Noise sources and stabilization strategies in frequency combs

Transcription

1 Noise sources and stabilization strategies in frequency combs ICTP Winter College on Optics Trieste, Italy February 17, 2015 Nathan Newbury National Institute of Standards and Technology, Boulder, CO

2 Outline Motivation for frequency combs Frequency comb Noise in fiber-based frequency combs Fixed point Making a quiet frequency comb Fiber frequency combs at NIST Overview of different designs since 2003 Current robust NIST frequency comb Conclusion

3 People Esther Baumann Hugo Bergeron Mick Cermak Ian Coddington Kevin Cossel Stefan Droste Fabrizio Giorgetta Dan Herman Nathan Newbury Laura Sinclair Bill Swann Gar-Wing Truong Eleanor Waxman Gabe Ycas Other non NIST collaborators: Brian Washburn (Kansas State) Jean Daniel Deschenes (U of Laval) Greg Rieker (CU) NIST collaborators: Scott Diddams, Dave Leibrandt, Craig Nelson, Scott Papp, Frank Quinlan, Kevin Silverman, Jeff Shainline, Rich Mirin,

4 Recent review articles RSI Review article on current NIST comb design: L.C. Sinclair, J. D. Deschênes, L. Sonderhouse, W. C. Swann, I.H. Khader, E. Baumann, N. R. Newbury, and I. Coddington, Invited Article: A Compact Optically Coherent Fiber Frequency Comb, Review of Scientific Instruments 86, (2015); See also: based digital control box phase stablization frequency comb.cfm Nanophotonics upcoming review on fiber combs: S. Droste, G. Ycas, B. R. Washburn, I. Coddington, NRN, Optical Frequency Comb Generation based on Erbium Fiber Lasers, Nanophotonics, to be published Fiber frequency Comb noise N. Newbury, W. Swann, J. Opt. Soc. Am. B, Low noise fiber laser frequency combs, 24, (2007)

5 Frequency Combs: Why are they special? Laser Frequency Comb Intensity comb teeth frequency spectral ruler n 1 n n+1 Clock broad spectrum coherent & bright calibrated frequency scale laser rf synthesizer

6 Applications of Frequency Combs Newbury, Nat. Phot., 5, 186 (2011) Diddams, JOSA B, 27, B51 (2010) Frequency Comb Applied to laser-based metrology/sensing systems As a spectral ruler - As a frequency divider As a time ruler - As a calibrated broadband source

7 Precision microwave generation (for RADAR) Example applications Precision molecular spectroscopy (for greenhouse gases) Precision spectroscopy (for exoplanet searches) Precision timing across synchronized network Precision Ranging NIST Others: Advanced communications Fundamental scientific tests

8 Outline Motivation for frequency combs Frequency comb Basic picture Types of Frequency combs Noise in fiber-based frequency combs Fixed point Noise sources Actuators Making a quiet frequency comb Fiber frequency combs at NIST Overview of different designs since 2003 Current robust NIST frequency comb Conclusion

9 Passively Modelocked Laser gain sat. abs. A Mode Locked Laser Time domain Outputs light at equally spaced modes of the laser Frequency Domain t Intensity optical frequency

10 A Free Running Mode Locked Laser Passively Modelocked Laser Time domain gain sat. abs. t Frequency domain I( f ) f rep f o 0 f n = nf rep + f 0

11 A Free Running Mode Locked Laser Passively Modelocked Laser Time domain gain sat. abs. t Frequency domain I( f ) f rep f o 0 With noise, output moves around... but basic comb structure is preserved. Comb can only translate and breathe f n = nf rep + f 0

12 Offset Frequency Stabilization Jones, et al. Science 288,635 (2000) Passively Modelocked Laser gain sat. abs. T = f r -1 t J. Hall T. Hänsch Spectrally broaden to an octave I( f ) f o f r 0 phase locked loop f o x2 Self referenced Lock f 0 = 2(nf rep + f 0 ) - 2nf rep + f 0

13 Stabilization of the Second Degree of Freedom Passively Modelocked Laser T = f r -1 J. Hall T. Hänsch gain sat. abs. t I( f ) f o A choice: Stabilize to an Optical or RF oscillator f r 0 Phase lock (stabilize) offset frequency, f o

