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Abstract
We have experimentally demonstrated the post-compression of a long-wave infrared (9.2 μm) 150 GW peak power pulse from 2 ps to less than 500 fs using a sequence of two bulk materials with negative group velocity dispersion (GVD). The compression resulted in up to 1.6-fold increase of the peak power and up to 2.8-fold increase of the intensity in the center of a quasi-Gaussian beam. The partial decoupling of the self-phase modulation and chirp compensation stages by using two materials with significantly different ratios of nonlinear refractive index to GVD provides accurate optimization of the compression mechanism and promises a viable path to scaling peak powers to supra-terawatt levels. During the preparatory study, we measured, for the first time to our knowledge, the nonlinear refractive indices of NaCl, KCl, and BaF2 for picosecond pulses in the long-wave infrared region.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Multi-terawatt peak power has been achieved recently in a 2 picosecond pulse at a long-wave infrared (LWIR) wavelength of 9.2 $\mathrm{\mu}$m via chirped-pulse amplification (CPA) in high-pressure, mixed-isotope CO$_2$ laser amplifiers [1]. Further progress towards shorter and correspondingly more powerful LWIR pulses is possible via 1) better utilization of the gain bandwidth of the CO$_2$ amplifiers, and 2) post-compression of the pulses after the CPA [2]. The shortest duration of a multi-joule LWIR pulse realistically achievable without post-compression is $\sim$500 fs. Such a pulse can be produced in an amplification scheme utilizing two vibrational-rotational bands of the CO$_2$ gain spectrum, $9R$ and $9P$, and requires a multi-millijoule 300 fs seed at 9.3 $\mathrm{\mu}$m. The pulse can be further post-compressed to a few-cycle duration (<100 fs) in a bulk nonlinear material with negative group velocity dispersion (GVD) [2]. Both segments of the path towards the few-cycle supra-terawatt LWIR pulses require extensive research and development. In this work we concentrate our efforts on one of these segments: the post-compression.
Post-compression schemes for high-peak-power near-infrared lasers usually involve spectrum broadening via self-phase modulation (SPM) in a nonlinear material followed by chirp compensation/compression with a chirped mirror [3]. A simpler scheme is possible if the nonlinear material has a negative group velocity dispersion: the self-phase modulation and the dispersive chirp compensation actions can then be combined in a single bulk-material optic. This scheme is especially promising for LWIR spectral range where most of the relevant optical materials exhibit a negative GVD. Compression of millijoule picosecond LWIR pulses to $\sim$600 fs was first observed by Corkum in a high-pressure CO$_2$ regenerative laser amplifier [4]. The amplifier was operated in a saturated regime and the compression was explained by the spectral broadening via SPM in the amplifier’s discharge plasma and negative GVD in NaCl windows of the amplifier. We note that the nonlinear properties of NaCl were not known sufficiently well at the time of Corkum’s pioneering work; attributing the SPM to the window material rather than the partially ionized active medium seems a more probable explanation of the observed pulse compression in view of present-day knowledge.
NaCl is a popular and relatively inexpensive material for LWIR laser optics. It has a high damage threshold ($\sim$0.5 J/cm$^2$ for a 2 ps pulse [4]) and is available in large sizes. This, together with its combination of nonlinear refractive index $n_2$ and group velocity dispersion $\beta _2$, seemingly make it a natural choice for post-compression of terawatt-class LWIR pulses. A scheme for compressing a 2.5 ps, 1.5 J, 10 $\mathrm{\mu}$m pulse in a super-Gaussian beam to 250 fs in bulk NaCl was suggested and numerically modeled in [5]. The proposed scheme consists of four plates of NaCl with total thickness of 19 cm separated by spatial filters and beam expanders. Multiple stages and spatial filtering are needed to achieve the required spectral broadening while avoiding small-scale self-focusing that occurs when the B-integral of an optical element exceeds 2–3. Matching of the spectral broadening and the group delay at each stage is achieved by adjusting the thickness of the material and the laser intensity, where the latter is controlled by the beam size.
