1. Introduction

Many applications of lasers require high-power, picosecond pulses generated in the mid to long-wave infrared (LWIR) range of 2–20 µm. This wavelength range is the most useful part of the spectrum for trace analysis of molecular components of air because it covers the fundamental rotational-vibrational bands of constituent gases, and there are a few low-loss transmission windows in the atmosphere.

Since powerful, pulsed mid to LWIR lasers are scarce, the standard approach in developing such sources is down-conversion of well-developed short pulse 1–2 µm solid-state lasers in a nonlinear crystal. Here, a high frequency near-infrared pump at ω₁ is mixed with a slightly longer wavelength component at ω₂ to generate a LWIR frequency ω₃ = ω₁ − ω₂ through the process of difference-frequency generation (DFG). In many situations of DFG, the field at ω₁ is an intense pump field, while the field at ω₂ is a weak signal field. DFG yields amplification of the signal field along with generation of another field of frequency ω₃, commonly called idler. This process, termed optical parametric amplification (OPA), has the same phase-matching conditions as DFG and differs from DFG only by the much higher parametric gain for the signal and idler waves [1].

Multiple techniques have been used for production of the two-color radiation needed for the generation of tunable mid to LWIR by a three frequency parametric process in a nonlinear crystal. The most natural path is to use two separate lasers. A Nd:glass laser and a tunable 1.1–1.4 µm Dye laser were mixed in a GaSe crystal to generate 1 ps pulses tunable in the range from 6 to 15 µm [2]. Also, an optical parametric generator pumped by the second harmonic of a 1 µm Nd:glass laser can generate high energy signal pulses around 1.2 µm. This approach to DFG resulted not only in a broad tunability but in rather energetic, ≥25 µJ pulses at 10 µm [3]. Despite the fact that high energy for the signal wave results in the highest efficiency of the DFG process, it requires an extra seed laser source.

A much simpler way to build the near-IR seed in the 1–2 µm range is generation of a white light continuum (WLC) from ~1 µm radiation. At present, passive WLC generation in a simple dielectric plate [4] or in a nonlinear GeO₂ fiber [5] is the most common in laboratory experiments, sometimes simply achieved using the commercial TOPAS OPA system (Light Conversion). Characteristic of WLC, however, is a rather low spectral energy density at any selected signal frequency, which significantly limits the efficiency of DFG. Low efficiency is usually compensated by substantial increase in the 1 (0.8) µm pump laser energy which is expensive and ultimately limited by the damage threshold of the DFG crystal. The main question is whether the simplicity of a passive device (WLC generator) can be combined with the high energy of a signal wave approaching that of a separate laser source.

Raman shifters in the near-IR range are a well-established technology for production of frequency sidebands around the pump laser with a frequency shift corresponding to approximately 1000 cm⁻¹ [6]. Efficiency of the first Stokes line generated in this process can exceed 50% for nanosecond pulses [7, 8]. For the much shorter picosecond pulses having a time duration close to the dephasing time T₂, the conversion efficiency decreases rapidly [9]. Therefore, new ways to efficiently generate Raman sidebands in a transient gain regime required for short pulse mid to LWIR DFG sources need to be explored.

Here we demonstrate an efficient 10.6 µm DFG when the phase-matched GaSe crystal is pumped by a common picosecond 1.06 µm Nd:glass laser and simultaneously is seeded by a shifted light at 1.18 µm of the first Stokes sideband generated in a Raman shifter. The choice of material C₆D₆ was dictated by a 944.7 cm⁻¹ Raman frequency that coincides with the 10P(20) transition of a CO₂ laser. This frequency corresponds to the highest gain in a CO₂ active medium and is suitable for amplification of LWIR pulses as short as a few picoseconds to GW power levels [10]. Additionally, for seeding a CO₂ amplifier on a resonant frequency, the Raman shifter has to be tuned around the Raman frequency. We show that in the transient stimulated Raman regime, the efficiency of Stokes production and the central wavelength can be controlled by chirping the pump pulse such that it provides compensation of the self-phase modulation in a Raman medium. All together, this allows for a simple way to generate pulses in the LWIR range with a high efficiency.