14 Frequency Comb needs a Reference Oscillator RF oscillator (Quartz / DRO / H maser) 10 MHz 10 GHz Optical Oscillator (cavity stabilized Laser) 200 THz Amplitude (lin. units) 1 Hz Frequency offset (Hz) Pound Drever Hall Cavity Lock Quartz/DRO: small, compact, cheap RF comb stabilization easy No optical coherence in comb Broad optical teeth Not small, not compact, not cheap Optical comb stabilization hard Optically coherent comb Delta function teeth

15 RF Stabilization Passively Modelocked Laser T = f r -1 J. Hall T. Hänsch gain sat. abs. t RF oscillator I( f ) f o f r RF phase locked loop 0 Phase locked offset frequency, f o f n = nf rep + f 0

16 Optical Stabilization Passively Modelocked Laser T = f r -1 J. Hall T. Hänsch gain sat. abs. t I( f ) f o Optical Clock = Narrow linewidth laser Laser Optical phase locked loop 0 Phase locked offset frequency, f o f Opt

17 Optical Reference Laser Frequency comb f rep clk Rf synth. f Opt f rf f Laser Loop filter Optical Phase Locked Loop filter Phase comparison Intensity f rf =f Opt f Laser rf Rad 2 /Hz Hz 2 /Hz Frequency Deviation Optical heterodyne ResBW 93 Hz spectrum Frequency (MHz) Phase/Frequency Noise PSD Fourier Freq. Counted Frequency Time Allan deviation in loop measures of comb phase coherence and frequency stability

18 RF vs Optical Stabilization: Lever Arm Difference RF I( f ) For an RF lock: Phase locked f RF phase noise is multiplied by n o 2 up to optical Broad optical linewidths Cavity Stabilized Optical teeth central position defined absolutely Laser For an Optical Lock : Optical phase locked loop Optical phase noise divided by n 2 down to rf Narrow optical linewidths across comb (if reference laser narrow) 0 Phase locked f o f Opt

19 Other Stabilization Options: double pinning Passively Modelocked Laser T = f r -1 J. Hall T. Hänsch gain sat. abs. t Laser Laser I( f ) f o 0 f Opt, 1 f Opt, 2 NO Offset frequency stabilization > no need for octave supercontinuum But no absolute frequency knowledge (unless cavity separately measured)

20 Other Stabilization Options: free running laser Passively Modelocked Laser T = f r -1 J. Hall T. Hänsch gain sat. abs. t RF frequency counter (nf rep ) Free running Laser I( f ) f o 0 Phase locked offset frequency, f o f n = nf rep + f 0 Avoids need for cavity stabilized laser Retains qbsolute frequency knowledge

21 Femtosecond Laser Frequency Combs A unique source for sensing and spectroscopy an array of millions of phase-coherent CW oscillators large spectral coverage: 300 nm - 10 microns precisely known frequencies (~1 Hz resolution) high peak power for efficient nonlinear optics Harmonic Generation and Continuum Difference Frequency Generation and Continuum Ti:sapphire Yb:fiber Er:fiber Tm:fiber wavelength (nm) courtesy of S. Diddams et al. Ti:Sapphire laser Er:fiber laser

22 Some Frequency Combs Ti:Sapphire Combs NIST ~2000 Er Fiber Combs Laser Freq. Comb Table Top (1 m 2 ) Courtesy S. Diddams 10 GHz Ti:sapphire Laser NIST/OFS 04 Yb fiber comb (10W!) A. Bartels,, Science 326, 681 (2009). Schibli, et al. Nature Photonics 2, (2008) (IMRA America & JILA) MicroCombs? Caltech ~2004 Parametric Comb Chip Scale (1 cm 2 ) Del Haye, Nature, 450, 1214, 2007; Levy, Nat. Phot. 4, 32 (2010), Papp, Diddams, PR A 84, (2011), EPFL, OE waves, Cornell, CalTech, MPQ, NIST... Many others Er:Yb glass Thulium Fiber combs Cr:Forsterite

23 Most universal solution: Fiber Laser Based Combs Advantages of fiber frequency comb Compact, inexpensive design Potential for stable hands-free operation Compatible with highly reliable telecommunication components Covers the Infrared region of the spectrum Under development at: Menlo, Toptica, MPQ, PTB, AIST, IMRA, OFS, U. Konstanz, Kansas State, Arizona, NIST, etc. etc. Rest of talk will focus on fiber frequency combs but many of the results/analysis are general and apply to other frequency combs as well.

