverse-bias by modulating the width of the depletion region thereby sweeping the carriers in and out of the waveguide.

2 The electrical to optical frequency response |S21| of a Mach Zehnder modulator with 0.25 mm long p+in+-sections in forward bias operation and a 6 mm long device in reverse bias operation has been measured (see Figure 3a). For the forward bias regime, the electrical bandwidth f3dB is about ~200MHz. In this mode of operation, the bandwidth is carrier lifetime limited. Due to surface recombination, the lifetime of this device is expected to be τ≈1ns, f3dB ≈1/2πτ=160MHz, which is consistent with the measurement. The optimum bias voltage is ~1V with a current of ~10mA. The electrical power consumption for a 0.5mm long device at 25% modulation depth is shown in Fig. 3.b. At low frequencies 10MHz, only 1µW of RF drive power is necessary to achieve 25% modulation depth. Even at 10GHz, only 20mW is needed. A VπL product of 0.02 Vcm at 10MHz was achieved for forward biased operation in a separate measurement for a 1-mm arm-length device. Under reverse biased operation the modulator is expected to have broad 7 bandwidth only limited by the saturation velocity 10 cm/s in silicon resulting in f3dB = 2.4/2πτdrift≈80GHz [4]. However, sofar the measured bandwidth is limited to f3dB~2GHz. The response of the device under reverse bias is much weaker, thus it requires a longer arm length of 6.0 mm. The optimum bias voltage was ~9 V with a current less than 2 µA for reverse bias operation.

Frequency Response 0.5 mm, 25% 30

Forward Bias 20 0.00 Reverse Bias

10

-10.00 0

Power Input [dBm] [dBm] Input Power -10 Amplitude (dB) Amplitude -20.00

-20

-30.00 10 100 1000 10000 -30 Frequency (MHz) 10 100 1000 10000 100000 Frequency [MHz] (a) (b) Fig. 3. (a) Frequency response of a 0.25 mm long Mach Zehnder modulator operated in forward bias, and a 6.0 mm long Mach Zehnder modulator in reverse bias. (b) Power Consumption of a 0.5 mm long Mach Zehnder in forward bias with 25% modulation depth

References: [1] R.A. Soref, “Silicon-based optoelectronics,” Proc. IEEE 81, 1687–1706 (1993). [2] Dainesi, P. et al. “CMOS compatible fully integrated Mach-Zehnder interferometer in SOI technology,” IEEE Photon. Technol. Lett. 12, 660-662 (2000). [3] A. Liu, Dean Samara-Rubio, L. Liao, and M. Paniccia. “Scaling the Modulation Bandwidth and Phase Efficiency of a Silicon Optical Modulator”. IEEE J. of Selected Topics in Quantum Electronics, Vol. 11, No. 2, March/April 2005. [4] Shun Lien Chuang, Physics of Optoelectronic Devices, Wiley, New York (1995). [5] F. Gan and F. X. Kärtner, “High-speed Silicon Electro-optic Modulator Design,” IEEE Photonics Technology Letters, 17, 1007-1009, (2005). [6] F. Gan, F. J. Grawert, J. Schley, S. Akiyama, J. Michel, K. Wada, L. C. Kimerling, F. X. Kärtner, “Design of All-Optical Switches Based on Carrier-Injection in Si/SiO2 Split-Ridge Waveguides (SRW's)”, IEEE J. of Lightwave Technology 2006, Vol.24, No. 9, September2006

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Unpolarized Supercontinuum Sources for Broadband Studies of 1D and 3D Photonic Crystals

Sponsors National Science Foundation (MRSEC) – DMR-0213282 Air Force Office of Scientific Research (AFOSR) - FA9550-04-01-0011

Project Staff Peter T. Rakich, Hideyuki Sotobayashi, Juliet T. Gopinath, Jason W. Sickler, Chee Wei Wong, Steven G. Johnson, Minghao Qi, Elefterios Lidorikis, Henry I. Smith, John D. Joannopoulos and Erich P. Ippen

High-index contrast photonic crystal waveguides are of interest for an increasing variety of applications. However, the measurements required to understand the basic physical phenomena of photonic crystal devices often present serious experimental challenges. In many cases it is necessary to perform spectral measurements over 50 – 100% of the center frequency of the device (i.e. as much as an octave) in order to understand the bandgap-related phenomena. Additionally, due to the nano-scale dimensions of such devices, high insertion losses and low throughput are typical in a laboratory setting. It is for this reason that high-brightness sources such as tunable lasers are typically used to scan the broad spectral features of photonic crystals. Unfortunately, tunable laser sources spanning the entire 1 – 2 µm spectral range, critical for the study of telecom-centered devices, are not readily available. To facilitate the science and study of photonic crystals and integrated photonic devices, we develop practical femtosecond fiber-laser- based supercontinuum sources (SC) spanning the 1.2 – 2.0 µm wavelength range and broadband SC based measurement techniques. These techniques are then applied to the study of high index contrast photonic crystal devices, enabling a host of new photonic crystal studies. Experiments involving both 1-D photonic crystal microcavity waveguides and 3-D periodic photonic crystals with embedded point defects are described. Experimental findings are compared with rigorous electromagnetic simulations[1,2].

Earlier applications of SC sources to the study of photonic devices have utilized solid-state Ti:Sapphire-based SC sources (centered at 800 nm) to study two-dimensional photonic crystal slab waveguides with a system utilizing free-space optics [3,4]. While this is an effective means of generating supercontinuum centered at 800 nm, it is difficult to efficiently extend the spectral range past 1.5 microns. Furthermore, the short lengths of photonic crystal fiber used to construct such sources exhibit severe polarization drift, over time. This can be detrimental to the study of polarization sensitive devices such as photonic crystal waveguides and cavity modes. In contrast, we have developed unpolarized all-fiber SC sources centered at telecommunications wavelengths (1.55 µm) and an all-fiber measurement apparatus for the study of photonic crystals and integrated circuits at telecom wavelengths. To minimize the losses and complexity produced by broadband free-space optics, we focus instead on all-fiber methods for broadband polarization control, and coupling. Additionally, through sensitive detection and careful normalization many of the undesirable aspects of a typical SC source can be mitigated, producing high fidelity measurements over the entire 1.2 – 2.0 µm wavelength range[1,2].

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Figure 1: (a) Schematic of supercontinuum source, which consists of a femtosecond fiber-laser and a length of highly nonlinear dispersion shifted fiber. (b) Optical power spectrum of the fiber laser output before and after passing through the nonlinear fiber.

The SC source developed in this work consists of a length of highly nonlinear dispersion-shifted fiber (HNL-DSF) seeded by a femtosecond stretched-pulse fiber laser, shown in Fig. 1(a). The laser consists of a 55.6 cm length of bismuth oxide-based erbium-doped fiber (Bi-EDF), 1.8 m of low-nonlinearity single-mode fiber (LNL-SMF), two polarization controllers, and a polarizing beam-splitter. The rejection port of the polarizing beam splitter forms the output coupler of the laser, while a bi-directionally pumped length of Bi-EDF fiber serves as a the gain medium, providing a broad gain bandwidth and high gain per unit length [5]. To balance the dispersion of the Bi-EDF, and manage the intracavity nonlinearity, 1.8 m of LNL-SMF is included in the laser. Mode-locked operation of the laser was obtained through nonlinear polarization evolution [6]. For pump powers of 350 mW, a 28 mW average output power was obtained with center wavelengths and spectral full-width half maxima of 1571 nm and 58 nm respectively. Through external compression with a 1.8 m segment of LNL-SMF 100 fs pulses were obtained, providing a peak pulse power of ~8.5 kW, which was sufficient for the generation of a broad SC spectrum. Pulses are injected into 500 m of HNL-DSF having a zero-dispersion wavelength of 1565 nm and a nonlinear coefficient of 21 km-1 W-1 to generate SC. The laser spectra before and after the HNL- DSF are shown in Fig. 2(b). It should be noted that the supercontinuum light generated by this method is unpolarized when measured at millisecond time scales due to nonlinear polarization evolution produced in the HNL-DSF. Additionally, the nonlinear nature of the SC generation makes the shape of the spectral output very sensitive to changes in laser state[7].

