Simulating spatiotemporal dynamics of ultra-intense ultrashort lasers through imperfect grating compressors

Zhaoyang Li; Zhaoyang Li; Jun Liu; Yi Xu; Yuxin Leng; Yuxin Leng; Ruxin Li; Ruxin Li; Ruxin Li; Ruxin Li

doi:10.1364/OE.473439

1. Introduction

Strong-field quantum electrodynamics (SF-QED) is a very important research field in the modern physics [1,2]. When beyond the intensity ∼10²³ W/cm², quantum effects like vacuum birefringence would appear [3,4]. When near the critical intensity (Schwinger limit) ∼10²⁹ W/cm², electron-positron pairs can be directly generated from vacuum, which is also known as “strong-field vacuum breakdown” [5–9]. In a nonideal vacuum at a laboratory environment, a recent study shows residual electrons would trigger QED cascade, i.e., nonlinear Compton scattering and nonlinear Breit–Wheeler process, which happens from the intensity ∼10²⁵ W/cm² and then predicts an upper limit intensity ∼10²⁶ W/cm² [10]. One important physical objective of our under-constructed project of the Station of Extreme Light 100 PW laser (SEL-100PW) in Shanghai, China is to observe and study these SF-QED effects in experiments [11]. The currently reported highest intensity directly produced by a laser is 10²³ W/cm² [12], which is still many orders of magnitude lower than the expected value of 10²⁶ or 10²⁹ W/cm². The optical intensity of a driven laser is the fundamental condition for SF-QED, although many plasma methods have been proposed to further increase the radiation intensity by reducing light wavelengths in spectrum (accordingly focal spots in space) and shortening pulse durations in time [13–17]. The SEL-100PW laser is designed with a 1500 J energy, a 15 fs duration, and accordingly a 100 PW peak-power. When the beam is focused with a spot size of 10, 5, and 2 µm, respectively, the achieved intensity would be 1.3 × 10²³, 5.1 × 10²³, and 3.2 × 10²⁴ W/cm². This simple estimation is based on an ideal pulse beam without any spatiotemporal coupling distortion, which is reasonable in a long-pulse narrow-beam laser but incorrect in a short-pulse large-beam laser, such as ELI-NP [18], SULF-10PW [19], and SEL-100PW [11] lasers. In a traditional chirped pulse amplification (CPA) or optical parametric chirped pulse amplification (OPCPA) laser, some precision-dispersion elements [20,21] are used to compensate the residual temporal dispersion for the Fourier-transform limit pulse, and deformable mirrors [22] are introduced to correct the wavefront error for the diffraction limit focal-spot. However, the dispersion management is spatial-independent and the wavefront correction is spectral-independent (or temporal-independent), and consequently the spatiotemporal coupling distortion cannot be removed which would degrade the focused intensity at the target [23–29]. In an ultra-intense ultrashort laser, the nature of the major spatiotemporal coupling distortion is different frequencies of a broadband pulse beam have different wavefronts in space-spectrum, and after coherent superposition, the optical field has a coupled distortion in space-time [30]. The traditional linear spatiotemporal coupling distortion, for example pulse-front curvature [31,32] and pulse-front tilt [33], has been well studied, which can be easily removed [34–36]. However, a recently reported complex spatiotemporal coupling distortion [24,25], caused by the grating wavefront error in a large-aperture grating compressor, cannot be removed by the traditional methods. In our earlier works, we have introduced this distortion in space-time/spectrum [24,25] for a common single-pass double-pair grating compressor (i.e., single-pass symmetrical four-grating compressor). In the future, this problem will get worse as the development of the ultra-intense ultrashort laser from 10 PW to 100 PW, because the bottleneck of a 100 PW laser changes from the high-energy pulse-amplification to the large-aperture pulse-compression, as well as the following beam focusing. Here, to meet the development requirement of the future Exawatt-class laser, especially the technical and engineering requirement of our SEL-100PW laser project, we have improved our model and studied more complete spatiotemporal dynamics, aiming at providing a clear understanding and a scientific reference for both the current project and the future development. This work is also important for all CPA/OPCPA femtosecond lasers from millijoules to kilojoules.

2. Improved model and simulation parameter

The spatiotemporal phase coupling induced by the grating wavefront error has been introduced in our previous works [24,25]: a 2 D [(1 + 1) D] and a 3 D [(2 + 1) D] space-time models were developed; the optical field after the compressor was given; and a common configuration of the single-pass double-pair grating compressor was considered. In the improved model, two important factors of the spatio-spectral clipping induced by the limited grating size and the spatiotemporal amplitude coupling induced by the grating amplitude modulation are added in the 3 D model; the optical field inside the compressor is given; and another configuration of the single-pass single-pair grating compressor is considered for comparison. The improved model is closer to the reality than the previous model, and the comparison between two compressor configurations facilitates the engineering design.

A moving coordinate system of x–y–z is defined on the pulse beam, which propagates with the pulse beam through the grating compressor, as well as the following focusing optics, and eventually arrives at the target. The z–axis is along the central optical ray at the center frequency, and the x–y plane is on the phase-front of the center frequency. A 3 D matrix is used to describe the (2 + 1) D optical field in space-time/spectrum, and the horizontal, vertical and longitudinal directions of the matrix denote the x–, y– and t/ω–axes of the pulse beam, respectively. The grating grooves are along the y–axis, and then the angular dispersion happens in the x–z plane.

2.1 Single-pass double-pair grating compressor

The single-pass double-pair grating compressor has four gratings G1-4. Because “G1 and G4” or “G2 and G3” have the same spatio-spectral coupling (i.e., the beam at G1 and G4 has no spatial chirp, and the beam at G2 and G3 has the same spatial chirp), the imperfections of G4 and G3 are overlaid onto those of G1 and G2, respectively, and the overlaid imperfections of G1&4 and G2&3 are considered for simplification [24,25], like combining “like terms” in mathematics. In this article, although G1&4 and G2&3 have the same overlaid imperfection, which have a relative shift in space to avoid a “phase up” or “phase down” superposition. The spatio-spectral amplitudes of the pulse beam before, in (between G2 and G3), and after the compressor modulated by the spatio-spectral clipping and the grating amplitude modulation are given by

(1)$$\left\{ {\begin{array}{c} {{A_{before}}({x,y,\omega } )= A(\omega )A({x,y} )}\\ {{A_{Din}}({x,y,\omega } )= A(\omega )A({x - \delta {x_\omega },y} ){C_G}({x,y} ){M_{G1\& 4}}({x - \delta {x_\omega },y} ){M_{G2\& 3}}({x,y} )}\\ {{A_{Dafter}}({x,y,\omega } )= A(\omega )A({x,y} ){C_G}({x + \delta {x_\omega },y} ){M_{G1\& 4}}({{x_\omega },y} ){M_{G2\& 3}}({x + \delta {x_\omega },y} )} \end{array}} \right.. $$

