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

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

Introduction: Output of a Mode-Locked Laser 10 ns Time Domain Power 10 fs time 0.1 THz 10 MHz Frequency Domain Power Frequency Small Dt => Broad Spectral Coverage

Supercontinuum Ti:sapphire Laser Microstructure Fiber

Optical Frequency Metrology Mode-Locked Lasers Nonlinear Optical Fibers Radio Frequency Standards Optical Frequency Metrology Molecular Spectroscopy

Part One: Mode-locked Fiber Lasers 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

Passively Mode-locked Lasers Elements of mode-locked lasers Pump source Gain element Saturable absorber for mode-locking Dispersion compensation for shortest pulses

Fiber Lasers: Advantages and Disadvantages 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

Gain Medium: Erbium-Doped Fiber (EDF) EDF Gain Bandwidth 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

Saturable Absorber for Mode-Locking 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

Fiber Dispersion and Nonlinearities Group Velocity Dispersion (GVD) Fiber

Fiber Dispersion and Nonlinearities Self Phase Modulation (SPM) Fiber

Characterizing Dispersion and Nonlinearity in an Optical Fiber Assume single mode and no birefringence Concerned with phase matched nonlinearities Assumptions leads to SPM and GVD only

Characterizing Dispersion and Nonlinearity in an Optical Fiber 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

The Nonlinear Schrödinger Equation 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

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

Figure Eight Laser Output

Nonlinear Loop Mirror: Linear Operation No phase shift between interferometer arms

Nonlinear Loop Mirror: Nonlinear Operation

Figure Eight Laser Performance AMP Temporal FWHM <100 fs Average Power= 100 mW Center Wavelength= 1560 nm

Stretched Pulse Laser Normal Dispersion Anomalous Dispersion

Nonlinear Polarization Rotation Ey Ex

Nonlinear Polarization Rotation Ey Ex

Nonlinear Polarization Rotation Ey Ex

Nonlinear Polarization Rotation Ey Ex

Nonlinear Polarization Rotation Ey Ex

Stretched-Pulse Operation intensity time

Stretched-Pulse Fiber Laser Isolator Polarizer Polarization Controllers EDF 980 nm Pump WDM 90/10 Splitter Output

Stretched-Pulse Laser Performance Temporal FWHM <100 fs Average Power= 100 mW Center Wavelength= 1560 nm AMP

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

Electric Field from a Mode-locked Laser Time domain (Pulses in time) Time domain (Pulses in time) E(t) E(t) Df Df 2Df 2Df Carrier-envelope phase slip from pulse to pulse because group and phase velocities differ Carrier-envelope phase slip from pulse to pulse because group and phase velocities differ t t repetition rate repetition rate Frequency domain (Comb of lines) fn = nfr + fo I(f) f fo = fr Df/2p repetition frequency fr Stable frequency comb if Repetition rate (fr) locked Offset frequency (f0) (phase slip) locked

Acoustic Frequency Metrology: Guitar Tuning Known Frequency, fk Unknown Frequency, fun Df=0.5 Hz Df=0.01 Hz

Optical Frequency Metrology fun fn = nfr + fo I(f) f fo = fr Df/2p repetition frequency fr RF Beat 1550 nm 193,548,387,096,774.2 Hz 10,000,000.0 Hz Locking Electronics Stability and accuracy of RF standard passed to optical frequencies Cesium Time Standard ~9 GHz Hydrogen Maser 10 MHz

Stabilize frequency comb by Self-reference frequency locking fo I(f) f fn = n fr + fo x2 f2n = 2nfr + fo Measure offset frequency fo as shown and lock to zero Phase-lock fr directly to an rf synthesizer To Lock comb to an RF oscillator

Supercontinuum Frequency Comb

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)

All-Fiber Supercontinuum Source HNLF 1480 nm pump 1480 nm pump Er fiber SMF pigtail 980 nm pump Er fiber isolator Continuum after 20 cm DF - HNLF

Highly Nonlinear Fiber (HNLF) 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

f-to-2f Interferometer An octave of supercontinuum allow the generation of CEO beat frequencies with a SNR of 30 dB

Phase-locked Frequency Comb f-to-2f Interferometer Supercontinuum generation in highly nonlinear fiber (HNLF), 23 cm of length Amplifier: 100 mW output, FWHM < 100 fs Oscillator: 20 nm FWHM pulses, 50 MHz rep rate

Fiber Laser-Based Frequency Comb f-to-2f interferometer Supercontinuum Source (all fiber)

Frequency Stability - Optical comb phase locked to RF source - Any optical comb line known absolutely by fn = nfr + fo

Phase Noise Measurements 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

Optical Frequency Metrology Mode-Locked Lasers Nonlinear Optical Fibers Radio Frequency Standards Optical Frequency Metrology Molecular Spectroscopy

Standard Reference Materials Standards for Wavelength Division Multiplexing

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)

Metrology with Supercontinuum Comb fn = nfr + fo I(f) f fo = fr Df/2p repetition frequency fr RF Beat fun fr 2fr Fiber-based Frequency Comb Tunable CW Laser 12C2H2 ESA Computer

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

Thank you for your time! Brian R. Washburn National Institute of Standards and Technology Optoelectronics Division 815.03 brianw@boulder.nist.gov

EXTRA SLIDES

Four-Wave Mixing and Self-Phase Modulation Nonlinear effects in fused-silica are due to the c(3) susceptibility Four-Wave Mixing is the result of the instantaneous component of c(3) (Kerr effect) Four Wave Mixing (FWM) - Specific conditions needed to assure phase matching Self-Phase Modulation (SPM) - Completely degenerate FWM - Automatically phase-matched Intensity dependent Index

Solitons Soliton Propagation GVD Only SPM Only

Stimulated Raman Scattering (SRS) SRS is from the non-instantaneous component of the c(3) susceptibility SRS typically leads to a frequency downshift of the incident light The Raman gain curve (gR) characterizes the frequency downshift (Dn) acquired by the incident light

The NLSE 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

Including SRS To include the effect of SRS, the c(3) susceptibility was broken into fast (SPM) and slow (SRS) portions The measured Raman gain curve (gR) can be implemented using

Extended NLSE for Including SRS Describes spectral features developed over a frequency range of up to a third of the carrier frequency . Uses the experimental nonlinear Raman response of fused-silica

Soliton Propagation Solitons are formed after a balance of GVD and SPM Higher order dispersion and nonlinearities cause soliton breakup

Pulse Propagation Regimes N=1 Soliton Axis of Evil

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

Soliton vs. Nonsoliton Regime Sidebands (Kelly sidebands) indicative of soliton propagation Inhibiting soliton formation increases spectral bandwidth

Femtosecond-Laser-Based Optical Synthesizer reference m-wave m-wave out optical out fn = nfr + fo I(f) f fo fr 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

Details on Locking Electronics CEO Frequency Locking Electronics Repetition Rate Locking Electronics

Frequency Stability verses Gate Time Normalized Frequency Uncertainty (/favg) Normalized Frequency Uncertainty (/favg) Gate Time (ms) Uncertainty on locked repetition rate (Frep) is near the system floor Uncertainty on counted CEO beat (f0) is larger due to linewidth of the beat Gate Time (ms)

Spectrum of Figure-Eight Laser

Spectrum of Stretched-Pulse Laser