The SC spectrum generated in the HNL-DSF is coupled into the apparatus shown in Fig. 2(a) for waveguide transmission studies. The unpolarized SC light is first passed through a broadband fiber-optic coupler, splitting the continuum into two ports, signal and reference. The signal is then sent through an inline polarizer and polarization controller, which define the polarization at the input of the waveguide. A lensed fiber is then used to couple the signal into the waveguide. A second lensed fiber collects the waveguide output that is sent through a polarization controller and inline polarizer for polarization analysis. The signal and reference are then imaged through a monochromator onto two identical photodetectors, for real-time normalization of the SC fluctuations and spectral changes. Detection is performed with Peltier cooled IR-enhanced InGaAs photodiodes and lock-in amplifiers to achieve low noise measurements (with a noise equivalent power of 28 fW/√Hz) and enable rapid scans (less than one minute) with as little as 4 mW of SC light.

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Figure 2: (a) A schematic of measurement apparatus. A small fraction of SC light is diverted by a coupler for reference (Ref) measurement while the remainder (Signal) is passed through the waveguide. The signal and reference are then imaged through a monochromator onto identical photo-detectors for real time normalization. (b) Polarization extinction obtained through polarization control method depicted in Fig 2(a).

Polarization control of the light launched into the waveguide and polarization analysis of the light collected from the guide were performed with use of broadband inline polarizers and strain-type polarization controllers as depicted in Fig 2(a). As can be seen in Fig. 2(b), this provides greater than 20 dB of polarization extinction over most of the spectral range of the SC source. However, critical to broadband performance is (1) the type of inline polarizer used, and (2) minimization of polarization mode dispersion (PMD) which follows the polarizer. Laminated inline polarizers of the type described in ref [8] were used, providing high extinction and low insertion losses over the entire 1 – 2 µm wavelength range. PMD was managed by minimizing the length of fiber between the polarizer and lensed fiber, as well as any bending experienced by the fiber. For the measurement shown in Fig 2(b), fiber lengths were kept below 30 cm. Additionally, through a slight change in the state of the polarization controller >25 dB contrast can be achieved at any wavelength in the 1.2 – 2.0 µm range, enabling higher polarization extinction through more than one wavelength scan if needed.

This method was applied to the study of a number of HIC devices, however, in this paper we examine a 1-D photonic bandgap microcavity and 3-D photonic crystal with point defects [2]. The 1-D photonic crystal microcavity, which has been studied extensively over the past several years, consists of a silicon strip on top of an oxide layer, forming a waveguide with a single TE-like mode over much of the 1 – 2 µm wavelength range [9,10]. A photonic crystal is patterned in the waveguide by etching a periodic array of holes through the silicon strip. The photonic crystal defect is then defined by increasing one hole spacing from a (the lattice constant) to ad (the defect length). A device schematic and scanning electron micrograph (SEM) are shown in Fig. 3(b). For comparison with experiments, simulations of the device band structure and power transmission were performed based on the parameters extracted from SEM measurements [11,12]. Results of the band-structure computations can be seen in Fig 3(a) while the dashed curve of Fig 3(c) shows the simulated power transmission.

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Figure 3: (a) Band diagram (TE-like bands only) based on SEM measurements of device. Grey region indicates states above the light line. (b) SEM of microcavity (top) and cross-section of waveguide (bottom). Device parameters extracted from SEM are a = 424 nm, ad = 649 nm, w = 494 nm, tg = 195 nm, to = 350 nm, and D = 179 nm. (c) A transmission measurement (solid) and simulated transmission (dashed) of photonic crystal microcavity (TE polarization). The transmission measurement is normalized to that of a similar waveguide without etched holes. (d) High resolution (0.1 nm) measurement (solid) and simulation (dashed) of the microcavity resonance.

Superposed on the theoretical photonic crystal power transmission (dash) of Fig. 3(c) is the measured transmission spectrum (solid). The experimental spectrum was obtained by measuring the photonic crystal waveguide transmission and normalizing to a calibration scan of an identical waveguide without a photonic crystal. Normalization is important to remove wavelength dependence of waveguide coupling, waveguide propagation losses as well as spectral variations of the SC source. However, a comparison of theory with experiment reveals that normalization is quite effective. Remarkable agreement is seen between experiment and theory for wavelengths between 1400 – 2000 nm. A 265 nm stop-band is clearly visible in the experiment from approximately 1425 – 1690 nm. In addition, the high resolution spectrum shown in Fig. 3(d) reveals a sharp microcavity resonance can be seen at 1542 nm, demonstrating efficient power coupling through the photonic crystal, with approximately 52% transmission. This is in reasonable agreement with the simulated transmission efficiency of 68%.

A similar supercontinuum based technique was applied to the study of a 3D photonic crystal with embedded point defects, enabling high spatial resolution studies (with a 2.5 µm spot size) of a small number of embedded point defects which were randomly distributed within the PhC. An SEM of the 3-D PhC under study can be seen in Fig. 4(c), and was fabricated in Silicon through a layer-by layer process utilizing several successive e-beam lithography steps. This 3-D photonic crystal exhibits a 21% complete photonic bandgap centered at telecom wavelengths. The details of this fabrication process can be found in reference [1]. The fabricated structure consists of alternating layers of two complementary 2-D photonic crystal slabs, one layer of dielectric rods and another of air holes in a dielectric slab. Embedded within the PhC are randomly distributed defects, each consisting of a completely filled air hole. Defects of this type produce a spatially localized photonic crystal mode, having numerous resonant states within the photonic bandgap, which couple to radiation. These defects are dispersed within the photonic crystal with a density

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of 15%. Despite the remarkable fabrication quality, inhomogeneity in the environment of these point defects was unavoidable, resulting in inhomogeneous broadening of defect states throughout the PhC. For this reason it was necessary to probe very small areas of the PhC to resolve the energy spectrum of individual defect cavities. Spectroscopic studies of these defects over small areas proved difficult with thermal white light sources due to their low brightness. However, SC based measurement techniques yielded high fidelity measurements of a small number of nano-scale PhC defects, allowing the energy spectrum of individual defects to be fully resolved.

In this study, supercontinuum-based confocal reflection and transmission measurements were used to examine a small number of defects embedded within the PhC. An average of 3 PhC defects could be studied with use of a Gaussian spot size of 2.5 µm generated by a lensed fiber. The supercontinuum source used in these studies consisted of a Ti:Sapphire pumped optical parametric oscillator (OPO) which was used to seed the SC generation in a highly nonlinear fiber, generating SC spanning 1.2 – 2.0 µm. Further details about the SC source are described in Rakich et. al. [13]. In these experiments, a reference channel was used to normalize for any spectral variations; however, unpolarized SC light was sufficient to observe the defect resonances, making polarization control unnecessary.

Figure 4: (a) photo of lensed fiber and photonic crystal 3D PhC device under test (b) Theoretical (aqua) and experimental (red) transmission spectra of 3D PhC with defects. Theoretical transmission of PhC without defect states (green dash). (c) SEM of 3D fabricated SEBL (d) Theoretical (aqua) and experimental (red) reflection spectra of 3D PhC with point defects.

Spatially localized reflection measurements, taken by this method, were performed at numerous positions on the photonic crystal. Some characteristic reflection and transmission measurements can be seen in Figs. 4(b) and (d) along with the corresponding theoretical transmission and reflection spectra computed through 3D FDTD computations. The experimental geometry for the

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transmission measurement is depicted in the inset of Fig. 4(a). Here a lensed fiber forms a 2.5 µm Gaussian spot size on the PhC, while a flat-cleaved single mode fiber optic was used to collect the light transmitted through the PhC over a narrow range of transverse wave-vectors (corresponding to ~1° half angle). The PhC transmission spectrum was then normalized to a similar measurement through the same substrate, without the PhC in the path. We can see that the bandgap of the PhC is clearly resolved along with two peaks in the transmission spectrum (denoted by I & II in Fig. 4(b)), corresponding to resonant transmission through the multi-mode point defects. This can be seen by comparing the theoretical (aqua) and experimental (red) transmission spectra. Such peaks in transmission are not found in simulations of the structure without defect states (green), clearly indicating that these spectral features result from resonant transfer of power through the defect modes. The spectral signatures of the defect modes are somewhat less pronounced for the transmission spectrum, however, more striking features resulting from the defect states are observed as dips in the reflection spectrum. This is because the reflection measurement probes a large transverse wave-vector range (corresponding to a 15.5° half angle), which is more suitable for coupling to localized defect states which tend to radiate over large solid angles. A detailed comparison of the experimental (red) and theoretical (aqua) reflection spectra can be made from Fig 4(d). Three dips are observable in the reflection spectrum at approximately 1.4 µm, 1.5 µm and 1.6 µm wavelengths (denoted by III, IV & V in Fig. 4(d)), which result from resonant coupling to localized defect states within the PhC. The observed stop band and the positions of the defect resonances are in remarkable agreement with the simulated reflection spectrum. It should also be noted that all parameters used to simulate the transmission spectra shown below were extracted from SEMs of the device, and no free parameters were used.