A(ω) is the m-order super-Gaussian spectral amplitude, A(x, y) is the n-order super-Gaussian spatial amplitude, C_G(x, y) is the clipping function by G2&3, M(x, y) is the grating amplitude modulation function, δx_ω is the frequency-dependent x-axis beam shift in the compressor with respect to the center frequency ω₀, and the above are given by

(2)$$A(\omega )= {A_0}\exp \left[ { - {2^{m - 1}}\ln 2{{\left( {\frac{{\omega - {\omega_0}}}{{\Delta \omega }}} \right)}^m}} \right], $$

(3)$$A({x,y} )= \exp \left\{ { - {2^{n - 1}}\ln 2\left[ {{{\left( {\frac{x}{{{B_{FWHM}}}}} \right)}^n} + {{\left( {\frac{y}{{{B_{FWHM}}}}} \right)}^n}} \right]} \right\}, $$

(4)$${C_G}({x,y} )= rect\left( {\frac{x}{{{L_G}\cos \alpha }}} \right)rect\left( {\frac{y}{{{W_G}}}} \right), $$

(5)$$M({x,y} )= 1 + \eta \cdot r({x,y} ), $$

(6)$$\delta {x_\omega } ={\pm} ({\tan {\beta_0} - \tan {\beta_\omega }} )\frac{{{\omega _0}{d^2}{{\cos }^3}{\beta _0}}}{{2\pi }}\frac{{\Delta T}}{{\Delta \lambda }}\cos \alpha. $$

A₀ is the amplitude, Δω and B_FWHM are the FWHM (full-width at half maximum) spectral bandwidth and beam aperture, L_G and W_G are the grating length and width, η is the grating amplitude modulation coefficient, r(x, y) is a random function within [−1, 1], α is the incident angle, β₀ and β_ω are the diffraction angles of ω₀ and ω, d is the grating constant, and ΔT/Δλ is the chirp ratio of each grating pair G1&2 or G3&4. Here, + and – in Eq. (6) applies to the case with an incident angle larger and smaller than the Littrow angle, respectively.

The spatio-spectral phases of the pulse beam in (between G2 and G3) and after the compressor modulated by the spatio-spectral clipping and the grating wavefront error are given by

(7)$$\left\{ {\begin{array}{c} {{\phi_{Din}}({x,y,\omega } )= \frac{\omega }{c}[{{f_{G1\& 4}}({x - \delta {x_\omega },y,0,0} )+ {f_{G2\& 3}}({x,y,{\varphi_x},{\varphi_y}} )} ]{C_B}({x - \delta {x_\omega },y} ){C_G}({x,y} )}\\ {{\phi_{Dafter}}({x,y,\omega } )= \frac{\omega }{c}[{{f_{G1\& 4}}({x,y,0,0} )+ {f_{G2\& 3}}({x + \delta {x_\omega },y,{\varphi_x},{\varphi_y}} )} ]{C_B}({x,y} ){C_G}({x + \delta {x_\omega },y} )} \end{array}} \right.. $$

In the first equation of Eq. (7), the spatially-uniformed temporal chirp ϕ_TC(ω) of the incident chirped-pulse beam is not included. f(x, y, φ_x, φ_y) is the wavefront function of the pulse beam modulated by the grating wavefront error, C_B(x, y) is the beam aperture function, and the above are given by

(8)$$f({x,y,{\varphi_x},{\varphi_y}} )= \frac{{{H_l}}}{2}\left[ {\sin \left( {2\pi \frac{x}{{L\cos \alpha }} + {\varphi_x}} \right) + \sin \left( {2\pi \frac{y}{L} + {\varphi_y}} \right)} \right] + \frac{{{H_h}}}{2}r({x,y} ), $$

(9)$${C_B}({x,y} )= rect\left( {\frac{x}{{{B_{FW}}}}} \right)rect\left( {\frac{y}{{{B_{FW}}}}} \right). $$

H_l and H_h are the peak-to-valley (PV) values of low- and high-spatial frequency wavefront errors, L is the spatial period of the low-spatial frequency wavefront error on the grating surface, φ_x and φ_y denote the horizontal and vertical relative shifts between two overlaid wavefronts of G1&4 and G2&3, respectively, and B_FW is the FW (full-width) beam aperture.

The complex amplitudes of the pulse beam in (between G2 and G3) and after the compressor are given by

(10)$$\left\{ {\begin{array}{c} {{E_{Din}}({x,y,\omega } )= {A_{\textrm{Din}}}({x,y,\omega } )\exp [{i{{{\phi_{TC}}(\omega )} / 2} + i{\phi_{Din}}({x,y,\omega } )} ]}\\ {{E_{Dafter}}({x,y,\omega } )= {A_{\textrm{Dafter}}}({x,y,\omega } )\exp [{i{\phi_{Dafter}}({x,y,\omega } )} ]} \end{array}} \right., $$

where, ϕ_TC(ω)/2 is the uncompensated temporal chirp after the first grating pair G1&2.

2.2 Single-pass single-pair grating compressor

The single-pass single-pair grating compressor has two gratings G1–2, and the spatio-spectral amplitude of the pulse beam after the compressor modulated by the spatio-spectral clipping and the grating amplitude modulation is given by

(11)$${A_{Safter}}({x,y,\omega } )= A(\omega )A({x - \delta {x_\omega },y} ){C_G}({x,y} ){M_{G1}}({x - \delta {x_\omega },y} ){M_{G2}}({x,y} ). $$

The spatio-spectral phase of the pulse beam after the compressor modulated by the spatio-spectral clipping and the grating wavefront error is given by

(12)$${\phi _{Safter}}({x,y,\omega } )= \frac{\omega }{c}[{{f_{G1}}({x - \delta {x_\omega },y,0,0} )+ {f_{G2}}({x,y,{\varphi_x},{\varphi_y}} )} ]{C_B}({x - \delta {x_\omega },y} ){C_G}({x,y} ). $$

C_G(x, y) is the clipping function by G2, ΔT/Δλ is the chirp ratio of the single grating pair G1&2, and φ_x and φ_y denote the horizontal and vertical relative shifts between two wavefronts of G1 and G2, respectively. The complex amplitude of the pulse beam after the compressor is given by

(13)$${E_{Safter}}({x,y,\omega } )= {A_{\textrm{Safter}}}({x,y,\omega } )\exp [{i{\phi_{Safter}}({x,y,\omega } )} ]. $$

2.3 Electric field in space-time

For both the single-pass double- and single-pair grating compressors, the electric field after pulse compression (defined as the near-field) is given by

(14)$${E_n}({x,y,t} )= {\raise0.7ex\hbox{$1$} \!\mathord{/ {\vphantom {1 {2\pi }}} }\!\lower0.7ex\hbox{${2\pi }$}}\int {{E_{after}}({x,y,\omega } )\exp ({i\omega t} )d\omega }, $$

and which after beam focusing (defined as the far-field) is given by

(15)$${E_f}({x^{\prime},y^{\prime},t} )= \int\!\!\!\int {{E_n}({x,y,t} )\exp \left( { - i\frac{{2\pi }}{\lambda }\frac{{x^{\prime}x + y^{\prime}y}}{f}} \right)dxdy}, $$

where f is the focal length.

