A germanium acousto-optic modulator was recently reported (Shim et al., Optics Letters, 31, 838, 2006) that is capable of generating phase and amplitude shaped femtosecond pulses directly in the mid-infrared. In this paper, the design, implementation and performance of this novel mid-IR shaper is described in detail as is the sub-50 fs optical parametric amplifier that provides large bandwidth for generation of complex pulse shapes. These details include the acoustic power and wavelength dependence of the deflection efficiency, the phase stability of the shaper, the synchronization of electronics, and a study on how the mid-IR bandwidth of the optical parametric amplifier depends on its optical configuration. With these details quantified, the accuracy of the device is tested by creating a series of shaped pulses that are characterized by cross-correlation with well-known mid-IR reference pulses and by simulations. Test waveforms include optimally compressed, phase-chirped and amplitude-modulated mid-IR pulses. The shaped pulses are of sufficient quality that they will enable new experiments in 2D IR spectroscopy and in the coherent control of vibrations in ground electronic states.
©2006 Optical Society of America
Multidimensional infrared spectroscopies are becoming increasingly important tools for studying the structures, environments and dynamics of molecules [1, 2]. The most common of these techniques is two-dimensional infrared (2D IR) spectroscopy, which probes molecular structures through vibrational frequencies, couplings, and transition dipole angles. Environmental dynamics are probed through lineshape analysis. These techniques are especially adept at monitoring dynamics of evolving structures or the kinetics of chemical reactions since they have both fast time-resolution (fs/ps) and good structural sensitivity. They also have potential applications as analytical tools, since cross peaks help discern mixtures of solutions or the binding between chemical species. Collecting 2D or higher dimensional spectra requires sequences of femtosecond and/or picosecond mid-IR pulses whose time delays and phases can be specified. Currently, these pulse trains are generated using beamsplitters where the delays are controlled with translation stages [3–5]. This conventional approach is sufficient to generate simple 2D IR spectra, but difficult to extend to higher dimensions or to better extract desired quantities . Extending 2D IR requires more sophisticated control over the pulse frequencies and phases. For example, recent simulations have shown that the 2D IR cross peaks can be enhanced using pulse trains composed of pulses with sophisticated chirps . Another example is work done in the near-IR, where 2D electronic spectra were collected by cycling the phases of the pulses rather than using phase matching, in analogy to the way that 2D NMR spectra are often recorded . Thus, mid-IR pulse shaping promises to advance these new multidimensional infrared spectroscopies.
In a previous letter, we reported the initial workings of a germanium acousto-optic modulator (Ge AOM) that can generate arbitrarily shaped mid-IR pulse sequences . In comparison to other mid-IR shaping techniques [10,11], this pulse shaper has superior throughput efficiency and shaping resolution because it works directly in the mid-IR. In this paper, we report details of the AOM design and performance that are necessary for precise mid-IR pulse shaping. These details include the wavelength dependence and acoustic wave amplitude dependence of the deflection efficiency. The phase stability of the shaped mid-IR pulses is also quantified, which is improved over our previous publication  using an electronic phase-locked loop circuit to synchronize the arbitrary waveform generator to the laser oscillator. More complex pulses are also made possible by quadrupling the mid-IR bandwidth generated from the attached mid-IR optical parametric amplifier. Taken together, the bandwidth, precision, and phase stability of the resulting shaped mid-IR pulses are of sufficient quality that they can be incorporated into future multidimensional infrared spectroscopies.