This study provides an experimental demonstration of post-compression of picosecond LWIR pulses in the minimum viable configuration, which is suitable for future scaling up and optimization. For simplicity, the number of compression stages was limited to two. We have chose not to use interstage filtering and telescoping in this proof-of-principle demonstration. However, an important additional optimization parameter was provided by using different materials at each compression stage. In particular, using a material with smaller $n_2$ in later stages may eliminate the need for expanding the beam between stages. More importantly, by combining a high-$n_2$/low-dispersion material with a low-$n_2$/high-dispersion one, we partially decoupled the SPM spectrum broadening and the dispersive chirp compensation processes, thereby facilitating their independent and more efficient optimization. This design approach requires an accurate knowledge of the nonlinear responses of optical materials irradiated by intense picosecond LWIR pulses. The material database in this regime is presently very limited. Thus, we have started our research with a campaign of measuring nonlinear properties of LWIR materials. The data which we have acquired was used to identify promising material combinations for the post-compression process.
This paper is organized in the following way. First, we describe a single-shot method of measurement of nonlinear refractive index of the LWIR-transparent solids using a high-peak-power laser and present our results for three such materials: NaCl, KCl, and BaF$_2$. Next, a proof-of-principle post-compression experiment using KCl and BaF$_2$ in combination is described. Finally, the results of the experiment are compared with a numerical model and the potential for further development and optimization is discussed.
2. Characterization and selection of materials for post-compression
The single-shot method of measuring the nonlinear refractive index is based on analyzing the self-focusing of a quasi-Gaussian beam propagated through a test sample. Samples of three wide-bandgap materials regularly used for transmissive optics in the mid-wave and long-wave infrared were acquired for this research: NaCl (60 mm thickness, 100 mm diameter), KCl (50 mm thickness, 76 mm diameter), and BaF$_2$ (50 mm thickness, 76 mm diameter; two samples from different suppliers). Although BaF$_2$ is rarely used with CO$_2$ lasers due to its sharp increase in absorption at wavelengths above 9–10 $\mathrm{\mu}$m, we found that the absorption at 9.2 $\mathrm{\mu}$m, the operating point of our mixed-isotope laser, is tolerable: internal transmittance of a 50 mm thick sample is 87%. Also, due to the small refractive index, Fresnel reflection losses in uncoated BaF$_2$ are low, <3% per surface. Figure 1 shows the absorption curve measured using a line-tunable continuous-wave CO$_2$ laser (Access Lasers L4G-FC). This curve was used in the numerical calculations described in Section 4.
Nonlinear refractive indices of the sample materials were measured using the experimental setup schematically shown in Fig. 2. A reproducible, near-Gaussian beam of up to 500 mJ energy is produced in this scheme by sending the output of the terawatt LWIR laser through a 12.88 mm dia. aperture and allowing it to propagate 14 m through the atmosphere. The intensity distribution on the sample in this configuration is defined by far-field diffraction with virtually no dependence on the profile of the input beam [6]. The pulse energy is measured after the sample and a BaF$_2$ wedge window using a pyroelectric joulemeter (Gentec-EO QE95).
Fig. 2. Experimental setup for measuring the nonlinear refractive index of transparent materials. The distance between the sample and the BaF$_2$ wedge is 120 mm. The total propagation distance from the sample to the beam profiler is 1.63 m. The combination of BK7 blanks and gold mirrors in the zig-zag optimizes the signal level on the beam profiler.
To determine the energy after the sample, the measured energy is corrected for Fresnel losses on the surfaces and the internal absorption in the BaF$_2$ wedge. The combined losses in the sample and the wedge are accounted for to determine the energy before the sample. The complete spatio-temporal profile of the input pulse on the sample is then calculated for a specific energy using a comprehensive model of the laser system and beam propagation as described in [6]. At high pulse energies, the nonlinear refraction of air results in a measurable reduction of the beam size compared to a 14 m free-space propagation and pulse compression to 1.6–1.7 ps in the center of the beam. Both of these effects were verified experimentally and are in a good agreement with our model predictions.
