MSc in Photonics PHOTONICSBCN
Universitat Politècnica de Catalunya (UPC) Universitat Autònoma de Barcelona (UAB) Universitat de Barcelona (UB) Institut de Ciències Fotòniques (ICFO) http://www.photonicsbcn.eu
Master in Photonics
MASTER THESIS WORK
TEMPORAL AND SPECTRAL CHARACTERIZATION OF NEAR-IR FEMTOSECOND OPTICAL PARAMETRIC OSCILLATOR PULSES
Parisa Farzam
Supervised by Dr. Majid Ebrahim-Zadeh, (ICFO, ICREA) and Dr. Lukasz Kornaszewski (ICFO)
Presented on date 9th September 2009
Registered at
Temporal and spectral characterization of near-IR femtosecond optical parametric oscillator pulses
Parisa Farzam ICFO-Institut de Ciències Fotòniques, Nonlinear optics group, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
E-mail: [email protected]
Abstract. Recently, there has been growing interest in ultrashort pulse measurement techniques. The aim of this work is to utilize interferometric autocorrelator in order to characterize near- IR femtosecond optical parametric oscillator (OPO) pulses. Although considerable research has been devoted to using nonlinear crystals in the autocorrelators, an attractive alternative to this approach remains two-photon absorption in photodiodes. In the setup we have used a commercial semiconductor which has several advantages to second harmonic generation technique. Conventional methods in autocorrelation analysis use secant hyperbolic square (sech2) assumption to figure out the shape of pulse; but we have developed a software to find out the pulse shape by guessing the phase. The comparison between results from phase-guessing method and sech2 assumption shows that the first method is more flexible and gives much information but it needs to be enhanced in order to find the best phase automatically.
Keywords: ultrashort pulse measurement, autocorrelation, two-photon absorption, optical parametric oscillator.
1. Introduction The ultrashort pulse is a pulse whose duration is at most a few tens of picoseconds, and often in the range of femtosecond. It is usually generated by means of passive mode locking technique, but sometimes also with free electron lasers. Moreover it is possible to start with longer pulses and apply some methods of pulse compression. In dealing with ultrashort pulses new issues do arise; for instance, the shorter the pulse, the broader its spectrum [1]. The broad optical bandwidth of such pulses leads to problems such as the chromatic dispersion of lens materials, which leads to chromatic aberrations of the focusing optics unless special correction techniques are employed. Furthermore all optical components, for instance mirrors, lenses etc. should work properly in entire range of pulse bandwidth which is very wide. The other problem with ultrashort pulses is the characterization of them. As these pulses shrink in length and grow in utility, the ability to measure them becomes increasingly important. There are several reasons for this. First, precise knowledge of the pulse properties is necessary for verifying theoretical models of pulse creation. Second, in order to make even shorter pulses, it is necessary to understand the distortions that limit the length of currently available pulses. Third, in experiments using these pulses, it is always important to know at least the pulse length in order to determine the temporal resolution of a given experiment. Moreover, in many experiments additional details of the pulse’s structure play an important role in determining the outcome of the experiment. Of particular importance is the variation of frequency during the pulse, known as ‘‘chirp’’. [2] Measurement of pulse means finding intensity and phase in either time or frequency domain. In order to measure an event in time we need to use a faster event. But how can we measure the fastest event? Since no shorter event is available, we use the pulse to measure itself. [1] Temporal and spectral characterization of near-IR femtosecond optical parametric oscillator pulses