2.4 Simulation parameter

The following simulation and analysis will be based on the preliminary design of the SEL-100PW laser, however which won’t affect the generalizability of the improved model and the guiding value for other facilities. The input chirped-pulse beam to the compressor has a 12^th order super-Gaussian spectrum with a 210 nm FWHM bandwidth centered at 925 nm, a 4ns/210nm chirp ratio, and a 16^th order super-Gaussian beam with a 640 mm FWHM square aperture. The compressor has a groove density of 1320 g/mm, an incident angle of 61°, and a limited grating size of 1450 × 700 mm² which is the largest size in the world. The grating-pair perpendicular distances for the single-pass double- and single-pair grating compressors are 1464 mm and 2928 mm, respectively. Referring to a measured wavefront error of our current meter-sized golden grating, as shown by the inset of Fig. 1(a), we produced a sine-function wavefront error with a 600 mm period and a λ/3@800 nm PV value. When this wavefront error is projected from the grating surface into the beam aperture, the period changes from 600 mm to around 291 mm. Another random fast-varying (high-spatial frequency) wavefront error with a maximum PV of λ/10@800 nm and a fixed spatial period of 5 mm is added on the slow-varying (low-spatial frequency) wavefront error. Figure 1(a) shows the wavefront error could well represent the measured one for achieving a general study in this article. Figure 1(b) shows the random amplitude modulation is within [0.9, 1.1] (i.e., η=0.1) and has a fixed spatial period of 5 mm. The other simulation parameters include: the focal length of the focusing optics is 2 m; the simulation window and sampling period are 400 fs and 0.2 fs in time and 4 × 4 m² and 5 × 5 mm² in the near-field space, respectively; and those in spectrum (i.e., temporal frequency) and in the far-field space (i.e., spatial frequency) can be directly calculated according to the Fourier transform relationship.

Fig. 1. Wavefront error and amplitude modulation. (a) Wavefront error and (b) amplitude modulation of gratings used in this article. Inset in (a) shows measured wavefront of a meter-sized golden grating. x is transverse coordinate of beam cross-section, and wavefront error and amplitude modulation are projected from grating surface to beam cross-section.

Download Full Size | PDF

3. Distortion in (2 + 1) D space-time

Using the above improved model and given parameters, the (2 + 1) D spatiotemporal electric fields in the x-y-t domains are calculated. With the ideal compressor (doesn’t exist actually), Figs. 2(a) and 2(b) show the compressed and focused electric fields in the near- and far-fields, respectively. Figures 2(c) and 2(d) show the corresponding results with an imperfect single-pass double-pair grating compressor, respectively. In this article, for observing electric fields in space-time, the frequency of the carrier wave is multiplied by 0.5 to avoid a fast oscillation. Figure 2(a) shows the ideal compressor completely removes the temporal chirp without introducing any modulation and outputs the Fourier-transform limit pulse across the beam in the near-field. Figure 2(b) shows after an ideal beam focusing both the diffraction-limit focal spot and the Fourier-transform limit pulse appear in the far-field. When using an imperfect single-pass double-pair grating compressor, Fig. 2(c) shows the electric field in the near-field has spatiotemporal coupling distortion in the x–t plane and spatial-only distortion in the y–t plane. Figure 2(d) shows after beam focusing the electric field in the far-field also has spatiotemporal coupling distortion in the x–t plane and spatial-only distortion in the y–t plane. Because in the moving coordinate system of x–y–z grating grooves are along the y–axis, the angular dispersion, as well as the spatiotemporal coupling distortion, happens in the x–z plane. The spatial-only distortion in the y–t plane can be corrected by deformable mirrors. However, the spatiotemporal coupling distortion in the x–t plane cannot be easily removed, which will degrade the focused intensity. Because the spatial-only distortion has been well studied previously, here to reduce the simulation load and focus on the spatiotemporal coupling distortion, we will only simulate the (1 + 1) D fields in the x–t/Δf plane and (1 + 1) D phases in the x–Δf plane for different cases, where Δf is the frequency difference about the center frequency. Of course, by using the improved model, one can also simulate the complete (2 + 1) D optical fields in space-time/spectrum if required.

Fig. 2. (2 + 1) D electric fields. Compressed electric fields in the near-field with (a) ideal and (c) imperfect compressors. Focused electric fields in the far-field with (b) ideal and (d) imperfect compressors. Frequency of carrier wave is multiplied by 0.5 to avoid fast oscillation.

Download Full Size | PDF

4. Distortion in single-pass double-pair grating compressor

An ideal super-Gaussian chirped-pulse beam with plane wavefronts for all frequencies inputs to the compressor, where the initial temporal chirp is uniform in space. Figure 3(a) shows (1 + 1) D fields of the ideal compressor which are going to be used as a reference standard in this article. Figure 3(a)(i) shows the spatio-spectral intensity field I(x, Δf) = I(x)I(Δf), which is not changed before and after the ideal compressor. Figures 3(a)(ii) and 3(a)(iii) show the electric fields in the near- and far-fields E_n(t, x) = A_FTL(t)A(x) and E_f(t, x) = A_FTL(t)A_DL(x), where the subscripts FTL and DL denote Fourier-transform limit and diffraction limit, respectively. The on-axis pulse in the far-field is defined as the “on-target pulse”. The red curve in Fig. 1(b)(vi) shows the on-target pulse for the ideal compressor, which is normalized to the reference standard of “1” for comparison in this article.

