Lecture 27: Ultrafast Pulse Shaping

Transcription

1 ECE-616: Fall 2011 Lecture 27: Ultrafast Pulse Shaping Professor Andrew Weiner Electrical and Computer Engineering Purdue University, West Lafayette, IN USA 11/22/11 Lundstrom ECE-656 F11 1

2 Ultrafast Pulse Shaping Andrew M. Weiner Purdue University A few references Tutorial talk at CLEO 2010: "Femtosecond Pulse Shaping Using Spatial Light Modulators, A. M. Weiner, Review of Scientific Instruments, 71, (2000). "Ultrafast Optical Pulse Shaping: A Tutorial Review," A. M. Weiner, Optics Communications, 284, (2011).

3 Femtosecond Pulse Shaping Spectral Dispersers: Gratings Prisms VIPAs AWGs 4f configuration inherently dispersion-free Fourier synthesis via parallel spatial/spectral modulation Diverse applications: fiber communications, coherent quantum control, few cycle optical pulse compression, nonlinear microscopy, RF photonics Pulses widths from ps to few fs; time apertures up to ~1 ns Review article: A.M. Weiner, Rev. Sci. Instr. 71, 1929 (2000)

4 Dispersion-free Pulse Transmission through 4f Shaper 48 fs Input Output Weiner, Heritage, and Kirschner, J. Opt. Soc. Am B 5, 1563 (1988).

5 Reflective Pulse Shaper Collimator Grating Mirror LCM Lens Reduced size & component count Insertion loss as low as ~4 db (including circulator!) R.D. Nelson, D.E. Leaird, and A.M. Weiner, Optics Express (2003)

6 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).

7 Synthesis of Femtosecond Square Pulses Shaping via microlithographic amplitude and phase masks Amplitude mask: gray-level control via diffraction out of zero-order beam Cross-correlation data Power spectrum Theoretical intensity profile Weiner, Heritage, and Kirschner,J. Opt. Soc. Am B 5, 1563 (1988).

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

9 Intentionally Generated Noise Bursts Using Femtosecond Pulse Shaping π/2 -π/2 Pseudorandom phase pattern applied to spectrum of 100 fs pulses Intensity autocorrelations Pseudonoise intensity profiles (intensity cross-correlation technique) Weiner, Heritage, and Kirschner, J. Opt. Soc. Am B 5, 1563 (1988).

10 Shaping of Incoherent and Nonclassical Light Incoherent Light: Shaping the elec. field cross-correlation function ASE source (EDFA) Pulse shaper No shaping PD Spectrum & spectral phase Nonclassical Light: Shaping the two-photon wave function Entangled photon source (parametric down-conversion) Pulse shaper Ultrafast coincidence detector (sum frequency generation) Signal Idler Signal Idler Linear spectral phase Wavelength (nm) Sum frequency counts Wavelength (nm) Delay (ps) Wang and Weiner, Opt. Comm. 167, 211 (1999) Signal-idler delay (fs) Pe er, Dayan, Friesem, and Silberberg, Phys. Rev. Lett. 94, (2005) Signal-idler delay (fs)

11 Programmable Pulse Shapers: Spatial Light Modulators

12 Fourier Transform Pulse Shaping A variety of programmable modulator arrays Nuernberger, Vogt, Brixner and Gerber, Phys. Chem. Chem. Phys. 9, 2470 (2007)

13 Programmable Pulse Shaping Liquid Crystal Modulator (LCM) Arrays Weiner et al, IEEE JQE 28, 908 (1992) Wefers and Nelson, Opt. Lett. 20, 1047 (1995) One layer LCM: phase-only shaping Two layer LCM: independent amplitude and phase shaping ~ nm typical wavelength range - recently extended to 260 nm in the UV [(Tanigawa et al, Opt. Lett. 34, 1696 (2009)] Tens of milliseconds response time

14 Liquid Crystal Modulator Array (LCM) 1-layer LCM schematic No applied voltage With applied voltage Longitudinal field tilts molecules, changing birefringence Typically pixels on 100 µm centers Phase vs. voltage response 1-layer LCMs: input polarization (ŷ) aligned with LC molecules (ŷ) for phase-only response 2-layer LCMs: input polarization (ŷ) vs. 45 for LC molecules for phase-amplitude response Phase change 2π 0 10 Voltage (rms)

15 Pulse Shaping Results Using Phase and Amplitude (2-Layer) 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)

16 RF arbitrary waveform generator Programmable Pulse Shaping Acousto-optic modulators (AOM) Vibrates and changes refraction index Spectral amplitude-phase shaping via diffraction from a traveling acoustic wave Traveling-wave mask; generally applicable only to amplifier systems; reprogramming time ~ 10 µs (device dependent) Electronic arbitrary waveform generator provides amplitude-phase control, but care needed to account for acoustic attenuation and nonlinearities Dugan, Tull, and Warren, J. Opt. Soc. Am. B 14, 2348 (1997)

17 Programmable Pulse Shaping Acousto-optic modulators (AOM) ~800-nm pulse sequence exhibiting constant, linear, quadratic, cubic, and quartic spectral phases Mid-IR pulse shaping using Ge AOM RF drive Spectrum Dugan, Tull, and Warren, J. Opt. Soc. Am. B 14, 2348 (1997) 260 nm 5 µm demonstrated wavelength range Shim, Strasfeld, Fulmer, and Zanni, Opt. Lett. 31, 838 (2006) Continuous spatial modulation (time-bandwidth products of several hundred)

