1. Introduction

High resolution pulse shaping capabilities exist for wavelengths ranging from the visible to the near-infrared (NIR) [1, 2]. Extensions of high-power pulse shaping to the mid-infrared (MIR) and ultraviolet (UV) regions would have immediate applications in coherent control, spectroscopy and imaging. However, direct arbitrary phase and amplitude pulse shaping in these regimes is difficult. Liquid crystal modulators absorb in the UV and MIR; acousto-optic materials such as quartz and TeO₂ absorbs in the UV. Germanium, as an acousto-optical material though transparent in the MIR, has a low radio frequency bandwidth and hence limited modulation resolution.

One solution to the problem of modulator material limitations is to shape pulses in the visible or near-infrared wavelengths to control the shape of a pulse of another wavelength via a nonlinear optical process. There have been some recent successes in this approach. Phase locked pulse trains at about 14µm with a fixed delay have been created using difference frequency mixing of shaped NIR pulses in a GaSe crystal [3]. Adjustable linear frequency chirped pulses at similar wavelengths have also been produced by optical rectification process in GaAs using 800nm ultrashort pulses [4]. The shaped pulse energy produced from the two above mentioned experiments are in the fJ-pJ range. Witte and co-workers demonstrated programmable pulse shaping (~ 1µJ) in the 3–8µm regime using difference frequency mixing in a AgGaS₂ crystal between two shaped NIR pulses [5]. However, the mixing of two pulses of similar bandwidth places limitations on the resolution of shaped pulses that can be produced. We have recently shown that the optical parametric amplification of a broadband visible shaped signal pulse, pumped by a narrow spectral bandwidth pulse will parametrically force the NIR idler pulse to acquire the shape of the shaped visible signal pulse with high fidelity [6].

In this paper, we report that complicated (amplitude and phase modulated) microjoule energy MIR pulses can be manufactured from the amplification of NIR narrow bandwidth pulses with an arbitrarily shaped 800nm pump pulse using a KNbO₃ based OPA process. This offers the advantage of a fixed wavelength pulse shaping apparatus.

2. Theory

The OPA process can be described by the coupled wave equations [7]. In particular, the generation of the idler pulse of electric field E_i (z,ω) in the frequency domain is described by

The shape of the generated idler pulse is a convolution between the pump and the signal pulse. If the shape of the pump pulse is a near delta function in frequency domain E _p(ω)~δ(ω-ω_p), the idler will acquire the amplitude profile of the signal pulse with the conjugated phase profile reflected along the difference frequency between the pump and signal center frequency (ω _p and ω _s respectively).

Here the signal field E_s (ω) is centered at ω _s . In practice, this condition is close to being satisfied if the bandwidth of the shaped signal pulse is significantly greater than that of the pump (henceforth, we shall label the narrow bandwidth pulse as the spectral gate pulse), as was the case for a NOPA configuration [8, 9, 10], where in an earlier proof-of-principle experiment to transfer the shape of a visible signal pulse onto a NIR idler pulse, the ratio of the signal pulse to pump pulse is in excess of 10:1 [6]. In a previous work [11], we applied a similar scheme to a collinear potassium niobate based OPA (type I, 1mm) pumped at 800nm. The ratio of the bandwidth of the pump pulse to the signal amplification bandwidth was 1:4 leading to severe limitation in resolution of the transferred pulse shape. The ratio can be improved by reducing the bandwidth of the pump pulse. However, this would also reduce the energy source for the process, hence reducing the efficiency of the process.

We report in this article the results of using an alternative approach to create shaped pulses in the MIR. To achieve pulse shape transfer, one can also use the signal beam as the spectral gate in an OPA process to transfer the pump pulse shape onto the idler (i.e., E_s (ω) ~ δ(ω-ω _s )). Equation (1) becomes

In this case, since the spectral gate is not the energy source for the OPA process, the spectrum of the signal can be reduced to increase the resolution of the shape transfer without much compromise to the efficiency of the nonlinear optical process. Another advantage of this scheme is that the shaped pulse wavelength tunability is achieved by controlling the wavelength of the spectral gate pulse instead of adjusting the delicate optics in the pump pulse shaper.