Fig. 3. Comparison between ideal compressor and perfect single-pass double-pair grating compressor. (a) Dynamics of ideal compressor: (i) (x–Δf) intensity field (no change during propagation), and (x–t) electric fields after (ii) pulse compression and (iii) beam focusing. (b) Dynamics of perfect single-pass double-pair grating compressor: (i) schematic, (x–Δf) intensity fields (ii) in and (iii) after compressor, (x–t) electric fields after (iv) pulse compression and (v) beam focusing, and (vi) on-target (at x = 0) pulse (blue curve). Green curves in (a)(i), (b)(ii) and (b)(iii) illustrate intensity integrals in frequency. In (b)(vi), on-target (at x = 0) pulse (red curve) of ideal compressor is reference standard of “1”, and that (blue curve) of perfect single-pass double-pair grating compressor degrades to 0.88 due to spatio-spectral clipping. Δf, frequency about center frequency; t, local time; G1-4, grating 1-4; and F, ideal focusing optics.

Download Full Size | PDF

Figure 3(b) shows the result of the single-pass double-pair grating compressor which is quite different from the ideal compressor, even though the compressor has perfect gratings without any wavefront error and amplitude modulation. Figure 3(b)(i) gives the schematic, and Fig. 3(b)(ii) shows although the spatio-spectral intensity field in the compressor is clipped only in space by G2 and G3, because of the spatial chirp, the higher and lower frequencies are clipped at the upper and lower beam edges, respectively, resulting in spatio-spectral clipping. After the compressor, Fig. 3(b)(iii) shows although the spatial chirp is compensated, the intensity field still has spatio-spectral coupling modulation I(x, Δf) ≠ I(x)I(Δf), and Fig. 3(b)(iv) shows the electric field has spatiotemporal coupling distortion E_n(t, x) ≠ A_FTL(t)A(x). Because the spectra at the upper and lower beam edges are narrowed (red and blue shifted, respectively), the pulses at the upper and lower beam edges are broadened. At the focus, Fig. 3(b)(v) shows the electric field has obvious spatiotemporal tilt E_f(t, x) ≠ A_FTL(t)A_DL(x), and the blue curve in Fig. 3(b)(vi) shows the on-target pulse degrades to 0.88 with respect to the reference standard “1”. This spatiotemporal degradation has three factors of pulse broadening due to spectral narrowing at beam edges, focal spot enlarging due to beam reduction at higher and lower frequencies, and energy loss due to spatio-spectral clipping.

Next, we will analyze the influence of amplitude modulation and wavefront error of each grating. Because two overlaid imperfections of G1&4 and G2&3 are considered, we just need to study three cases of G1&4, G2&3, and G1-4 having the imperfection.

When G1&4 has the amplitude modulation, Fig. 4(a)(i) shows in the compressor the intensity modulation is smeared due to spatial chirp, however Fig. 4(a)(ii) shows after the compressor it appears due to spatial chirp compensation. Figures 4(a)(iii)-(v) show the additional influences on the electric fields in the near- and far-fields and the on-target pulse are negligible. When G2&3 has the amplitude modulation, the situation is opposite. Figure 4(b)(i) shows in the compressor the intensity modulation is obvious, and Fig. 4(b)(ii) shows it disappears after the compressor. Figures 4(b)(iii)-(v) show the electric fields and the on-target pulse almost remain unchanged. When G1-4 have the amplitude modulation, although Figs. 4(c)(i) and 4(c)(ii) show the intensity modulations exist both in and after the compressor, Figs. 4(c)(iii)-(v) show the additional influences on the electric fields and the on-target pulse are very weak. The current meter-sized golden gratings have very-uniform and high-efficiency diffraction across the aperture, and no significant slow-varying amplitude modulation is observed. Here, we can find that the change of spatial chirp can smear the adverse influence of the grating amplitude modulation (also known as spectral-dependent beam smoothing), and which is not a key factor to the degradation of the optical fields and the on-target pulse.

Fig. 4. Amplitude modulations and optical fields. When (a) G1&G4, (b) G2&G3, and (c) G1-4 have amplitude modulation, respectively, (x–Δf) intensity fields (i) in and (ii) after compressor, (x–t) electric fields after (iii) pulse compression and (iv) beam focusing, and (v) on-target (at x = 0) pulses (blue curve). Green curves in (i) and (ii) illustrate intensity integrals in frequency. On-target (at x = 0) pulses (blue curve) deviate from reference standard “1” (red curve) to (a)(v) 0.88, (b)(v) 0.88 and (c)(v) 0.87, respectively.

Download Full Size | PDF

When G1&4 has the wavefront error, Fig. 5(a)(i) shows in the compressor the phase is spatio-spectrally coupled due to spatial chirp, however Fig. 5(a)(ii) shows after the compressor it is only space-dependent due to spatial chirp compensation. Figure 5(a)(iii) shows after pulse compression the electric field has only space-dependent time delays across the beam, that is pulse- and phase-fronts distort but without any separation between pulse- and phase-fronts due to the same distorted wavefront for all frequencies. Figure 5(a)(iv) shows after beam focusing it has spatial side-lobes around the focal spot, and Fig. 5(a)(v) shows the on-target pulse degrades from 0.88 to 0.56. When G2&3 has the wavefront error, the situation is opposite. Figure 5(b)(i) shows in the compressor the phase is only space-dependent, however Fig. 5(b)(ii) shows after the compressor it becomes spatio-spectrally coupled. Figure 5(b)(iii) shows after pulse compression the electric field has serious spatiotemporal coupling distortion, which is caused by the coherent superposition of waves with different wavefronts at different frequencies. Figure 5(b)(iv) shows after beam focusing the electric field has spatiotemporally distorted side-lobes around the focal spot in space and pre/post-pulses around the main pulse in time, and Fig. 5(b)(v) shows the on-target pulse degrades from 0.88 to 0.55. When G1-4 have the wavefront error (the relative shift between two wavefront errors in space is 2π/3, i.e., 291mm/3), Figs. 5(c)(i) and 5(c)(ii) show the phases both in and after the compressor are spatio-spectrally coupled. Figures 5(c)(iii) and 5(c)(iv) show the spatiotemporal coupling distortions of the electric fields increase, and Fig. 5(c)(v) shows the on-target pulse further degrades to 0.44. The above result shows the wavefront error of gratings and the change of spatial chirp can introduce spatio-spectrally coupled phase and then spatiotemporally coupled electric field, which is a key factor to the degradation of the optical fields and the on-target pulse.

Fig. 5. Wavefront errors and optical fields. When (a) G1&G4, (b) G2&G3, and (c) G1-4 have wavefront error, respectively, (x–Δf) phases (i) in and (ii) after compressor, (x–t) electric fields after (iii) pulse compression and (iv) beam focusing, and (v) on-target (at x = 0) pulses (blue curve). On-target (at x = 0) pulses (blue curve) deviate from reference standard “1” (red curve) to (a)(v) 0.56, (b)(v) 0.55 and (c)(v) 0.44, respectively.

