Transcript Slide 1
All-Fiber, Phase-Locked Supercontinuum Source for Frequency Metrology and Molecular Spectroscopy Brian R. Washburn National Institute of Standards and Technology Optoelectronics Division 815.03 325 Broadway Boulder, CO 80305 BRW 5/2003 Acknowledgments S. A. Diddams, N. R. Newbury, S. L. Gilbert, W. Swann National Institute of Standards and Technology J. W. Nicholson and M. F. Yan OFS Laboratories, USA C. G. Jørgensen OFS Fitel Denmark I/S, Denmark BRW 5/2003 Introduction: Output of a Mode-Locked Laser Output of a Mode-Locked Laser Power 10 ns Time Domain 10 fs time Frequency Domain 10 MHz Power 0.1 THz Frequency Small Dt => Broad Spectral Coverage BRW 5/2003 Microstructure Fiber Spectral Intensity (dB) Ti:sapphire Laser 0 Supercontinuum -10 -20 -30 -40 600 800 1000 BRW 5/2003 1200 1400 Wavelength (nm) Mode-Locked Lasers Nonlinear Optical Fibers Radio Frequency Standards Optical Frequency Metrology Molecular Spectroscopy BRW 5/2003 Outline Part One: Mode-locked Fiber Lasers • Compare/contrast fiber lasers to free-space • • lasers Fiber Dispersion and Nonlinearities Mode-locking in fiber lasers Part Two: Optical Frequency Metrology • Components of the all-fiber supercontinuum • • source Phase-locking a fiber laser System performance Part Three: Molecular Spectroscopy BRW 5/2003 Passively Mode-locked Lasers CW pu Ultrashort mp Pulsed Output Ga in CW pump Ultrashort Pulsed Output Elements of mode-locked lasers – – – – Pump source Gain element Saturable absorber for mode-locking Dispersion compensation for shortest pulses BRW 5/2003 Fiber Lasers: Advantages and Disadvantages • Advantages – – – – – Easy to align fiber laser cavity Less sensitive to misalignment Passive optical elements are inexpensive Uses less power than Ti:sapphire laser More compact • Disadvantages – More sensitive to environment (polarization) – Optical fiber limits total laser power – All fiber cavity limits ability to easily experiment with laser design – Careful dispersion and nonlinearity management is needed for proper laser design BRW 5/2003 Gain Medium: Erbium-Doped Fiber (EDF) EDF Gain Bandwidth -35 Power (dBm) -40 -45 -50 -55 -60 -65 1530 1540 1550 1560 1570 Wavelength (nm) • • Use a fiber that is highly doped with Er as the gain element of the laser This fiber exhibits normal dispersion : D=-70 ps/nm-km BRW 5/2003 Power Power Power Saturable Absorber for Mode-Locking time • • • time A saturable allows the laser cavity to “favor” high peak power, ultrashort pulses An absorber created by Kerr lensing is typically used in solid state lasers Fiber nonlinearities are used in fiber lasers Need a complete understanding of fiber dispersion and nonlinearities BRW 5/2003 BRW 5/2003 Fiber Dispersion and Nonlinearities Group Velocity Dispersion (GVD) Normalized Power 1.0 Fiber 0.8 0.6 0.4 0.2 0.0 -400 -200 0 200 Time (fs) 400 Wavelength (nm) Spectral Intensity 1350 1400 1450 1500 1550 1600 1650 1700 1.0 0.8 0.6 0.4 0.2 0.0 -0.15 -0.10 -0.05 0.00 0.05 Frequency (1/fs) 0.10 0.15 BRW 5/2003 Fiber Dispersion and Nonlinearities Self Phase Modulation (SPM) Wavelength (nm) 