3. Experimental

The experimental setup is depicted in Fig. 1. We split a source beam at 800nm (~150fs duration, 0.5mJ energy per pulse) into two. The first portion of ~ 200µJ is sent to a acousto-optic pulse shaper (AOPS). We sent the second portion of ~ 300µJ to the first stage collinear OPA (OPA1). The modules that make up the rest of the setup consist of a NIR spectral gate (SG) that narrows the NIR pulse bandwidth out of OPA1 and a second stage collinear OPA (OPA2) that produces the idler shaped pulse from the shaped pump and the NIR seed signal pulse from the SG.

The AOPS consists of a 4-f configuration [1, 2]. The spectral components of the 150fs pulse are spatially dispersed by a 1400 lines/mm diffraction grating. They are then collimated by a f=46cm spherical mirror and the spectral spread of the pulse is mapped spatially in the fourier plane. On this plane is positioned an acousto-optical modulator (4.0cm long, 1.2cm thick TeO₂ crystal). Arbitrarily crafted radio frequency pulses generate acoustic waves along the AOM crystal axis creating a momentary diffraction grating. The first order diffraction of the beam acquires amplitude and phase modulation as dictated by the crafted RF pulse. The second set of spherical mirror and diffraction grating recombines the modulated spectrum to give the shaped pulse.

The beam directed to OPA1 is split into two. The first part (~2µJ) is focused onto a 2mm thick sapphire window to generate a stable single mode whitelight supercontinuum pulse. A second harmonic generation process (BBO-type I; 0.5mm) converts the second part of the beam to give a pulse at 400nm (~150fs, 80µJ). Controlling the relative delay between the supercontinuum pulse and the 400nm pump pulse controls the wavelength of the signal and idler pulse output in a collinear OPA process (BBO-type I; 4mm). The pump and idler pulses are sent through the BBO crystal for a second pass to obtain an idler pulse in the NIR wavelengths tunable from ~960–1250nm. Between 1050 to 1100 nm, we obtain a pulse energy of ~4µJ. We use a spectral gate (SG) to reduce the bandwidth of the NIR pulse. The SG is a 4-f setup with a 840 lines/mm diffraction grating and a f=12cm lens. At the Fourier plane, we place a plane mirror and an adjustable slit to control the NIR pulse bandwidth. We amplify this NIR seed signal pulse with the shaped pump pulse in a second collinear OPA process (KNbO₃-type I; 2mm). Shaped MIR idler pulses (1–2µJ) are generated in this OPA process. The wavelength of the shaped idler pulses can be tuned easily by translating the slit in the spectral gate (SG). This increases the ease of usage since the delicate alignment of the pulse shaping apparatus at 800nm need not be adjusted when changing from one MIR shaped pulse wavelength to another.

 

Fig. 1. Experimental setup of mid infrared pulse shaper. OPA: Optical parametric amplifier, AOPS: Acousto-optic pulse shaper, AWG: Arbitrary waveform generator (radio frequency), 2HG: Second harmonic generation, WL: White light continuum generation, P: Periscope to change polarization, D: Delay stage, SG: Spectral gate.

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We use frequency resolved optical gating (FROG) [12] and its variations to characterize our shaped pulses. Second harmonic generation (SHG) FROG is used to characterize our shaped pump and signal pulse. To characterize the shaped MIR pulses, we use a new variation of FROG which we named signal-idler cross-correlation FROG (SIXFROG), whereby a trace of the sum frequency generated spectrum between the amplified signal pulse and shaped idler pulse is obtained as a function of delay between the two beams. This is particularly useful in characterizing phase locked pulse trains. As noted earlier, the amplified signal retains a transform limited spectral phase profile, and the amplification using phase locked pump pulse train produces a signal pulse train with zero phase difference between them irregardless of the phase relationship of the pump phase locked pulses. The signal’s non varying phase relationship but similar delay profile can be used to cross correlate the shaped MIR pulse trains. SHG FROG has a two-fold ambiguity in characterizing the MIR phase locked pulses: if the relative phase is ϕ, then the relative phase ϕ+π also yields the same SHG FROG trace. This ambiguity is avoided if SIXFROG is used instead.