2. Generation of sidebands in transient Raman regime

Stimulated Raman scattering (SRS) is a nonlinear optical effect in which a pump laser excites some resonant mode in a medium and provides amplification of a family of sidebands that is generated from optical noise around the pump frequency. The comb line spacing is determined by the Raman frequency Ω_R of the scattering mode in the Raman-active material (see Fig. 1) and is typically in the range of 500-3000 cm⁻¹ for solids and liquids [11, 12]. The first sideband on the red side of the pump is called first Stokes and is usually the most energetic. It is this sideband that we want to mix with the same pump laser in a DFG crystal, as shown by the block diagram in Fig. 1, to generate LWIR wavelengths. The frequency of the generated LWIR light is simply the difference frequency between the pump and the Raman shifted frequency i.e. the frequency of the excited mode of the Raman medium. Several commercially available Raman-active materials with Raman frequencies near 1000 cm⁻¹ are listed in Table 1 that could be used in this scheme to generate 10 µm light from DFG.

 

Fig. 1 Energy diagram (left) of pump laser ω_L exciting a Raman medium and being down-shifted by the Raman frequency Ω_R to produce ω_Stokes = ω_L − Ω_R. Block diagram (right) describing the three wave mixing scheme for efficient down-conversion to LWIR wavelengths from a near-IR laser (~1 µm). The output frequency is equal to the Raman frequency of the Raman shifter material.

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Table 1. Raman-active materials that could be used to reach the LWIR range around 10 µm with the presented DFG scheme [6,13,14]

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An important timescale for SRS is the dephasing time of the excited mode T₂ = (πcΓ_R)⁻¹, where c is the vacuum speed of light and Γ_R is the Raman linewidth in cm⁻¹. The relative magnitude between T₂ and the pump laser pulse length τ_p significantly affects the gain dynamics of SRS and is often categorized as either the steady-state or transient regime. The technology of Raman shifters was developed to utilize the higher gain achievable in the steady-state regime where τ_p ≫ T₂ and has led to conversion efficiencies from pump to the first Stokes component of over 50% in many solids [12] and some liquids [8, 15]. If instead we have short pump pulses with τ_p ≤ T₂, then the interaction is classified as the transient regime of SRS. It is well known that a Stokes pulse generated in this regime has a reduced gain and is only amplified on the trailing end of the pump pulse in the time domain because it takes a finite amount of time for the resonant mode to grow in the medium [16]. Some earlier work indicates that it is possible to generate rather efficient first Stokes components even for picosecond pulses by operating at very high intensities (>25 GW/cm²) [17, 18]. However, this triggers undesirable self-phase modulation (SPM) and Kerr self-focusing that results in significant modification of the spectral and spatial properties of the pump beam, respectively, making the pulse unsuitable for efficient DFG.

In Fig. 2, we present a simplified concept in which a prechirped pulse allows for compensation of undesirable SPM in a transient Raman shifter. The figure shows snapshots of the evolution of pump and Stokes pulses as they propagate through a Raman cell, traveling from left to right. The transform-limited (TL) pump pulse in Fig. 2a first excites a vibrational mode in the medium with a time-delayed peak value because the medium is not fast enough to exactly follow the pump profile. The pump then scatters off this mode and produces light at the Stokes frequency with the same time delay. Upon further propagation, the Stokes pulse is subjected to an intensity-dependent refractive index produced by the pump pulse. This results in the frequency broadening effects of SPM for the pump pulse and cross-phase modulation (XPM) for the Stokes pulse. However, since the Stokes pulse is delayed in time, the XPM broadening is asymmetric and heavily favors the blue side, as shown in Fig. 2a.

 

Fig. 2 Transient SRS with a transform-limited (TL) pump pulse (propagating to the right) leads to a blue-shifted Stokes component by XPM from the pump (a). Adding a negative chirp to the pump compensates for SPM and removes the blue-shift from the Stokes pulse (b).