1450 1500 1550 1600 1650 1700 1.0 Spectral Intensity 1400 1.0 0.8 0.6 0.4 Fiber 0.2 0.0 -0.15 -0.10 -0.05 0.00 0.05 0.10 Frequency (1/fs) Normalized Power Spectral Intensity 1350 1350 1650 1700 0.8 0.6 0.4 0.2 0.0 -0.15 0.15 Wavelength (nm) 1450 1500 1550 1600 1400 -0.10 -0.05 0.00 0.05 0.10 Frequency (1/fs) 1.0 0.8 0.6 0.4 0.2 0.0 -400 -200 0 200 Time (fs) 400 BRW 5/2003 0.15 Characterizing Dispersion and Nonlinearity in an Optical Fiber Pi (r, ) = 0 Ej 0 Ej Ek El (1) ij j Dispersion (3) ijkl jkl Nonlinearity • Assume single mode and no • • birefringence Concerned with phase matched nonlinearities Assumptions leads to SPM and GVD only BRW 5/2003 Characterizing Dispersion and Nonlinearity in an Optical Fiber 2 0 T LD 2 () = n() c LNL 1 P0 n20 2 cr0 • The dispersion length (LD) is the length of fiber where a Gaussian pulse to temporally broadens by Sqrt(2) • The nonlinear length (LNL) is the length of fiber for which a pulse gains a phase of 1 radian BRW 5/2003 The Nonlinear Schrödinger Equation Nonlinearity Dispersion Absorption E ( z, t ) i m1 m i 2 = E m E i 1 E R(t ') E ( z , t t ') dt ' m z 2 m ! t 0 t 0 m=2 A beautiful equation which accurately describes a highly nonlinear optical system An understanding of this equation provides the ability to design and predict the behavior of active fiber devices • • • • Fiber lasers Erbium doped fiber amplifiers Nonlinear loop mirrors/switches TOADs BRW 5/2003 Mode-locking in Fiber Lasers • Active Mode-locking – Typically use AOM or Mach Zehnder to achieve mode locking • Sigma laser (Duling et al, Opt Lett Vol 21, 21 1996) – Advantage: Can achieve high repetition rates (10 GHz) • Passive Mode-locking – Interferometric designs based on gain and saturable absorber sections • Figure eight lasers (Sacnac switch) • Stretched Pulse Lasers – Advantage: sub-picosecond, high energy pulses BRW 5/2003 Figure Eight Laser Output isolator rejection port PD PC PZT PC 980 nm pump Er fiber BRW 5/2003 Nonlinear Loop Mirror: Linear Operation A 50/50 B Gain Linear Operation: No phase shift between interferometer arms BRW 5/2003 Nonlinear Loop Mirror: Nonlinear Operation A 50/50 B Gain Nonlinear Operation: Phase Difference: D n2 (G 1) I (t ) L BRW 5/2003 Figure Eight Laser Performance 3.0 isolator PC PZT PC Er fiber correlation signal (a.u.) rejection port PD AMP 2.5 2.0 1.5 1.0 0.5 0.0 -750 -500 -250 0 250 500 750 980 nm pump time (fs) Temporal FWHM <100 fs Average Power= 100 mW Center Wavelength= 1560 nm BRW 5/2003 Stretched Pulse Laser E r e b r fi Normal Dispersion Output 980 nm pump PZT Isolator/ polarizer PC PC Anomalous Dispersion BRW 5/2003 Nonlinear Polarization Rotation QWP Kerr HWP Polarizer intensity Polarizer time Ey Ex BRW 5/2003 Nonlinear Polarization Rotation QWP Kerr HWP Polarizer intensity Polarizer time Ey Ex BRW 5/2003 Nonlinear Polarization Rotation QWP HWP Kerr Polarizer intensity Polarizer time Ey Ex BRW 5/2003 Nonlinear Polarization Rotation QWP Kerr HWP Polarizer intensity Polarizer time Ey Ex BRW 5/2003 Nonlinear Polarization Rotation QWP Kerr HWP Polarizer intensity Polarizer time Ey Ex BRW 5/2003 