4. Results and discussion

We create pulses with an amplitude modulation as well as both phase and amplitude modulations using our setup. We narrowed the signal to 2nm centered at 1062nm. The corresponding seed pulse is ~ 800fs in duration. The pump pulse is shaped with the spectrum shown in Fig. 2(a). Figure 2(b) depicts the resultant amplitude modulated shaped idler pulse centered at 3.3µm. The resolution at that wavelength of the amplitude modulation features is about 30nm.

 

Fig. 2. Spectrum of (a) the amplitude modulated shaped pump pulse and (b) the resultant idler shaped pulse from the OPA process.

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Fig. 3. (0.17Mb) SIXFROG traces of MIR phase locked two pulse train with varying phase relationship, Δϕ. XX,XY,X̄ and XȲ denotes the interpulse phase difference of 0,π/2,π and 3π/4 rad respectively.

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We also created phase locked two-pulse trains with a variable delay between them. These pulses can be described as

where A(t) is the pulse envelope function of a pulse in the train,ω _L is the center frequency of the pulse, τ is the relative delay between the two pulses and ϕ’s are the pulse phases. The SIXFROG traces of phase locked pulses set at τ=1ps delay with phase differences of ϕ₂-ϕ₁≡δϕ=0,π/2 and π are depicted in Fig. 3 with the phase invariant signal pulse train as the reference. The duration of each pulse in the pulse train is 130fs FWHM and the time-bandwidth product is ~ 0.51. The shifting of the fringes details the phase relationship between the pulse pair. These shaped pulses will be used for an experiment to measure an optical free induction decay signal.

There are some limitations to the current setup. The particular AOM modulator that we are using has a damage threshold that limits the maximum shaped pump pulse energy to only ~ 50µJ. This is due to the tight focusing onto the modulator’s active aperture (~ 200µm in the direction perpendicular to the spectrum spread). Possible solutions are to spread out the beam somewhat more in the vertical direction (using cylindrical lenses); using a TeO₂ AOM with a larger active aperture and hence lower resolution (which would not be a limitation here, since in this setup, the resolution is limited by the bandwidth of the seed pulse); or to use a fused silica AOM which has an order of magnitude higher maximum optical power density, but significantly lower diffraction efficiency than TeO₂ [13]. Alternatively, a liquid crystal array modulator (LCM) [1], with the dispersed beam cylindrically focused at the Fourier plane can be used (Commercially available LCMs can have a vertical pixel aperture of 2mm [14]). Shaped pulse energy of up to 230µJ has been reported using a LCM based pulse shaper [15]. Nonetheless, our proof of principle experiments does illustrate the feasibility of obtaining MIR pulses using such pulse shape transfer scheme.

5. Optical free induction decay

We perform an experiment using phase locked pulses created using our MIR pulse shaper. In NMR spectroscopy, FID acquisition is routinely done to recover the linear NMR spectrum. A short RF pulse with a bandwidth covering the nuclear spin resonance frequencies creates magnetization, which in turn radiates electro-magnetic waves at the resonance frequencies. This emitted frequencies in the MHz region are sampled in quadrature as the FID signal. The analogous experiments with vibrational coherences (such as C-H and O-H stretches) will produce FID signals at frequencies in the MIR region. The ultrashort oscillations of the field (10fs per cycle at 3µm) is beyond the capabilities of the sampling method used in the NMR experiments. Longer wavelength FID signal (12.5µm), from intersubband transitions of quantum wells, has been measured using ultrafast electro-optics sampling [16]. We will need probe pulses of sub- 5fs duration in order to measure the 3µm FID signal using the electro-optics sampling technique [17].

 

Fig. 4. All four double sided Feynman diagrams above are included in the second order contributions to the perturbative expansion to the density matrix. The ϕ’s denote the phases acquired by the perturbative terms from the interacting pulses. The diagram in (a) pertains to the OFID signal which we distill from the sum contribution using the phase cycling procedure.