Such pulses are generally characterized using auto- or cross-correlation methods which conventionally involve splitting an ultrashort laser pulse by means of beam-splitter, adding a variable relative time delay between the split pulses, and spatially overlapping the two pulses in a nonlinear crystal (with the correct crystal orientation for phase-matching) for second-harmonic generation (SHG) or third harmonic generation (THG) followed by a linear detector for example: photo-multiplier tube (PMT) or charged coupled device (CCD). [3-5] The most common method used to infer the temporal width of a pulse is based on a Michelson- type autocorrelator and the generation of a phase-matched second harmonic signal. Although, frequency-resolved optical gating (FROG) [6] and spectral-phase interferometry for direct electric-field reconstruction (SPIDER) [7] have been successfully employed for the intensity and phase measurement of femtosecond optical pulses, interferometric autocorrelation (IAC) has considerable advantages over them. For instance: easy implementation, self-calibration from interferometric fringes, and alignment confirmation through symmetry and contrast ratio, and requirement for laser pulses of much lower intensities than either FROG or SPIDER because it does not resolve spectrally the second-harmonic or sum-frequency-generated spectrum of the laser pulse. Furthermore, it can also be utilized as a real-time diagnostic of several-cycle pulses because it explicitly reveals the number of cycles, and its fringe structure is sensitive to the intensity and phase of the pulse. Although there are some limits for IAC such as absence of unique pulse retrieval and lack of obvious shape-chirp correspondence, due to these experimental advantages, IAC can become a more powerful technique for the temporal characterization of femtosecond laser pulses, as long as it is accompanied by a good phase- retrieval algorithm. [8] There are various forms of autocorrelation in optics depending on what is being measured. The simplest optical autocorrelation is that of the field autocorrelation where the electric field, E, is what we are interested in. The electric field is a function of time and so we write its autocorrelation as:
′ −∞ ∗ ′ (1) 퐴1 푡 = −∞ 퐸 푡 퐸 푡 − 푡 푑푡.
Whereas 푡′ is the time delay introduced. A field autocorrelation is also referred to as a first order autocorrelation. It is related to the spectrum by a Fourier transform:
퐼 푓 = 퐹 퐴1 . (2)
Overlapping of two pulses (E t and E t − t′ ) in a SHG crystal will produce light at twice the frequency of input light with a field that is given by:
푆퐻퐺 ′ 퐸푠푖푔 = 퐸 푡 퐸 푡 − 푡 . (3)
This field has an intensity that’s proportional to the product of the intensities of the two input pulses: 푆퐻퐺 ′ 퐼푠푖푔 = 퐼 푡 퐼(푡 − 푡 ). (4)
SHG Detectors are usually too slow to time resolve Isig , this measurement produces the time integral, which is the definition of intensity autocorrelation.
∞ ′ ′ (5) 퐴2 푡 = −∞ 퐼(푡)퐼 푡 − 푡 푑푡.
In this work we deal with second order interferometric autocorrelation:
∞ ′ ′ 2 2 (6) 퐺2 푡 = −∞ 퐸 푡 + 퐸 푡 − 푡 푑푡. Temporal and spectral characterization of near-IR femtosecond optical parametric oscillator pulses
′ It can be measured experimentally. An example of measured signal of 퐺2 푡 is shown in figure1. 8
7
6
5
4 autocorrelation [a.u.] autocorrelation 3
2
1
0 -800 -600 -400 -200 0 200 400 600 800 delay [fs] Figure 1. Example of second order autocorrelation of an OPO.
′ In order to find the equations of upper and lower envelope we analyze 퐺2 푡 :
′ ∞ ′ 2 2 퐺2 푡 = −∞ 퐸 푡 + 퐸 푡 − 푡 푑푡 =
∞ ∞ + 2 퐼2(푡) 푑푡 + 4 퐼(푡)퐼 푡 − 푡′ 푑푡 + (7) − ∞ − ∞ 푘1 (푓=0) 푘2 (푓=0)
∞ ∞ + 퐸2 푡 퐸∗2 푡 − 푡′ 푑푡 + 퐸∗2 푡 퐸2 푡 − 푡′ 푑푡 + (8) − ∞ − ∞ 푘3푎 , 푘3푏 (푓=2푓0)
∞ ∞ + 2 퐸 푡 퐼(푡)퐸∗ 푡 − 푡′ 푑푡 + 2 퐸∗ 푡 퐼 푡 퐸 푡 − 푡′ 푑푡 + (9) − ∞ − ∞ 푘4푎 , 푘4푏 (푓=푓0)
∞ ∞ + 2 퐸 푡 퐼(푡 − 푡′ )퐸∗ 푡 − 푡′ 푑푡 + 2 퐸∗ 푡 퐼 푡 − 푡′ 퐸 푡 − 푡′ 푑푡. − ∞ − ∞ (10) 푘5푎 , 푘5푏 (푓=푓0)
Lower envelope of interferometric autocorrelation:
푀푖푛 퐺2 = 푘1 + 푘2 − 2. ( 푘4푎 + 푘5푎 − 푘3푎 ). (11)
Upper envelope of interferometric autocorrelation:
푀푎푥 퐺2 = 푘1 + 푘2 + 2. ( 푘4푎 + 푘5푎 + 푘3푎 ). (12)
The equation (6) is definition of interferometric autocorrelation. 푘1 is constant and just shows background intensity. k2 is intensity autocorrelation and k3 is second harmonic autocorrelation or second harmonic interferogram. [1,9] If we apply Fourier transform on autocorrelation we will attain its spectrum. Temporal and spectral characterization of near-IR femtosecond optical parametric oscillator pulses