In conclusion, newly developed supercontinuum sources and techniques provide a practical means of studying photonic devices over broad wavelength ranges in the NIR, enabling a host of new studies involving both 1-D periodic photonic crystal microcavities and 3-D periodic photonic crystals. An all-fiber apparatus enables very practical and low-loss means of utilizing supercontinuum sources over the 1.2 – 2.0 µm wavelength range for photonic crystal studies. Additionally, through sensitive detection and careful normalization many of the undesirable aspects of a typical SC source can be mitigated, producing high fidelity measurements of nano-scale photonic devices over the entire 1.2 – 2.0 µm wavelength range.

References 1 Qi, M. H. et al. A three-dimensional optical photonic crystal with designed point defects. Nature 429, 538-542 (2004).

2. Rakich, P. T. et al. Nano-scale photonic crystal microcavity characterization with an all-fiber based 1.2-2.0 mu m supercontinuum. Opt. Express 13, 821-825 (2005).

3. Neal, R. T. et al. Ultrabroadband transmission measurements on waveguides of silicon-rich silicon dioxide. Appl. Phys. Lett. 83, 4598-4600 (2003).

4. Netti, M. C. et al. Separation of photonic crystal waveguides modes using femtosecond time- of-flight. Appl. Phys. Lett. 81, 3927-3929 (2002).

5. Kuroiwa, Y. et al. in OFC 2001. Optical Fiber Communication Conference and Exhibition. Technical Digest, 17-22 March 2001 5-1 (Opt. Soc. America, Anaheim, CA, USA, 2001).

6. Haus, H. A., Tamura, K., Nelson, L. E. & Ippen, E. P. Stretched-Pulse Additive-Pulse Mode- Locking in Fiber Ring Lasers - Theory and Experiment. IEEE J. Quantum Electron. 31, 591- 598 (1995).

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7. Newbury, N. R., Washburn, B. R., Corwin, K. L. & Windeler, R. S. Noise amplification during supercontinuum generation in microstructure fiber. Opt. Lett. 28, 944-946 (2003).

8. Shiraishi, K., Hatakeyama, H., Matsumoto, H. & Matsumura, K. Laminated polarizers exhibiting high performance over a wide range of wavelength. J. Lightwave Technol. 15, 1042- 1050 (1997).

9. Foresi, J. S. et al. Photonic-bandgap microcavities in optical waveguides. Nature 390, 143- 145 (1997).

10. Wong, C. W. et al. Strain-tunable silicon photonic band gap microcavities in optical waveguides. Appl. Phys. Lett. 84, 1242-1244 (2004).

11. Johnson, S. G. & Joannopoulos, J. D. Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis. Opt. Express 8, 173-190 (2001).

12. Kunz, K. S. & Luebbers, R. J. The finite-difference time-domain method for electromagnetics. (CRC Press: Boca Raton, 1993).

13. Rakich, P. T. et al. in 2004 IEEE LEOS Annual Meeting Conference Proceedings, LEOS 2004, Nov 7-11 2004 813-814 (Institute of Electrical and Electronics Engineers Inc., Piscataway, NJ 08855-1331, United States, Rio Grande, Puerto Rico, 2004).

14. Rakich, P. T. et al. Invited Paper, in 2005 NOC Proceedings for European Conference on Networks and Optical Communications, July 5-7 2005 p 4-11 (University College London, London, UK)

15. Rakich, P. T. et. al. Invited Paper, Optics East Annual Meeting Conference Proceeding, Oct. 25-28 2005 (Copley Marriot, Boston MA, USA)

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Ultra-wide Tuning of Photonic Microcavities via Evanescent Field Perturbation

Sponsor Pirelli Research Labs, Milan Italy Air Force Office of Scientific Research (AFOSR) - FA9550-04-01-0011

Project Staff Peter T. Rakich, Miloš A. Popović, Dr. Michael R. Watts, Dr. Tymon Barwicz, Professor Henry I. Smith and Professor Erich P. Ippen

The field of integrated optics promises to provide a practical and scaleable means of routing and switching light for applications ranging from telecommunications networks to sensing and spectroscopy. However, a key barrier to the development of dynamic integrated optical circuits is the lack of a practical means of enabling large changes in waveguide effective-index (∆neff). Large ∆neff is critical for the development of widely tunable filters and for scaling active components to smaller size. Currently, thermo-optic tuning is the only widely implemented means of producing a ∆neff in optical circuits [1-3], but it has insufficient range and is slower than desired for many applications.

We have demonstrated ultra-wide tunability through evanescent perturbation of a large free- spectral-range (FSR) micro-ring resonator. Geometrical tuning mechanisms, such as evanescent tuning, have the distinct advantages that they are material-system independent and that they enable large ∆neff with small power dissipation. In what follows, a 1.7 % frequency shift is demonstrated (or 27 nm tuning near 1565 nm) in a microring resonator without significant distortion of the cavity resonance. Furthermore, complete recovery of the resonance is found when the perturbing body is removed. Experiments are carried out with a novel silica-fiber probe which provides access to the evanescent field of an air-clad high-index-contrast (HIC) ring- resonator mode. As the probe is advanced toward the ring resonator, the probe-ring distance is found through simultaneous nanometric distance calibration and force measurements.

For the purposes of this study, a silicon-rich silicon-nitride ring resonator of the type described in Ref. 4, but of first order, is considered. The ring resonator was designed for operation at 1.5 µm wavelengths, with an FSR of 27 nm. The mode of the air-clad ring resonator has an evanescent field extending outside the guide in the direction normal to the plane of the ring. Consequently, a dielectric body can be placed above the ring such that it uniformly penetrates the evanescent field of the ring (see inset of Fig. 1(b)). This produces an increase in effective index of the mode, resulting in a shift of resonance frequency. If the perturbing dielectric is comprised of silica, a maximum theoretical tuning range of 29.9 nm at an operating wavelength of 1565 nm is possible. The tuning closely approximates an exponential as a function of distance z from the ring, with a decay length of 1/α ≅ 91.6 nm, making it evident that a high degree of positional control is required.

The major challenge in a laboratory implementation of the geometry shown in Fig. 1(b) is the high degree of angular alignment required between the perturbing body and the ring resonator (typically microradians). This alignment issue is addressed through a novel probe design illustrated in Fig. 1(a). It utilizes a fiber-taper near the end of the probe, which allows the fiber end to lie parallel to the surface when in contact with the substrate of the ring resonator. The fabrication process for this probe is outlined in the inset of Fig. 1(a). First, the fiber is tapered to several microns, forming a flexible joint. Then the face of the probe (used to perturb the ring resonator) is formed by a fiber cleave, and annealed until a small amount of glass reflow occurs, ensuring an ultra-smooth surface.

The apparatus used to perform evanescent perturbation experiments can be seen in Fig. 1(a). It consists of the silica fiber probe (described above), which is mounted on a cantilever having a force constant of ~5000 N/m. The probe-cantilever assembly is advanced with a distance-

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calibrated piezo translation stage such that it can be brought in and out of contact with the ring- resonator device. Motion of the cantilever and probe relative to the device is monitored with an interferometer, one end of which is formed by the cantilever. Position is read through rapid interrogation of the interferometer with white light from an erbium-doped fiber amplifier (EDFA) and an optical spectrum analyzer (OSA). Force experienced by the probe can be precisely measured from the cantilever deflection. Broadband EDFA light is also coupled into and collected from the ring resonator device with lensed fibers to measure the micro-ring response. Experiments were performed by simultaneously measuring the ring resonator drop response, cantilever position, and forces of probe-sample interaction.