24 Some Different NIST Fiber Combs NIST/OFS Figure 8 stretched pulse ring laser Fiber Frequency Comb Fiber Frequency Comb Washburn et al., Opt. Lett. 29, 250 (2004) McFerran et al., Opt. Lett. 31, 1997 (2006) Swann, Opt. Lett. 31, 3046 (2006). stretched pulse ring laser with variable rep rate Fiber Frequency Comb Washburn et al, OE, 12, 4999 (2004) All fiber Free space Stretched pulse ring lasers Fiber Frequency Combs Coddington et al, PRA, 81, (2010) Ring laser with intracavity EOM Swann et al. OE, 19, (2011) Linear SESAM Linear cavity Fiber Frequency Comb Sinclair, OE, 22, 6996 (2014) Sinclair, RSI, 86, (2015);

25 Fiber Laser Frequency Comb f ceo f opt pump diode length Fiber amp Highly Nonlinear Fiber Detect comb parameters & feedback Stabilized Comb f ceo f opt - Stabilize offset frequency by feeding back to pump power - Stabilize f rep (or optical tooth) by feeding back to cavity length

26 Ring Laser: Soliton vs. Stretched pulse mode Soliton-mode: net dispersion < 0 25 nm Er Doped Fiber: + Dispersion CW pump Power (db) SM Fiber: - Dispersion Wavelength (nm) 1650 Stretched-pulse: net dispersion > 0 Ippen, Haus..., MIT CW pump Power (db) 90 nm Wavelength (nm) 1650 Either works for a frequency comb: low dispersion better for noise

27 Free-running Mode-locked laser E(f) 0.1 nj 100 fs 10 ns f pump diode A free-running frequency comb. Now need to broaden to octave-spanning supercontinuum

28 Highly Nonlinear Fiber (HNLF) for Er fiber combs index Index Profile Ge doped F 2 doped radius Dispersion (ps/nm- km) n ~ Ti:sapphire laser microstructure fiber dispersion nonlinearity : 8 to 15 1/W-km Effective Area : 13 m 2 loss : 0.7 to 1 db/km dispersion (1550 nm) : -10 to +10 ps/nm-km dispersion slope (1550 nm) : ps/nm2-km splice loss (to SMF) :0.18 db splice loss (to HNLF) :0.02 db wavelength (nm) Er laser HNLF dispersion BallComb-28 NRN 1/19/2004

29 Fiber Laser Frequency Comb Octave Spanning Comb 0.1 nj 100 fs pump diode Fiber amp Highly Nonlinear Fiber 1 m 1.5 m reality 2 m How noisy is the free-running comb? What causes this noise? How do we feedback against it? our cartoon

30 Free-running Linewidths Fiber Comb We would like 1 Hz linewidths (or rather sub-radian phase noise) Narrow cw laser I(f) f o 0 Rf power (db) f o 200 khz Frequency (MHz) nm Frequency (MHz) nm 5 khz 40 khz Frequency (MHz)

31 Noise Sources Pump Fluctuations pump diode Environmental perturbations (vibration & temperature, humidity) ASE Er+ Fiber amp ASE Supercontinuum generation in Highly Nonlinear fiber Shot Noise Degrades Signal-to-Noise (but not linewidth) Extra-cavity noise (white phase noise) Intra-cavity noise does broaden linewidth

32 How to characterize the frequency comb response to noise (and actuators)? 1. Use Fixed Point f n = nf r +f ceo temp ng to characterize noise by effect on f r and f ceo Don t! All* noise/actuators change f r But differ in their Fixed point 2. Use Frequency noise PSD Always characterize by frequency (or phase) noise power spectral density Linewidth is a (misleading) convenience (* except self phase modulation or external AOM)

33 Perturbation -> Comb Noise Must be accordion like From H. Telle and coworkers: H. R. Telle, B. Lipphart, and J. Stenger, APB, 74, 1 (2002) f r f o fn What is noise on this tooth? Correlated!!

34 Fixed-Point picture for Noise From H. Telle and coworkers: H. R. Telle, B. Lipphart, and J. Stenger, APB, 74, 1 (2002) f r f o f fix n-n fix f n What is noise n fix ) on this tooth? Any noise described by: 1. Fixed tooth that does not move 2. Repetition rate change about that point

35 Where is the fixed point? Three important cases Round trip & Carrier Phase shift together time frequency Round trip only Carrier phase only

36 How to characterize the frequency comb response to noise (and actuators)? 1. Use Fixed Point f n = nf r +f ceo temp ng to characterize noise by effect on f r and f ceo Don t! All* noise/actuators change f r But differ in their Fixed point 2. Use Frequency noise PSD Always characterize by frequency (or phase) noise power spectral density Linewidth is a (misleading) convenience (* except self phase modulation or external AOM)