4000
3500
3000 k , k 1 2 2500
2000
Intensity [a.u] Intensity 1500
k , k 1000 k , k 4a 5a 4b 5b k k 3a 500 3b
0 -2f -2f 0 f 2f Frequency 0 0 0 0 ′ Figure 2. Fourier transform of 퐺2 푡 corresponding to autocorrelation pattern of figure1, the entire trace is shifted so that the center of it coincides with zero frequency.
Optical autocorrelation using two-photon absorption (TPA) in commercial semiconductor devices provides a convenient, sensitive, and inexpensive alternative to standard techniques using nonlinear crystals. [9] The use of TPA for auto-correlation measurements offers several advantages over the SHG technique. [11] First, the process can be observed with low-intensity signals. Second, phase matching is not required, therefore process is available over a wide bandwidth. Third, each two-photon transition produces a carrier or photoelectron within the semiconductor that can be measured by simple direct electrical detection. Finally, compared with second-harmonic generation, two photon absorption exhibits less polarization sensitivity because it is primarily an energy transfer process. [12]
2. Measurement
2.1. Source (Titanium: sapphire, optical parametric oscillator) The source which we are going to measure the interferometric autocorrelation and spectrum of it is a femtosecond optical parametric oscillator (OPO). An OPO is a coherent light source based on parametric amplification within an optical resonator. It is similar to a laser, also using a kind of laser resonator, but based on optical gain from parametric amplification in a nonlinear crystal (in this case Periodically poled Lithium Niobate (PPLN)) rather than from stimulated emission. It converts an input laser wave, pump, into two output waves of lower frequency, signal and idler, by means of nonlinear optical interaction. The pump of our OPO is Ti: sapphire laser which operates at central wavelength of 813 nm and its power is 1.6 watts. The length of laser cavity is the same as the OPO cavity; therefore the repetition rate of the OPO is the same as Titanium: Sapphire (76 MHz). A main attraction of OPO is that the output wavelengths, which are determined by a phase- matching condition, can be varied in wide ranges. Thus it is possible to achieve wavelengths which are difficult or impossible to obtain from any laser, and wide wavelength tunability is also often possible. Our OPO operates in the range of 1350 nm to 1580 nm.
2.2. The Measurement Protocol The schema of autocorrelator is shown in the figure 3. Temporal and spectral characterization of near-IR femtosecond optical parametric oscillator pulses
PD
L t' Input Pulse
BS
Scanning
Mirror (M1)
Fixed Mirror (M2)
Figure 3. Schema of an autocorrelator based on Michelson interferometer. The beam-splitter (BS) splits the input pulse into two beams which travel through two different ways. M1 moves and makes a time delay between two beams (t′ ). Finally a lens will focus both beams onto a photodiode.
The output of OPO passes to the spectrometer that shows its central wavelength. After tuning the OPO for desirable wavelength we remove the spectrometer and send the OPO beam into the autocorrelator; it will split into two beams by means of a coated glass beam-splitter. It works properly in the range of 1200 nm to 1600 nm that can cover the output of our OPO. By moving the scanning mirror the optical path of one of two beams will change and a delay will be introduced to it. A calcium fluoride lens (focal length = 5 cm) focuses both beams onto the active area of a silicon photodiode. The photodiode is connected to an oscilloscope and the autocorrelation functions can be observed and saved from the oscilloscope. The scanning mirror (M1) is mounted on a speaker which oscillates, and the frequency of oscillation is 10 Hz. By oscillation of speaker the mirror will oscillate and a periodic change in optical path of one of split beams will be achieved. This change introduces a variable periodic time delay (t′) between two split beams. The combination of these two beams causes the autocorrelation pattern to appear. We made the measurement for fourteen different wavelengths of OPO signal.