The results of a tuning experiment can be seen in Figs. 1(c)-(e). Fig. 1(c) shows the ring resonance frequency as a function of the cantilever height measured by the interferometer. Each data point (circle) represents the resonant wavelength obtained from measurements of the drop port of the ring resonator. The force and force derivative experienced by the probe over the same range of cantilever displacement are displayed in Fig. 1(d-e). In Fig. 1(d) two trends can be seen: (1) for smaller positions (i.e. position ≤ 1270 nm) an exponential change in resonance wavelength covers a 25 nm tuning range; (2) for positions larger than 1270 nm (indicated by the vertical dashed line) there is a very gradual change in ring resonance frequency. In interpreting these two tuning regimes, the forces of interaction between the probe and sample (seen in Fig. 1(b)) provide insight. For the evanescent tuning regime attractive forces (negative in sign) are experienced by the probe, which are due to a combination of capillary and Van der Waals interactions as the probe approaches flush contact [5]. Snap-down of the probe can be seen at 1270 nm most clearly through a sharp increase in the derivative of the force, corresponding to the maximum in the exponential portion of the tuning curve. After this point, the probe remains flush with the device resulting in compression of the probe, which is seen as a large positive slope in the force curve.

Fig. 1. (a) Tuning apparatus and (inset) probe fabrication process; (b) measured resonance wavelength of microring vs. distance of probe from ring surface (inset – schematic of tuning geometry); (c,d,e) resonance wavelength, force and force derivative vs. cantilever position.

Through an analysis of the force and force derivative measurements, the probe-ring distance can be placed on an absolute scale and compared with theory, as seen in Fig. 1(b). An exponential fit of the tuning versus probe-ring distance reveals a decay length of 87 ± 4 nm and a maximum tuning of 24.8 nm, which agrees with the theoretical decay length of 91.6 nm and maximum

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tuning range of 29.9 nm. Tunings as large as 27 nm were obtainable by contacting the ring using unique points of the probe face, indicating that conformation of the probe surface plays a role in limiting the maximum possible perturbation. High-speed acquisition of spectra shows that throughout the tuning process the resonance shape appears to be preserved. Additionally, when the fiber is raised again the unperturbed resonance is fully recovered, demonstrating a negligible degree of hysteresis, which suggests no material exchange between the probe and ring.

In conclusion, high-fidelity reversible tuning was demonstrated over 1.7% frequency range through evanescent tuning. In this experiment, a uniform silica perturbing body was used, although it should be noted that with higher-index perturbing structures, upwards of 3% tuning could be implemented through the same range of motion. Furthermore, higher index-contrast waveguides (such as silicon) can tolerate stronger perturbation before coupling to radiation modes occurs, which should further enhance tuning ranges. For more information see Refs [6-7].

References 1. P. Heimala, P. Katila, J. Aarnio and A. Heinamaki, "Thermally tunable integrated optical ring resonator with poly-Si thermistor," J. Lightwave Tech. 14, 2260-7 (1996).

2. D. Geuzebroek, E. Klein, H. Kelderman, N. Baker and A. Driessen, "Compact wavelength- selective switch for gigabit filtering in access networks," IEEE Photon. Tech. Lett. 17, 336-8 (2005).

3. H. M. H. Chong and R. M. De La Rue, "Tuning of photonic crystal waveguide microcavity by thermooptic effect," IEEE Photon. Tech. Lett. 16, 1528-1530 (2004).

4. T. Barwicz et al. "Microring-resonator-based add-drop filters in SiN: fabrication and analysis," Opt. Express 12, 1437-1442 (2004).

5. W.M. van Spengen, R. Puers and I. de Wolf, "A physical model to predict stiction in MEMS," J. Micromech. and Microeng. 12, 702 (2002).

6. Rakich, P.T., et al., “Ultrawide tuning of photonic microcavities via evanescent field perturbation,” Opt. Lett., 31,1241-3 (2006)

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Propagation without Diffraction in a 2D Photonic Crystal for Optical Interconnects

Sponsors: MRSEC/NSF Microelectronics Advanced Research Corporation DARPA – 2003-IT-674 Office of Naval Research – N00014-01-1-0803 Air Force Office of Scientific Research – FA9550-04-01-0011

Project Staff: Marcus S. Dahlem, Peter T. Rakich, Dr. Sheila N. Tandon, Dr. Mihai Ibanescu, Dr. Gale S. Petrich, Prof. Marin Soljačić, Prof. John D. Joannopoulos, Prof. Leslie A. Kolodziejski, Prof. Erich P. Ippen

One of the interesting effects observed in photonic crystals (PhCs) is the propagation of optical beams without diffraction. Referred to as super-collimation (or self-collimation), this optical effect allows diffraction-free propagation of micron-sized beams over centimeter-scale distances. It is a natural result of the unique dispersive properties of PhCs, and no nonlinearities or physical waveguides are required. Self-collimation was first observed by Kosaka et al. in a 3D PhC [1] and by Wu et al. in 2D triangular [2] and square [3] lattices, over relatively short distances (hundreds of microns). We have recently reported centimeter-scale super-collimation in a large-area 2D photonic crystal [4]. A natural metric for the scale of collimation experiments is the isotropic diffraction-length over which a Gaussian optical beam would normally spread by a factor of 21/2 in 2 an isotropic medium: Ld = π.ω / λx where ω is the Gaussian beam waist radius and λx = 2π / kx is the wavelength of the light in the direction of propagation. A figure of merit for super-collimation is the ratio of the observed length of collimated propagation to the isotropic diffraction length Ld. The utility of super-collimation is strongly linked to the distance over which it can be maintained, and the figure of merit is important since it dictates the maximum density and complexity of optical circuits based on super-collimation. Previous experimental studies showed figures of merit smaller than 6 [5]. In this work we observe figures of merit of more than 600.

Figure 1 – Super-collimation over a 0.3 cm sample. (a) SEM image of the fabricated large-area PhC. (b) Top view of the TE-light guided along a 0.3 cm-long PhC, acquired with an IR camera, and NSOM images of the collimated beam at positions labeled (1)-(3) (corresponding to 0.02, 0.10 and 0.30 cm along the device), and beam cross-section with Gaussian fit, obtained from the intensity map at position (3).

Super-collimation is studied over centimeter-length-scale distances in a large-area 2D PhC with a square lattice of air holes in a thin silicon film – Figure 1(a). Our 2D PhC was fabricated in a silicon on insulator (SOI) wafer, using interferometric lithography and reactive ion etching [6], and

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was designed to operate in the 1500 nm wavelength range for TE radiation (electric field parallel to the 2D plane), in the lowest energy band (close to the edge of the bandgap). The lattice constant is a = 350 nm and the hole radius is r = 0.3a. The projected band structure of the PhC slab under study was computed with a 3D frequency-domain eigenmode solver, and around λ = 1500 nm the computed surfaces showed remarkably little spatial dispersion in the transverse wavevector.

We experimentally observed that the optimum wavelength for super-collimation was approximately 1500 nm, and we measured losses of (3.6 ± 0.5) dB/mm. A coarse contact-mode near field scanning optical microscopy (NSOM) technique [7] was used to obtain high resolution images of the beam profile at different positions along the PhC, showing that a 2 µm-wide beam was conserved over 0.3 cm of propagation – Figure 1(b). The beam profiles were fitted to Gaussian functions yielding full widths at half maximum (FWHMs) in intensity of 2.1, 2.1 and 2.3 (±0.2) µm, for positions (1)-(3), respectively. In addition, high-resolution confocal measurements confirmed super-collimation after 0.5 cm of propagation – Figure 2.

Figure 2 – Confocal image (displayed as a surface-plot) at the output of a 0.5 cm-long PhC, Figure 3 – Frequency dependence and disorder showing the TE beam profile at the effects on super-collimation. (a-c) Experimental super-collimation wavelength. The inset shows a results. (d-f) Simulated results through BPM. Gaussian fit to the data and returns a FWHM of 2.2 µm.

The results of this experiment show figures of merit as high as 376, which correspond to super-collimation over more than 14,200 lattice constants. Additional studies of a 0.8 cm-long PhC device yielded measurements of beams with similar transverse profiles, and figures of merit closer to 600. Both frequency dependence and effects of disorder were observed experimentally – Figure 3(a-c) – and studied through the beam propagation method (BPM), based on the computed dispersion surfaces – Figure 3(d-f). For a normalized frequency of ω = a/λ = 0.233 the beam divergence is negligible. The discrepancy between measurements and simulations is 2%, and the beam break up is due to short scale disorder, such as fabrication roughness (RMS fluctuation in the hole-radius of 0.6 nm). We show that super-collimation possesses inherent robustness with respect to short-scale disorder and this work presents an important step toward enabling flexible high density optical interconnects.