After passing through the sample, the beam is attenuated by reflecting it from the front surface of the BaF$_2$ wedge. It is then directed to a pyroelectric array beam profiler (Ophir Spiricon Pyrocam IV) via an optical zig-zag where a combination of gold mirrors (reflectance >99%) and BK7 glass plates (surface reflectance $\sim$40%) is used to further attenuate the beam and to match its intensity to the dynamic range of the beam profiler. The total distance between the sample and the beam profiler is 1.63 m; it was experimentally adjusted to provide roughly a factor of two self-focusing related reduction of the beam size at highest pulse energy of $\sim 500$ mJ. The beam profiler is used without a protective window to eliminate any material effect on the measurement results. Representative examples of measured beam profiles for the KCl sample are shown in Fig. 3(a).
Fig. 3. Determination of the nonlinear refractive index of KCl. (a) Examples of normalized measured beam profiles labeled with the input energy. (b) Determination of $n_2$ by fitting to the propagation model. (c) Verification of the result by comparing the beam profiles measured at different energies with model predictions.
The one-dimensional beam profile (fluence as a function of the distance from the beam center) is determined by averaging the values of all pixels at fixed radial intervals from the centroid and assigning this averaged value to each point in the resulting curve. This azimuthal averaging procedure maximizes the accuracy of the measurement by using all information contained in the two-dimensional beam profile. The absolute calibration of the beam profiler is performed by comparing the measured energy after the sample with the integrated signal on the beam profiler. Representative beam profiles measured with the KCl sample at different input pulse energies are shown in Figs. 3(b) and 3(c) with solid curves.
Self-focusing in the sample material affects the divergence of the beam and manifests itself in the deviation of the measured beam profile from a profile obtained without the sample. The nonlinear interaction of an attenuated beam with air is negligible. Therefore, the observed beam focusing can be used for the evaluation of the nonlinear refractive index of the sample. Figure 3(b) shows one of the measured beam profiles and the results of numerical modeling performed assuming different values of $n_2$.
Modeling of the pulse interaction with the sample is performed using the co2amp software [7] which employs a split-step algorithm that is briefly described in Section 4 and is similar to the approach reported in [5]. Because the thickness of the sample is small compared to the self-focusing distance, the beam profile variation inside the sample is ignored. Propagation after the sample is modeled with a free-space Fresnel integral calculated in the frequency domain.
Comparing the experimental curve with the theoretical ones, we determine $n_2(\textrm {KCl}) = 3.4\times 10^{-20}$ m$^2$/W. We verified this result by using it for modeling the material interaction with pulses of different energy and comparing the model predictions with the measured beam profiles as shown in Fig. 3(c). A very good agreement between the model and the experiment is achieved at low and medium pulse energies. A stronger deviation at high energies is due to a relatively strong nonlinear pulse interaction with air during the 14 m beam-forming propagation. Even though this interaction is accounted for in the model, it affects the overall error bar of the measurement procedure; for example, assuming <5% error in the measurement of energy is sufficient to explain the discrepancy between the experiment and the model at 423 mJ in Fig. 3(c).
The above procedures for measurement and data analysis were also used for NaCl and BaF$_2$, yielding the $n_2$ values listed in Table 1. Similarly to the analysis performed in [6] for $n_2$(air), we estimate the error bar for the resulting values of $n_2$ of solid materials as $^{+20\%}_{-0}$. This asymmetric error corresponds to the confidence interval of the input intensity, as determined using the pulse characterization procedure described in [1].
Table 1. Properties of studied materials at 9.2 $\mathbf{\mu}$m.
We are unaware of any previous measurements of the nonlinear refractive indices of KCl and BaF$_2$ at LWIR wavelengths. For NaCl, an upper estimate $n_2\leq 5.3\times 10^{-20}$ m$^2$/W was reported earlier for a comparatively long (1 ns) 10.6 $\mathrm{\mu}$m pulse (Watkins et al. as cited in [8]). Our result agrees with this estimate.
Table 1 also lists the linear refractive index $n_0$ and the group velocity dispersion $\beta _2$ values calculated using the Sellmeier equations reported in [9] for NaCl and KCl and in [10] for BaF$_2$. Among these three materials, KCl has the highest absolute $n_2/\beta _2$ ratio, exceeding that of NaCl by roughly a factor of two and BaF$_2$ by more than a factor of eight. This led to the choice of KCl for the first element of the compressor, which is primarily responsible for the SPM part of the process, and BaF$_2$ for the downstream element, which provides the dispersive compensation of the chirp.
