Programmable Femtosecond Pulse Shaping

Transcription

1 Programmable Femtosecond Pulse Shaping Andrew M. Weiner Purdue University School of Electrical and Computer Engineering West Lafayette, IN Phone: (765) Fax: (765) Support: NSF, ARO

2 Outline Pulse shaping basics Results from pulse shaping theory System issues Programmable pulse shaping Liquid crystal spatial light modulators Acousto-optic modulators Movable and deformable mirrors Applications New directions in pulse shaping Summary

3 Outline (cont.) Not covered in any detail: Femtosecond sources, amplifiers, measurement techniques Pulse shaping review articles: A. M. Weiner, Prog. Quantum Electron. 19, 161 (1995) A. M. Weiner, Rev. Sci. Instrum. 71, 1929 (2000)

4 Pulse Shaping Basics

5 Pulse Shaping by Linear Filtering ( ) ( ) e out (t) = dt h t t ein t E ( ω ) = H( ω)e ( ω) out in

6 Femtosecond Waveform Synthesis Fourier synthesis via parallel spatial/spectral modulation Diverse applications: fiber communications, coherent quantum control... Computer programmable pulse shapers can be fiber pigtailed with ~ 5 db fiber to fiber loss Pulse widths ranging from picoseconds to below 10 femtoseconds

7 Pulse Shaping Data (Intensity Cross-correlation) E(ω) ω ω Temporal analog to Young s two slit interference experiment Highly structured femtosecond waveform obtained via simple amplitude and phase filtering Weiner, Heritage, and Kirschner, J. Opt. Soc. Am B 5, 1563 (1988).

8 Synthesis of Femtosecond Square Pulses Power spectrum Cross-correlation data Theoretical intensity profile Spectral shaping using fixed, microlithographically fabricated phase and amplitude masks Weiner, Heritage, and Kirschner, J. Opt. Soc. Am B 5, 1563 (1988).

9 Pulse Shaping via Spectral Phase Control τ ω = ω Linear phase Quadratic phase Cubic phase φω= B φω= C ω ω ( ) A( ω ω) A>0 A=0 A<0 o ( ) φω= ( ) ( ω ω ) 2 ( ) ( ) 3 chirp compensated φ( ω) o chirped o Pulse position modulation Linear chirp Nonlinear chirp Weiner et al, IEEE J. Quant. Electron. 28, 908 (1992) Efimov et al, J. Opt. Soc. Am. B12, 1968 (1995)

10 Pulse shaping via Phase-Only Filtering A pseudorandom spectral phase filter produces an ultrafast pseudonoise burst. +1 E(ω) Periodic repetitions of such phase filters produce fsec pulse trains. -1 Phase filters may be designed using either known codes or by using numerical optimization methods. Control of temporal intensity, with temporal phase left unspecified.

11 A Selected Chronology of Fourier Transform (FT) Pulse Shaping 1) FT shaping (~30 ps input pulses) 2) Pulse shaping in a fiber-grating pulse compressor (~1 ps) 3) First theory of diffraction effects in FT shaping 4) Grating-lens pulse stretchers Froehley et al, in Progress in Optics 20, 65 (1983) Heritage et al, Appl. Phys. Lett. 47, 87 (1985); Opt. Lett. 10, 609 (1985) Thurston et al, IEEE JQE 22, 682 (1986) Martinez,IEEE JQE 23, 59 (1987) 5) FT shaping (~100 fs) 6) Early applications of FT shaping Weiner et al, J. Opt. Soc. Am. B 5, 1563 (1988) Weiner et al, PRL 61, 2445 (1988); Opt. Lett. 13, 300 (1988); IEEE JQE 25, 2648 (1989); Science 247, 1317 (1990)

12 A Selected Chronology of Fourier Transform (FT) Pulse Shaping (cont) 7) Programmable pulse shaping (phase-only liquid crystal modulator) 8) Pulse shaping below 20 fs 9) Time scanning pulse shapers (moving mirror) 10) Programmable pulse shaping (acousto-optic modulator) 11) Programmable pulse shaping (phase-and-amplitude LCM) 12) Adaptive pulse shaping 13) Programmable pulse shaping (deformable mirror) 14) Applications to coherent quantum control Weiner et al, Opt. Lett. 15, 326 (1990) Reitze et al, Appl. Phys. Lett. 61, 1260 (1992) Kwong et al, Opt. Lett. 18, 558 (1993) Hillegas et al, Opt. Lett. 19, 737 (1994) Wefers et al, Opt. Lett. 20, 1047 (1995) Yelin et al, Opt. Lett. 22, 1793 (1997) Zeek et al, Opt. Lett. 24, 493 (1999) Lots of authors; ~ present

13 Results from Pulse Shaping Theory

14 Pulse Shaping Theory (I): Basics out ( ω ) = ( αω) ( ω) E M E in x α= = ω spatial dispersion e (t) = e (t) m(t/ α) out in 1 ( ) j ω m(t / α ) = M αω e t dω 2π For a transform-limited input pulse, pulse shaping generally does not decrease the pulse duration (bandwidth is not increased).