Download Full Size | PDF

To improve the on-target intensity, the spatio-spectrally coupled phase induced by the grating wavefront error need to be corrected. Based on the result in Fig. 5(c), a deformable mirror is positioned before/after the single-pass double-pair grating compressor to correct the slow-varying (low-spatial frequency) wavefront error, which matches with the wavefront at the center frequency. Because the correction is spectral-independent, Fig. 6(a)(i) shows only the slow-varying (low-spatial frequency) wavefront at the center frequency is corrected, and the phase is still spatio-spectrally coupled. Figures 6(a)(ii) and 6(a)(iii) show the electric fields are changed but still spatiotemporally coupled, and Fig. 6(a)(iv) shows the on-target pulse just slightly improves from 0.44 to 0.49. This shows the traditional (spectral-independent) wavefront detection and correction are useless now [22], and the spectral-dependent method becomes necessary for the current and the future ultra-intense ultrashort lasers [37–39]. For example, we can position one deformable mirror before/after the single-pass double-pair grating compressor to remove the slow-varying (low-spatial frequency) wavefront error induced by G1&4 and another deformable mirror between G2 and G3 to correct that induced by G2&3. We can also use the pre-compensation method introduced in Ref. [39] to correct the slow-varying (low spatial frequency) wavefront error of G2&3 before the compressor by imaging the pre-compensation into the compressor. When the slow-varying (low spatial frequency) wavefront errors induced by G1-4 are removed [only remain fast-varying (high spatial frequency) wavefront errors induced by G1-4], Fig. 6(b)(i) shows the value of the spatio-spectral phase distortion is very small, Figs. 6(b)(ii) and 6(b)(iii) show the electric fields have very weak spatiotemporal coupling distortions, and Fig. 6(b)(iv) shows the on-target pulse dramatically improves from 0.44 to 0.84, very near 0.88. This shows, to obtain a high on-target intensity, the slow-varying (low spatial frequency) wavefront errors of all gratings, especially G2 and G3, in a single-pass double-pair grating compressor should be detected and corrected, while the fast-varying (high spatial frequency) ones can be left alone.

Fig. 6. Wavefront corrections and optical fields. All G1-4 have wavefront error, when (a) spectral-independent and (b) spectral-dependent wavefront corrections are introduced to remove low-spatial-frequency (slow-varying) wavefront error, respectively, (i) (x–Δf) phases after pulse compression, (x–t) electric fields after (ii) pulse compression and (iii) beam focusing, and (iv) on-target (at x = 0) pulses (blue curve). On-target (at x = 0) pulses (blue curve) deviate from reference standard “1” (red curve) to (a)(iv) 0.49 and (b)(iv) 0.84, respectively.

Download Full Size | PDF

5. Distortion in single-pass single-pair grating compressor

Compared with a single-pass double-pair grating compressor, it is easier in engineering to correct the wavefront errors of all gratings in a single-pass single-pair grating compressor [40]. Figure 7(a) schematically shows the perpendicular distance of the grating pair is enlarged from 1464 mm to 2928 mm to remove the temporal chirp, and the output spatially-chirped beam is directly focused by an ideal focusing optics, which is also known as “spatiotemporal focusing” in optical micro-fabrications [41–43].

Fig. 7. Spatio-spectral clipping and optical fields in single-pass single-pair grating compressor. (a) Schematic. (b) Dynamics of perfect single-pass single-pair grating compressor: (x–Δf) intensity fields (i) before and (ii) after compressor, (x–t) electric fields after (iii) pulse compression and (iv) beam focusing, and (v) on-target (at x = 0) pulse (blue curve). Green curves in (i) and (ii) illustrate intensity integrals in frequency. In (v), on-target (at x = 0) pulse (blue curve) deviates from reference standard “1” (red curve) to 0.73 due to spatio-spectral clipping. G1 and G2, gratings 1 and 2; and F, ideal focusing optics.

Download Full Size | PDF

Figure 7(b)(i) shows the input spatio-spectral intensity field, and Fig. 7(b)(ii) shows both the spatial chirp and the spatio-spectral clipping increase (the spectral narrowing and blue/red shifting at the upper/lower beam edge increase). Figure 7(b)(iii) shows the pulse broadening at the upper and lower beam edges increases, Fig. 7(b)(iv) shows the spatiotemporal tilt of the focused electric field increases, and Fig. 7(b)(v) shows the on-target pulse degrades from 1 to 0.73, lower than 0.88 for the single-pass double-pair grating compressor.

When G1 has the imperfection (both wavefront error and amplitude modulation), Fig. 8(a)(i) shows after the compressor the intensity modulation is smeared due to spatial chirp, however, Fig. 8(a)(ii) shows the phase becomes spatio-spectrally coupled. Figures 8(a)(iii) and 8(a)(iv) show both the electric fields after pulse compression and beam focusing have spatiotemporal coupling distortions, and Fig. 8(a)(v) shows the on-target pulse degrades from 0.73 to 0.47. When G2 has the imperfection, Figs. 8(b)(i) and 8(b)(ii) show both the intensity and the phase have only space-dependent modulations, and Fig. 8(b)(iii) shows the compressed electric field has only space-dependent time delays across the beam without any separation between pulse- and phase-fronts due to the same distorted wavefront for all frequencies. Figure 8(b)(iv) shows the focused electric field has only spatial side-lobes around the focal spot, and Fig. 8(b)(v) shows the on-target pulse degrades from 0.73 to 0.44. When G1&2 have the imperfection (the relative shift between two wavefront errors in space is 2π/3, i.e., 291mm/3), Figs. 8(c)(i) and 8(c)(ii) show the spatio-spectral couplings of both the intensity field and the phase increase, Fig. 8(c)(iii) shows the compressed electric field has increased spatiotemporal coupling distortion, Fig. 8(c)(iv) shows the focused electric field has both side-lobes and pre/post-pulses in space-time, and Fig. 8(c)(v) shows the on-target pulse dramatically degrades to 0.31. If we position two deformable mirrors before and after the compressor to correct the wavefront errors of G1 and G2, respectively, that is the slow-varying (low-spatial frequency) wavefront errors of all gratings are removed, and the fast-varying (high-spatial frequency) wavefront errors and the amplitude modulations of two gratings are left. Figure 8(d)(i) shows although the modulated intensity field has no changes, Fig. 8(d)(ii) shows the spatio-spectral coupling of the phase is controlled within a small range. Figures 8(d)(iii) and 8(d)(iv) show the electric fields after pulse compression and beam focusing have negligible spatiotemporal coupling distortions, and Fig. 8(d)(v) shows the on-target pulse improves from 0.31 to 0.70, very near 0.73.