3. Experimental demonstration of post-compression
For a proof-of-principle demonstration of pulse post-compression, we have modified the experimental setup as shown in Fig. 4. The following setup modifications, relative to the experimental setup shown in Fig. 2 were implemented: 1) the KCl and BaF$_2$ plates were installed in the position of the sample at $\sim$20 mm separation; 2) an $F$=55 cm BaF$_2$ lens was used for imaging the output surface of the BaF$_2$ plate on the crystal of a single-shot autocorrelator; and 3) all elements of the optical zig-zag were replaced by gold mirrors to optimize the autocorrelation signal.
Fig. 4. Experimental setup for studying the post-compression of the laser pulse. The distance between the KCl and the BaF$_2$ plates is 20 mm. The distance between the output surface of the BaF$_2$ plate and the sampling wedge is 120 mm. All BK7 blanks in the optical zig-zag from the measurement configuration in Fig. 2 have been replaced by gold mirrors to maximize the autocorrelation signal.
The single-shot autocorrelator [1,11] provides accurate measurement of LWIR pulse durations down to $\sim$300 fs. In the used scheme, the 9.2 $\mathrm{\mu}$m input beam is split in two equal parts that then intersect on a 10 mm-diameter, 1 mm-thick AgGaSe$_2$ crystal. When two pulses overlap in time within a crystal, a sum-frequency 4.6 $\mathrm{\mu}$m beam is generated. The relative tilt of the wave fronts of the two beams causes a variation in the time delay between them across the crystal. The transverse profile of the sum-frequency signal, thus, represents the temporal intensity autocorrelation of the input pulse. For optimum performance, the autocorrelator crystal must be homogeneously illuminated and the temporal variation of the pulse structure within the crystal must be small. To ensure the latter, the output surface of the BaF$_2$ plate is imaged on the crystal with 2$\times$ magnification. This way, only a relatively flat, 5 mm diameter central part of the beam is analyzed.
Autocorrelation traces were recorded at different pulse energies; a list of selected shots used in the data analysis is given in Table 2. At pulse energies >400 mJ, a nonlinear attenuation of the central portion of the beam in the samples was observed, making the calculation of the input energy based on the readout of the joulemeter, which is located after the samples, ambiguous. Therefore, uncorrected energy readouts are shown in the table along with the input energy and the peak intensity calculated neglecting the nonlinear attenuation. The input energy and the peak fluence values of the high-energy shots $\#$7, $\#$8, and $\#$9 must thus be considered as lower-limit estimates.
Table 2. List of representative laser shots. Asterisk marks the optimal-compression shot.
Representative autocorrelation traces are shown in Fig. 5(a). Horizontal projections of the autocorrelation traces are shown in Fig. 5(b) and Fig. 5(c) for the shots with negligible and non-negligible nonlinear attenuation, respectively. Compression to sub-picosecond durations is observed for all pulses with input energies exceeding 200 mJ. The highest peak intensity among the pulses compressed in a regime with negligible nonlinear attenuation was achieved in shot $\#$6 (278 mJ joulemeter readout). At higher energies, the signal intensity starts to decrease despite the continued shortening of the pulse. In addition, the intensity distribution in the autocorrelation trace becomes spatially modulated (i.e., the two high-energy shots in Fig. 5(a)).
Fig. 5. The measured intensity autocorrelation of pulses compressed in a sequence of a 50 mm thick KCl and a 50 mm thick BaF$_2$ plates. (a) Examples of the raw autocorrelation data individually normalized and labeled with the measured energy. (b) Processed autocorrelation curves for shots with negligible nonlinear absorption. (c) Processed autocorrelation curves for shots with non-negligible nonlinear absorption. The same normalization factor is used for all curves in (b) and (c).