2.3. Calibration of Autocorrelator We want to find a relationship between the oscilloscope display scale and the real time delay to be able to convert those numbers to real time delay. The fixed mirror is used for this purpose. We make a movement (d) in M2. Because of this movement, the light travel extends by 2d. This movement shifts the whole trace of autocorrelation as much as 푑푡. We know that the real time shift that the movement of M1 will cause is: 2푑 푑푡′ = 푐 Where c is the speed of light. We repeat this procedure for several times to find the factor which converts the oscilloscope scale to real time.
3. Data Analysis 3.1. Idea (autocorrelation comparison and phase guess) In pulse measurement with autocorrelation, it is common to assume sech2 as the pulse shape. In this method, the full width at half maximum (FWHM) of measured intensity autocorrelation will be divided by a constant (1.543), and then sech2 with FWHM equal to the result of division will be drawn. But this method is not suitable for OPO pulses, because OPO pulses can be very complicated and it is not safe to simulate them with sech2 pulses. The method which is used in this work is shown in figure 4. Temporal and spectral characterization of near-IR femtosecond optical parametric oscillator pulses
Adding guessed phase E( f ) I( f ) I() I( f ) φ(f)
i( f ) 1 E( f ) E( f ).e E(t) F (E( f )) G2[E(t)]
If they are similar E(t ) is a good approximation. Comparison between
G2 and G 2 (measured) If they are not similar we should guess a new phase.
Figure 4. The flowchart of data analysis. The details are explained in the text.
First, the measured intensity versus wavelength (spectrum) will be interpreted to intensity versus frequency, because Fourier transformation is not applicable in wavelength space. Next, from the square root of intensity the amplitude of electric field corresponding to the shortest possible pulse will be found. Then we will guess a phase and by applying this phase to amplitude, the electric field as a function of frequency will be found. Inverse Fourier transform will transfer the electric field in frequency space to electric field in time space. Finally from electric field as a function of time we can calculate autocorrelation. To find if the guessed phase ′ is a good approximation or not we will compare the envelope of calculated (G2) autocorrelation and measured autocorrelation (G2). If they are not similar we should guess another phase and perform this procedure again until we achieve a good approximation. In this work a Matlab program is prepared in order to execute the procedure; the guessed phase will be given manually. In this program we define the phase as Taylor series.
2 3 4 Phase (f) =푎(푓 − 푓0) + 푏(푓 − 푓0) + 푐(푓 − 푓0) + ⋯. (13)
Whereas f0 is the central frequency of measured pulse. Therefore whenever we want to guess the phase, it is enough to guess just three numbers (a, b, and c) because higher orders of dispersion can be safely neglected.
3.2. Results
Several pulse measurements have been done during this work, but here I have put the graphs of four measurements in figure 4. Each picture contains three different graphs that all three are related to one pulse. The first graph from top has two curves. The blue curve shows the spectrum (intensity versus wavelength) and the green curve shows a candidate phase as a function of wavelength. The middle graph shows the result of simulation which is the retrieved pulse (intensity versus time). The blue pulse is the one which is obtained from phase-guessing method; and the red curve is the pulse which is obtained from sech2 assumption. The blue curve shows more details of pulse, whereas green curve is symmetric. It means for all initial pulses which are probably asymmetric, with sech2 assumption we always attain a symmetric pulse and we will lose considerable amount of information. The last graph is the autocorrelation. The blue lines are measured interferometric autocorrelation and the green line is intensity autocorrelation obtained from it. The red curve is the envelope which is calculated from phase-guessing method.