In the visible and near-IR spectral regions it is very common to use pulse shaping to create trains of pulses or pulses with complicated chirps. These wavelength regions access excited electronic states and can be used to optimize processes such as fluorescence, ionization and photodissociation [12–14]. Most experiments have utilized these wavelength regions the most because there exist a number of commercially available devices for shaping visible and near-IR light, including liquid crystal modulators [15,16], TeO2 acoustooptic modulators , and deformable mirrors . However, these devices do not work in the mid-IR. Liquid crystal modulators and TeO2 absorb wavelengths longer than 1.5 microns while deformable mirrors have insufficient translation for a π-phase shift beyond λ=900 nm. Shaped mid-IR pulses have been created indirectly, by shaping in the near-IR using a commercial shaper and transferring that shape to the mid-IR via difference frequency mixing [10, 11, 19, 20]. However, the nonlinearity of difference frequency mixing results in poor resolution and mid-IR intensities that strongly depend on the pulse shape and phase. As a result, indirect shaping methods have limited utility in 2D IR spectroscopy. A better way is to shape directly in the mid-IR. In this manner, intense mid-IR pulses can first be generated from transform limited near-IR pulses and then shaped with a resolution and efficiency dictated only by the design of the pulse shaper. Based on groundbreaking work in TeO2 acousto-optic pulse shaping by Warren and co-workers , our Ge AOM pulse shaper directly modulates the phase and amplitude of femtosecond mid-IR pulses, providing superior resolution and efficiency .
The complexity of the shaped pulses is limited not only by the shaper frequency and phase resolution, but also by the bandwidth of the pulses prior to shaping. For this reason, we also report the measured bandwidths and intensities of mid-IR pulses generated from systematic alterations to the configuration of our optical parametric amplifier (OPA). In this manner, the OPA can be designed for the best compromise between pulse duration and power. We have generated pulses with bandwidths exceeding 850 nm, corresponding to 43 fs pulses at 5 microns.
The layout of our optical parametric amplifier (OPA) and pulse shaper are shown in Fig. 1. The design of the OPA is similar to others [22, 23]. The OPA is pumped by 1 mJ, 45 fs transform limited pulses from a 1 kHz Ti:sapphire regenerative amplifier (Spectra-Physics) seeded by a home-built Ti:Sapphire oscillator. Downconversion of the 800 nm into signal and idler pulses (140 µJ) takes place in a type II BBO (θ=25.9°) crystal in two stages with collinear alignment. Mid-IR pulses are generated by difference frequency mixing the signal and idler beams into a type II AgGaS2, cut at θ=50.4°. The signal and idler beams are 2 mm dia. before focusing with f=30 cm spherical mirrors. The generated mid-IR beam is collimated with a spherical gold mirror. The residual signal and idler are removed by a 1-mm-thick Ge filter, which is also used to overlap a collinear HeNe alignment beam on top of the mid-IR beam path.
The pulse shaper  is aligned in a 4-f geometry using a pair of diffraction gratings (200 grooves/mm) and a pair of cylindrical mirrors (f=125mm). In this geometry the gratings, cylindrical mirrors and AOM are all separated by the focal length with the Ge AOM placed at the Fourier plane. The shaper design incorporates gratings placed in quasi-Littrow configuration and tilted in the vertical direction which allows easy adaptability to multiple light sources such as a HeNe and mid-IR . Before inserting the Ge AOM, the 4-f geometry of the cylindrical mirrors and gratings was initially set using three parallel propagating HeNe beams diffracted from the first grating with orders of 7, 8 and 9. The Ge AOM (Isomet), when placed in the Fourier plane, deflects the mid-IR at the Bragg angle of ~2° with amplitude and phase according to the acoustic wave passing through the crystal. Since the HeNe beam does not transmit through Ge, we compensate for the 2° angular deviation using the folding mirrors (FM, Fig. 1) immediately before and after the Ge AOM. The deflection also adds a linear chirp to the pulse , which was compensated by translating the second grating while maximizing the second harmonic signal (SHG) of the shaped beam through a 0.5-mm thick doubling AgGaS2 crystal (θ=33°). The AOM was designed to operate at a 75 MHz center frequency and has a bandwidth of 50 MHz. A 300 Msample/s arbitrary waveform generator is used to create an acoustic wave that propagates along the length of the AOM at 5.5 mm/µs. Given a crystal aperture of 5.5 cm×1 cm, the time aperture of the AOM is 10 µs. The frequency resolution of the shaper is dictated by the product of the time aperture and the usable RF bandwidth, which is optimally 500, but is measured to be 190 under the current focusing conditions . Tighter focusing at the crystal by either expanding the mid-IR beam or using shorter focal length cylindrical mirrors will improve the resolution. Since the acoustic wave appears static on the timescale of the ultrafast pulse traversing the Ge AOM, the acoustic wave acts as a modulated grating, deflecting desired frequencies with amplitude and phase specified by the acoustic wave. As a result, the phase of the shaped mid-IR pulses is set by the phase of the acoustic wave. Thus, for pulses with reproducible phase from one laser shot to the next, it is imperative that the arbitrary waveform generator is synchronized to the repetition rate of the laser. To accomplish this synchronization, a photodiode monitors the repetition rate of the Ti:sapphire oscillator as a reference. A divider circuit uses the resulting 88 MHz reference to generate a 1 kHz trigger pulse for both the arbitrary waveform generator and the amplifier YLF pump laser. A 300 MHz signal is also generated from the 88 MHz reference wave using a phaselocked loop circuit that serves as an external clock for the arbitrary waveform generator. This electronic configuration produces clock and trigger pulses synchronized to within 0.6 ns.