To gain better insight into the observed attenuation and spatial modulation of the autocorrelation traces at high pulse energies, the effect of pulse energy on the intensity distribution was studied by imaging the output surface of the BaF$_2$ plate on the beam profile monitor instead of the autocorrelator crystal. Examples of the measured profiles are shown in Fig. 6. Beam profiles of low-energy pulses (sub-figures (a) and (b)) are not visibly distorted by the compressor materials. A speckle-like structure starts to appear in the beam when the pulse energy approaches the energy of the optimal compression (c). At higher energies (d), the central part of the beam becomes highly spatially modulated. An accurate analysis of high-energy profiles shows that the energy is not simply redistributed, but is partially absorbed in the crystal. The observed behavior of the intensity distribution in the beams corresponding to high-energy pulses transmitted through the KCl+BaF$_2$ combination agrees with the reduction of the peak pulse intensity and the inhomogeneous intensity distribution in the autocorrelation traces.
Fig. 6. Measured beam profiles at the output surface of BaF$_2$ (individually normalized). The 5 mm diameter portion of the beam used for autocorrelation measurements is shown by the dotted circles.
The observed spatial modulation of the beam can be explained by small-scale self-focusing. Such an effect is expected when the B-integral exceeds 2–3 [5,12]. Optimal compression in our configuration is observed when the B-integral in the center of the beam is $\sim$2.6 for each component of the compressor, or $\sim$5.2 total (the B-integral is calculated using the model described in Section 4.). Small-scale self-focusing results in the formation of microfilaments and the threshold of nonlinear absorption can be reached inside the filaments, thus leading to the observed nonlinear attenuation. If this explanation is valid, then spatial filtering of the beam between the KCl and the BaF$_2$ components may allow for increasing the input pulse intensity before the onset of the nonlinear attenuation.
No measurable compression and spatial modulation was observed with one of the plates (KCl or BaF$_2$) removed.
In a separate measurement, a broadening of the spectrum of the pulse during post-compression was observed. Pulse spectra before and after post-compression were measured with 8 nm resolution using a home-built, single-shot, slitless spectrometer [1,11] installed in the position of the imaging lens in Fig. 4. Pulse spectrum after the KCl plate (with BaF$_2$ removed) was also measured. These spectra are shown in Fig. 7. The broadened spectra shown are for pulses with energy matching that required for optimal post-compression. The fine structure of the spectra is due to the rotational modulation of the gain spectrum of the CO$_2$ laser amplifiers [1]. The slitless spectrometer accepts the entire beam. Thus the measured spectra must be considered as the beam-average.
Fig. 7. Typical measured spectra of the uncompressed pulse, the pulse after the KCl plate, and the fully compressed pulse at the energy corresponding to optimal compression (full beam).
4. Comparison with theoretical model predictions
Results of numerical modeling using the co2amp software [7] are shown in Figs. 8 and 9.
Fig. 8. Comparison of measured autocorrelation traces of compressed pulses with model predictions for low (a) and high (b) nonlinear absorption. The experimental curves in (a) and (b) correspond to Fig. 5(b) and Fig. 5(c), respectively.
Fig. 9. Results of numerical modeling of the pulse compression in the conditions corresponding to shot $\#$6 in Table 2. (a),(b) Temporal and spectral profiles of the 5 mm dia. central portion of the beam. (c),(d) Temporal and spectral profiles averaged over the entire beam.
The post-compressor model uses the results from comprehensive modeling of the chirped-pulse amplification of a picosecond LWIR pulse in a chain of high-pressure, mixed-isotope CO$_2$ laser amplifiers [1] followed by propagation in air [6] as input. A split-step algorithm is used to model the interaction of the laser pulse with a material. In this algorithm, the material plate is represented by a series of thin slices. Interaction of the pulse with each slice is modeled as follows. First, the nonlinear effect (the $n_2$-related phase delay) of half of the slice on the pulse is calculated in the time domain. Then, the linear part of the interaction (spectral dispersion and linear absorption) is modeled for the entire thickness of the slice in the frequency domain. Finally, the nonlinear effect of the remaining half of the slice is calculated in the time domain. This procedure is repeated for each slice of the material and for each position in the one-dimension spatial calculation grid (radial symmetry is assumed). The slice thickness used in the calculations is 1 mm. This thickness has been validated by confirming that the use of a smaller thickness doesn’t noticeably affect the results. This model neglects the beam size variation inside the material; this is justified by the relatively small thickness of the material and the small divergence of the centimeter-scale beam. Nonlinear absorption and small-scale filamentation are also neglected. Fresnel losses on the surfaces of the compressor elements are accounted for in the model.