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One alternative way to detect the FID signal is to convert the polarization into population with a second pulse at delay τ, which can then be detected to measure the FID at that delay point [18, 19, 20]. This population ${\mathrm{\rho }}_{11}^{\mathit{\text{FID}}}$(τ), is related to the quantity ρ11a(τ,ϕ₁,ϕ₂) which can be described by the double sided Feynman diagram [21] as depicted in Fig. 4(a). It represents the evolution of the on-diagonal element (first vibrational excitation state population) of a term in the second order contributions to the perturbative expansion of the density matrix. Assuming that the pulses are short compared to the dephasing lifetimes, ρ11a(τ,ϕ₁,ϕ₂) and its relation to ${\mathrm{\rho }}_{11}^{\mathit{\text{FID}}}$ can be written down as

where ω₀ is the vibrational resonance frequency and Γ₁₀ is the dephasing rate of the vibrational coherence. g(τ) is the Fourier transform of g(ω-ω₀), the distribution in resonance frequency due to inhomogeneity. However, there are other second order perturbative terms that leads to the population ρ₁₁ as well, as represented in Figs. 4(b),(c) and (d) (The fourth order contribution is minimal here, since the experiment is set up such that the laser intensity incident is sufficiently low). The different terms contributing to the population have different dependences on the relative phase of the pulse pair. In particular, ρ_11a(τ,ϕ₁,ϕ₂) has a distinct dependence on ϕ₁-ϕ₂. Phase cycling uses this phase dependence to extract ${\mathrm{\rho }}_{11}^{\mathit{\text{FID}}}$(τ) [23]. At each time delay τ, four sets of experiments with phase locked pulses of phase differences 0,π/2,π and 3π/4 are used to create population, with the resultant population denoted by ${\mathrm{\rho }}_{11}^{\text{XX}}$(τ),${\mathrm{\rho }}_{11}^{\text{XY}}$(τ),${\mathrm{\rho }}_{11}^{\text{X}\bar{\text{X}}}$(τ) and ${\mathrm{\rho }}_{11}^{\text{X}\bar{\text{Y}}}$(τ) respectively. The desired ${\mathrm{\rho }}_{11}^{\mathit{\text{FID}}}$(τ) is obtained by summing the four population as follows

A phase locked three pulse experiment with appropriate phase cycling is able to measure a 2D correlation spectrum useful in studying ultrafast molecular structural dynamics [23].

 

Fig. 5. Schematic for the acquisition of OFID. PD: Photodetector, BS: Beamsplitter.

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Experimentally, the excited state population can be detected as fluorescence [20, 22]. An alternate way is to detect the population as directly proportional to the amount of light absorbed. The attenuation of the incident phase locked pulse pair energy is proportional to the excited state population. The schematic of the experimental setup for the measurement of the OFID signal is depicted in Fig. 5. A 2mm Ge window splits the MIR phase locked pulses from the pulse shaper. Each beam is directed to a PbSe photodiode. In one arm, the sample is placed in the beam path. Chloroform in tetrachloromethane (1:8 volume) is placed in a sample cell of 1mm pathlength. The total signal from this arm is normalized by dividing it by the total signal from the other arm yielding a signal S(τ,δϕ). The signals are summed in accordance to Eq. (6) to yield the real (XX-XX̄) and imaginary (XY-X̄) parts of the resultant OFID signal (depicted in Fig. 6). The laser center frequency is defined at 3081cm^-1. The absorption peak of chloroform is at 3019cm^-1 and the observed oscillation occurs in the rotation frame of laser frequency, i.e. at -62cm^-1.

6. Conclusions

We have implemented a nonlinear optical technique to create arbitrarily shaped pulses in the MIR. This method may have significant advantages over other pulse shaping approaches, since the gratings in the pulse shaper do not have to be realigned to change wavelengths. We created amplitude modulated pulses as well as pulse trains with controllable delay and interpulse phase. An experiment to obtain the complex valued optical free induction decay of a C-H vibrational mode of chloroform is performed.

 

Fig. 6. Complex optical free induction decay of the C-H stretch of Chloroform obtained from experimental signal S(τ,δϕ).

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