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To compensate for the effect of XPM on the Stokes frequency, we suggest to use a pump pulse that initially has a small negative chirp, as illustrated in Fig. 2b. In this way, the red photons from the pump are scattered from the vibrational mode and produce a red-shifted Stokes pulse. Both pulses continue to propagate in the medium and experience the same SPM and XPM effects. But this time, a blue-shift to the Stokes pulse from XPM counters the shift from the initial chirp and can result in the nominal Stokes frequency. Thus, the Raman frequency will appear to be the same as (or close to) the nominal transition frequency Ω_R, where the gain is maximum. This technique of chirping the pump pulse therefore allows for fine tuning of the Stokes central frequency.

To study the interaction between the resonant effect of SRS and the nonresonant effect of SPM in the transient SRS regime, we simulated the propagation of diverging 1060 nm pulses in liquid C₆H₆, the material with nonlinearities close to that for C₆D₆, using the cylindrically-symmetric Generalized Nonlinear Schrodinger Equation (GNLSE) [19]. The choice of a quasi-3D simulation over 1D allowed us to include the spatial evolution of the beam as it is affected by self-focusing. The GNLSE is solved using the split-step Fourier method [20] where the diffractive term is calculated spectrally by performing a Hankel transform [21,22]. We used a nonlinear index of 1×10⁻¹⁵ cm²/W as given in [23] and the dispersion relation measured in [24] for benzene. The Raman response is modeled as an exponentially decaying sinusoid with a frequency of ~30 THz and a bandwidth of ~60 GHz, consistent with the Raman fluorescence measurements presented in [15]. Stochastic noise with a standard deviation equal to the square root of the photon number in one temporal discretization bin was included as prescribed in [25].

The simulation results can be split into two cases: pump pulses with a duration faster than T₂, and pump pulses on order of T₂. In the first case, transform-limited 1.5 ps pump pulses were focused to ~10 GW/cm² and the pulse evolution is dominated by self-focusing in the liquid. As shown in Fig. 3a, the beam profile develops a ring structure in the first 8 cm of propagation. The ring results from the symmetry of our GNLSE model, and is indicative of significant self-focusing, resulting in disruption of the SRS process. For the second case, we used 4 ps pulses with an intensity of ~4 GW/cm², which was enough of a change to limit self-focusing of the beam over 15 cm of propagation. However, the first Stokes sideband appeared on the blue side of where it was expected to be based on steady-state SRS, which is explained by our simplified picture. Results from modeling both positively and negatively chirped pumps are shown in Fig. 3b. The higher efficiency obtained for the negative chirp may be attributed to continuous SRS close to the nominal Raman transition frequency, where the gain is the highest.

 

Fig. 3 Simulation results from the GNLSE modeling in C₆H₆. (a) The beam profile of 1.5 ps pump pulses shows significant self-focusing. The color bar is intensity in units of GW/cm². (b) Stokes pulse conversion efficiency and central wavelength depend on sign of the chirp on 4 ps pump pulses.

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3. Experimental setup

The pump pulse used in these experiments emanates from a Nd:glass CPA laser capable of producing 2 mJ pulses at 1060 nm with a 5 Hz rep rate. The laser bandwidth of the oscillator is narrowed such that 1.5 ps pulses are transform-limited and longer pulses are generated by either under compression or over compression with the CPA gratings. All pulse lengths are measured with a multishot, second harmonic autocorrelator. As shown in Fig. 4, the pump laser is split with a 50/50 beam splitter and sent through separate arms of the optical setup. In the first arm, there is a 5-inch-long cell filled with the Raman-active material C₆D₆, whose Raman frequency from the ring-breathing vibrational mode is 28.3 THz [13]. The first Stokes sideband generated from the 1060 nm pump is therefore expected to be near 1180 nm for both positive and negative chirped cases. It is assumed that the nonlinearity of deuterated benzene is very similar to that of benzene, having a nonlinear refractive index of 1×10⁻¹⁵ cm²/W [23]. Note that this large n₂ of C₆D₆ means that the 1 µm beam has a peak power much above the critical power for Kerr self-focusing (~1 MW). To prevent complete collapse of the pump beam, the deuterated benzene Raman cell is placed downstream of a focusing lens such that the beam is diverging when it enters the cell.

 

Fig. 4 Experimental setup with a 50/50 beam splitter BS, beam combiner BC, and variable delay line DL.