Post-compression for pulses at the energies of the representative shots listed in Table 2 was modeled. For a direct comparison with the experimentally measured autocorrelation signals, the average pulse shape inside the 5 mm dia. central portion of the beam and its autocorrelation function were calculated in all cases. A comparison of the numerical calculations with corresponding experimentally measured autocorrelation signals is shown in Fig. 8. This figure uses the same color codes for the shots as Fig. 5. The shots with negligible nonlinear attenuation are shown in Fig. 8(a); very good agreement between the experiment and the model is observed in this case. At high pulse energies (Fig. 8(b)) the model predicts higher intensities than observed in the experiment. This is due to neglecting the filamentation and the nonlinear absorption in our model.
It is important to note that the model accurately reproduces the experiment at the pulse energies corresponding to the optimal post-compression regime. This is the regime that is most relevant for the design of a post-compression scheme and allows us to use the model for deeper insight into the performance of a compressor operating under optimal conditions. The calculation results corresponding to the conditions of shot $\#$6 are summarized in Fig. 9. The pulse evolution at different stages of post-compression (at the input, after the first element, and at the output of the post-compressor) is shown by dotted black, solid blue, and solid red lines, respectively. Sub-figures (a) and (b) correspond to the 5 mm dia. central portion of the beam; sub-figures (c) and (d) represent averaging across the entire beam. The output pulse profile in Fig. 9(a) represents the same pulse as the dashed red curve in Fig. 8(a), but without calculating its autocorrelation. The broadened spectra averaged across the entire beam (blue and red curves in Fig. 9(d)) agree reasonably with the spectra measured experimentally under similar conditions (blue and red curves in Fig. 7 respectively). This agreement provides confidence in the accuracy of the model.
Note that the duration of the input pulse is shorter in the beam center than in the outer areas of the beam. For the 5 mm diameter central part of the beam, the duration is 1.6 ps versus 1.85 ps when averaged over the entire beam. This is due to pulse compression in air, which occurs in the same manner as compression in bulk solids (i.e., SPM accompanied by negative GVD) but requires a longer propagation length due to the orders-of-magnitude smaller $n_2$ and dispersion. Compression of picosecond LWIR pulses in air has been previously observed [13]. We have also experimentally confirmed the 1.6 ps duration of the pulse in the 5 mm diameter central portion of the beam using an autocorrelation measurement in the experimental configuration of Fig. 4 with KCl and BaF$_2$ plates removed.
5. Discussion
Good agreement between the experimentally measured and numerically calculated pulse autocorrelations and spectra at the energies relevant for pulse compression applications leads us to conclude that our model accurately describes the observed pulse evolution in the regime of interest. This is the basis of our conclusion that a 1.6 ps (FWHM) LWIR laser pulse has been successfully compressed to <300 fs in the quasi-flattop central region of a near-Gaussian beam, thus resulting in a 180% increase of the beam’s peak intensity in the central region. The time-bandwidth product of the 290 fs pulse in Fig. 9(a,b) is $\sim$0.4 indicating that the pulse compressed in optimal conditions is nearly transform-limited. When averaged across the entire beam profile, a 1.85 ps pulse has been compressed to <500 fs, corresponding to a 60% increase of the peak intensity.
Partial decoupling of the SPM and dispersive chirp compensation is achieved by using a combination of two materials with substantially different $n_2/\beta _2$ ratios. Pulse compression after the first element of the compressor (a KCl plate) is almost negligible while the spectral broadening by SPM is substantial, corresponding to roughly half the total broadening achieved in the compressor (Fig. 9). This allows matching of the nonlinear spectral broadening and group-delay dispersion of the system and also maintaining optimal B-integrals of the individual components while eliminating the need to adjust the beam size between components.