The resolution of our shaper is characterized in the time-domain by auto- and cross-correlations. The auto- and cross-correlations utilize interferometers with 2 mm-thick ZnSe beam splitters and HgCdTe detectors. The autocorrelator is constructed with a parabolic mirror and a 0.5 mm-long type I AgGaS2 (θ=33°) doubling crystal to minimize additional dispersion. The cross-correlator overlaps the shaped beam collinearly with an unshaped beam split prior to the shaper and divides the recombined beam equally onto two HgCdTe detectors for balanced heterodyne detection. Time domain scans are taken with computer controlled delay stages that translate one of two ZnSe wedged optics cut at 5±0.2 deg, changing the amount of material that the mid-IR pulses pass through . The time-resolution of this delay stage configuration is 0.02 fs. Over a 2 ps time-delay, the pulses broaden <0.16 fs due to the change in material thickness.
3. Results and discussion
Pulses used in 2D IR spectroscopy or coherent control experiments need to be intense and phase stable with large bandwidth and accurate pulse shapes. In this section, we demonstrate these capabilities. First, we report how the power and bandwidth of the mid-IR pulses depend on the OPA configuration. Second, we describe the shaper efficiency and phase stability. Finally, we report pulse shaping to optimally compress the mid-IR pulses as well as to programmably generate a variety of functional shapes. Pulse shapes were characterized with cross-correlation measurements and simulations show that their shapes are accurately produced by the programmed waveform.
3.1 Optimizing mid-IR bandwidth from optical parametric amplifier
The factors that ultimately limit the sophistication of the shaped pulses are the shaper frequency resolution, the phase resolution, and the bandwidth of the input pulse. In this section we address the latter limitation, focusing on optimizing the OPA configuration to generate the maximum bandwidth. Significant amounts of dispersion occurs when pulses of <50 fs duration pass through even small amounts of material. Furthermore, the thicknesses of the non-linear crystals must be optimized for bandwidth and power. Figure 2 shows how the MIR spectrum depends upon the components constituting our OPA. Starting with a 4 mm BBO and a 1.5 mm AgGaS2 crystal, which are typical thicknesses in mid-IR OPAs , the OPA produced mid-IR pulses with a bandwidth of 200 nm and ~4 µJ of energy (Fig. 2, blue). Since the cube polarizer (14 mm thick) that controls the white light generation stretches the 800 nm pulses from 50 to 77 fs, we began by removing the cube polarizer. This change increased the bandwidth to ~300 nm (Fig. 2, green) without altering the energy of the mid-IR (the white light continuum was instead optimized by translating the sapphire crystal along the beam focus). Turning to the crystals, we changed the 1.5 mm to a 1.0 mm thick AgGaS2 crystal which brought the bandwidth to 400 nm, again without power reduction (Fig. 2, red). Changing to a 2 mm-thick BBO instead of a 4 mm BBO (Fig. 2, cyan) did not alter the mid-IR spectrum, but the shot-to-shot stability of the mid-IR improved and the power increased (~6 µJ). The shot-to-shot stability improved because the signal and idler were no longer spontaneously generated without the white light seed present. Finally, a 0.5 mm AgGaS2 dramatically increased the bandwidth to 850 nm (Fig. 2, purple), with only a slight sacrifice of energy (~5 µJ). Thus, the largest improvements are made by proper choice of AgGaS2 crystals, which is consistent with the phase-matching bandwidths of AgGaS2 increasing inversely to crystal thickness (570, 850 and 1700 nm for crystals with thicknesses of 1.5, 1.0, and 0.5 mm, respectively). In the end, with proper selection of crystals and optics, the bandwidth could be nearly quadrupled without significant loss of intensity, corresponding to pulse durations as short as 43 fs if compressed.