18 ULTRAFAST OPTICS AND OPTICAL FIBER COMMUNICATIONS LABORATORY Acousto-optic Programmable Dispersive Filter (AOPDF) An in-line pulse shaping technology especially for amplified systems Phase matched polarization conversion mediated by acoustic wave Due to birefringence, output temporal profile related to acoustic spatial profile (controlled by radio-frequency arbitrary waveform generator) Representative numbers: 2.5 cm TeO 2 crystal, n 2 -n 1 =0.04 Acoustic velocity: 10 5 cm/s Acoustic frequencies: 20 MHz around 52.5 MHz Optical frequencies: 150 THz around 375 THz (800 nm) Time aperture for pulse shaping: 3.3 ps Acoustic transit time: 25 µs Verluise, Laude, Cheng, Spielmann, and Tournois, Opt. Lett. 25, 575 (2000)

19 Results from Pulse Shaping Theory

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

21 The Complexity of a Shaped Pulse spectral resolution ~ 1/time aperture (T) bandwidth time aperture pulse duration ~ 1/bandwidth (B) Time-bandwidth product (BT = B/δf = T/δT) provides a measure of potential complexity of a shaped pulse Equal to # of independent features in either frequency or time domain Favors large optical bandwidth / very short pulses Spectral resolution (and time aperture) limited by minimum SLM feature size, finite optical spot size (related to the resolution of a grating spectrometer!)

22 Pulse Shaping Masks: Intensity Gray-level masks utilizing diffraction (square pulse generation example)

23 Same Intensity Mask Out of Focus Image Emulates what happens in the actual pulse shaper: importance of spectral resolution

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

25 Pulse Shaping Theory: Effect of Diffraction 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 e out (t) ~ e in (t) m(t / α)exp wot /8α Spectral smearing due to finite spot size time window Equivalent to a window function in the time domain Thurston, Heritage, Weiner, and Tomlinson, IEEE JQE 22, 682 (1986); A.M. Weiner, Ultrafast Optics (Wiley, 2009)

26 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)

27 Selected Applications

28 Applications in Optical Communications Dynamic spectral processor Spectral disperser Spectral combiner Broadband input - Ultrashort pulse - CW plus modulation Processed output - Multiple wavelengths Spatial light modulator Control of phase, intensity, polarization Frequency-by-frequency, independently, in parallel -Pulse shaping -Dynamic spectral equalizers -Dynamic wavelength processing

29 Pulse Shaping in WDM: Intensity Control Manipulation on a wavelength-by-wavelength basis No concern for phase or for coherence between channels Wavelength selective add-drop multiplexer (and wavelength selective switches) Ford et al, J. Lightwave Tech. 17, 904 (1999) [Lucent] Spectral gain equalizer MEMS version Liquid crystal version: Patel and Silberberg, IEEE PTL 7, 514 (1995) Ford et al, IEEE JSTQE 10, 579 (2004) [Lucent]

30 Programmable Fiber Dispersion Compensation Using a Pulse Shaper: Subpicosecond Pulses Spectral phase equalizer Coarse dispersion compensation using matched lengths of SMF and DCF Fine-tuning and higher-order dispersion compensation using a pulse shaper as a programmable spectral phase equalizer Similar ideas apply to DWDM tunable dispersion compensation and few femtosecond pulse compression. A.M. Weiner, U.S. patent 6,879,426 ( ) τω= ψ( ω) ω

31 Higher-Order Phase Equalization Using LCM Input and output pulses from 3-km dispersion-compensated link Input pulse Output pulse (without phase correction) already compressed several hundred times Output pulse (with quadratic & cubic correction) No remaining distortion! Chang, Sardesai, and Weiner, Opt. Lett. 23, 283 (1998) Applied phase

32 Intensity cross-correlation (a.u.) 460 fs transmission over 50 km SMF Commercial DCF module (as is) with spectral phase equalizer without DC by pulse shaper second-order DC by pulse shaper both second- and thirdorder DC by pulse shaper Essentially distortion-free! Time (ps) Phase (rad) π π (A) (B) Pixel # ~ 5 ns after SMF 13.9 ps after DCF 470 fs after quadratic/cubic phase equalization Z. Jiang, Leaird, and Weiner, Opt. Lett. 30, 1449 (2005) 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

33 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)

34 Quantum Control of Two Photon Absorption in Cesium 2 Sinusoidal spectral phase ψ( ω ) =αcos ω ωo ψ( ω ) =αsin ω 2 Anti-symmetric around ω ο /2 ω 2 o E 1 Narrowband TPA 1 Dark Pulse no TPA! Shaping spectral phase to manipulate interference between two photon absorption pathways for creation of user selectable dark or light pulses Similar effects occur in second harmonic generation later applied for MIIPS pulse measurement technique Meshulach and Silberberg, Nature 396, 239 (1998) Symmetric around ω o /2

35 High Power Pulse Compression in the 5-fs Regime MIIPS traces pre compensation post compensation Phase scan (rad) Compression results Pulse shaper used both for measurement* and compensation! *Multiphoton intrapulse interference phase scan (MIIPS) -e.g., Xu, Gunn, Dela cruz, Lozovoy and Dantus, JOSA B 23, 750 (2006) Wang, Wu, Li, Mashiko, Gilbertson, and Chang, Optics Express 16, (2008)

36 Ultrabroadband Radio-Frequency Photonics RF Arbitrary Waveform Generation 1.2/2.5/4.9 GHz FM Waveform 48/24 GHz FM Waveform RF THz Phase Modulation Optical Time (ns) Time (ps) Exploitation of optical pulse shaping technology for cycle-by-cycle synthesis of arbitrary RF waveforms beyond the speed of electronics solutions Approach scales from Gigahertz to Terahertz

37 Impulse Excitation of Frequency-Independent Antennas Precompensation of antenna dispersion McKinney, Peroulis, and Weiner, IEEE. Trans. MTT 56, 710 (2008) Input voltage Impulse ~195 ps Output voltage Chirped: ~2.17 ns Predistorted Compressed ~264 ps