Temporal and spectral characterization of near-IR femtosecond optical parametric oscillator pulses
1.54 1.56 1.58 1.6 1.62 1.64 1.66 1.68 1
0.5 0
phase [rad] phase spectrum [a.u.] 0 1.54 1.56 1.58 1.6 1.62 1.64 1.66 1.68 wavelength [µm] 1 from () 2
0.5 sech intensity [a.u.] 0 -800 -600 -400 -200 0 200 400 600 800 time [fs]
8 measured 7 measured calculated 6
5
4
3
autocorrelation [a.u.] autocorrelation 2
1
0 -800 -600 -400 -200 0 200 400 600 800 delay [fs] (a)
1.48 1.5 1.52 1.54 1.56 1.58 1.6 1.62 1.64 1
0.5 0
phase [rad] phase spectrum [a.u.] 0 1.48 1.5 1.52 1.54 1.56 1.58 1.6 1.62 1.64 wavelength [µm] 1 from () 2
0.5 sech intensity [a.u.] 0 -800 -600 -400 -200 0 200 400 600 800 time [fs]
8 measured 7 measured
6 calculated
5
4
3
autocorrelation [a.u.] autocorrelation 2
1
0 -800 -600 -400 -200 0 200 400 600 800 delay [fs] (b) Temporal and spectral characterization of near-IR femtosecond optical parametric oscillator pulses
1.48 1.5 1.52 1.54 1.56 1.58 1.6 1.62 1.64 1
0.5 0
phase [rad] phase spectrum [a.u.] 0 1.48 1.5 1.52 1.54 1.56 1.58 1.6 1.62 1.64 wavelength [µm] 1 from () 2
0.5 sech intensity [a.u.] 0 -800 -600 -400 -200 0 200 400 600 800 time [fs]
8 measured 7 measured
6 calculated
5
4
3
autocorrelation [a.u.] autocorrelation 2
1
0 -800 -600 -400 -200 0 200 400 600 800 delay [fs] (c)
1.44 1.46 1.48 1.5 1.52 1.54 1.56 1.58 1
0.5 0
phase [rad] phase spectrum [a.u.] 0 1.44 1.46 1.48 1.5 1.52 1.54 1.56 1.58 wavelength [µm] 1 from () 2
0.5 sech intensity [a.u.] 0 -800 -600 -400 -200 0 200 400 600 800 time [fs]
8 measured 7 measured
6 calculated
5
4
3
autocorrelation [a.u.] autocorrelation 2
1
0 -800 -600 -400 -200 0 200 400 600 800 delay [fs] (d)
Figure 5. The plotted graphs of the experiment, each picture (a, b, c, or d) hast three parts: the first part is spectrum and phase; the second is a comparison between the pulse from sech2 assumption and from phase-guessing method; the last graph is intensity and interferometric autocorrelation and envelop which is fitted to it. Central wavelength of pulse is: (a) 1580 nm, (b) 1552 nm, (c) 1517 nm, (d) 1499 nm. Temporal and spectral characterization of near-IR femtosecond optical parametric oscillator pulses
4. Conclusion
To recapitulate, we have characterized pulses of an OPO using phase-guessing method. It was done using non-linear current detection in a photodiode instead of usual SHG crystal. Both interferometric and intensity autocorrelation signals are achieved by this technique. The main problem of this method is finding the best phase; for some pulses it is very difficult and time consuming. It should be improved by means of an automatic phase-guessing software. Furthermore the pulse which is attained by means of phase-guessing is not unique. Comparison between pulse which is retrieved from phase-guessing technique by the sech2 shows that they are similar, but in the first case there is much information than sech2. Either the initial pulse is symmetric or not the sech2 pulse is always symmetric and significant amount of information will be lost. To sum up, this method provide much accurate results but it needs to be enhanced from phase- guessing mechanism point of view.
Acknowledgments
It is an honor for me to thank Professor Majid Ebrahim-Zadeh who helped me from the first day of master courses to the last day of this project. This thesis would not have been possible without help of Dr. Lukasz Kornaszewski who was abundantly helpful and offered invaluable support, and guidance. Finally I thank ICFO and all colleagues in the optical parametric oscillators group for their friendly assistance especially Dr. Adolfo Esteban Martin for providing the access of OPO.
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