3.2 Pulse shaper phase stability
One way that the pulse shaper would augment 2D IR spectroscopy is to provide one or more shaped pulses in a pulse train. In order for shaped pulses to be generally incorporated into a coherent 2D IR pulse sequence, they must be phase stable since the 2D IR signal is collected interferometrically. Interferometric stability is degraded by changes in pathlength that are usually caused by variations in mirror pointing stability. These fluctuations can be actively compensated with stabilized beampaths or passive correction [3–5]. Besides pathlength drift, phase instability can be caused by the Ge AOM electronics. Since the phase of the acoustic wave sets the phase of the mid-IR pulse, the acoustic wave must be reliably triggered to within a fraction of the 75 MHz center frequency for each laser pulse. A timing jitter of 6.7 ns would lead to randomly phased pulses. In our previous paper , the phase could not be set to better than 3.3 ns because the 300 MHz internal clock of the arbitrary waveform generator was not synchronized to the laser leading to a phase jitter of no better than λ/4 . In this report, we use the divider and phase-lock circuits described in the Experimental to generate trigger pulses and an external 300 MHz clock that are synchronized to the Ti:sapphire oscillator to within 0.6 ns. Shown in Fig. 3 is a plot of the phase stability that can be obtained with this setup. We quantified the phase stability of the shaped mid-IR relative to the unshaped mid-IR with our cross-correlator. The phase was measured by setting the delay stage to a position where the cross-correlation signal amplitude is close to zero so that the intensities are linearly related to the phase. Each point in the plot of Fig. 3 is averaged over 5 laser shots and standard deviation over the 100 second experiment gives a phase stability of λ/27. When normalized for shot-to-shot noise, this is about half the phase stability of a standard 2D IR optical setup without a shaper . Since the period of the acoustic wave corresponds to 13.3 ns, with 0.6 ns electronic jitter, we do not expect better than λ/50 phase stability. Electronic jitter might be further reduced by locking to a higher harmonic of the Ti:Sapphire oscillator. Phase drift on longer timescales can be measured and corrected .
3.3 Pulse shaper efficiency
The shaper efficiency is of paramount importance in achieving sufficient pulse energies to be of use in 2D IR and coherent control experiments [2,26,27]. Furthermore, the position dependence of the shaper efficiency needs to be measured so that pulse shapes can be accurately programmed. Shown in Fig. 4(a) is the deflection efficiency of AOM as a function of acoustic wave amplitude. The deflection efficiency scales nearly linearly with acoustic wave amplitude up to 0.5 of the maximum voltage of the arbitrary waveform generator. This linear correlation holds across the aperture. Shown in Fig. 4(b) is the AOM deflection efficiency as a function of position along the aperture for an acoustic wave amplitude of 0.5. The maximum deflection efficiency is ~70% and drops to ~50% at 1.5-cm from the end of the aperture due to divergence of the acoustic wave. In the shaped pulses that are demonstrated below, we include the aperture position and acoustic wave amplitude dependent deflection efficiencies in the algorithm to design the shaped pulses. The total power of our shaped pulses is typically ~1.5 µJ when starting from an OPA output of 5 µJ.
