The results of multiple successful experimental campaigns [1 –3] in the field of relativistic laser–plasma physics have motivated the rapid development of state-of-the-art laser systems, with over 50 petawatt-class lasers under construction or operational worldwide [4]. The continuous improvement in laser system performance enables exciting future applications, such as relativistic electron beams for high energy colliders [5], energetic ion beams for precision cancer therapy, and even inertial confinement fusion to generate a self-sustaining energy source [6]. However, achieving the next levels in laser peak power requires new techniques to overcome the limitations of present-day laser systems employing the chirped pulse amplification (CPA [7]) scheme. While a substantial increase in laser pulse energy—and therefore, laser peak power—is often principally possible, an expensive aperture scaling of the back-end (i.e., final amplifier, beamline optics, and compressor) is required to avoid permanent material damage at high fluences. Additionally, the large beam diameters and long propagation distances present in the final power amplifiers, such as those at the petawatt-class POLARIS [8] laser system at the Friedrich Schiller University and Helmholtz Institute in Jena, Germany, can lead to a significantly aberrated output beam profile [9,10] with a high local fluence that further limits the final laser pulse energy due to the laser-induced damage threshold.

An increase in the laser peak power can also be achieved through a reduction in the pulse duration. Here, a large spectral bandwidth is required, which is limited in CPA systems by the unamplified seed pulse spectrum, emission spectrum of the laser-active materials, and, in some cases, hard-clipping in the stretcher–compressor setup. Even with a broad bandwidth, achieving the Fourier transform limited (FTL) pulse duration is often difficult, due to the existence of uncompensated higher-order dispersion terms [11] or even spatial phase aberrations within the CPA system’s stretcher [12] that lead to high frequency spectral phase distortions. Due to the multiple limitations within the CPA chain, a further significant shortening of the pulse duration must be accomplished after the final pulse compression, i.e., post-CPA. Here, the high intensities of the compressed laser pulse can trigger nonlinear processes such as self-phase modulation (SPM), through which the laser spectrum can be broadened and the pulse subsequently recompressed using a compact chirped mirror pair, thereby directly increasing the peak power. This is particularly important for Yb-based ultrashort laser systems, such as POLARIS, which require nearly three times the energy to achieve the same peak power as Ti:sapphire systems, due to the smaller bandwidth of Yb-doped materials.

Recently, common optical materials such as fused silica (FS) have been explored to generate moderate spectral broadening [13] in the near-field via SPM (NF-SPM), with the potential [14,15] for significant pulse compression after multiple passes. In this Letter, we report on the results of an investigation on multiple commercially available nonlinear materials that exhibit even higher nonlinear refractive indices and a near-zero absorption, ideal for various spectral broadening applications within the laser system. Furthermore, following a proper material selection, we demonstrate that the post-CPA pulse compression technique can enable a pulse duration shortening by a factor of three with a single-pass setup that can be installed directly after the CPA chain of any existing high peak power laser system.

Present-day high peak power laser systems are readily capable of achieving pre-focus, post-CPA pulse intensities in excess of $1 \;{\rm TW}/{{\rm cm}^2}$. Nevertheless, with such laser pulses, enabling significant spectral broadening using SPM in the near-field using a thin (1 mm) material requires a nonlinear refractive index of at least ${{10}^{- 7}} \;{{\rm cm}^2}/{\rm GW}$, which is three orders of magnitude larger than that of the noble gases (e.g., argon or neon [16]) commonly utilized in far-field SPM schemes. Furthermore, to ensure a net increase in the peak power and mitigate the impact of thermal effects on the nonlinear sample, the material absorption and selected thickness must be minimal, such that the anti-reflection (AR)-coated samples provide a near-unity optical transmission. In this section, multiple nonlinear plastics produced by Goodfellow GmbH—allyl diglycol carbonate (CR39) [17], amorphous polyethylene terephthalate (PET) [18], polymethyl methacrylate (PMMA) [19], and cellulose acetate (CA) [20]—are selected as possible candidates for the post-CPA pulse compression method and characterized according to their nonlinear refractive indices and transmission. The results are compared to that of FS, a common optical glass that has been recently tested [13] for NF-SPM using a joule-class, high peak power pulse.

 

Fig. 1. Schematic of the ${n_2}$ characterization setup. A 75 µJ, 126 fs laser pulse induces degenerate four-wave mixing (DFWM) in a thin, nonlinear material. By comparing the DFWM amplitude to the reference, the ${n_2}$ can be determined.

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The nonlinear refractive indices (${n_2}$) of the characterized samples were extracted from degenerate four-wave mixing (DFWM [21]) measurements using the calibrated setup depicted in Fig. 1. Here, a 75 µJ, 126 fs laser pulse from the POLARIS laser system enters the setup and is separated into two nearly equal amplitude components, which are then focused and temporally synchronized inside the designated sample with length $L$, inducing a nonlinear interaction that produces a background-free DFWM signal $A$. The ${n_2}$ of the sample can then be characterized by comparing the resulting DFWM yield to that of a suitable reference material with a known nonlinear refractive index ${n_{{2,{\rm ref}}}}$ via [22]

Table 1. DFWM-Based ${n_2}$ Characterization

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Fig. 2. Optical transmission measurements of the 1 mm (*0.5 mm for PMMA and CA) uncoated nonlinear samples using a spectrophotometer. The data between 825 nm and 900 nm are not considered due to a detector switch within this range.

