Spectral Line-by-Line Pulse Shaping A.M. Weiner*, Z. Jiang, D.E. Leaird, C.-B. Huang, and J. Caraquitena Purdue University amw@purdue.edu http://ece.www.ecn.purdue.edu/~amw ecn purdue edu/ * On sabbatical at JILA/NIST, Boulder, Colorado Funding:
Outline Introduction ti What s new when combs and pulse shaping are put together? Shaper spectral resolution vs. comb mode spacing: a parameter mismatch Shaping with hybridly mode-locked laser comb Illustrations of requirements for high fidelity waveform generation Shaping with phase modulated d CW laser combs Programmable shaping at the 1 line level
Femtosecond Pulse Shaping Typical spectral resolution: 1s or 1s of GHz Fourier synthesis via parallel spatial/spectral modulation Diverse applications: fiber communications, coherent quantum control, few cycle optical pulse compression, nonlinear microscopy, RF photonics Liquid crystal modulator (LCM) arrays: Typically 128 pixels (up to 64), millisecond response Functionalities: phase-only, independent phase and intensity, polarization A.M. Weiner, Rev. Sci. Instr. 71, 1929 (2)
Femtosecond Frequency Combs S.T. Cundiff, J. Phys. D: Appl. Phys. 35 (22) R43 R59 E(t) ΔΦ I(f) δ 2πδ = ΔΦ f rep f rep Stabilized frequency combs available at repetition rates up to ~1 GHz t f 1/f n = n f rep + δ f rep Comb-offset frequency δ directly related to pulse-to-pulse phase difference ΔΦ Enabler for revolutionary advances in optical frequency metrology; 25 Nobel Prize in Physics to Hall & Hänsch
Spectral Line-by-Line Pulse Shaping Shaping: group of lines f rep Frequency domain Shaping: individual lines f rep Μ f rep frequency frequency 1/(Μ f rep ) Repetition period (1/f rep ) Time domain Overlapped regime 1/f rep 1/f rep time 1/f rep 1/f rep time Conventional pulse shaping: isolated, low duty factor waveforms Line-by-line spectral filtering: overlapped, 1% duty factor waveforms Sensitive to frequency shifts, pulse-to-pulse phase
Spectral Line-by-Line Pulse Shaping A step towards true optical arbitrary waveform generation (since now individual lines are controlled) Opportunity for construction of waveforms with ultrafast time structure AND long-term coherence Potential applications: Spectroscopy coherent control at single line frequency resolution, enhancement cavities, Engineering applications short pulse communications, laser radar,
Application Motivation: Ultrafast Spread Sprectrum Multiple-Access Communications Via Coded Optical Waveforms Potential advantages: Enhanced security, simplified network control, flexible bandwidth provisioning Transmitter Encoder Programmable Spectral Phase Decoder Nonlinearity EDFA Other users Other users Receiver Approximately coherent matched filtering Spectral encoding Spectral ldecodingdi
Application Motivation: Ultrafast Spread Sprectrum Multiple-Access Communications Via Coded Optical Waveforms Potential advantages: Enhanced security, simplified network control, flexible bandwidth provisioning Transmitter Encoder Receiver Synchronized shaped LO Other users Other users Integrator Approximately coherent matched filtering Spectral encoding Spectral ldecodingdi Linear receiver structures based on line-by-line homodyne Truly coherent multiwavelength processing!