3.4 Chirp compensation by scanning second and third-order dispersion coefficients
Mid-IR pulses generated from the OPA are not necessarily transform-limited. Bragg deflection at the AOM also adds a significant amount of linear chirp to the pulse and the Ge AOM itself causes material dispersion . As described in the experimental section, we reduced the linear chirp by translating the second grating in the shaper to maximize the SHG of the shaped beam using a AgGaS2 crystal, taking advantage of the fact that the 4-f shaper is essentially a grating-pair compressor. Following grating optimization, we use the AOM to refine the linear chirp compensation as well as compensate for higher order phase distortions in the pulses. In fact, in order to program pulses with well-defined shapes, it is essential to first remove the phase distortions of the input pulses. The phase of the electric field in the frequency domain can be written:
where ϕ n are the dispersion coefficients, each of which can be independently varied using the Ge AOM. To create transform limited pulses, we varied the 2nd and 3rd-order dispersion coefficients (ϕ 2 and ϕ 3) while recording the resultant SHG signal, shown in Fig. 5(a). The optimum values resulting in the maximum SHG were ϕ 2=0.06 ps2 and ϕ 3=0.06 ps3, which corresponds to the shortest pulse duration. With these optimum coefficients, the duration measured from the autocorrelation in Fig. 5(c) was reduced to 69±7 fs from 96±7 fs in Fig. 5(b). While this process produces transform limited pulses, the pulse duration is not as short as might be expected from the bandwidth of the pulses emitted directly from the OPA (Fig. 2) because the deflection efficiency of the shaper effectively reduces the pulse bandwidth (Section 3.3, above).
3.5 Characterization of unshaped pulses by autocorrelation
For the remainder of this paper we characterize the shaped pulses by cross-correlating them with the unshaped pulses which act as a reference. If the reference pulses were infinitely short in duration, this would permit a perfect characterization of the shaped pulse electric field. In practice, the unshaped pulses are finite duration and are emitted from the OPA slightly chirped, as described above, which distorts the resulting cross-correlation trace. In this section we characterize the phase distortion of the unshaped pulses using a technique called modified-spectrum autointerferometric correlation (MOSAIC) . These phase distortions are then included in simulations of the cross-correlations discussed in the following sections.
Figure 6 shows the spectrum, autocorrelation, and MOSAIC traces for the unshaped mid-IR pulses prior to the shaper (Fig. 1). The measured duration is 53±2 fs from the fwhm of the 2nd-order autocorrelation in Fig. 6(b). Although the wings present in the autocorrelation are a clear sign of chirp, the autocorrelation alone is not sensitive enough to quantify the phase distortions. To retrieve the temporal amplitude and phase information from femtosecond pulses, it is common to use interferometric methods such as FROG, SPIDER and GRENOUILLE [29–31]. These measurements involve elaborate experimental setups that are difficult to implement in the mid-IR where the laser beams are invisible. Furthermore, these techniques require mid-IR array detectors or up-conversion with 800 nm pulses that is not trivial at wavelengths longer than 5 microns. The MOSAIC algorithm has recently shown that linear and nonlinear chirp can be determined accurately from conventional 2nd-order interferometric autocorrelation traces . MOSAIC reshapes autocorrelation traces numerically by spectral filtering. It produces two curves, which are depicted in Fig. 6(c) for the autocorrelation of Fig. 6(b). The lower envelope contains chirp information, while the upper trace conveys pulse duration only. We fit the MOSAIC envelopes assuming a laser pulse having an electric field given by E(ω)=Ẽ(ω)exp[iϕ(ω)] where Ẽ(ω) is the square root of the corresponding spectrum [Fig. 6(a)] and ϕ(ω) is expanded as in Eq. (1). The coefficients ϕ 2 and ϕ 3 are adjusted to fit. The theoretical MOSAIC envelopes shown in Fig. 6(c) were calculated with ϕ 2=±0.0763 ps2, ϕ 3=∓0.0246 ps3 and the others set to zero. To determine the signs of ϕ 2 and ϕ 3, we measured the cross-correlation (not shown) between the unshaped beam and the transform limited pulse from the shaper described in Section 4 above, giving ϕ 2=0.0763 ps2 and ϕ 3=-0.0246 ps3. Simulations shown below used these parameters to convolute the unshaped pulses and simulate the measured cross-correlations.