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The second arm of the experiment serves two purposes. First, it has an adjustable path length to provide timing control and ensure temporal overlap between pulses from both arms in the DFG crystal. The second purpose is that it delivers a pump pulse with a clean spatial profile, free from distortions caused by the onset of self-focusing. This new pump pulse is spatially combined with the Raman-shifted light from the other arm using a dichroic mirror designed to reflect wavelengths less than 1100 nm and transmit longer wavelengths. The two colors are then mixed in a 1 cm long GaSe crystal via type II (e-oe) phase-matching. The λ/2 waveplate shown in the figure rotates the polarization before the Raman cell so that the Stokes light is orthogonally polarized to the pump from the other arm. Phase-matching is achieved by angle-tuning with an internal angle of 14.5°, however, this crystal can only be cleaved perpendicular to the optical axis and must be rotated to an external angle near 40°. Gallium selenide was chosen because it is one of the few nonlinear crystals that is transparent at both 1 µm and 10 µm and it has a very large χ⁽²⁾ nonlinearity. All spectral measurements were done with an iHR-550 imaging spectrometer (HORIBA Scientific). A Golay cell detector was used for all energy measurements with a germanium filter to dump 1 µm light.

4. Results and discussion

4.1. Raman shifter

Two pulse lengths were studied in the experiment: transform-limited 1.5 ps and chirped 4 ps pump pulses with the same energy of 1 mJ. The 1.5 ps pulses produced flashes of light inside the cell with a strongly diverging beam leaving the cell. Continuum light was observed extending from the pump to past 1.3 µm but with no clear Raman peak, as shown in Fig. 5a. This configuration is analogous to the WLC from a dielectric plate or fiber. The longer 4 ps pump pulses produced a different spectrum; a Raman Stokes peak was observed with negligible WLC background and with no flashes of light inside the cell. Changing the sign of the chirp on the pump affected both the measured pump and Stokes pulses. A positively chirped pump (blue lines in Fig. 5b) resulted in a broader pump spectrum after the Raman cell than with the negative chirp (red lines in Fig. 5b). When using a positively chirped pump, the measured transient Raman frequency was 903 cm⁻¹, which is smaller than Ω_R by 42 cm⁻¹. For the negatively chirped pump, the measured Raman frequency was 936 cm⁻¹-a decrease of only 9 cm⁻¹ from the nominal 944.7 cm⁻¹ frequency of C₆D₆. Energy conversion to Stokes was 2% for the negative pump chirp and 0.3% for positive pump chirp. In Fig. 6, the onset of self-focusing of the 4 ps pump pulses is seen from the measured beam profiles before and after the Raman cell.

 

Fig. 5 Spectra measured after the Raman cell are shown for three cases: 1.5 ps transform-limited (green, a), 4 ps with a negative chirp (red, b), and 4 ps with a positive chirp (blue, b).

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Fig. 6 Beam profiles of the pump laser before (left) and after (right) the Raman cell for the 4 ps case as measured by a pyroelectric array. The onset of self-focusing is observed.

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It is clear from both experiment and simulations that the 1.5 ps pump pulse case is dominated by self-focusing and SPM effects, causing SRS to be disrupted. This prevents significant amplification of the first Stokes sideband. Although some Stokes light was generated on-axis in the simulation, we believe the beam diverges too quickly after strong self-focusing in the cell to be collected efficiently in the experiment. Ultimately, the observed WLC could be used with a filter, but this does not seem to have an advantage over the established methods of generating a WLC [4, 5]. However, switching to 4 ps pump pulses was enough of a change to limit self-focusing in the 5-inch cell and produce efficient SRS. There was still noticeable broadening of the pump spectra from SPM, but more so with the positive chirp than negative chirp case. This is expected because SPM always generates a positive chirp. The SPM-induced chirp reinforces an initial positive chirp and counteracts an initial negative chirp, resulting in broader bandwidth for the former and narrower bandwidth for the latter. As mentioned before, XPM can also shift the Stokes frequency to the blue. An analytic expression for this shift ∆ν_S was developed by Zinth and Kaiser [26].