References 1 H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212-1214 (1999).

2 L. J. Wu, M. Mazilu, and T. F. Krauss, “Beam steering in planar-photonic crystals: from superprism to supercollimator,” J. Lightwave Technol. 21, 561-566 (2003).

3 L. Wu, M. Mazilu, J.-F. Gallet, and T. F. Krauss, “Square lattice photonic-crystal collimator,” Photonics and Nanostructures - Fundamentals and Applications 1, 31-36 (2003).

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4 P. T. Rakich, M. S. Dahlem, S. N. Tandon, M. Ibanescu, M. Soljačić, G. S. Petrich,, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, “Achieving centimetre-scale supercollimation in a large-area two-dimensional photonic crystal,” Nature Mater. 5, 93-96 (2006).

5 H. Kosaka, T. Kawashima, A. Tomita, T. Sato, and S. Kawakami, “Photonic-crystal spot-size converter,” Appl. Phys. Lett. 76, 268-270 (2000).

6 S. N. Tandon, M. Soljačić, G. S. Petrich, J. D. Joannopoulos, and L. A. Kolodziejski, “The superprism effect using large area 2D-periodic photonic crystal slabs,” Photon. and Nanostruct. 3, 10-18 (2005).

7 S. Bourzeix, J. M. Moison, F. Mignard, F. Barthe, A. C. Boccara, C. Licoppe, B. Mersali, M. Allovon, and A. Bruno, “Near-field optical imaging of light propagation in semiconductor waveguide structures,” Appl. Phys. Lett. 73, 1035-1037 (1998).

Laser Micro-Machining of Photonic Devices

Sponsors National Science Foundation – ECS-0501478 Air Force Office of Scientific Research – F9550-040-1-0011

Project Staff Dr. Jung-Ho Chung, Yu Gu, Dr. Kenya Suzuki, Vikas Sharma, Dr. Andrew M. Kowalevicz, Professor James G. Fujimoto

Micromachining using femtosecond laser pulses is a powerful and versatile technique for fabricating photonic devices. It is capable of writing three-dimensional structures and has the potential for high-density integrated photonic circuits, thus providing enhanced functionality not possible in planar geometries. In contrast to the conventional semiconductor-based fabrication process, the micromachining process utilizes relatively simple equipments, allowing for rapid construction of a variety of devices. Important elements of the fabrication system consist of a femtosecond laser and computer controlled three-dimensional stages.

Specifically, we are using a three-axis air-bearing stage system that provides nanometer resolution and full three-dimensional computer control. Typically glass samples are located on top of the stages and moved according to software commands, while femtosecond pulses are focused inside the samples. In our case, those pulses are emitted from a homemade extended cavity Kerr-lens-modelocking Ti:Sapphire laser with ~150-nJ energy. The repetition rate and pulse duration of the oscillator are 5.85 MHz and 45 fs, respectively [1]. In contrast to amplified lasers, it has the repetition rate high enough to accumulate heating effects, which enables device fabrication approximately three orders of magnitude faster than the amplified laser case. Moreover, generally MHz-range lasers are advantageous for fabricating waveguide devices since the photomodification is caused mainly by thermal diffusion, resulting in symmetric cross-sections of modified regions, while kHz amplified lasers cause elliptical cross-sections due to nonlinear absorption and plasma generation highly dependent on the focal volume [2]. Finally, the relative high energy in our laser system enables us to overcome the restriction to very high numerical aperture objectives, thus giving greater flexibility and versatility to the machining process.

Since the first demonstration for modifying refractive indices in glass materials [3], various structures have been fabricated via direct writing using femtosecond lasers [4-17]. They include not only a wide variety of planar devices, such as several types of couplers [4-7], interferometers [8, 9], and active waveguides [10, 11] but also three-dimensional structures, such as optical splitters [12, 13], interconnections [14], wavelength-division multiplexing couplers [15], and

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directional couplers [16, 17]. In following sections, we will discuss the telecom-wavelength characterization of waveguides and measurement results of 3x3 couplers we recently fabricated.

1. Basic Characterization of Waveguides

After photonic devices are directly written in a glass substrate, usually its surfaces where the beam is coupled are polished for efficient light coupling. Then, it is located on a waveguide manipulator sandwiched between two XYZ stages holding fibers. Either amplified spontaneous emission (ASE) from an Erbium-doped fiber amplifier (EDFA) or the light emitted from a 1.5µm tunable laser source is coupled into waveguides written in the substrate. Another butt coupled fiber at the other side of the substrate picks up waveguide outputs, enabling readings from an optical spectrum analyzer or power meter. To minimize coupling losses, index matching oil is applied between the fiber tips and waveguide surfaces. A charge-coupled device (CCD) camera with a microscope objective is used for alignment.

To analyze basic properties of direct written waveguides, we fabricated the structure shown in Fig. 1(a), consisting of straight and curved waveguides, in soda lime glass substrates (Corning 0215, n=1.515), while varying the parameters, such as laser power, beam polarization, bending radius, and writing speed. When the writing speed was too fast and the writing power was too low, we observed weaker confinement of light, leading to larger output beam profiles. On the other hand, when the exposure is too high, i.e., in the case of high power and low speed, multimode guiding occurs. Typically, nicely guided single-mode beam profiles, as shown in Fig. 1(b), were observed when the pulse energy is approximately ~15 nJ and the writing speed ranges from 5 mm/s to 20 mm/s.

(a) (b)

Figure 1. (a) Layout of the structure for measuring basic properties of direct written waveguides. (b) Typical near-field beam profile at the waveguide exit

One important property of a waveguide is its loss. We measured losses of straight and curved waveguides for different parameters. In the straight waveguide case (bottom part in Fig. 1(a)), while varying the beam polarization and writing speed, we measured insertion losses for different lengths of waveguides to find out propagation and coupling losses. Fig. 2(a) shows the losses as functions of writing speed when the pulse energy was ~18 nJ. For both polarizations, the propagation loss was the lowest with the speed of 10-20 mm/s and the coupling loss got slightly lower when the speed decreased. Typical propagation and coupling losses were approximately 0.4dB/cm and 4 dB, respectively. In the curved waveguide case, we fabricated the S-type bend consisting of two arcs with identical bending angles of 15 degrees but radii of curvatures opposite in sign, as shown in Fig. 1(a). We used radii of 5, 10, 20, 50, and 100 mm. When the insertion loss is measured for the waveguide, it will include transition losses between straight and curved parts and between the arcs. However, the loss caused by radiation along the curved parts dominates. Fig. 2(b) shows the insertion loss as a function of bending radius, as measured for different writing speeds. As well known, the bending loss increases as the radius gets smaller.

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Also, the plot shows that as the writing speed decreases, the bending loss gets lower, indicating that the curves with higher refractive-index cores have reduced radiation.

1.0 10 0.9 9 0.8 8 TM 0.7 7 0.6 6 TE Writing speed 0.5 5 0.4 TE 4 TM 0.3 3

Fiber coupling loss, dB loss, coupling Fiber 0.2 2 Propagation loss, dB/cm loss, Propagation 0.1 1 0.0 0 0 1020304050 Writing speed, mm/s (a) (b)

Figure 2. Losses as functions of writing speed (a) for straight waveguides with transverse-magnetic (TM) and transverse-electric (TE) polarized fields and (b) for S-bends with speeds of 2, 5, 10, and 20 mm/s

2. 3x3 Couplers

One of the important applications of optical, symmetric 3x3 directional couplers [18] is optical interferometer-based sensors because they enable the detection of the direction of an interferometer arm phase change caused by an analyte. A Michelson interferometer-based low- coherence reflectometer and optical coherence tomography have already been demonstrated via symmetric 3x3 couplers for optical signal processing [19, 20]. Although those couplers were based on fiber optics, the integrated optical type is preferable because it offers such advantages as flexibility in photonic circuit configuration and mass production. Even in an integrated optic form, it is important to maintain the symmetry of the waveguide arrangement in the coupling region in order to be able to detect the direction of phase change efficiently in Mach-Zehnder interferometer-based sensors. In contrast to conventional waveguide fabrication techniques utilizing photolithography and dry etching, direct writing via femtosecond lasers is suitable for realizing three-dimensional devices such as symmetric 3x3 directional couplers.