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In addition to the nonlinear refractive index, the absorption of the nonlinear plastics must be characterized as well, to ensure suitability for the post-CPA pulse compression technique at petawatt-class peak powers. For this purpose, optical transmission measurements, with the results displayed in Fig. 2, were conducted for each sample using a Shimadzu SolidSpec-3700 spectrophotometer that covers the spectral range for both Ti:sapphire and Yb-based laser systems. While AR-coated versions of the nonlinear plastics were not available during this investigation, the surface reflection losses at normal incidence could be calculated using literature refractive index values measured nearest to the POLARIS central wavelength of 1030 nm, providing an adequate estimate for the absorption of each material: 0.04% for CR39 ($n = 1.495$ [26]), 0.73% for PET ($n = 1.551$ [18]), 0.03% for PMMA ($n = 1.483$ [19]), and 3.64% for CA ($n = 1.470$ [20]). Here, AR-coated CR39 and PMMA are capable of providing a near-unity optical transmission, with an absorption even lower than that of FS (0.05%, with $n = 1.450$ [27]). For PET and CA, however, the low but nevertheless non-negligible absorption limits their use in high energy, petawatt-class laser systems such as POLARIS, in which joule-level pulse energies present within the large diameter beams are absorbed by the millimeter-thin uncooled plastic, leading to thermally induced material deformation and a spatially varying SPM-broadened spectrum and compressible pulse duration.

Following the promising results of the nonlinear material characterization, the extent of the achievable spectral broadening through near-field self-phase modulation (NF-SPM) was tested using the designated samples. Here, each nonlinear plastic (1 mm thickness) was individually placed in the optical path of a 2 mJ, 126 fs laser pulse from the output of the first POLARIS CPA stage, with a reduced beam size (1.1 mm FWHM) to match the $1 \;{\rm TW}/{{\rm cm}^2}$ peak intensity of the fully amplified, pre-focus POLARIS laser pulse. A simple beam shaping method involving a telescope and aperture combination was employed to smoothen the spatial profile and mitigate spatiospectral inhomogeneities. A brief discussion and alternative solution to beam shaping are presented as well below. After NF-SPM, the broadened spectra were then measured using a Flame-S (Ocean Optics) spectrometer. As seen in Fig. 3, the ${n_2}$ of CR39 is indeed larger than that of PMMA and CA, with an improvement in the spectral broadening by 20% and 12%, respectively, matching the expected behavior given by the results in Table 1. Furthermore, the use of 1 mm CR39 as the nonlinear medium resulted in a doubling of the FWHM spectral bandwidth in a single pass, while 1 mm amorphous PET provided a near tripling.

 

Fig. 3. Single-pass near-field self-phase modulation using 1 mm CR39, PET, PMMA, and CA, with the initial spectrum in black. The spectral bandwidth, with FWHM values displayed in the legend, of the 2 mJ, 126 fs pulse was doubled after a single pass through CR39 and tripled after PET.

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While the absorption of PET limits its applicability to high energy, ultrashort pulses, the significant spectral broadening enabled by the nonlinear plastic can be employed to correct, e.g., gain narrowing in a millijoule-class multi-pass or regenerative amplifier. For this purpose, the 1 mm PET sample was placed within a Yb:FP15-based regenerative amplifier at POLARIS that amplifies the low power (5 nJ, 20 ps) input pulses up to 2 mJ at a repetition rate of 1 Hz. The potential of this gain narrowing compensation technique is shown in Fig. 4, with the single nonlinear plastic providing a 40% increase in the spectral bandwidth, thereby reducing the compressible pulse duration from 156 fs to 111 fs. The 2 mJ output energy was maintained by rotating the uncoated PET sample for incidence at Brewster’s angle (${\approx} {{57}^ \circ}$ at 1030 nm) to mitigate the losses due to surface reflections, while the 0.73% absorption was accounted for by increasing the pump pulse energy. Although the output beam size initially increased from 0.82 mm to 0.9 mm FWHM due to Kerr lensing, the post-broadening spectral and spatial profiles remained unaltered after long-term operation (${\gg} 1000$ shots) of the SPM-enhanced amplifier, indicating that thermally induced PET deformation was negligible. The residual nonlinear spectral phase terms induced by the influence of intracavity SPM on the chirped amplified pulse [28] can be corrected, e.g., using an acousto-optic programmable dispersive filter—not only to improve the temporal rising edge, but also to achieve an FTL pulse duration shorter than that of the pre-SPM case, due to the enhanced spectral bandwidth.

 

Fig. 4. Gain narrowing compensation using 1 mm PET within a mJ-class Yb:FP15-glass amplifier. The amplified spectrum (left) was broadened by 40% while maintaining the output 2 mJ pulse energy and Gaussian-like spatial profile (right). The spectral fringes are the result of interference between the 20 ps pulse and residual surface reflections due to the uncoated PET.