37 Frequency Noise PSD Can use phase noise PSD to by just dividing by f 2 FFT Frequency Noise PSD: S n How far tooth moves Frequency Noise S f (dbhz 2 /Hz) Random Walk FM White FM White PM Frequency, f, (Hz) How fast tooth moves

38 Fixed-Point picture for Noise From H. Telle and coworkers: H. R. Telle, B. Lipphart, and J. Stenger, APB, 74, 1 (2002) f r f o f fix n fix ) n-n fix f n What is noise on this tooth? Frequency Noise PSD Noise on any tooth is just scaled repetition rate noise

39 Quantifying the Noise on the Comb Summing Frequency Noise PSD Pump noise pump diode Environmental Perturbations (temp, vibration) ASE Er+ Fiber amp ASE Shot Noise f n What is noise on the nth tooth? Sum of noise from each effect = from temperature + from + from amplified + vibrations spontaneous emission from pump noise

40 Environmental Perturbations -> Cavity length Environmental perturbations (vibration, RH temperature,) T = f r -1 t length fluctuation I( f ) FIXED POINT FOR CAVITY LENGTH 0 f o Temperature: 10-5 per degree C (very sensitive) Vibration/Humidity: very sensitive S ~1/f behavior

41 Quantifying the Noise on the Comb Summing Frequency Noise PSD Pump noise pump diode Environmental Perturbations (temp, vibration) ASE Er+ Fiber amp ASE Shot Noise f n What is noise on the nth tooth? Sum of noise from each effect = from temperature + from + from amplified + vibrations spontaneous emission from pump noise

42 Effect of Amplified Spontaneous Emission Direct Timing Jitter Often called Quantum Limit for mode-locked lasers H. A. Haus and A. Mecozzi, IEEE J. Quantum Electron. 29, 983 (1993). R. Paschotta, Appl Phys. B 79, 163 (2004). ASE Er-doped fiber (gain) t arrival + ASE = t arrival t = Round Trip Timing Shift Comb expands/contracts about center of spectrum S ASE ~ white noise (broadband) * phase jitter gives S-T linewidth

43 Effect of Amplified Spontaneous Emission Indirect Timing Jitter H. A. Haus and A. Mecozzi, IEEE J. Quantum Electron. 29, 983 (1993). R. Paschotta, Appl Phys. B 79, 163 (2004). ASE Er-doped fiber (gain) spectral shifts + ASE = Random spectral shifts + Dispersion = Timing shift Comb expands/contracts about center of spectrum This effect dominates ASE timing jitter at high cavity dispersion

44 Quantifying the Noise on the Comb Summing Frequency Noise PSD Pump noise pump diode Environmental Perturbations (temp, vibration) ASE Er+ Fiber amp ASE Shot Noise f n What is noise on the nth tooth? Sum of noise from each effect = from temperature + from + from amplified + vibrations spontaneous emission from pump noise

45 How to solve for the Response of the Fiber-Laser Frequency Comb (1) Heuristic derivation Physical insight Ad hoc Numerical factors sometimes obscure Implementation: L. Xu, et al. Opt. Lett., vol. 21, 1996, Haverkampf, APB 78, 2004, etc. Three Options (2) Master Equation & Perturbation Theory Analytic, selfconsistent treatment Rigorous bookkeeping Requires analytic perturbations (e.g. Lorentzian gain.) Master equation is an approximation Implementation: Haus and Mecozzi, JQE., vol. 29, But add chirp, gain dynamics, all perturbations (3) Numerical integration of Nonlinear Schrödinger Eq. Full solution of NLSE Include all effects Significant computation (pulse width vs round trip vs response time) Potential loss of physical insight Implementation: Paschotta, Appl. Phys. B, vol. 79, 2004.