Line-by-Line Pulse Shapers High spectral resolution shaper High rep rate comb f f LCM Grating Lens Mirror Shaper #1 ~18 mm diameter beam size 5. GHz 1541.9 1542. 1542.1 Wavelength (nm) Shaper #2 Telescope 2.6 GHz 1542.6 1542.7 1542.8 Wavelength (nm) Collimator Fibers Circulator 2 1 Polarization Controller Input pulse: 3 harmonically modelocked fiber laser (9-1 Output shaped pulse GHz rep rate) (NOT self-referenced) e e e Grating Lens f Beam Diameter Diffraction angle Shaper #1 11 / mm 75 mm 18 mm 57 o Shaper #2 12 / mm 1 mm 18 mm 65 o Z. Jiang et al, Opt. Lett. 3, 1557 (25); Optics Express 13, 1431 (25)
Harmonic Waveform Generation Line-by-Line Intensity Control Spectra Waveforms 1 GHz 31.5dB (1 db/div) 2 GHz 29 db 4 GHz 28 db Sampling Scope Intensity cross-correlation 5 GHz 26 db 154 1541 1542 1543 1544 1545 Wavelength (nm) -1-5 5 1
Importance of Strong Spectral Line Suppression 1 db/div 15 db 1 db/div 25 db 1 db/div 38 db Line positions 1541.7 1541.9 1542.1 Wavelength (nm) 1541.7 1541.9 1542.1 1541.7 1541.9 1542.1 1542.3 Wavelength (nm) Wavelength (nm) 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 Earlier pulse shaper design (#1) (~5 GHz resolution) Recent pulse shaper design (#2) (~2.6 GHz resolution) Obvious harmonic distortion for lower resolution shaper Unwanted line suppression is critical for high fidelity waveform generation! RF Spectrum 43 db 1 2 3 4 5 Frequency (GHz)
High Fidelity Arbitrary Waveform Generation (AWG) Amplitude : Phase: 1 1 1 1 π π π π High fidelity pulse shaping, closely matched to theory O-AWG transferable to RF-AWG 1 db/d div 1541.8 1542 1542.2 1542.4 1542.6 Wavelength (nm) O-AWG RF-AWG [π π] Solid: calculation Circles: x-correlation [ π π] -1-5 5 Fast photodetector 1-1 -5 5 1
Temporal Talbot effect T rep T Perioidic pulse train Dispersive medium Temporal self-image T = T / r rep Temporal self-imaging, with possibility of rep rate multiplication, for certain values of quadratic spectral phase Single-mode fibers and linearly chirped fiber Bragg gratings traditionally used as dispersive media Analogous effects with periodically sampled spatial beams and diffraction Programmability of line-by-line shaping leads to high fidelity demonstrations of this effect J. Caraquitena, Z. Jiang, D.E. Leaird, and A.M. Weiner, Opt. Lett. 32, 716 (27)
Temporal Talbot effect 6 Example: 3X multiplication INPUT Pha ase (π) 4 2-2 Comb lines Φ 2 T 2 H( ω) = exp i ω 2-4 -6-6 -4-2 2 4 6 Relative frequency ( ω ω / ω ) o rep OUTPUT Quadratic phase-filter Periodic phase-filter Temporal Talbot effect is a particular case of a periodic line-by-line phase filter!
Repetition-rate multiplication: Experimental results Extremely good uniformity in multiplied trains 1% 1.5% 1.5% 2% INPUT TRAIN 2X 3X 4X 5X Peak-peak k variations Multiplication factor Pulse Trains n.u.) Intensity ( -1-5 5 1 Optical Spectra Inten nsity (a.u.) 1541 1542 1543 1544 Wavelength (nm) RF Spectra 1 db/div 46 db 41 db 39 db 34 db 1 2 3 4 5 Frequency (GHz) J. Caraquitena, Z. Jiang, D.E. Leaird, and A.M. Weiner, Opt. Lett. 32, 716 (27)
Stability Issues of Mode-Locked Laser Fluctuations of fcomb-offset Frequency δ Φ Φ Spectral lines fluctuate 8.5 GHz 1541.7 1541.9 1542.1 Wavelength (nm) 1.5 GHz 1541.7 1541.9 1542.1 Wavelength (nm) Comb-offset frequency δ fluctuates 2πδ = ΔΦ f rep Phase between pulses ΔΦ fluctuates π π Overlapped regime fluctuates -2-1 1 2-2 -1 1 2 Input pulse positions Stabilized frequency comb is required for line-by-line pulse shaping Self-referenced high-rep-rate mode-locked lasers have not been available Z. Jiang et al, Opt. Lett. 3, 1557 (25) Time
Simulate Effect of Frequency Shifts (Phase: ) Unshifted lines 4 GHz max shift Fi ields (a.u.) 1 8.8.6.4 2.2-3 -2-1 1 2 3 Frequency (GHz) Frequency (GHz) Small intensity change (~1 %) Small energy change Almost in group of lines regime Intensit ty (a.u.) 1.8.6.4.2-25 -2-15 -1-5 5 1 15 2 25 Experiments e give similar results. C.-B. Huang, Jiang, Leaird, and Weiner, Opt. Exp. 14, 13164 (26)
Simulate Effect of Frequency Shifts (Phase: π) Unshifted lines 4 GHz max shift Fi ields (a.u.) Intensit ty (a.u.) 1.5 -.5-1 -3-2 -1 1 2 3 Frequency (GHz) 1.8.6.4.2 Frequency (GHz) -25-2 -15-1 -5 5 1 15 2 25 C.-B. Huang, Jiang, Leaird, and Weiner, Opt. Exp. 14, 13164 (26) Large intensity change (~68 %) Large energy change Waveform also changes Far from group of lines regime Experiments give similar results.