(a) (b) Figure 3. (a) Schematic configuration of a 3x3 directional coupler, and (b) Typical coupling characteristics of an optical, symmetric 3x3 directional coupler.

We demonstrated and characterized symmetric 3x3 three-dimensional directional couplers. Fig. 3 shows the schematic configuration of a symmetric 3x3 coupler and its typical coupling characteristics. The coupler consists of three input waveguides, a transition region, a coupling region, a second transition region, and output waveguides. Fig. 3(b) shows the calculated coupling characteristics of an ideal symmetric coupler, where an optical signal is launched into input port waveguide 1. It should be noted that the optical power of waveguide 1 gradually couples with waveguides 2 and 3 at the same ratio, but it never falls to zero. This is because part of the input optical signal, which couples with waveguide 2, is transferred back to waveguides 3 and 1. The same is true of the part of the input signal that couples with waveguide 3, and is transferred back to waveguides 2 and 1. In other words, if we launch an optical signal from input

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port 1 and monitor output 1, then the coupler becomes an asymmetric directional coupler. Therefore, output 1 does not fall to zero.

The center-to-center separations between the input and output waveguides were fixed at 80 µm, while the separation in the coupling region was varied between 15, 20, and 25 µm in order to investigate the coupling characteristics. The horizontal length of the transition waveguide regions was fixed at 5 mm. Therefore, the junction angles between the transition waveguide regions and the input and the output, and the coupling waveguide region, varied from 0.43 to 0.36 degrees, according to the waveguide separation and the length of the coupling region. This variation in angle has a negligible effect on the coupling characteristics. Fig. 4 shows the coupling characteristics of the various 3x3 directional couplers at a wavelength of 1530 nm. The solid and dotted lines represent the coupling characteristics for TM and TE polarized modes, respectively. Only a small polarization dependence of 11 % in the coupling ratio is observed in the coupler with a separation of 25 µm and a coupling interaction length of 7.2 mm. This fact supports the idea that a waveguide fabricated with a high-repetition-rate ultra short pulse laser does not show polarization dependence [21]. The measured losses were 6.6 dB and varied only by 0.2 dB as the separation distance was varied from 25 µm to 15 µm. The excess loss includes propagation loss as well as fiber coupling loss. The small loss variation of 0.2 dB with waveguide separation distance was caused by the discontinuities between waveguides, implying that the effect of the nonadiabatic connection along transition waveguide was negligible. As shown in Fig. 4, the separation S between the waveguides in the coupling region clearly affected the coupling characteristics. Fig. 4(a) illustrates that almost no coupling occurred for a coupling length of 0 µm for a separation of 25 µm. On the other hand, with separations of 20 and 15 µm, a nonzero amount of power has already been transferred when the straight waveguide interaction length is 0 µm, as shown in figures 4(b) and (c). This is because the coupling between the waveguides in the transition region becomes dominant. In either case, the measured coupling characteristics oscillated as a function of the straight waveguide interaction length. This indicates that, despite some errors, it is possible to realize coupled mode functions that are sinusoidal. However, it should be noted that the optical power of waveguide 1 falls to zero for interaction lengths of 7000, 3000, and 800 µm for separations of 25, 20, and 15 µm, respectively. Through numerical calculation, we found that this error resulted from deviations from symmetry dominated by vertical position errors of the coupling waveguide.

(a) (b) (c) Figure 4. Coupling characteristics of a fabricated 3x3 directional coupler with an optical signal incident from input port 1. The separation S were designed to be (a) 25 µm, (b) 20 µm, and (c) 15 µm. The solid lines and dotted lines correspond to TM and TE polarization modes, respectively.

References [1] A. M. Kowalevicz, A. T. Zare, F. X. Kartner, J. G. Fujimoto, S. Dewald, U. Morgner, V. Scheuer, and G. Angelow, "Generation of 150-nJ pulses from a multiple-pass cavity Kerr- lens mode-locked Ti : Al2O3 oscillator," Optics Letters 28(17): 1597-99 (2003). [2] S. M. Eaton, H. B. Zhang, and P. R. Herman, "Heat accumulation effects in femtosecond laser-written waveguides with variable repetition rate," Optics Express 13(12): 4708-16 (2005). [3] K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, "Writing waveguides in glass with a femtosecond laser," Optics Letters 21(21): 1729-31 (1996).

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[4] D. Homoelle, S. Wielandy, A. L. Gaeta, N. F. Borrelli, and C. Smith, "Infrared photosensitivity in silica glasses exposed to femtosecond laser pulses," Optics Letters 24(18): 1311-13 (1999). [5] C. B. Schaffer, A. Brodeur, J. F. Garcia, and E. Mazur, "Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy," Optics Letters 26(2): 93-5 (2001). [6] A. M. Streltsov and N. F. Borrelli, "Fabrication and analysis of a directional coupler written in glass by nanojoule femtosecond laser pulses," Optics Letters 26(1): 42-43 (2001). [7] K. Minoshima, A. M. Kowalevicz, I. Hartl, E. P. Ippen, and J. G. Fujimoto, "Photonic device fabrication in glass by use of nonlinear materials processing with a femtosecond laser oscillator," Optics Letters 26(19): 1516-18 (2001). [8] K. Minoshima, A. M. Kowalevicz, E. P. Ippen, and J. G. Fujimoto, "Fabrication of coupled mode photonic devices in glass by nonlinear femtosecond laser materials processing," Optics Express 10(15): (2002). [9] C. Florea and K. A. Winick, "Fabrication and characterization of photonic devices directly written in glass using femtosecond laser pulses," Journal of Lightwave Technology 21(1): 246-53 (2003). [10] R. Osellame, S. Taccheo, M. Marangoni, R. Ramponi, P. Laporta, D. Polli, S. De Silvestri, and G. Cerullo, "Femtosecond writing of active optical waveguides with astigmatically shaped beams," Journal of the Optical Society of America B (Optical Physics) 20(7): 1559-67 (2003). [11] Y. Sikorski, A. A. Said, P. Bado, R. Maynard, C. Florea, and K. A. Winick, "Optical waveguide amplifier in Nd-doped glass written with near-IR femtosecond laser pulses," Electronics Letters 36(3): 226-27 (2000). [12] S. Nolte, M. Will, J. Burghoff, and A. Tuennermann, "Femtosecond waveguide writing: a new avenue to three-dimensional integrated optics," Applied Physics a-Materials Science & Processing 77(1): 109-11 (2003). [13] V. Sharma, A. M. Kowalevicz Jr, R. Huber, J. G. Fujimoto, and K. Minoshima, "Three dimensional waveguide splitters fabricated in glass using a femtosecond laser oscillator," paper presented at Conference on Lasers and Electro-Optics, CLEO, Baltimore, MD, May 22-27, 2005. [14] Y. Nasu, M. Kohtoku, Y. Hibino, and Y. Inoue, "Three-dimensional waveguide interconnection in planar lightwave circuits by direct writing with femtosecond laser," Japanese Journal of Applied Physics Part 2-Letters & Express Letters 44(46-49): L1446- L48 (2005). [15] W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, "Wavelength division with three-dimensional couplers fabricated by filamentation of femtosecond laser pulses," Optics Letters 28(24): 2491-93 (2003). [16] A. M. Kowalevicz, V. Sharma, E. P. Ippen, J. G. Fujimoto, and K. Minoshima, "Three- dimensional photonic devices fabricated in glass by use of a femtosecond laser oscillator," Optics Letters 30(9): 1060-2 (2005). [17] K. Suzuki, V. Sharma, J. G. Fujimoto, and E. P. Ippen, "Characterization of symmetric [3x3] directional couplers fabricated by direct writing with a femtosecond laser oscillator," Optics Express 14(6): 2335-43 (2006). [18] S. K. Sheem, "Optical Fiber Interferometers with [3by3] Directional-Couplers - Analysis," Journal of Applied Physics 52(6): 3865-72 (1981). [19] K. Takada, H. Yamada, and M. Horiguchi, "Optical Low-Coherence Reflectometer Using [3x3] Fiber Coupler," Ieee Photonics Technology Letters 6(8): 1014-16 (1994). [20] M. A. Choma, C. H. Yang, and J. A. Izatt, "Instantaneous quadrature low-coherence interferometry with 3 x 3 fiber-optic couplers," Optics Letters 28(22): 2162-64 (2003). [21] R. Osellame, N. Chiodo, V. Maselli, A. Yin, M. Zavelani-Rossi, G. Cerullo, P. Laporta, L. Aiello, S. De Nicola, P. Ferraro, A. Finizio, and G. Pierattini, "Optical properties of waveguides written by a 26 MHz stretched cavity Ti:sapphire femtosecond oscillator," Optics Express 13(2): 612-20 (2005).

