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Spatiotemporal Coherent Control of Lattice Vibrational Waves

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Science  17 Jan 2003:
Vol. 299, Issue 5605, pp. 374-377
DOI: 10.1126/science.1078726

Abstract

We achieved automated optical control over coherent lattice responses that were both time- and position-dependent across macroscopic length scales. In our experiments, spatiotemporal femtosecond pulse shaping was used to generate excitation light fields that were directed toward distinct regions of crystalline samples, producing terahertz-frequency lattice vibrational waves that emanated outward from their multiple origins at lightlike speeds. Interferences among the waves resulted in fully specified far-field responses, including tilted, focusing, or amplified wavefronts. Generation and coherent amplification of terahertz traveling waves and terahertz phased-array generation also were demonstrated.

Ultrafast optical control over electronic and/or vibrational responses of atoms, molecules, and crystals has advanced dramatically in recent years (1–8). Experiments in this field have typically been conducted with femtosecond pulse shaping techniques (9) for generation of complex excitation light fields that yield specified coherent responses or that manipulate complex phenomena such as photochemical reactions. Typically, these light fields, as well as the material responses generated by them, are specified as a function of time but not of macroscopic spatial location. For ultrafast responses that move coherently across macroscopic distances, more complete optical control over both spatial and temporal evolution requires the use of time- and position-dependent excitation fields. Here we demonstrate versatile, programmable, spatiotemporal coherent control over terahertz-frequency lattice waves that propagate at lightlike speeds through crystalline solids. This capability may find application in the multiplexed generation of tailored terahertz signals that could be propagated and used inside or outside the crystalline sample in which they were generated.

The lattice coherences manipulated in our experiments are phonon-polariton waves, which are admixtures of polar lattice vibrations (transverse optic phonons) and electromagnetic waves (10). A femtosecond excitation laser pulse exerts a sudden (“impulse”) driving force on the crystal through impulsive stimulated Raman scattering (ISRS) (11), launching coherent vibrations that propagate at lightlike speeds (about one-sixth the speed of light, c) away from the excitation region. Recently developed methods in spatiotemporal femtosecond pulse shaping (12, 13) were used to transform a single 800-nm pulse of 50-fs duration into an array of such pulses, arriving at different times and different locations in a lithium tantalate (LiTaO3) single crystal. Vibrational waves were thereby created at multiple programmably specified times and points of origin in such a way that after some propagation, the waves began to overlap and undergo constructive or destructive interference to produce spatiotemporally controlled responses. The initial lattice vibrational amplitudes and phases at each point of origin were fully specified through spatiotemporal shaping of the optical intensity profile, because the ISRS excitation process is governed by the optical intensity and not the optical phase (11).

Real-space images of the propagating waves were recorded at different times by probe pulses that were variably delayed with respect to the excitation pulses. Spatiotemporal imaging (14,15) of phonon-polaritons in this manner is possible because of the substantial refractive index changes induced by the lattice vibrational displacements. The excitation pulses, probe pulses, and phonon-polariton electric fields were all polarized along the optic axis of a 2-mm-thick LiTaO3 crystal at 295 K. An amplified, 1-kHz repetition rate Ti:sapphire laser system was used, and after pulse shaping, a total of 10 to 50 μJ of energy was typically distributed among all of the excitation pulses. For all experiments, the crystals were kept at 295 K. The phonon-polaritons had frequencies in the 0.2- to 2-THz range, and their phase and group velocities were approximately constant at c/6.4 (16). Thus, the lattice waves we generated propagated coherently at about one-sixth the speed of light in vacuum, and even single-cycle waves with terahertz bandwidths showed negligible spreading or loss of bandwidth as they moved across millimeter distances over durations of tens of picoseconds. The excitation and detection processes are illustrated schematically in Fig. 1.

Figure 1

Schematic illustration of the spatiotemporal coherent control experiment. A single beam with a single femtosecond pulse is transformed by the pulse shaper into many excitation beams and pulses that reach specified sample locations at specified times. These launch lattice phonon-polariton waves that move through the sample at lightlike speeds, superposing coherently to form a far-field response that is dictated by the excitation spatial and temporal profiles. Variably delayed probe pulses are passed through the sample and projected onto a charge-coupled device camera to monitor the phonon-polariton spatial and temporal evolution.

Phonon-polariton responses to excitation light fields consisting of one, two, four, and nine spots oriented along a line parallel to the LiTaO3 optic axis are illustrated in Fig. 2. Each spot received just one excitation pulse, and all of the excitation pulses arrived at the same time (t = 0). Near to the optical excitation sources (i.e., in the near field), the separate wavelets can be independently observed and monitored. After some propagation, which occurs preferentially in the direction perpendicular to the polarization, constructive and destructive interferences begin to occur among wavelets that originated from different sources. Finally, in the far field, the superposition is complete and results in a phonon-polariton wavefront whose properties are dictated by both the spatial and temporal features of the shaped optical excitation waveform. In the case of nine-pulse excitation, the near-field response is too short lived to view here. Experiments were conducted with up to 50 distinct excitation spots. All figures contain excerpts from far more complete sets of images that, when viewed in rapid succession, appear as “movies” of phonon-polariton propagation (15).