er b i f Er Output 980 nm pump PZT Isolator/ polarizer PC intensity Stretched-Pulse Operation time PC BRW 5/2003 Stretched-Pulse Fiber Laser WDM 980 nm Pump 90/10 Splitter EDF Isolator Output Polarization Controllers Polarizer Polarization Controllers BRW 5/2003 Stretched-Pulse Laser Performance Temporal FWHM <100 fs Average Power= 100 mW Center Wavelength= 1560 nm ber i f r E PC AMP PZT Isolator/ polarizer PC Normalized Normalized AC AC Intensity Intensity Output 980 nm pump 1.0 1.0 AC FWHM 91 fs Pulse FWHM ~ 60 fs FWHM 743 fs 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 -1500 -1500 -1000 -1000 -500 -500 0 0 500 500 Delay Delay(fs) (fs) 1000 1000 1500 1500 BRW 5/2003 Part Two: Optical Frequency Metrology Mode-Locked Lasers Nonlinear Optical Fibers Radio Frequency Standards Optical Frequency Metrology New way to connect microwave and optical frequencies BRW 5/2003 Electric Field from a Mode-locked Laser Time domain (Pulses in time) Df E(t) 2Df Carrier-envelope phase slip from pulse to pulse because group and phase velocities differ t repetition rate Frequency domain (Comb of lines) I(f) 0 fo = fr Df/2 repetition frequency fr fn = nfr + fo f Stable frequency comb if 1) Repetition rate (fr) locked 2) Offset frequency (f0) (phase slip) locked BRW 5/2003 Acoustic Frequency Metrology: Guitar Tuning Known Frequency, fk Unknown Frequency, fun Df=0.5 Hz Df=0.01 Hz BRW 5/2003 Optical Frequency Metrology fun I(f) fo = fr Df/2 RF Beat repetition frequency fr f 0 fn = nfr + fo 1550 nm Locking Electronics Cesium Time Hydrogen Standard Maser ~9 GHz 10 MHz 193,548,387,096,774.2 Hz 10,000,000.0 Hz Stability and accuracy of RF standard passed to optical frequencies BRW 5/2003 Stabilize frequency comb by Self-reference frequency locking fr I(f) fo f 0 fn = n fr + fo x2 f2n = 2nfr + fo fo To Lock comb to an RF oscillator • Measure offset frequency fo as shown and lock to zero • Phase-lock fr directly to an rf synthesizer BRW 5/2003 Supercontinuum Frequency Comb 0 E0() F 0 0 0 Hz Tuning Fork ? Hz Tuning Fork ? Hz Extended Ti:sapphire frequency comb Ti:sapphire gain bandwidth upercontinuum BRW 5/2003 A Fiber Laser-Based Frequency Comb Translate Ti:Sapphire results to Fiber-based system • • Most existing frequency combs limited to Ti:Sapphire laser-based systems No self-referenced frequency combs from a mode-locked fiber laser in use – Locking of a fiber laser to other stabilized sources have been achieved* – Until recently a full octave from fiber laser not available* • A fiber-based frequency comb can provide – Compact, inexpensive design – Potential for stable “hands-free” operation – Optical frequency metrology in the IR * References F. Tauser et al, Opt. Express 11, 594 (2003) F.