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Publications, Presentations, Thesis and Books

Journal Articles

1. J. Kim, J. R. Birge, V. Sharma, J. G. Fujimoto, F. X. Kaertner, V. Scheuer, and G. Angelow, “Ultrabroadband beam splitter with matched group-delay dispersion”, Opt. Lett. 30, 1569 (2005). 2. R. Ell, G. Angelow, W. Seitz, M. J. Lederer, H. Huber, D. Kopf, J. R. Birge, and F. X. Kaertner, “Quasi-synchronous pumping of modelocked few-cycle Titanium-Sapphire lasers”, Optics Express 13, 9292 (2005). 3. A. Winter, F. Ö. Ilday, O. D. Mücke, R. Ell, H. Schlarb, P. Schmüser, and F. X. Kärtner, “Towards high-performance optical master oscillators for energy recovery linacs,” Nucl. Instr. and Meth. A 557, 299 (2006). 4. L. Matos, O. D. Mücke, J. Chen, and F. X. Kärtner, “Carrier-envelope phase dynamics and noise analysis in octave-spanning Ti:sapphire lasers,” Opt. Express 14, 2497 (2006). 5. A. Gordon and F. X. Kärtner, “Quantitative modeling of single atom high harmonic generation”, Phys. Rev. Lett. 95, 223901 (2005). 6. A. Gordon, R. Santra, and F. X. Kärtner, “Role of the Coulomb singularity in high harmonic generation”, Phys. Rev. A 72, 063411 (2005). 7. R. Huber, M. Wojtkowski, K. Taira, J.G. Fujimoto, and K. Hsu, “Amplified, frequency swept lasers for frequency domain reflectometry and OCT imaging: design and scaling principles”, Optics Express, 13(9): 3513-28 (2005). 8. R. Huber, M. Wojtkowski, J. G. Fujimoto, J. Y. Jiang, A. E. Cable, “Three-dimensional and C- mode OCT imaging with a compact, frequency swept laser source at 1300 nm“, Optics Express, 13(26): 10523-38 (2005). 9. R. Huber, M. Wojtkowski, and J. G. Fujimoto, "Fourier Domain Mode Locking (FDML): A new laser operating regime and applications for optical coherence tomography," Optics Express, 14: 3225-37 (2006). 10. A. Gordon, C. Jirauschek, and F. X. Kärtner, “Numerical solver of the time dependent Schrödinger equation with Coulomb singularities”, Phys. Rev. A 73, 042505 (2006). 11. A. Gordon, F. X. Kärtner, N. Rohringer, and R. Santra, “Role of many-electron dynamics in high harmonic generation”, Phys. Rev. Lett. 96, 223902 (2006). 12. J. R. Birge, F. X. Kärtner, “Efficient analytic computation of dispersion from multilayer structures,” Applied Optics, 45, 1478 (2006). 13. H.A. Haus, M.A. Popović and M.R. Watts, “Broadband hitless bypass switch for integrated photonic circuits,” IEEE Photon. Technol. Lett. 18, 1137 (2006). 14. M.A. Popović, C. Manolatou and M.R. Watts, “Coupling-induced resonance frequency shifts in coupled dielectric multicavity filters”, Opt. Express 14, 1208 (2006). 15. S. Akiyama, M.A. Popović, P.T. Rakich, K. Wada, J. Michel, H.A. Haus, E.P. Ippen and L.C. Kimerling, “Air trench bends and splitters for dense optical integration in low index contrast,” J. Lightwave Technol. 23, 2271 (2005). 16. T. Barwicz, M.A. Popović, M.R. Watts, P.T. Rakich, E.P. Ippen and H.I. Smith, “Fabrication of Add-Drop Filters Based on Frequency-Matched Microring Resonators,” J. Lightwave Technol. 24, 2207 (2006). 17. Ch. Jirauschek, L. Duan, O. D. Mücke, F. X. Kärtner, M. Wegener, and U. Morgner, ”Carrier-envelope phase-sensitive inversion in two-level systems”, JOSA B, 22(10), 2065-2075 (2005)

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18. Ch. Jirauschek and F.X. Kärtner, “Gaussian pulse dynamics in gain media with Kerr Nonlinearity” J.Opt. Soc. Am. B. 23(9), 1776-1784 (2006). 19. O. D. Mucke, R. Ell, A. Winter, J. Kim, J. R. Birge, L. Matos, and F. X. Kartner” Self- Referenced 200 MHz Octave-Spanning Ti:Sapphire Laser with 50 Attosecond Carrier- Envelope Phase Jitter”, OPTICS EXPRESS, 13(13): 5163 (2005) 20. F. Ö. Ilday and F. X. Kärtner, “Cavity-enhanced optical parametric chirped-pulse Amplification”, OPTICS LETTERS, 31(5):637, (2006) 21. D. Kielpinski and M. Cetina J.A. Cox and F.X. Kartner, “Laser cooling of trapped ytterbium ions with an ultraviolet diode laser”, Optics Letters, 31(6): 757-9,(2006) 22. T. Binhammer, E. Rittweger, U. Morgner, R. Ell, F. X. Kartner, “Pulse Shaping and Temporal Superresolution towards Single-Cycle Pulses”, Optics Letters, 31(10) : 1552-4 (2006) 23. A.D. Aguirre, N. Nishizawa, J.G. Fujimoto, W. Seitz, M. Lederer, and D. Kopf, “Continuum generation in a novel photonic crystal for ultrahigh resolution optical coherence tomography at 800 nm and 1300 nm,” Optics Express, 14(3): 1145-60 (2006).

Accepted Journal Articles: 24. F. W. Gan, F. J. Grawert, J. Schley, S. Akiyama, J. Michel, K. Wada, L. C. Kimerling, F. X. Kärtner, Design of All-Optical Switches Based on Carrier-Injection in Si/SiO2 Split-Ridge Waveguides (SRW’s), IEEE Journal of Lightwave Technology. 25. M.A. Popović, T. Barwicz, M.R. Watts, P.T. Rakich, L. Socci, E.P. Ippen, F.X. Kärtner and H.I. Smith, “Multistage high-order microring-resonator add-drop filters,” Opt. Lett. 31, no. 17, Sep 1, 2006 26. M.A. Popović, E.P. Ippen and F.X. Kärtner, “Universally balanced photonic interferometers,” Opt. Lett. 31, no. 18, Sep 15, 2006.

Journal Articles, Submitted for Publication

R. Huber, D. C. Adler, and J. G. Fujimoto, “Buffered Fourier Domain Mode Locking (FDML): Unidirectional swept laser sources for OCT imaging at 370,000 lines per second,” submitted to Optics Letters.

Conference Proceedings

1. O. D. Mücke, R. Ell, A. Winter, J. Kim, J. R. Birge, L. Matos, and F. X. Kaertner, “Self- Referenced 200 MHz Octave-Spanning Ti:Sapphire Laser With 0.10 Radian Carrier- Envelope Phase Error,” talk 2 in session 4, 1st ESA International Workshop on Optical Clocks, European Space Research and Technology Centre of the European Space Agency, Noordwijk, The Netherlands, June 8-10, 2005. 2. F. X. Kärtner, O. D. Mücke, P. Wagenblast, R. Ell, A. Winter, J. Kim, A. Siddiqui, and L. Matos, “Solid-State Lasers for Frequency Metrology,” invited talk TuB1.1, IEEE LEOS Summer Topical 2005 on Optical Frequency & Time Measurement and Generation, San Diego, CA, July 25-27, 2005. 3. R. Huber, K. Taira, M. Wojtkowski, T. H. Ko, J. G. Fujimoto, and K. Hsu, "High speed frequency swept light source for Fourier domain OCT at 20 kHz A-scan rate," Coherence Domain Optical Methods and Optical Coherence Tomography in Biomedicine IX, San Jose, CA, Jan 23-26, 2005. 4. R. Huber, K. Taira, T. H. Ko, M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, and K. Hsu, "High-speed, amplified, frequency swept laser at 20 kHz sweep rates for OCT imaging," paper presented at Quantum Electronics and Laser Science Conference (QELS), Baltimore, MD, May 22-27, 2005.