4.2. Difference frequency generation

The last stage of the experiment was mixing a new pump pulse with the Raman-shifted Stokes pulse in a nonlinear crystal for DFG to produce light near 10 µm. All DFG measurements were carried out with a negatively chirped, 4 ps pump when Raman conversion efficiency is maximized. As mentioned before, GaSe can only be cleaved perpendicular to the optical axis (or z-cut), and since it is a negative crystal, it should be rotated in the same plane as the polarization of the pump beam. For our frequencies, both type I (e-oo) and type II (e-oe) phase-matching are possible through angle-tuning of the crystal at room temperature. The main difference between these two is the polarization of the 10 µm idler wave—either an o- or e-wave, respectively. Both cases require a large external angle near 40°, so we operated with type II phase-matching to minimize 10 µm Fresnel losses. With this setup, we generated 3 µJ of 10 µm light—an external energy conversion efficiency of 0.15% from the Nd:glass pump. A phase-matching curve for the internal crystal angle is shown in Fig. 7a. For monochromatic light, the angle width of a phase-matching curve can serve as a measure of effective crystal length. However, in our case both pump and signal pulses were not transform-limited and the phase-matching width is dominated by the broad spectra. For this case, the effective crystal length is limited by group velocity mismatch between the pump and idler waves to about 7 mm for our pulse lengths.

 

Fig. 7 Experimental results of DFG in 1 cm GaSe between pump and Stokes pulse from transient SRS. (a) Phase-matching measurements are compared with theory for plane-wave and fixed-field approximations. (b) Measured 10 µm idler spectra after the DFG crystal. The black vertical line marks the 10P(20) transition and peak gain of a CO₂ laser.

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In a separate measurement, we studied the 10 µm idler spectrum and show two examples in Fig. 7b; the first is for the highest conversion efficiency (blue, phase-matched). Then, by tuning the crystal angle, we added an intentional red-shift (red, small mismatch) in order to match the 10P(20) transition of a CO₂ laser. Note that the maximum efficiency is not perfectly aligned with the nominal Raman frequency value, but the central frequency can be slightly shifted. Alternatively, finer tuning of the pump chirp may also accomplish this goal. A small drop in conversion efficiency for the detuned case is an indication that the Stokes pulse has a very large bandwidth.

Autocorrelation measurements at 10 µm were hindered due to a lack of instruments, therefore we did cross-correlation measurements between the pump and signal waves to estimate the duration of the LWIR pulse, under the assumption that the temporal profile of the LWIR pulse follows that of the signal pulse. We used the same GaSe crystal and measured the energy at 10 µm as a function of delay in the pump pulse with respect to the Stokes pulse. The resulting measurement, shown in Fig. 8, is a convolution of the pump and Stokes pulses. A width of 3.7 ps for the main peak matches the 4 ps pump closely (within error), thus the duration of the Stokes pulse must be short compared to the pump since there is not any broadening observed in the cross correlation trace. Finally, since both input waves for DFG are ≤4 ps, it is assumed that the 10 µm output wave is on the same scale.

 

Fig. 8 Cross correlation measurement between pump and Stokes pulses in the GaSe DFG crystal. The x-axis is a delay on the pump pulse with respect to the Stokes pulse.

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5. Summary

We have presented a new method for creating and seeding the signal wave required for LWIR light generation by DFG. The signal seed is a Stokes pulse generated by a near-infrared pump laser through transient SRS in liquid deuterated benzene. This transient process was characterized and the conversion efficiency was optimized by controlling the time-bandwidth product and chirp sign of the pump laser. To prevent significant self-focusing of the 1 mJ pump by Kerr self-focusing in the Raman cell, it was necessary to stretch the pulse to 4 ps from the transform-limited value of 1.5 ps. It was found that having a small positive chirp on the pump led to a Stokes pulse shifted to the blue of its expected frequency. However, by giving the pump a small negative chirp, the effects of SPM and XPM could be compensated and the blue shift was reduced. Maintaining the central frequency close to Ω_R also improved the conversion efficiency to the Stokes pulse and therefore maximized signal seed energy for DFG in the GaSe crystal. With this method, we demonstrated the generation of picosecond, 3 µJ pulses of 10 µm light through DFG pumped by 1 mJ pulses from a 1 µm Nd:glass laser.