46 Effect of Pump Power Noise on Comb Pump Fluctuations CW pump Er-doped fiber (gain) Pump power change Gain change Pulse Energy & Width Gain filtering Nonlinear selffrequency shift Frequencydependent loss Non-lorentzian resonant gain shift Self-phase modulation Third-Order- Dispersion Self-Steepening Spectral Shift Resonant Group Velocity Carrier Phase Shift Round Trip Timing Shift N. R. Newbury and B. R. Washburn, JQE, 41, 1388 (2005)

47 Response Bandwidth and Laser Stability (Gain-Pulse Energy Coupling) Gain g Pump (P P ) Saturation of SAM w 2 SAM Energy = w Net gain 0 unstable stable Pulse energy (w) Slope = /2 nonlinear loss Energy round trip Gain round trip Coupled differential equations 1 T w w 2 gw T 1 T g g g Tg r w w w 1 1 g Erbium 3dB 3dB P P P P P System is unstable without extra nonlinear loss Gain saturation too slow to counteract SAM Parameters support simple exponential decay No relaxation oscillations (see Namiki et al, APL, 69,3969 (1996))

48 Dynamics Pump Power Noise on Comb Responds as a Low-Pass Filter Pump Fluctuations Pump Nonlinear loss Er+ fiber : ~khz response gain w 2 Self-Amplitude Modulation Magnitude (db) Response to Pump Power change More stable Less stable Bare Erbium Gain response Frequency Overdamped system -> No Relaxation Oscillations!! Consequences: Finite response to pump fluctuations Slows laser response to pump power feedback But can phase compensate for a simple rolloff with a capacitor! Namiki et al, APL, 69,3969 (1996), JOSAB 14, 2099 (1997); J. McFerran et al, Opt. Lett. 31, 1997 (2006) & APB, 86, (2007); Newbury and Washburn, JQE, 41, 1388 (2005)

49 Response Bandwidth: Experiment Input CW pump P P Er-doped fiber (gain) Output ( f rep, f CEO, power) L Magnitude (db) Fig-8 laser 4.5 khz ( =1/2) Er gain =1.6 khz Erbium 3dB (As measured outside of laser) Ring laser 20 khz ( ~1/10) Frequency (Hz) Signal (db) f ceo beat Frequency (MHz)

50 Effect of Pump Power Noise on Comb Pump Fluctuations CW pump Er-doped fiber (gain) Pump power change Gain change Pulse Energy & Width Gain filtering Nonlinear selffrequency shift Frequencydependent loss Non-lorentzian resonant gain shift Self-phase modulation Third-Order- Dispersion Self-Steepening Spectral Shift Resonant Group Velocity Carrier Phase Shift Fixed Point = - Infinity (overall shift of comb) Round Trip Timing Shift Fixed Point = Carrier Frequency N. R. Newbury and B. R. Washburn, JQE, 41, 1388 (2005)

51 Change in f rep : Theory (Part I) Spectral Shifts & Third-Order Dispersion Contributions Effective Group Velocity depends on spectrum center and width ( ) Spectral Shift rms spectrum Slope = Round Trip Time Shift Spectral Shifts Third-order dispersion 0 Cause of Spectral Shifts : gain Curvature, D g 1.) Gain pulls frequency toward gain peak 2.) Loss pushes frequency up or down Raman SFS Pulling 0 loss 3.) Raman SFS pushes frequency down 1 l l 2D g, NL

52 Changes in f rep : Theory (Part II) Resonant Gain Contribution g g : Homogenous Gain bandwidth index Round Trip Time Shift + Resonant gain dispersion gain 0 Group index of the Er gain fiber depends on the Er gain inversion For Lorentzian gain with gain bandwidth 5 nm, maximum shift: 10 ppm or 500 Hz out of 50 MHz rep. rate

53 Pump Fluctuations CW pump Effect of Pump Power Noise on Comb Summary Non-lorentzian resonant gain shift Er-doped fiber (gain) Self-phase modulation Pump power change Third-Order- Dispersion Gain change Pulse Energy & Width Self-Steepening Gain filtering Nonlinear selffrequency shift Frequencydependent loss Spectral Shift Resonant Group Velocity Carrier Phase Shift Round Trip Time Shift Self-Steepening Third-Order Dispersion f r / P (Hz/mW) Spectral Shift Resonant Dispersion D a ta T h eo ry Spectral Shift Pump Power (mw) 70

54 Pump Fluctuations CW pump Effect of Pump Power Noise on Comb Summary Non-lorentzian resonant gain shift Er-doped fiber (gain) Self-phase modulation Pump power change Third-Order- Dispersion Gain change Pulse Energy & Width Self-Steepening Gain filtering Nonlinear selffrequency shift Frequencydependent loss Spectral Shift Resonant Group Velocity Carrier Phase Shift (fixed point = -infinity) Round Trip Timing Shift (fixed point = carrier frequency) small Usually timing shift dominates But verify experimentally N. R. Newbury and B. R. Washburn, JQE, 41, 1388 (2005

