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Fundamentals of Frequency Combs: What They Are and How They Work

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Fundamentals of Frequency Combs: What They Are and How They Work Fundamentals of frequency combs: What they are and how they work Scott Diddams Time and Frequency Division National Institute of Standards and Technology Boulder, CO KISS Worshop: “Optical Frequency Combs for Space Applications” 1 Outline 1. Optical frequency combs in timekeeping • How we got to where we are now…. 2. The multiple faces of an optical frequency comb 3. Classes of frequency combs and their basic operation principles • Mode-locked lasers • Microcombs • Electro-optic frequency combs 4. Challenges and opportunities for frequency combs 2 Timekeeping: The long view Oscillator Freq. f = 1 Hz Rate of improvement f = 10 kHz since 1950: 1.2 decades / 10 years f = 10 GHz “Moore’s Law”: 1.5 decades / 10 years f = 500 THz Gravitational red shift of 10 cm Sr optical clock ? f = 10-100 PHz ?? S. Diddams, et al, Science (2004) Timekeeping: The long view Oscillator Freq. f = 1 Hz f = 10 kHz f = 10 GHz f = 500 THz Gravitational red shift of 10 cm Sr optical clock ? f = 10-100 PHz ?? S. Diddams, et al, Science (2004) Use higher frequencies ! Dividing the second into smaller pieces yields superior frequency standards and metrology tools: 15 νoptical 10 ≈ ≈ 105 νmicrowave 1010 In principle (!), optical standards could surpass their microwave counterparts by up to five orders of magnitude ... but how can one count, control and measure optical frequencies? 5 Optical Atomic Clocks Atom(s) νo Detector At NIST/JILA: Ca, Hg+, Al+, Yb, Sr & Slow Δν Laser Control Atomic Resonance Counter & Laser Read Out Fast Laser (laser frequency comb) Control •Isolated cavity narrows laser linewidth and provides short term timing reference Isolated Optical Cavity •Atoms provide long-term stability and accuracy— now now at 10-18 level! •Laser frequency comb acts as a divider/counter Outline 1. Optical frequency combs in timekeeping • How we got to where we are now…. 2. The multiple faces of an optical frequency comb 3. Classes of frequency combs and their basic operation principles • Mode-locked lasers • Microcombs • Electro-optic frequency combs 4. Challenges and opportunities for frequency combs 7 Multiple faces of a frequency comb 1. A ruler for light frequencies Hz fr Δν Intensity Frequency 2. A perfectly-spaced train of optical pulses 1 1 fr Δν Time 8 Multiple faces of a frequency comb 3. An optical clockwork Frequency ν1 Comb • Comb uncertainty at the 20th decimal place • Measurement of optical ratios (e.g. ν : ν ) µ-wave 1 2 Cs, Rb, etc . ν2 • Direct connection from optical to microwave domains 9 Outline 1. Optical frequency combs in timekeeping • How we got to where we are now…. 2. The multiple faces of an optical frequency comb 3. Classes of frequency combs and their basic operation principles • Mode-locked lasers • Microcombs • Electro-optic frequency combs 4. Challenges and opportunities for frequency combs 10 Mode-Locked Laser: Basis of the Frequency Comb Time domain E(t) Δφ 2Δφ Key Concept: t Direct link between optical and microwave τr.t = 1/fr frequencies Frequency domain I(f) ν n = nfr + fo fo fr n ~105 f 0 Hänsch & Hall, Nobel Lectures 11 Group and phase velocity in modelocked lasers Laser High Cavity Output Reflector Free Space Coupler animation from Steve Cundiff The femtosecond mode-locked laser comb f Pulsed output of femtosecond laser mode N + 1 mode N L Femtosecond LaserFemtosecond FrequencyComb Laser Cavity → Cavity modes are locked in phase to generate a short pulse once every roundtrip time 2L/vg How does it work? à All Femtosecond lasers require: • Laser cavity + broadband gain source and optical components • Dispersion control • Power-dependent gain or loss ideal mode spacing: • Phase modulation c 2L L real “cold” cavity Ideal cavity modes modes f à Due to dispersion, the cavity modes are not evenly spaced à However, the nonlinear phase-modulation in a mode-locked laser provides the required synchronization of the modes, yielding a strictly uniform mode comb. GHz Rep Rate Ti:Sapphire Combs T. Fortier, A. Bartels, D. Heinecke, M. Kirchner 1 GHz Octave Spanning Laser M3 OC PUMP M1 M2 Al+ 10 GHz Self-referenced Ti:sapphire Laser Yb CaSr Hg+ A. Bartels, H Kurz, Opt. Lett. 27, 1839 (2002) T. Fortier, A. Bartels, S. Diddams, CLEO(2005) T. Fortier, A. Bartels, S. Diddams, Opt. Lett. 31, 1011 (2006) • Stabilized Comb = 106 Modes • Hz-level linewidths • Residual frequency noise at 1×10-19 level A. Bartels, D. Heinecke, S. Diddams, Science 326, 681 (2009). 