15 Pulse Shaping Theory (II): Effect of Diffraction w o Mask with sharp feature Assume spatial filter selects fundamental Gaussian mode (e.g., single-mode fiber, regenerative amplifier) ( ) ( ) 2 2 E ω ~ dx M(x) exp -2 x-αω w E ( ω) out o in Filter function Spectral smearing due to finite spot size out in o ( 2 2 2) e (t) ~ e (t) m(t / α)exp w t /8α time window Equivalent to a window function in the time domain Thurston, Heritage, Weiner, and Tomlinson, IEEE JQE 22, 682 (1986)

16 The Complexity of a Shaped Pulse Shortest temporal feature related to bandwidth: Bδt 0.44 Temporal window related to spectral resolution: δft 0.44 Complexity : η = B/δf = T/δt (# of independent features in either frequency or time domain) η increases with larger input beams, more dispersive gratings, shorter input pulses. Typically η ~ several hundred for 100 fs pulses.

17 Phase-to-Amplitude Conversion due to Diffraction Pseudorandom phase mask with abrupt 0-π phase transitions Each phase transition leads to a deep hole in the power spectrum. Such data validate theoretical treatment of diffraction effects in pulse shaping. Sardesai, Chang, and Weiner, J. Lightwave Tech. 16, 1953 (1998)

18 Pulse Shaping Theory (III) Further analysis predicts a time-dependent spatial shift of the shaped waveform prior to any spatial filtering [Wefers and Nelson, IEEE JQE 32, 161 (1996)]. The spatial filter converts the time-dependent spatial shift into a (position independent) time window. These effects are relatively small when the pulse shaper spectral resolution is adequate to resolve the spatial features on the mask.

19 System Issues

20 Control Strategies for Femtosecond Pulse Shaping Open loop control Requires pulse shaper calibration and specification of input and output pulses Adaptive control Requires specification of an observable to be optimized Sample application: coherent quantum control, where the Hamiltonian may not be known with sufficient precision

21 Adaptive Pulse Shaping Highly chirped pulse from a Ti:sapphire laser (Interferometric Autocorrelation Data) 14 fs pulse compressed via adaptive pulse shaping (1000 iterations) Liquid crystal phase modulator controlled using a simulated annealing algorithm to maximize second harmonic generation Yelin, Meschulach, and Silberberg, Opt. Lett. 22, 1793 (1997)

22 Pulse Shaping in Amplified Systems Laser Amplifier Shaper Laser Shaper Amplifier Post-shaping Pre-shaping Introduces loss Must design to avoid damage Distortion in amplifier is independent of pulse shape Amplifier saturation mitigates loss Damage not an issue Possible pulse shape dependent nonlinear distortion In either case, the pulse shaper may be programmed to compensate distortion.

23 Programmable Pulse Shapers: Liquid Crystal Spatial Light Modulators

24 Programmable Pulse Shaping using a Liquid Crystal Modulator (LCM) Array Either phase-only (pictured here) or phase-and-amplitude shaping is possible.

25 Liquid Crystal Phase Modulator Array Input polarization along ŷ LC aligned along ŷ Voltage applied along ẑ Phase-only as well as phase-amplitude configurations available Typically 128 pixels on 100 µm centers; up to 512 pixels reported Weiner et al, IEEE JQE 28, 908 (1992)

26 Programmable Fiber Dispersion Compensation Using a Pulse Shaper Approximate dispersion compensation using matched lengths of SMF and DCF For fs applications, both dispersion and dispersion slope must be matched Fine-tuning using a pulse shaper as a programmable spectral phase equalizer

27 Higher-Order Phase Correction Using LCM Input and output pulses from 3-km SMF-DCF-DSF link Input pulse Output pulse (without phase correction) already compressed several hundred times Output pulse (with quadratic & cubic correction) Chang, Sardesai, and Weiner, Opt. Lett. 23, 283 (1998) Applied phase

28 Spectral Phase Profile from a 400-fs, 10 km Dispersion Compensation Experiment 3 Phase (π) LCM pixel number Phase can be applied modulo 2π. Quadratic, cubic, and higher order phase can be applied independently. Magnitude of phase sweep eventually limited by need to adequately sample using fixed number of pixels Shen and Weiner, IEEE PTL 11, 827 (1999)