At the optimal energy, the B-integrals of the two components of the compressor (50 mm KCl and 50 mm BaF$_2$ plates) are roughly equal ($\sim$2.6 in both cases, or 5.2 total). The achieved compression is in good agreement with the analytical expression for SPM spectral broadening of a transform-limited Gaussian pulse [14]:
where $(\Delta \omega )_0$ and $\Delta \omega$ are the spectral bandwidths of the pulse before and after the nonlinear interaction with the material, and $B$ is the B-integral. It has been noted that Eq. (1) remains quite accurate for pulses with shapes that substantially deviate from Gaussian [12]. For $B=5.2$, Eq. (1) gives a factor of 4.7 for spectral broadening; if the resulting chirp is perfectly compensated, the compression factor should be the same. The observed compression factor in the center of the beam is $\sim$5.5, which is in reasonable agreement with the analytical expression. The small discrepancy between the values can be attributed to the fact that Eq. (1) ignores pulse compression during propagation through the nonlinear material due to negative GVD. The numerical model used in our analysis, however, accurately accounts for the simultaneous action of SPM and negative GVD.The total B-integral, corresponding to optimal compression in our experiment, is substantially higher than the rule-of-thumb limit for small-scale self-focusing (2–3) [5,12] despite the absence of spatial filtering and the small propagation distance between the elements of the compressor. We believe that this can be explained by the high quality of the beam achieved by using far-field diffraction on a hard-edge aperture. This method of ensuring high beam quality necessitates the loss of a large fraction of the pulse energy. Thus a more efficient approach must be used in any practical design of a high-energy post-compressor. We are presently investigating the potential of spatial filtering before the post-compressor and between its elements. An additional benefit of spatial filtering is the ability to preserve the super-Gaussian profile of a beam delivered by our laser amplifier operating in a saturated regime. A flattened beam profile will maximize the fraction of the beam that experiences optimal post-compression.
Based on two considerations, we conclude that the post-compression achieved in the center of the beam in this experiment is very close to the maximum compression that can be achieved in a practical two-component post-compression scheme: 1) the B-integrals of the elements of the post-compressor demonstrated in this work under optimal conditions are close to the threshold of small-scale self-focusing for a realistic beam; and, 2) the observed compression agrees both with the detailed numerical model and with the estimation based on a simplified expression Eq. (1). According to Eq. (1), one should expect roughly a factor-of-5 compression of a pulse in a well-optimized two-component scheme with $B=3$ for both components. Detailed numerical modeling provides a slightly more optimistic factor of 7. Thus, the minimal pulse duration achievable with a maximally efficient post-compression of a 2 picosecond LWIR pulse in a two-component scheme is 300–400 fs. A post-compression scheme with an increased number of compression stages can be considered for the production of even shorter LWIR pulses. If, however, a 0.5 ps pulse duration will be achieved in the future in a CPA CO$_2$ laser operating on two vibrational-rotational bands, a two-component post-compressor scheme will be sufficient for achieving the few-cycle LWIR regime.
6. Conclusion
We have proposed a two-component bulk-material LWIR post-compressor scheme with partial separation of Kerr-based spectral broadening and dispersive chirp compensation between the components. While the two components of this scheme contribute roughly equally to the total spectral broadening, the dispersive compression occurs almost exclusively in the second component, thus simplifying the system design and optimization. We have experimentally demonstrated efficient post-compression of sub-terawatt long-wave infrared pulses to <500 fs duration. It is expected that a properly scaled and optimized setup can be utilized in a reliable full-energy post-compressor for multi-terawatt LWIR laser pulses.
As a prerequisite for an accurate design of a post-compressor, the nonlinear refractive indices, $n_2$, of three popular infrared materials, NaCl, KCl, and BaF$_2$, were measured with 2 picosecond 9.2 $\mathrm{\mu}$m pulses. To the best of our knowledge, this is the first reported measurement of $n_2$ of these materials in the picosecond LWIR regime.
Funding
Office of Science (DE-SC0012704).
Acknowledgments
This work was supported by the the US Department of Energy Accelerator Stewardship Program grant, B&R $\#$KA2601020 (PI Mikhail Polyanskiy) and BNL Laboratory Directed Research and Development grant $\#$20-010 AD/NPP (PI Igor Pogorelsky).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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