55 Experimental Data for Comb Response to Pump Power Not hard to measure the fixed point Stimulate comb & measure response! Frequency Counter Data CW pump P P Er-doped fiber (gain) f 0 (MHz) 20f rep (MHz) Repetition frequency Offset frequency L Time (ms) x10 3 Here fixed point = 150 THz fixed point

56 Frequency Noise PSDs vs Pump Noise Vary Pump RIN (pump current dependent) I(f) f o CW pump Fiber Comb Narrow cw laser John McFerran, APB 86, 219 (2006) 0 Frequency Noise (dbhz 2 /Hz) Frequency (Hz)

57 Noise Sources Pump Fluctuations pump diode Environmental perturbations (vibration & temperature, humidity) ASE Er+ Fiber amp ASE Supercontinuum generation in Highly Nonlinear fiber Shot Noise Degrades Signal-to-Noise (but not linewidth) Extra-cavity noise (white phase noise) Intra-cavity noise does broaden linewidth

58 Effect of Different Noise Source on Frequency Comb f 0 frequency Ideal Output Environmental Effects PSD ~ 1/f Pump Noise PSD ~ low pass filter ASE-induced Quantum Noise PSD ~ white noise Extra-cavity noise (ASE, shot noise) N. Newbury & W. Swann, JOSA B, 8, (2007); fixed point: H. R. Telle, B. Lipphart, and J. Stenger, APB, 74, 1 (2002)

59 Quieting Down The Comb Phase-lead compensation to overcome laser response H(f) f Pump power feedback 1480 nm pump diode Operate pump at lowest RIN (highest power) Attenuator Er+ Isolate & Reduce loss Fiber amp Narrow cw laser f o Detection High bandwidth PZT fiber stretcher Cavity length feedback Narrow linewidth cw reference laser McFerran et al, Opt. Lett., 31, 1997 (2006) N. R. Newbury and B. Washburn, IEEE JQE, 41, 1388 (2005) Swann et al., Opt. Lett. 31, 3046 (2006).

60 Free-running Frequency Noise at 1 m (far edge of comb) Noisiest part of comb! Frequency noise (Hz 2 /Hz) Environment* Pump-noise Quantum ASE SNR Limit 100 Hz 1 khz 10 khz 100 khz 1 MHz Fourier frequency (Hz) (Corresponding Linewidth is ~ 10 s of khz)

61 Phase-Locked Frequency Noise at 1 m (far edge of comb) Noisiest part of comb! 60 Frequency noise (Hz 2 /Hz) f o locked fully locked unlocked Fourier Frequency (Hz) Quantum Limit from intra-cavity ASE Unlocked phase noise ~ 200 radians Locked phase noise ~ 0.6 radians

62 Optical Coherence Between Combs with IMRA America Swann, I Hartl, M. Fermann, Opt. Lett. 31, 3046 (2006). free-running cw fiber laser Comb 1 Comb 2 optical filter 3 khz RBW 0.3 Hz RBW Sub-Hz level residual linewidth ~50% of RF power in coherent peak

63 Prescription for using a stabilized Frequency Comb 1. Measure the offset frequency Hard to do requires octave spanning continuum 2. Detect either an optical beat or high harmonic of the repetition rate (optical vs rf stabilization) 3. Understand and minimize noise Check fixed point of pump power modulation if low dispersion cavity! 4. Feedback to actively cancel leftover noise High bandwidth feedback Two or more actuators (or signal processing on comb) 5. Design the rest of the experiment to not re introduce noise we just cancelled Minimize out of loop paths.

64 Limits to Comb Performance For frequency stability or linewidth: Limit is set by out of loop fiber/free-space and not comb Optical Source f r Frequency Comb opt filter Out of loop Fiber 10-5 /C Vibrations Humidity. f 0 Typical limits for a few meters of fiber taped to optical table Hz linewidths ~ second Larger System or Experiment

65 A Few General Rules of Thumb for Frequency combs Comb has no intrinsic accuracy > needs an external reference Flat supercontinuum not achievable Challenge for spectroscopy Sometimes solved with multiple supercontinuum branches Hard to detect offset frequency (f ceo ) with enough SNR! f 2f requires octave spanning continuum 2f 3f requires less bandwidths but more power The Fixed Point picture is the best way to analyze the noise and the stabilization. Coherent narrow linewidth comb requires careful design & high bandwidth feedback. Frequency stability (Allan deviation) depends on more experiment than the comb Out of Loop paths almost always dominate frequency stability