-L. Hong et al, Opt. Lett. 28, 1 (2003) J. Rauschenberger et al., Opt. Express 10, 1404 (2002) BRW 5/2003 All-Fiber Supercontinuum Source Er fiber 980 nm pump isolator Er fiber Continuum after 20 cm DF - HNLF 1480 nm HNLF pump SMF pigtail Supercontinuum Spectrum (dB) 1480 nm pump 0 Octave of Bandwidth -5 -10 -15 1000 1200 1400 1600 1800 2000 2200 2400 Wavelength (nm) BRW 5/2003 Highly Nonlinear Fiber (HNLF) Index Profile Dn ~ 0.2-0.3 F2 doped radius Dispersion (ps/nm - km) index Ge doped 100 nonlinearity : 8 to 15 1/W-km Effective Area : 13 mm2 loss : 0.7 to 1 dB/km dispersion (1550 nm) : -10 to +10 ps/nm-km dispersion slope (1550 nm) : 0.024 ps/nm2-km splice loss (to SMF) :0.18 dB splice loss (to HNLF) :0.02 dB Ti:sapphire laser Er laser 50 0 HNLF dispersion -50 microstructure fiber dispersion -100 600 800 1000 1200 1400 wavelength (nm) 1600 1800 BRW 5/2003 f-to-2f Interferometer 1100 nm /2 1100 nm PD SMF polarizer 1100 nm bandpass 10 -30 Repetition Rate, fr 0 -40 -10 -20 -50 Fundamental optical filter 2200 nm RF Spectral Power (dB) Spectral Power (dBm) SHG (LiIO3) Optical Intensity (dBm) f-to-2f interferometer fr-f0 beat SHG -30 -60 fr+f0 beat -40 -50 -70 -60 25 30 35 1000 40 45 1050 50 55 1100 60 65 1150 Frequency wavelength(MHz) (nm) 70 75 1200 An octave of supercontinuum allow the generation of CEO beat frequencies with a SNR of 30 dB BRW 5/2003 Phase-locked Frequency Comb 1480 nm pump Amplifier Er fiber 1480 nm pump HNLF SMF isolator rejection port PD PZT PC SHG (LiIO3) 2200 nm 1100 nm /2 Oscillator PC f-to-2f interferometer 980 nm pump Er fiber Locking Electronics 1100 nm PD SMF polarizer 1100 nm bandpass • Oscillator: 20 nm FWHM pulses, 50 MHz rep rate • Amplifier: 100 mW output, FWHM < 100 fs • Supercontinuum generation in highly nonlinear fiber (HNLF), 23 cm of length • f-to-2f Interferometer BRW 5/2003 Fiber Laser-Based Frequency Comb f-to-2f interferometer Supercontinuum Source (all fiber) BRW 5/2003 Frequency Stability 49872643.010 fr(Hz) 49872643.005 49872643.000 49872642.995 0.5 mHz standard deviation (Counter limited) 49872642.990 f0 (Hz) 64000000.1 64000000.0 63999999.9 10 mHz standard deviation 0 20 40 60 Time (minutes) 80 - Optical comb phase locked to RF source - Any optical comb line known absolutely by fn = nfr + fo BRW 5/2003 Phase Noise Measurements CEO Frequency Lock -6 10 -4 1.6x10 -7 2 Phase Noise (rad /Hz) -4 1.4x10 -8 10 -4 -9 1.2x10 -10 1.0x10 -11 8.0x10 10 -4 10 -5 10 -12 10 -5 6.0x10 -13 10 -5 4.0x10 -15 2.0x10 10 -5 10 -16 10 2 -14 Integrated Phase Noise (rad ) 10 0.0 0 10 1 10 2 10 3 10 4 10 5 10 6 10 Frequency (Hz) • • CEO frequency lock : integrated phase error for 2.07 MHz signal (DC to 25 MHz) was ~10 mrad Repetition rate lock : integrated phase error (DC to 25 MHz) was <1 mrad BRW 5/2003 Mode-Locked Lasers Nonlinear Optical Fibers Radio Frequency Standards Optical Frequency Metrology Molecular Spectroscopy BRW 5/2003 Standard Reference Materials Standards for Wavelength Division Multiplexing BRW 5/2003 Spectroscopy of Acetylene Wavemeter Frequency Uncertainty: ~1.8 MHz Typical wavemeters: ~20 MHz (0.15 pm at 1550 nm) Reference: Swann and Gilbert, JOSA B Vol. 17,7, (2000) BRW 5/2003 Metrology with Supercontinuum Comb repetition RF fBeat frequency r 2fr fr I(f) fo = fr Df/2 fun f 0 fn = nfr + fo Fiber-based Frequency Comb Tunable CW Laser ESA 12C H 2 2 Computer BRW 5/2003 Conclusions • Stabilized frequency combs have revolutionized optical clocks – Previous systems limited to 400 nm