15 Er:fiber based frequency combs à mode-locking based on nonlinear polarization rotation Launched Ultrashort Nonlinearly- polarization pulse train rotated state polarization ellipse WDM + Iso. λ/2 λ/4 SMF λ/4 PBS λ/2 SMF 980 nm pump(x2) erbium-EDFdoped fiber 16 Polarization-maintaining Er:fiber laser comb • Laser + amplifier + self-referencing are all constructed “in-line” with polarization-maintaining (PM) fiber optics. • Laser is mode-locked with saturable absorber mirror • Robust against environmental perturbations. (Newbury group at NIST) Frequency comb operates phase-locked in a moving vehicle. L. Sinclair, et al. Opt. Express 22, 6996-7006 (2014) 17 High-power Yb:fiber laser frequency comb • Linear cavity design • Saturable absorber end mirror for mode-locking • Fiber Bragg grating provides output coupling and dispersion control • External amplification to ~80 W followed by compression to ~100 femtosecond pulses Schibli, et al. Nature Photonics 2, 355 - 359 (2008) 18 Frequency Comb Extension via Nonlinear Optics • Using a combination of harmonic generation, difference frequency generation and super-continuum, frequency combs have been extended from the UV to the infrared Difference Frequency Harmonic Generation Generation and Continuum and Continuum Er:fiber Yb:fiber Ti:sapphire 100 500 1000 1500 2000 10000 wavelength (nm) • Some examples: o Extreme ultraviolet via harmonic generation: Phys. Rev. Lett. 94, 193201 (2005); Nature 436, 234- 237 (2005); Science 307, 400 (2005); o Mid-infrared comb generation via OPO, DFG and supercontinuum: Opt. Lett. 34, 1330 (2009); Opt. Lett. 37, 1400 (2012); Lett. 39, 2056 (2014); Opt. Lett. 36, 2275-2277 (2011). 19 Multiple faces of a frequency comb 3. An optical clockwork Frequency ν1 Comb • Comb uncertainty at the 20th decimal place • Measurement of optical ratios (e.g. ν : ν ) µ-wave 1 2 Cs, Rb, etc . ν2 • Direct connection from optical to microwave domains 20 Controlling the femtosecond laser comb For most applications with the femtosecond laser frequency comb, we need to measure and control the two degrees of freedom of the frequency comb: fo (offset frequency) and fr (repetition rate) νn = nfr + fo • fo measured by “self-referencing” ØNeed an octave-span spectrum • fr controlled with a microwave source or a CW laser 21 The laser comb and its control f -1 o f fr = N / νo Δφ = 2π fr Pulsed output fo νn = nfr + fo x2 mode N +1 mode N locked in phase CW laser νο t Operation is fully reversible: Can lock at microwave and synthesize optical 22 T. W. Hänsch and J. Hall, Nobel Lectures; D. J. Jones, et al., Science 288, 635 (2000); S. Diddams, Th. Udem, et al., Science 293, 825 (2001) Microstructure optical fiber continuum generation photos courtesy of Jinendra Ranka Lucent Technologies CLEO Postdeadline (CPD8) Baltimore (1999). J. Ranka, R. Windeler, A. Stentz, Opt. Lett. 25, 25 (2000). •Tight confinement~20 microns of light leads to high nonlinearity and anomalous dispersion in the wavelength regime of femtosecond Ti:sapphire lasers •Such fibers are available from commercial sources (ThorLabs, Crystal Fibre) and are developed in research labs (OFS, Univ. of Bath) 23 Octave-Span Supercontinuum 1 GHz Ti:sapphire 100 MHz Er:fiber also…. Yb:fiber OC Yb:crystalline 532 nm Tm:fiber PUMP ….. S. Diddams, JOSA B (2010) A. Bartels, H Kurz, Opt. Lett. 27, 1839 (2002) L. E. Nelson et al., APB 65, (1997) Nonlinear interferometer for measuring f0 Nonlinear Fiber fs Laser Infrared Visible KNbO3 For SHG fo fr - fo Polarizer Filter f0 Other interferometer designs exist: • inline with waveguide PPLN • Michelson 25 First Self-Referenced Mode-locked Lasers Ti:Sapphire Cr:forster- Cr:LiSAF Er:fiber Er:Yb Tm:fiber Jones 2000, ite Yb:fiber Yb:KYW Holzwarth Washburn Glass Phillips Apolonski Kim 2005, Hartl 2007 Meyer 2008 2001 2004 Stumpf 2009 2011 2000 2006 center λ 800 nm 894 nm 1560 nm 1275 nm 1040 nm 1030 nm 1560 nm 1950 nm pulse ~10-50 fs ~50 fs 80-200 fs 30 fs 70-100fs 290 fs 170 fs 70 fs length 532 nm, 980 or Pump 650 nm 1075 nm 976 nm 980 nm 976 nm 793 nm doubled 1480 nm source diode fiber laser diode diode diode diode Nd:YVO diode Repetit- 0.1 - 10 50-300 93 MHz 420 MHz 0.1-1 GHz 180 MHz 75 MHz 72 MHz ion rate GHz MHz E-to-O ~0.1% 1-2% ~1% ~0.5% 1-2% ~2-3% ~2-3% ?? Efficiency 26 Outline 1. Optical frequency combs in timekeeping • How we got to where we are now…. 2. The multiple faces of an optical frequency comb 3. Classes of frequency combs and their basic operation principles • Mode-locked lasers • Microcombs • Electro-optic frequency combs 4. Challenges and opportunities for frequency combs 27 Moving from Lab Scale to Chip Scale NIST ~1983 NIST ~2000 Frequency Chain Laser Freq. Comb Laboratory (100 m2) Table Top (1 m 2) ~104 size Potential Impact: reduction • Operation in any environment • Chip scale clocks • Inexpensive and mass produced • Communication and navigation • Sensing (environment, medical, ~1 cm2 manufacturing...) Future: Photonic Integrated Circuits A Tiny Revolution in Frequency Combs 4-Wave Mixing 1. Energy conservation: 2ωP = ωS + ωI m m+1 2. Momentum conservation: linear + nonlinear CW Input Comb Output m 3.
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