29 Post-compensation of Pulse Distortion in a 100-fs Chirped-Pulse Amplifier SHG-FROG trace of original, phase distorted amplified pulses SHG-FROG trace after phase equalization Phase equalization compresses the pulse close to the bandwidth-limit! Brixner, Strehle, and Gerber, Appl. Phys. B 68, 281 (1999)

30 Pulse Shaping Using Phase-and-Amplitude LCM Array Independent phase and amplitude control available at each wavelength Wefers and Nelson, Opt. Lett. 20, 1047 (1995)

31 Pulse Shaping Results Using Phase and Amplitude LCM Square pulse Pulse sequence Pulse sequence with different chirp rates Time (ps) Time (ps) Time (ps) Independent phase and amplitude control allows generation of nearly arbitrarily shaped waveforms. Kawashima, Wefers, and Nelson, Annu. Rev. Phys. Chem. 46, 627 (1995)

32 Liquid Crystal Spatial Light Modulators: Summary Independent gray-level spectral amplitude and phase control Pixellated spatial modulation (128 pixels typical, 512 reported) Mask static once programmed; applicable to CW modelocked sources and to amplified systems Reprogramming time 10 ms Low attenuation ~ > Demonstrated to below 10 fs Phase and amplitude response must be calibrated.

33 Programmable Pulse Shapers: Acousto-optic Modulators

34 Programmable Pulse Shaping Using an Acousto-optic Modulator (AOM) Pulse sequence exhibiting constant, linear, quadratic, cubic, and quartic spectral phases Spectral phase and amplitude control implemented via diffraction from a modulated traveling acoustic wave Dugan, Tull, and Warren, J. Opt. Soc. Am. B 14, 2348 (1997)

35 Frequency-Swept Pulses from an AOM Pulse Shaper Experimental STRUT trace 5 Theoretical STRUT trace 5 delay (ps) 0 delay (ps) Wavelength (nm) Wavelength (nm) [ ] (1 i ) + µ Target pulse e(t) ~ sech( γt) leads to a hyperbolic tangent frequency sweep, which is visible in the STRUT traces. Fetterman, Goswami, Keusters, Yang, Rhee, and Warren, Opt Express 3, 366 (1998)

36 Acousto-optic Modulators: Summary Independent gray-level spectral amplitude and phase control Continuous spatial modulation (time-bandwidth product > 1000 available) Traveling-wave mask; generally applicable only to amplifier systems Reprogramming time ~ 10 µs (device dependent) High attenuation (acoustic nonlinearities limit operation to low diffraction efficiency regime) Demonstrated to ~ 50 fs; diffractive nature of the mask may impose minimum pulsewidth limitations (needs investigation) Acoustic attenuation must be calibrated (and compensated when possible)

37 Programmable Pulse Shapers: Movable and Deformable Mirrors

38 Rapid Scanning Optical Delay Line Based on a Pivoting Mirror Pulse Shaper ( ) τ ω = φ( ω) ω Pivoting mirror provides a linear spectral phase shift, hence a delay! π phase shift yields ~ one pulsewidth delay. 10 ps delay scan achieved at 2 khz, useful for real-time OCT. Optical phase and delay are decoupled and can be independently controlled. Origin of time-space coupling easily apparent. Kwong, Yankelevich, Chu, Heritage, and Dienes, Opt. Lett. 18, 558 (1993); Tearny, Bouma, and Fujimoto, Opt. Lett. 22, 1811 (1997)

39 Pulse Compression using a Deformable Mirror Pulse Shaper Deformable mirror consists of gold-coated silicon nitride film suspended over array of actuator electrodes Precompensation of phase distortions in a CPA leading to nearly transform-limited 15 fs pulses at 1 mj energy Zeek, Bartels, Murnane, Kapteyn, Backus, and Vdovin, Opt. Lett. 25, 587 (2000)

40 Deformable Mirror Pulse Shapers: Summary Spectral phase-only control Reprogramming time ~1 msec Low attenuation Continuous spatial modulation, 4 µm maximum deflection Demonstrated devices controlled by a 13-element (by 3 row) electrode array Best suited to applications requiring relatively weak phase-only control Adaptive control may be preferred

41 Selected Applications in Photonics and Coherent Quantum Control

42 Arrayed-Waveguide-Grating Pulse Shaper NTT A double-pass arrayed-waveguide grating with a spatial phase filter forms a nearly integrated pulse shaper. Has been demonstrated for fixed dispersion slope compensation for 2 40 WDM channels in C- and L-bands simultaneously Takenouchi, Goh, and Ishii, OFC 2001, paper TuS2