Comb Source Alternatives for Line-by-Line Shaping Self-referenced mode-locked lasers Highest frequency stability Not available at sufficiently high rates (until recently) Pulse shapers with higher h resolution spectral dispersers? Filter cavities to increase comb spacing (NIST, MIT ) Hybridly mode-locked lasers Poor frequency stability, or lack of easy offset frequency tunability Phase-modulated CW sources Good frequency stability Easy tuning of offset frequency Limited optical bandwidth (may be enhanced by nonlinear propagation) (enabled experimental tests of pulse shape changes due to comb offsets)
Shaping at the 1 Line Level Phase-Modulated CW Comb (tunable) Adiabatic soliton compression Z. Jiang, Huang, Leaird, and Weiner, Nature Photonics (to appear)
Shaping at the 1 Line Level Spectral Intensity Control a #1 Spectra 1537.2 1537.6 #18 Intensity Cross-correlations 1.65 ps 2 ps Intensity (a a. u.) (Linear sca ale) b 1537.2 1537.6 Intensity (a. u.) 1535 1536 1537 1538 1539 Wavelength (nm) 154-2 -1 1 2 Alternate comb lines excised yields doubling of repetition rate
Shaping at the 1 Line Level Spectral Phase Control Intensity (a.u.) T/5 Delay 2T/5 3T/5 4T/5 2 1-1 -2 Applying linear spectral phase yields temporal delay ( ) τω= ψ( ω) ω
Complex Optical Arbitrary Waveform Generation a b c Intensity (a.u.) Intensity (a.u.) ) 1 1 Measurement Calculation Measurement Calculation -2-1 1 2.3.2.1-1 -5 5 15π Linear plus cubic phase examples.3 Measurement and calculation.2 agree closely:.1 high fidelity waveforms! Unwrapped phase (rad) d 15π 2π Spectral phase function Wra apped phas se (rad) π 1535 1536 1537 1538 1539 154 Wavelength (nm)
Optical Frequency Comb Generator (OFCG) Source RF at f m f m Input CW Position v Input CW v LiNbO 3 waveguide for phase modulation Fabry-Perot Cavity formed by coated mirrors Optical Frequency Comb Generator v 1539 154 v 1541 1542 1543 1544 1545 Wavelength (nm) Output Comb www.optocomb.com Spectral Phases π π Modified version of phase modulated CW, a laser-like cavity configuration Stable, smooth and broadband comb; simple and known spectral phases Two pulses per modulation period v M. Kourogi, K. Nakagawa, M. Ohtsu, IEEE J. Quantum Electron., pp. 2693-271, 1993. In collaboration with K. Imai and M. Kourogi
Int tensity (a a.u.) Line-by-Line Pulse Shaping on OFCG Spectra Cross-correlations 64 lines 2.78 ps 2.93 ps Long wavelength half 32 lines Short wavelength half 32 lines 2.88 ps 2.83 ps OFCG output Spectral amplitude filtering 1539 154 1541 1542 1543 1544 1545 Wavelength (nm) 64 lines Spectral 1.6 ps phase filtering -1-5 5 1 Coherent combination of two pulses to one pulse! Jiang, Leaird, Huang, Miao, Kourogi, Imai, and Weiner, IEEE J. Quant. Electron. (submitted)
Coherent Two-to-One Pulse Combination Transform-limited pulse Auto-correlations Data Theory Linear Scale 1.6 ps FROG Measurement -6-4 -2 2 4 6 Measured Spectrogram Retrieved Spectrogram 1 db B/div Log Scale Data Theory 24 db Intens sity (a. u.) 1.5 2 Phas se (rad) -1-5 5 1 Retrieved Spectrum -2-5 5 Retrieved Pulse
Bit-Error-Rate Measurements OFCG + Shaping: a suitable source for fiber communication Comparable to 1-GHz harmonically mode-locked laser BER 1e-3 1e-5 NRZ-like 1 Gb/s PRBS: 2 23-1 Whole comb before shaper (two pulses in each period) 64 lines after shaper without phase correction (two pulses in each period) 64 lines after shaper with phase correction (single pulse in each period) 1e-7 RZ 4 fs pulse from 1 GHz mode-locked laser 1e-9-26 -24-22 -2-18 -16-14 Optical Power (dbm) -12-1
Summary: Spectral Line-by-Line Pulse Shaping Resolving and addressing individual comb lines: A step towards optical arbitrary waveform generation Bringing frequency combs and pulse shaping together: Manipulation i on the ultrafast time scale and long term coherence Future opportunities and challenges: Line-by-line shaping with self-referenced sources Many more spectral lines Rapid update Applications Acknowledgements Zhi Jiang, Dan Leaird, Robin Huang, Jose Caraquitena, Houxun Miao (Purdue) K. Imai, M. Kourogi (Optocomb) S. Diddams, L. Hollberg (NIST), S. Cundiff (JILA)