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Fig. 5. Temporal profile measurements of the POLARIS laser pulse after the first CPA system. Using the post-CPA pulse compression technique with NF-SPM in 1 mm CR39, the initial 126 fs pulse was shortened by factors of 2.4 and 3.2 for incident pulse intensities of $1 \;{\rm TW}/{{\rm cm}^2}$ and $2 \;{\rm TW}/{{\rm cm}^2}$, respectively.

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For petawatt-class peak power applications of the post-CPA pulse compression method, the highly nonlinear CR39, which, simultaneously, exhibits an order of magnitude lower absorption than that of PET, has been selected as the most suitable material out of the characterized samples. To verify the compressibility of the previously utilized $1 \;{\rm TW}/{{\rm cm}^2}$ POLARIS laser pulse after spectral broadening via NF-SPM in 1 mm CR39, a chirped mirror pair (Layertec GmbH) and second-order autocorrelator (TOPAG GmbH) were installed within the experimental setup. The bandwidth-doubled laser pulse was then compressed using the compact chirped mirror pair ($6 \times - 250\;{{\rm fs}^2}$/bounce) to 52 fs FWHM—2.4 times shorter than the 126 fs input pulse duration—as seen in autocorrelation traces in Fig. 5, which employ a ${{\rm sech}^2}$ fit and are integrated across the full (unsampled) beam profile. A further spectral bandwidth enhancement from the initial 15 nm up to 47 nm FWHM was subsequently accomplished by increasing the laser pulse intensity to $2 \;{\rm TW}/{{\rm cm}^2}$ through a reduction in the beam diameter, enabled by the near-zero absorption offered by CR39. The spectral phase compensation by the chirped mirrors allowed for a compressed pulse duration of 40 fs FWHM—likely a slight underestimation of the actual value, due to the influence of higher-order spectral phase terms that are evident by the post-compression pulse wing formation in Fig. 5—resulting in an approximate $3.2 \times$ enhancement of the laser pulse peak power after a single pass through the 1 mm nonlinear plastic.

While the scope of this Letter covers the characterization and demonstration of nonlinear plastics such as CR39 for post-CPA pulse compression, multiple relevant limitations [29] including beam breakup via filamentation, nonlinear absorption, and spatiospectral homogeneity must be considered for high energy, petawatt-class laser pulses and are a matter of further investigation. A solution to the latter issue is currently being developed, in which the thickness of the CR39 sample is spatially varied to prevent the otherwise inhomogeneous spectral broadening along the input (e.g., Gaussian-like) beam profile. The resulting spatiotemporal optical path difference (OPD) profile induced by the curved plastic material can then be corrected by an inversely formed compensation plate that exhibits both a minimal absorption and nonlinear refractive index (e.g., ${\rm MgF}_2$ [30]). Here, a spatially homogeneous broadened spectrum and compressible pulse duration can be enabled for multiple beam types, while avoiding the losses incurred using common beam shaping techniques.

In conclusion, a substantial shortening of the pulse duration at an intermediate stage within the POLARIS laser system has been demonstrated via NF-SPM and post-CPA pulse compression using a compact, single-pass setup comprising a highly nonlinear 1 mm plastic and a chirped mirror pair. An investigation to determine the proper material was first conducted, in which the nonlinear refractive indices of multiple samples—CR39, PET, PMMA, and CA—were characterized in a DFWM-based measurement setup, with FS as the reference material. Each tested plastic exhibited an ${n_2}$ value sufficient for NF-SPM using the $1 \;{\rm TW}/{{\rm cm}^2}$ transport intensities readily achievable in high peak power laser systems. With the additional results from broadband optical transmission measurements, CR39, with ${n_{2}} = 6.24 \times {10^{- 7}}\; \frac{{{{{\rm cm}}^2}}}{{{\rm GW}}}$ and a near-zero absorption, was selected for post-CPA pulse compression within the POLARIS laser chain.

The viability of NF-SPM using the designated nonlinear samples was further tested using a 2 mJ, 126 fs laser pulse, with the results confirming the DFWM-based ${n_2}$ measurements and providing an increase in the spectral bandwidth by a factor of two after 1 mm CR39 and a factor of three after 1 mm PET. The non-negligible absorption of PET prevents high energy applications, but was instead utilized to compensate for gain narrowing within a millijoule-class Yb:FP15-glass amplifier, offering a 40% enhancement of the spectral bandwidth. Finally, the post-CPA pulse compression technique employing the optimal 1 mm CR39 was verified using the POLARIS laser pulse after the first CPA stage, inducing NF-SPM in a single-pass configuration with a doubling and tripling of the spectral bandwidth at pulse intensities of $1 \;{\rm TW}/{{\rm cm}^2}$ and $2 \;{\rm TW}/{{\rm cm}^2}$, respectively. Subsequent pulse compression with a chirped mirror pair resulted in an increase in peak power by a factor of 3.2, demonstrating the potential of the post-CPA pulse compression technique using CR39 to enable a significant intensity enhancement without large-scale, costly changes to the existing high peak power laser system.