to 1300 nm • Fiber laser-based frequency comb demonstrated – Potentially more robust than Ti:sapphire laser based frequency comb – Extend phase-lock frequency combs into the IR • Permit unprecedented accuracy in IR frequency metrology – Can lock frequency comb to Cesium time standard or other atomic standard BRW 5/2003 Thank you for your tim Brian R. Washburn National Institute of Standards and Technology Optoelectronics Division 815.03 [email protected] BRW 5/2003 EXTRA SLIDES BRW 5/2003 Four-Wave Mixing and Self-Phase Modulation Nonlinear effects in fused-silica are due to the (3) susceptibility (3) Pi (r, t ) = 0 ijkl (t t1 , t t2 , t t3 )Ej Ek El dt1dt2 dt3 jkl Four-Wave Mixing is the result of the instantaneous component of (3) (Kerr effect) • Four Wave Mixing (FWM) - Specific conditions needed to assure phase matching • Self-Phase Modulation (SPM) - Completely degenerate FWM - Automatically phase-matched (3) Pi () = 0 ijkl Ej Ek El jkl 3 2 (3) PSPM (t ) = 0 xxxx E E 4 Intensity dependent BRW 5/2003 Transform Limited =1550 nm Solitons ? SMF Soliton Propagation 1.0 0.5 0.6 0.0 0.4 -0.5 Intensity Phase 0.2 0.0 -400 -300 -200 -100 0 100 Time (fs) -1.0 200 300 0.5 0.6 0.0 0.4 -0.5 Intensity Phase Chirp -d/dt 0.2 0.0 Temporal Phase 0.8 -400 -300 -200 -100 0 100 -1.0 200 300 400 Time (fs) 1.0 400 SPM Only Intensity Phase 25 Chirp -d/dt 0.8 20 0.6 15 0.4 10 0.2 5 BRW 5/2003 0.0 -400 -300 -200 -100 0 100 200 300 400 0 Temporal Phase (radians) 0.8 Temporal Intensity 1.0 Temporal Phase (radians) Temporal Intensity Before Fiber Propagation Temporal Intensity 1.0 GVD Only 1.0 After Stimulated Raman Scattering (SRS) Raman Gain in Fused-Silica SMF 0.04 2 m/W) 2 2 ((t1 +t2 )/(t1 t2 ))exp(-t/t2)sin(t/t1) -13 hR(t)= 1.0 0.8 Raman Gain gR, (x 10 Raman Response, hR (1/fs) 0.06 Peak at 13.2 THz 0.6 0.02 0.4 0.00 0.2 -0.02 -50 0 50 100 150 Time (fs) • • • 200 250 300 0.0 0 6 12 18 24 30 Frequency Shift D, (THz) 36 SRS is from the non-instantaneous component of the (3) susceptibility SRS typically leads to a frequency downshift of the incident light The Raman gain curve (gR) characterizes the frequency downshift (D) acquired by the incident light BRW 5/2003 42 The NLSE 2 2 (PNL (r, t ) PL (r, t )) E ( r , t ) 2 E (r, t ) 0m0 = m0 2 t t 2 Assumptions 1) The nonlinear polarization PNL(r,t) can be treated as a small perturbation to PL(r,t). 2 The linear response is instantaneous. 3) The optical field maintains its polarization along the fiber length so a scalar approach is valid 4) E(r,t) is quasi-monochromatic. 5) The slowly varying envelope approximation (SVEA) 6) The mode profile is single mode, specifically LP01 Nonlinearity Dispersion Absorption E ( z, t ) i m1 m i 2 = E m E i 1 E R(t ') E ( z , t t ') dt ' m z 2 m ! t 0 t 0 m=2 BRW 5/2003 Including SRS To include the effect of SRS, the (3) susceptibility was broken into fast (SPM) and slow (SRS) portions R(t ) = (1 f R )(t ) f R hR (t ), The measured Raman gain curve (gR) can be implemented using 0 (3) g R () = f R Im F hR (t ) cn0 BRW 5/2003 Extended NLSE for Including SRS Nonlinearity Dispersion Absorption