Figure 2

Phonon-polariton spatiotemporal coherent control. Responses to impulsive excitation with (A) one, (B) two, (C) four, and (D) nine excitation regions are shown. The time delay between successive frames is 6.7 ps. Phonon-polariton responses moving from left to right are shown. Their counterparts moving in the opposite direction are not shown. arb., arbitrary.

Programmable manipulation of the far-field wavefront is illustrated inFig. 3. By varying the times at which excitation pulses arrive at distinct spots (Fig. 3, left), different control objectives, including wavefront tilting, focusing, and the direction of responses toward specified sample regions, or “addresses,” were achieved. For example, a linear delay sweep in the excitation waveform generated a phonon-polariton plane wavefront with a downward tilt (Fig. 3A), whereas the superposition of a linear and a parabolic delay sweep produced phonon-polaritons that focused about a millimeter away from the excitation region with either an upward or a downward tilt (Fig. 3, B and C, respectively). This type of terahertz phased-array generation is reminiscent of array sources that are ubiquitous in radar and ultrasound technologies (17), which operate at far lower frequencies. The single-cycle phonon-polariton responses propagate with no measurable dispersion across macroscopic distances, in agreement with the simulations shown in the bottom panels of Fig. 3, A to C (18, 19). Although single pulses were used at each excitation region, multiple pulses or complex time-dependent waveforms could be used, permitting, for example, periodic excitation at each spot with the far-field wavefront manipulated through phase or frequency scanning as well as the time-delay scanning illustrated here.

Figure 3

Phonon-polariton phased-array generation. Responses to excitation pulses with specified arrival times and sample locations are shown. The top panels in each row show experimental results, and the bottom panels show the corresponding simulations. The panel to the left of each row illustrates the type of excitation waveform used in each case. (A) Tilted phonon-polariton wavefronts resulting from four pulses arriving at the sample at progressively later times, with a linear relation between temporal delay and the spatial location of the spot. The direction of propagation depends on the slope of temporal delay versus position in the excitation waveform. (B) and (C) Phonon-polariton focusing plus steering specified through a parabolic-plus-linear relation between temporal delay and the spatial location of ∼50 spots.

Further spatiotemporal coherent control schemes allow for coherent manipulation of a propagating response by an excitation field that moves along with it through the sample. In Fig. 4A, the coherent addition of phonon-polariton wave packets as they propagate through the host crystal is demonstrated. The output of the pulse shaper is cylindrically focused so that each beam reaches a vertical “line” that is ∼1 mm high and 50 μm wide at the sample. The ∼20 beams are separated horizontally, and the time between pulses is delayed so that the pulses move from left to right across the crystal at a speed that matches the phonon-polariton group velocity. The phonon-polariton response generated by the first excitation pulse and traveling to the right is thereby amplified by successive excitation events, yielding an ∼10-fold increase in phonon-polariton amplitude and an ∼100-fold increase in intensity. By comparison, the data also show left-propagating responses that originate from each excitation region and that are not amplified and appear much weaker.

Figure 4

Phonon-polariton generation and amplification. (A) Amplification is realized by a series of “line” sources moving from left to right at a rate that matches the phonon-polariton group velocity. The last excitation pulse arrives before the fourth frame. Thereafter the amplified response continues moving to the right. Phonon-polariton amplification is shown as a function of (B) the delay between two regions and (C) the number of amplifying beams.

A systematic scan of the delay time between adjacent excitation regions corroborates that the amplification is maximal when the group velocity of the propagating phonon-polariton wave packet is properly matched. In Fig. 4B, the maximum is found at a sweep velocity of 50 ± 10 μm/ps, which is in agreement with the group velocity of 47 μm/ps (20) for the experimentally determined central wave vector of 420 cm−1. The gain as a function of the number of excitation pulses is illustrated in Fig. 4C and demonstrates that substantial terahertz wave amplification may be accomplished through spatiotemporal coherent control. In conjunction with internal or external terahertz focusing elements, our results permit large-amplitude phonon-polariton wave packet generation. A comparable amplitude is not achievable with just a single excitation pulse, because its intensity would be well above the damage threshold of the crystal. Although the principle of constructive addition of phonon-polaritons has been demonstrated previously with just two manually adjusted pulses (21), a prior attempt at multiple-pulse constructive addition produced barely detectable results because of an incompletely developed pulse-shaping apparatus (22).

Our results also demonstrate extensive control over terahertz electromagnetic waves, either inside the crystal or in free space after the waves emerge from a crystal edge. In this respect, our results extend previous efforts at control over terahertz radiation with temporal-only shaping of ultrafast light fields to irradiate single or multiple terahertz sources (23–25). These results also point toward spectroscopic applications, including the programmable steering of phonon-polaritons into integrated terahertz waveguide structures (26) for multiplexed, waveguide-based, terahertz spectroscopy measurements. The generation of amplified and focused high-intensity phonon-polaritons may enable nonlinear terahertz spectroscopy and control of nonlinear lattice dynamics, anharmonic crystals near structural phase transitions, or liquid-state intermolecular dynamics (27).

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