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5. R. Huber, K. Taira, M. Wojtkowski, and J. G. Fujimoto, "Fourier Domain Mode Locked Lasers for OCT imaging at up to 290kHz sweep rates," Optical Coherence Tomography and Coherence Techniques II, Munich, Germany, 2005. 6. R. Huber, K. Taira, and J. G. Fujimoto, "Fourier Domain Mode Locking: Overcoming limitations of frequency swept light sources and pulsed lasers," paper presented at Conference on Lasers and Electro-Optics Europe/ European Quantum Electronics Conference (CLEO/Europe - EQEC 2005), Munich, Germany, 2005. 7. N. Nishizawa, A.D. Aguirre, and J.G. Fujimoto, “Super continuum generation for real time ultrahigh resolution optical coherence tomography,” paper presented at Photonics West, San Jose, California, January 21-26, 2006, invited talk. 8. R. Huber, K. Taira, M. Wojtkowski, and J. G. Fujimoto, "Fourier domain mode-locked lasers for swept source OCT imaging at up to 290 kHz scan rates," Coherence Domain Optical Methods and Optical Coherence Tomography in Biomedicine X, San Jose, CA, 2006. 9. F. Ö. Ilday, A. Siddiqui, O. D. Muecke, and F. X. Kärtner, “Cavity-Enhanced Optical Parametric Chirped-Pulse Amplification,” talk CFN3, CLEO, Long Beach, California, May 21- 26, 2006. 10. O. D. Mücke, L. Matos, J. Chen, and F. X. Kärtner, “Carrier-envelope phase dynamics and noise analysis in octave-spanning Ti:sapphire lasers,” talk CTuP2, CLEO, Long Beach, California, May 21-26, 2006. 11. R. Ell, J. R. Birge, M. Araghchini, and F. X. Kärtner, “Control of carrier-envelope phase by a composite glass plate”, CLEO, Long Beach, California, May 21-26, 2006. 12. J. R. Birge, R. Ell, F. X. Kärtner, “Two-dimensional spectral shearing interferometry (2DSI) for ultrashort pulse characterization”, CLEO, Long Beach, California, May 21-26, 2006. 13. J. Kim, F. Ö. Ilday, A. Winter and F. X. Kärtner, “Timing Distribution and RF-Synchronization with Mode-Locked Lasers”, Paper WB3.4, IEEE/LEOS Summer Topical Meeting on Optical Frequency & Time Measurement and Generation 2005, San Diego, CA, Jul 2005. 14. J. Kim, T. R. Schibli, L. Matos, H. Byun and F. X. Kärtner, “Phase-coherent spectrum from ultrabroadband Ti:sapphire and Cr:forsterite lasers covering the visible to the infrared” (Invited talk), Paper M3-5, Ultrafast Optics (UFO/HFSW) 2005, Nara, Japan, Sep 2005. 15. J. Kim, F. Ludwig, D. Cheever, F. Ö. Ilday, J. Burnham and F. X. Kärtner, “A Balanced Optical-RF Phase Detector”, Paper CTuP5, Conference on Lasers and Electro Optics (CLEO) 2006, Long Beach, CA, May 2006. 16. J. Kim, J. Burnham, J. Chen, F. X. Kärtner, F. Ö. Ilday, F. Ludwig, H. Schlarb, A. Winter, M. Ferianis, D. Cheever, “An Integrated Femtosecond Timing Distribution System for XFELs”, Paper THOPA03, European Particle Accelerator Conference (EPAC) 2006, Edinburgh, UK, Jun 2006 17. M. Park, J. Kim, F. Kaertner and M. Perrott, “An Optical-Electrical Sub-Sampling Receiver Employing Continuous-Time ∆Σ Modulator”, Paper A2L-D, European Solid-State Circuits Conference (ESSCIRC) 2006, Montreux, Switzerland, Sep 2006. 18. A. Gordon, C. Jirauschek and F. X. Kärtner, "Scaling of the keV HHG photon yield with drive wavelength", paper F1-4 Ultrafast Optics (UFO/HFSW, Nara, Japan (2005) 19. A. Gordon and F. X. Kärtner, "The Ehrenfest theorem and quantitative predictions of HHG based on the three-step-model", paper TuP-2 Ultrafast Optics (UFO/HFSW), Nara, Japan (2005). 20. A. Gordon and F. X. Kärtner, "Scaling of the keV HHG photon yield with drive wavelength", paper JTuA3, OSA annual meeting, Tucson AZ, USA (2005). 21. A. Gordon, R. Santra and F. X. Kärtner, "Quantitatively-reliable analytic approximation for the single-atom HHG spectrum", paper JTuD73, CLEO, Long Beach, CA, USA (2006).

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22. C. Y. Wang, L. Diehl, F. Capasso, A. Gordon, C. Jirauschek, F. Kärtner, A. Belyanin D. Bour, S. Corzine, G. Höfler, P. Grant, H. C. Liu, T. Maier, H. Schneider, and J. Faist, “Coherent instabilities and self-pulsations in quantum cascade lasers”, paper CMN4, CLEO, Long Beach, CA, USA (2006). 23. F. W. Gan, F. X. Kärtner, “Low Insertion Loss, High-Speed Silicon Electro-Optic Modulator Design”, Integrated Photonics Research and Applications Topical Meeting (IPRA), April, Uncasville, CT, USA. 2006 24. M.A. Popović, Hermann A. Haus and M.R. Watts, “General approach to hitless switching and FSR extension for resonators in integrated photonic circuits,” in Optical Fiber Communication Conference (OFC/NFOEC), Anaheim, California, March 5-10, 2006, paper OWI66. 25. M.A. Popović, T. Barwicz, E.P. Ippen and F.X. Kärtner, “Global design rules for silicon microphotonic waveguides: sensitivity, polarization and resonance tunability,” in Conference on Lasers and Electro-Optics (CLEO), Long Beach, California, May 21-26, 2006, paper CTuCC1. 26. M.R. Watts, M. Qi, T. Barwicz, M. Popović, P. Rakich, L. Socci, E.P. Ippen, F. Kaertner and H.I. Smith, “Towards polarization independent high-index contrast microphotonics,” presented at XXVIIIth General Assembly of the International Union of Radio Science (URSI), New Delhi, India, Session D07A, Oct 28, 2005. 27. M.R. Watts, T. Barwicz, M.A. Popović, M. Qi, P.T. Rakich, L. Socci, E.P. Ippen, F.X. Kärtner, H.I. Smith and M. Romagnoli, “High-index-contrast microphotonics, from concept to implementation (Invited),” in Conference on Lasers and Electro-Optics (CLEO), OSA Technical Digest (Optical Society of America, Washington DC, May 21-26, 2006), paper CTuM3. 28. T. Barwicz, M.A. Popović, P.T. Rakich, M.R. Watts, F.X. Kärtner, E.P. Ippen and H.I. Smith, “Fabrication control of the resonance frequencies of high-index-contrast microphotonic cavities,” in Proceedings of the Integrated Photonics Research and Applications and Nanophotonics Topical Meeting (IPRA/Nano), Uncasville, Connecticut, April 2006, paper JWA3.

Theses

29. M. Fan, Efficient Out-of-Plane Microphotonic Fiber-to-Chip Coupler Designs, M. Eng. Thesis, Department of Electrical Engineering and Computer Science, MIT, 2006.

Books

1 O. D. Mücke, L. Matos, and F. X. Kärtner, “Solid-State Laser Technology for Optical Frequency Metrology”, in Solid-State Lasers and Applications, edited by A. Sennaroglu, chapter 10, 76 pages, in press (CRC Press, 2006, ISBN 0849335892).

2 J. M. Schmitt, R. Huber, and J. G. Fujimoto, “Limiting Ischemia by Fast Fourier-Domain Imaging” in Handbook on Cardiovascular OCT, ed. E. Regar (to be published, 2006/2007).

Patents

R. Huber, K. Taira, and J. G. Fujimoto, U.S. Patent Application Serial No.: 11/337,105; “Mode Locking Methods and Apparatus”

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