Fig. 8. Amplitude modulations, wavefront errors, wavefront correction, and optical fields. When (a) G1, (b) G2 and (c) G1&G2 have both wavefront error and amplitude modulation, respectively, (i) (x–Δf) intensity fields after compressor, (ii) (x–Δf) phases after compressor, (x–t) electric fields after (iii) pulse compression and (iv) beam focusing, and (v) on-target (at x = 0) pulses (blue curve). Green curves in (i) illustrate intensity integrals in frequency. On-target (at x = 0) pulses (blue curve) deviate from reference standard “1” (red curve) to (a)(v) 0.47, (b)(v) 0.44, and (c)(v) 0.31, respectively. (d) When spectral-dependent wavefront correction is introduced to remove low-spatial-frequency (slow-varying) wavefront error, (i) (x–Δf) intensity field after compressor is not changed, (ii) (x–Δf) phase after compressor and (x–t) electric fields both after (iii) pulse compression and (iv) beam focusing are improved, and (v) on-target (at x = 0) pulse (blue curve) improves from (c)(v) 0.31 to (d)(v) 0.7.

Download Full Size | PDF

6. On-target intensity comparison

The single-pass double- and single-pair grating compressors have their own advantages and disadvantages. Because of the same grating size, the same compressor design (i.e., chirp ratio, incident angle, beam aperture, grating density) but different spatial chirps, the spatio-spectral clipping in the single-pass double-pair grating compressor is weaker than that in the single-pass single-pair grating compressor. Then with perfect gratings (PG), the “PG” case in Fig. 9 shows the on-target intensity of the single-pass double- and single-pair grating compressor is 0.88 and 0.73, respectively, showing the single-pass double-pair grating compressor has a higher upper limit. If the gratings that diffract the spatially-chirped beam can be enlarged (limited by the current largest size of 1450 mm), the spatio-spectral clipping can be reduced.

Fig. 9. On-target (at x = 0) intensity comparison. PG: cases for perfect gratings. SDC and SIDC: cases for spectral-dependent and spectral-independent wavefront corrections. G1&4, G2&3, G1-4: cases for gratings G1&4 or G2&3 or G1-4 have wavefront error for single-pass double-pair grating compressors, respectively. G1, G2, G1&2: cases for grating G1 or G2 or G1&2 have wavefront error for single-pass single-pair grating compressors, respectively. Individual and overlaid wavefront errors are used in single-pass single- and double-pair grating compressors, respectively. Single-pass single-pair grating compressor has λ/3 PV individual wavefront error. Single-pass double-pair grating compressor having λ/3 and λ/2 PV overlaid wavefront errors are compared.

Download Full Size | PDF

The amplitude modulation is not a key factor to the on-target intensity, however which influences safe operation, especially when near the damage threshold of gratings. The wavefront error determines the on-target intensity, and we have considered three cases. First for the single-pass single-pair grating compressor, when the wavefront error appears on G1, G2, and G1&2, the “(G1)”, “(G2)” and “(G1&2)” cases in Fig. 9 show the normalized on-target intensity is 0.47, 0.44, and 0.31, respectively. Second for the single-pass double-pair grating compressor, when the wavefront error appears on G1&4, G2&3, and G1-4, the “G1&4”, “G2&3” and “G1-4” cases in Fig. 9 show the normalized on-target intensity is 0.56, 0.55, and 0.44, respectively. It is worth nothing that: in the single-pass double-pair grating compressor, the wavefront error represents the overlaid wavefront error of G1&4 and G2&3, respectively; while in the single-pass single-pair grating compressor, it represents the individual wavefront error of G1 and G2, respectively. When we increase the PV value of the overlaid wavefront error in the single-pass double-pair grating compressor from λ/3@800 nm to λ/2@800 nm, Fig. 9 shows the normalized on-target intensities for the three cases decrease from 0.56 to 0.33, from 0.55 to 0.29, and from 0.44 to 0.20, respectively. In our previous work, we also have introduced that the PV value instead of the period of the slow-varying (low-spatial frequency) wavefront error dominates the on-target intensity, which decreases with increasing the PV value (see Fig. 9(b) in Ref. [25]). Consequently, when with the same grating wavefront error, the single-pass single-pair grating compressor should have a higher on-target intensity. Moreover, it is worth noting that the focusing dynamics of a spatially-chirped beam is quite different from that of a Gaussian beam, and the intensity quick-change and the spatiotemporal tilt may influence some applications such as particle acceleration, radiation generation, and so on.

When the traditional spectral-independent wavefront correction is applied in the single-pass double-pair grating compressor, the “SIDC” case in Fig. 9 shows the on-target intensities improve to 0.23 and 0.49 for λ/3@800 nm and λ/2@800 nm PV values, respectively, showing this method is almost useless. When the spectral-dependent wavefront correction removes the slow-varying (low-spatial frequency) wavefront errors of all gratings, the “SDC” case in Fig. 9 shows the on-target intensities of the single-pass single- and double-pair grating compressors improve to 0.7 and 0.84, respectively, showing the single-pass double-pair grating compressor has a higher on-target intensity.

Recently, the correction of the slow-varying (low-spatial frequency) wavefront error of all gratings, especially G2&3, in the single-pass double-pair grating compressor attracts more and more attentions [39,44–46], which can enhance the on-target intensity. Meanwhile, although the fast-varying (high-spatial frequency) wavefront error in the grating stretcher and compressor does not cause obvious on-target intensity degradation, it does affect spatiotemporal contrast [47,48] and needs to be studied in the next step.

It should be emphasized that Fig. 9 gives the relative values normalized to the reference standard of the ideal compressor. When estimating the absolute values, the diffraction efficiency of each grating should be considered for the case of an energy-limited input to the compressor. However, in most cases the bottleneck is the damage of the output (last) grating, where the shortest pulse, as well as the highest intensity, appears. Once the energy fluence on the output (last) grating is fixed by carefully controlling the input energy, the results in Fig. 9 do not change.

7. Discussion

Figure 10 shows, also as introduced in Section 2, that the current work adds two additional influence factors, a new optical field result and a new compressor configuration, compared to the previous work [24,25]. However, the current model still has some discrepancies from the reality. Because the spatio-temporal/spectral coupling in an imperfect grating compressor is very complex and the current work mainly focuses on the influences of phase and amplitude imperfections at different grating positions in two different compressor configurations, only a given error has been considered for the wavefront based on the concept of controlled variable approach. The given wavefront error has two fixed high- and low-spatial frequencies, although which is based on the measured result of our meter-sized golden grating. Anyway, in the future work, the power spectral density (PSD) analysis with different low-, mid-, and high-spatial frequencies for both wavefront and amplitude errors is required, and the specific influences of different PSDs should be understood.

Fig. 10. Introduction and comparison of previous, current, and future works.