43 Applications of Pulse Shapers to WDM Ford et al, J. Lightwave Tech. 17, 904 (1999) Manipulation on a wavelength-by-wavelength basis, without concern for coherence between channels (unlike ultrafast optics) Experiments include: Multiple-wavelength add-drop switch using tilting micromirror arrays (see figure) Multiple-wavelength add-drop switch using liquid crystal arrays [Patel and Silberberg, IEEE PTL 7, 514 (1995)] Spectral gain equalizer using micromechanical amplitude modulator array [Ford and Walker, IEEE PTL 10, 1440 (1998)] Byte-parallel crossbar switching using optoelectronic smart pixel arrays [Krishnamoorthy et al, IEEE JSTQE 5, 261 (1999)]

44 Dark Solitons in Fibers Odd-symmetry pulses Even symmetry pulses Input Fiber output (low power) TIME (psec) Fiber output (at soliton power) TIME (psec) Fibers with normal dispersion support propagation of dark solitons. Fundamental dark solitons are odd-symmetry pulses (π phase shift). Experiments with shaped pulses confirm both dark soliton propagation and importance of π phase shift. Weiner, Heritage et al, Phys. Rev. Lett. 61, 2445 (1988)

45 Multi-wavelength Modelocked Diode Laser With Intracavity Pulse Shaper SOA G Wavelength tuning curves M2 DC RF DIAGNOSTICS L M1 SF Actively modelocked external cavity semiconductor diode laser Wavelength (3nm/div) Multiple wavelength bands selected via intracavity pulse shaper Each wavelength band contains a 2.5 GHz train of 12 ps pulses Synchronization between wavelength bands due to nonlinear interactions within the amplifier chip Applications to novel hybrid WDM-TDM photonics Wavelength (1.5nm/div) Shi, Finlay, Alphonse, Connolly, and Delfyett, IEEE Phot. Tech. Lett. 9, 1439 (1997)

46 Multiple-Pulse Control of Impulsive Stimulated Raman Scattering (α-perylene) Fsec pulse sequences allow selective amplification of optical phonons matched to the pulse repetition rate. (α-perylene) Weiner, Leaird, Wiederrecht, and Nelson, Science 247, 1327 (1990); J. Opt. Soc. Am. B8, 1264 (1991)

47 Effect of Sinusoidal Spectral Phase on TPA in Cesium 2 φω ( ) =αcos ω ωo φω ( ) =αsin ω 2 Anti-symmetric around ω ο /2 ω 2 o E 1 Narrowband TPA 1 Dark Pulse no TPA! Spectral phase control manipulates the interference between two photon absorption pathways Certain phase modulations yield dark pulses! Extended for enhancement of TPA with an intermediate resonance Meshulach and Silberberg, Nature 396, 239 (1998) Symmetric around ω o /2

48 Quantum Control of Photofragmentation Yields amplified Ti:S pulse LCM pulse shaper Changing the pulse shape changes the ratio of photofragmentation products. Assion et al, Science 282, 919 (1998)

49 Enhancement of Single High-order Harmonic Increase brightness by up to factor of 33 Optimized pulse only 4 fs longer than transform-limited pulse Nonlinear chirp assists in constructive interference of x-ray bursts from successive light cycles Bartels et al, Nature 406, 164 (2000)

50 New Directions in Pulse Shaping Phase filtering of broadband incoherent light, allowing manipulation of electric field coherence functions. Multi-dimensional pulse shaping Direct space-to-time pulse shaping Integrated pulse shaping devices Pulse shapers based on arrayed-waveguide-gratings Patterned fiber Bragg gratings Aperiodically poled second harmonic generation crystals Acousto-optic programmable filters

51 New Directions in Pulse Shaping (II) Pulse Shaping with Nonlinear Optics Frequency conversion to access new wavelength bands Femtosecond Source Pulse Shaper Frequency Conversion Process Results demonstrated for THz, Mid-IR Liu et al, IEEE JSTQE 2, 709 (1996) Park et al, IEEE JQE 35, 1257 (1999) Eickemeyer et al, Opt. Lett. 25, 1472 (2000) Spectral holography and spectral nonlinear optics Two or more waveforms interact in a holographic or nonlinear medium placed within a pulse shaper. This allows storage, recall, time-reversal, and correlation processing of femtosecond optical waveforms, as well as time-space and parallel-serial conversion.

52 Time-to-Space Mapping via Spectral Holography The temporal profile of the input signal pulse is converted into a spatial profile at the output. Changing the delay of the signal pulse causes the output spot observed on a CCD camera to move across the screen in real-time. Nuss, Li, Chiu, Weiner and Partovi, Opt. Lett. 19, 664 (1994).

53 Summary Synthesis of nearly arbitrary ultrafast optical waveforms under computer control via parallel spectral phase and amplitude filtering Demonstrated applications ranging from photonics to pulse compression to coherent control Opportunities for a broad range of new applications For example: active phase control of broadband fsec continuum pulses to reach the subfemtosecond regime