E ( z, t ) i m1 m i 2 = E m E i 1 E R(t ') E ( z , t t ') dt ' m z 2 m ! t 0 t 0 m=2 R(t ) = (1 f R )(t ) f R hR (t ), Nonlinearity SPM Raman Effect Self Steepening 2 i 2 2 i E E E E i 1 E hR (t ') E ( z , t t ') dt ' 0 t 0 t 0 • Describes spectral features developed over a frequency range of up to a third of the carrier frequency . • Uses the experimental nonlinear Raman response of fusedsilica 2 ( ) BRW 5/2003 Soliton Propagation • Solitons are formed after a balance of GVD and SPM LD N = an integer LNL 2 2 N 2 N PN = = 3.11 2 T0 Dt 2 2 2 • Higher order dispersion and nonlinearities cause soliton breakup BRW 5/2003 Positive GVD 0 Negative GVD 1/(Dispersion Length), 2/T0 2 Pulse Propagation Regimes + GVD SPM Selfsteepening SRS + GVD SPM Breakdown of the SVEA Include FWM - GVD SPM - GVD SPM Selfsteepening SRS 1/(Nonlinear Length), Po SPM: Self-phase modulation FWM: Four Wave Mixing SRS: Stimulated Raman scattering Analytic Solutions : Nonlinear Coefficient GVD: Group velocity dispersion BRW 5/2003 How to Choose Fiber Lengths? • Need enough EDF to provide sufficient gain in • the laser cavity Need enough SMF to provide adequate nonlinear polarization • Net cavity dispersion is anomalous: – Soliton Regime • Net cavity dispersion is slightly normal – Stretched-pulse Regime • Net cavity dispersion is strongly normal – No mode-locking BRW 5/2003 Soliton vs. Nonsoliton Regime • Sidebands (Kelly sidebands) indicative of soliton propagation • Inhibiting soliton formation increases spectral bandwidth BRW 5/2003 Femtosecond-Laser-Based Optical Synthesizer m-wave reference Optical Synthesizer I(f) optical reference m-wave out fo fr optical out fn = nfr + fo f Sounds great, but can you do it? – Ti:Sapphire femtosecond laser + novel nonlinear fiber (‘00) D. J. Jones et al. Science 288, 635 (2000) – Broadband Ti:Sapphire femtosecond laser (‘01/’02) Morgner et al., PRL, 86, 5462,’01, T. Ramond et al., Opt. Lett 27, 1842 – Femtosecond Er Fiber laser + novel nonlinear fiber (‘03) Washburn et al., accepted to Opt. Lett, Oct. ‘03 BRW 5/2003 Details on Locking Electronics f0 control to current source Locking Electronics error Loop out Phase Filter Detector 512 1.064 GHz Syn. 2.078125 MHz fr control to PZT HV Source Loop Filter 64 MHz from f-to-2f Syn. 1.0 GHz Syn. ~49.8 MHz from fr • CEO Frequency Locking Electronics • Repetition Rate Locking Electronics BRW 5/2003 10 -5 Counted f0 Sys. noise floor avg Uncertainty Normalized (/f(/f) avg) Frequency Uncertainty Normalized Frequency Frequency Stability verses Gate Time 10 10 10 10 10 10 -6 -7 -8 -9 -10 Counted Frep System noise floor -11 10 0 10 1 10 2 10 3 10 4 Gate Time (ms) • • Time (ms) rate (F Uncertainty on locked Gate repetition rep) is near the system floor Uncertainty on counted CEO beat (f0) is larger due to linewidth of the beat BRW 5/2003 Spectrum of Figure-Eight Laser 0.006 Power (mW) 0.005 0.004 0.003 0.002 0.001 0.000 1540 1560 1580 1600 Wavelength (nm) BRW 5/2003 Spectrum of Stretched-Pulse Laser Spectral Intensity 0.004 FWHM 19 nm 0.002 0.000 1500 1520 1540 1560 1580 1600 1620 Wavelength (nm) BRW 5/2003