Download Full Size | PDF

Another problem is that the geometric optics is used to analyze the spatio-spectral coupling, and the propagation diffraction inside the compressor (i.e., from the first grating to the last grating), which can transfer modulation between phase and amplitude (especially for the fast-varying modulation) and also transfer spatial modulation between two orthogonal directions, is ignored for the following reasons. The distance inside the compressor (around 6 and 3 m for single-pass double- and single-pair grating compressors, respectively) is short compared to the beam aperture (640 mm); the simulation load is very huge when using the Fresnel diffraction equation because the angular spectrum method is not applicable here; and the geometric optics (ray tracing) method could reflect well most of the effects we are interested in, except for the exact distribution of the fast-varying phase/amplitude modulations [49]. Figure 10 also shows, in the future work, the geometric optics method should be replaced by the wave optics method for a more accurate simulation and analysis.

8. Conclusion

We have improved the model of the spatiotemporal coupling in a grating compressor and studied the spatiotemporal dynamics of an ultra-intense ultrashort laser passing through an imperfect grating compressor. The research subjects include: influences of spatio-spectral clipping, grating wavefront error, and grating amplitude modulation; imperfections at different gratings; and comparison between two grating compressor configurations. The simulation results include optical fields in & after the compressor and after beam focusing. The grating wavefront error, which can induce spatiotemporal coupling, is a key factor to the on-target intensity degradation. The grating amplitude modulation, which has weak influence on the optical field distortion, determines safe operation. In different grating compressor configurations, the spatio-spectral clipping determines the upper-limit on-target intensity, while the spatiotemporal coupling distortion caused by the grating wavefront error dominates the actual achievable on-target intensity that is usually much lower than expected. Our view is that controlling the slow-varying (low-spatial frequency) wavefront error of all gratings in a grating compressor is key to the successful achievement of a 100 PW peak-power in the near-field and a 10²³–10²⁴ W/cm² peak-intensity in the far-field.

Funding

Shanghai Zhangjiang Laboratory.

Acknowledgments

The authors thank Cheng Wang and Ding Wang for their contributions to the geometrical design of the SEL-100PW compressor. This work was supported by the Zhangjiang Laboratory.

Disclosures

The authors declare no conflicts of interest.

Data availability

All models and data presented in this study are available from the corresponding author upon reasonable request.

References

1. M. Marklund and P. K. Shukla, “Nonlinear collective effects in photon-photon and photon-plasma interactions,” Rev. Mod. Phys. 78(2), 591–640 (2006). [CrossRef]

2. A. D. Piazza, C. Müller, K. Z. Hatsagortsyan, and C. H. Keitel, “Extremely high-intensity laser interactions with fundamental quantum systems,” Rev. Mod. Phys. 84(3), 1177–1228 (2012). [CrossRef]

3. Y. Nakamiya and K. Homma, “Probing vacuum birefringence under a high-intensity laser field with gamma-ray polarimetry at the GeV scale,” Phys. Rev. D 96(5), 053002 (2017). [CrossRef]

4. B. Shen, Z. Bu, J. Xu, T. Xu, L. Ji, R. Li, and Z. Xu, “Exploring vacuum birefringence based on a 100 PW laser and an x-ray free electron laser beam,” Plasma Phys. Control. Fusion 60(4), 044002 (2018). [CrossRef]

5. F. Sauter, “Über das Verhalten eines Elektrons im homogenen elektrischen Feld nach der relativistischen Theorie Diracs,” Z. Für Phys. 69(11-12), 742–764 (1931). [CrossRef]

6. W. Heisenberg and H. Euler, “Folgerungen aus der Diracschen Theorie des Positrons,” Z. Für Phys. 98(11-12), 714–732 (1936). [CrossRef]

7. J. Schwinger, “On Gauge Invariance and Vacuum Polarization,” Phys. Rev. 82(5), 664–679 (1951). [CrossRef]

8. A. R. Bell and J. G. Kirk, “Possibility of Prolific Pair Production with High-Power Lasers,” Phys. Rev. Lett. 101(20), 200403 (2008). [CrossRef]

9. Y. J. Gu, O. Klimo, S. V. Bulanov, and S. Weber, “Brilliant gamma-ray beam and electron–positron pair production by enhanced attosecond pulses,” Commun. Phys. 1(1), 93 (2018). [CrossRef]

10. Y. Wu, L. Ji, and R. Li, “On the upper limit of laser intensity attainable in nonideal vacuum,” Photonics Res. 9(4), 541–547 (2021). [CrossRef]

11. R. Li, “Progress on the 10PW laser facility at Shanghai,” Proc. SPIE 11514, 1151407 (2020). [CrossRef]

12. J. W. Yoon, Y. G. Kim, I. W. Choi, J. H. Sung, H. W. Lee, S. K. Lee, and C. H. Nam, “Realization of laser intensity over 10²³ W/cm²,” Optica 8(5), 630–635 (2021). [CrossRef]

13. K. Landecker, “Possibility of Frequency Multiplication and Wave Amplification by Means of Some Relativistic Effects,” Phys. Rev. 86(6), 852–855 (1952). [CrossRef]

14. S. V. Bulanov, T. Esirkepov, and T. Tajima, “Light Intensification towards the Schwinger Limit,” Phys. Rev. Lett. 91(8), 085001 (2003). [CrossRef]

15. S. Gordienko, A. Pukhov, O. Shorokhov, and T. Baeva, “Coherent Focusing of High Harmonics: A New Way Towards the Extreme Intensities,” Phys. Rev. Lett. 94(10), 103903 (2005). [CrossRef]

16. H. Vincenti, “Achieving Extreme Light Intensities using Optically Curved Relativistic Plasma Mirrors,” Phys. Rev. Lett. 123(10), 105001 (2019). [CrossRef]

17. L. Chopineau, A. Denoeud, A. Leblanc, E. Porat, P. Martin, H. Vincenti, and F. Quéré, “Spatio-temporal characterization of attosecond pulses from plasma mirrors,” Nat. Phys. 17(8), 968–973 (2021). [CrossRef]

18. F. Lureau, C. Richard, C. Radier, O. Chalus, G. Matras, S. Ricaud, S. Laux, O. Casagrande, H. Besaucele, and C. Simon-Boisson, “10 petawatts laser operation within beam transport section at ELI-NP,” Proc. SPIE 11666, 1166605 (2021). [CrossRef]