3.6 Phase and amplitude pulse shaping
With the shaped and unshaped pulses characterized, we now generate a variety of pulse shapes and measure them with cross-correlations. As examples, we focus on shapes that are useful in mid-IR coherent control and 2D IR spectroscopies. We converted the cross-correlation traces to 2-dimensional time/frequency representations by Winger transformation,
which give the time-evolution of the pulse frequency. Figure 7 shows Wigner plots from cross-correlations for various shaped pulses created from a range of ϕ 2, ϕ 3 and ϕ 4 dispersion coefficients. In Figs. 7(a) to 7(c), Wigner plots are given for experimental and simulated pulses that are linearly chirped with ϕ 2=-1.0 ps2. Negative linear chirps are useful for populating highly excited vibrational states because the frequency sweep can be made to match the energy spacing between vibrational levels in anharmonic potentials. Although linear chirps can be easily generated using either a pair of gratings or materials, complex shapes may be more efficient at ladder climbing . Figures 7(d) through 7(i) show higher-order chirped pulses, generated with ϕ 3=-0.5 ps3 and ϕ 4=0.2 ps4, respectively.
Notice that the Wigner diagram of the linearly chirped pulse in Fig. 7(a) is slightly curved. This deviation from linearity is not caused by the shaped pulse, but is a consequence of the chirped unshaped pulse used in the cross-correlation. Shown in Fig. 7(b) is a simulation of the cross-correlation calculated with the chirp in the unshaped reference beam that was characterized in Sect. 3.5. The simulated Wigner diagrams agree reasonably well with the experimental plots. Also shown in Fig. 7(c) is the Wigner diagram that would appear if the reference pulse were transform limited, revealing that the deviation from linear chirp is indeed caused by the imperfect reference pulse. Simulated Wigner diagrams are also shown for the higher order chirped pulses (Figs. 7(e)–7(f), 7(h)–7(i)).
Nonlinear spectroscopies, such as 2D IR spectroscopy, rely on trains of pulses with controllable phases and time delays. These pulse trains are conventionally created using beam splitters, but pulse shaping has the potential of generating arbitrary numbers of pulses with control over the envelope and phase of each pulse. Here, we create a double pulse train with variable time-delay and relative phase. Double pulse trains are the simplest example of a pulse shape created by modulating the input beam intensity. Figure 8(a) shows the Wigner diagram from the cross-correlation of two pulses with a time interval of 500 fs. Once again, slight distortions are created in the measured cross-correlation by the chirped reference pulse supported by simulations in Figs. 8(b) and 8(c). Since the time-dependence of the shaped pulse is related to the AOM acoustic wave by a Fourier transform, the period and phase of sinusoidal modulation on the acoustic wave intensity sets the time spacing and relative phase between the two pulses. Thus, the AOM resolution sets the maximum time delay and minimum step size that can be taken. With a frequency resolution of 500, it should be possible to generate delays as large as 35 ps. Control over the relative phase between two pulses was demonstrated in our previous paper and had a precision of 0.008π rad . With good control over the delay and phase of double pulses, our mid-IR shaper should be useful in phase cycling experiments .
Mid-IR pulse shaping has been previously limited to simple linear chirps using material or gratings and to indirect shaping methods with low resolution and power [10,11,19,20]. Although simply shaped, applications of these pulses demonstrated vibrational ladder climbing and optimized pulse compression [26,34]. In this paper, we demonstrated pulse shaping directly in the mid-IR using a Ge AOM with high efficiency and resolution. We generated a series of phase and amplitude pulses, the accuracy of which is tested with simulations. Phase-stable mid-IR shaping could be used in multidimensional IR spectroscopies to map solution phase potentials, monitor energy transfer, and study solutesolvent interactions. In fact, simulation studies suggest that well-designed pulses can populate certain high vibrational modes , control intra- and inter-molecular proton transfer [1,36–38], control electron transfer through vibrational excitation , and direct isomerization . Considering that 2D IR experiments are usually carried out with <1 µJ of power  and that vibrational populations have recently been inverted with only 2.2 µJ , it stands to reason that this new shaper promises to open a new class of experiments geared to understanding and optimizing ground state control.
This work is supported by the Packard Foundation, the National Science Foundation, and the Beckman foundation. S.-H. Shim acknowledges the Kwanjeong Educational Foundation for a fellowship.
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