19. W. Li, Z. Gan, L. Yu, C. Wang, Y. Liu, Z. Guo, L. Xu, M. Xu, Y. Hang, Y. Xu, J. Wang, P. Huang, H. Cao, B. Yao, X. Zhang, L. Chen, Y. Tang, S. Li, X. Liu, S. Li, M. He, D. Yin, X. Liang, Y. Leng, R. Li, and Z. Xu, “339 J high-energy Ti:sapphire chirped-pulse amplifier for 10 PW laser facility,” Opt. Lett. 43(22), 5681–5684 (2018). [CrossRef]

20. P. Tournois, “Acousto-optic programmable dispersive filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140(4-6), 245–249 (1997). [CrossRef]

21. Z. Li, C. Wang, S. Li, Y. Xu, L. Chen, Y. Dai, and Y. Leng, “Fourth-order dispersion compensation for ultra-high power femtosecond lasers,” Opt. Commun. 357, 71–77 (2015). [CrossRef]

22. F. Druon, G. Chériaux, J. Faure, J. Nees, M. Nantel, A. Maksimchuk, G. Mourou, J. C. Chanteloup, and G. Vdovin, “Wave-front correction of femtosecond terawatt lasers by deformable mirrors,” Opt. Lett. 23(13), 1043–1045 (1998). [CrossRef]

23. G. Pariente, V. Gallet, A. Borot, O. Gobert, and F. Quéré, “Space-time characterization of ultra-intense femtosecond laser beams,” Nat. Photonics 10(8), 547–553 (2016). [CrossRef]

24. Z. Li, K. Tsubakimoto, H. Yoshida, Y. Nakata, and N. Miyanaga, “Degradation of femtosecond petawatt laser beams: Spatio-temporal/spectral coupling induced by wavefront errors of compression gratings,” Appl. Phys. Express 10(10), 102702 (2017). [CrossRef]

25. Z. Li and N. Miyanaga, “Simulating ultra-intense femtosecond lasers in the 3-dimensional space-time domain,” Opt. Express 26(7), 8453–8469 (2018). [CrossRef]

26. A. Borot and F. Quéré, “Spatio-spectral metrology at focus of ultrashort lasers: a phase-retrieval approach,” Opt. Express 26(20), 26444–26461 (2018). [CrossRef]

27. V. Leroux, S. W. Jolly, M. Schnepp, T. Eichner, S. Jalas, M. Kirchen, P. Messner, C. Werle, P. Winkler, and A. R. Maier, “Wavefront degradation of a 200 TW laser from heat-induced deformation of in-vacuum compressor gratings,” Opt. Express 26(10), 13061–13071 (2018). [CrossRef]

28. V. Leroux, T. Eichner, and A. R. Maier, “Description of spatio-temporal couplings from heat-induced compressor grating deformation,” Opt. Express 28(6), 8257–8265 (2020). [CrossRef]

29. A. Jeandet, S. W. Jolly, A. Borot, B. Bussière, P. Dumont, J. Gautier, O. Gobert, J.-P. Goddet, A. Gonsalves, A. Irman, W. P. Leemans, R. Lopez-Martens, G. Mennerat, K. Nakamura, M. Ouillé, G. Pariente, M. Pittman, T. Püschel, F. Sanson, F. Sylla, C. Thaury, K. Zeil, and F. Quéré, “Survey of spatio-temporal couplings throughout high-power ultrashort lasers,” Opt. Express 30(3), 3262–3288 (2022). [CrossRef]

30. Z. Li and J. Kawanaka, “Efficient method for determining pulse-front distortion in an ultra-intense laser,” J. Opt. Soc. Am. B 37(9), 2595–2603 (2020). [CrossRef]

31. Z. Bor, “Distortion of femtosecond laser pulses in lenses,” Opt. Lett. 14(2), 119–121 (1989). [CrossRef]

32. Z. Bor, Z. Gogolak, and G. Szabo, “Femtosecond-resolution pulse-front distortion measurement by time-of-flight interferometry,” Opt. Lett. 14(16), 862–864 (1989). [CrossRef]

33. C. Fiorini, C. Sauteret, C. Rouyer, N. Blanchot, S. Seznec, and A. Migus, “Temporal aberrations due to misalignments of a stretcher-compressor system and compensation,” IEEE J. Quantum Electron. 30(7), 1662–1670 (1994). [CrossRef]

34. S. W. Bahk, J. Bromage, and J. D. Zuegel, “Offner radial group delay compensator for ultra-broadband laser beam transport,” Opt. Lett. 39(4), 1081–1084 (2014). [CrossRef]

35. B. Sun, P. S. Salter, and M. J. Booth, “Pulse front adaptive optics: a new method for control of ultrashort laser pulses,” Opt. Express 23(15), 19348–19357 (2015). [CrossRef]

36. S. Li, Z. Li, C. Wang, Y. Xu, Y. Li, Y. Leng, and R. Li, “Broadband spectrographic method for precision alignment of compression gratings,” Opt. Eng. 55(8), 086105 (2016). [CrossRef]

37. C. Dorrer and S.-W. Bahk, “Spatio-spectral characterization of broadband fields using multispectral imaging,” Opt. Express 26(25), 33387–33399 (2018). [CrossRef]

38. Y. G. Kim, J. I. Kim, J. W. Yoon, J. H. Sung, S. K. Lee, and C. H. Nam, “Single-shot spatiotemporal characterization of a multi-PW laser using a multispectral wavefront sensing method,” Opt. Express 29(13), 19506–19514 (2021). [CrossRef]

39. Z. Li and J. Kawanaka, “Complex spatiotemporal coupling distortion pre-compensation with double-compressors for an ultra-intense femtosecond laser,” Opt. Express 27(18), 25172–25186 (2019). [CrossRef]

40. S. Du, X. Shen, W. Liang, P. Wang, J. Liu, and R. Li, “Multistep pulse compressor based on single-pass single-grating-pair main compressor,” arXiv:2201.09157v1 (2022).

41. G. Zhu, J. V. Howe, M. Durst, W. Zipfel, and C. Xu, “Simultaneous spatial and temporal focusing of femtosecond pulses,” Opt. Express 13(6), 2153–2159 (2005). [CrossRef]

42. F. He, H. Xu, Y. Cheng, J. Ni, H. Xiong, Z. Xu, K. Sugioka, and K. Midorikawa, “Fabrication of microfluidic channels with a circular cross section using spatiotemporally focused femtosecond laser pulses,” Opt. Lett. 35(7), 1106–1108 (2010). [CrossRef]

43. F. He, B. Zeng, W. Chu, J. Ni, K. Sugioka, Y. Cheng, and C. G. Durfee, “Characterization and control of peak intensity distribution at the focus of a spatiotemporally focused femtosecond laser beam,” Opt. Express 22(8), 9734–9748 (2014). [CrossRef]

44. J. Liu, X. Shen, Z. Si, C. Wang, C. Zhao, X. Liang, Y. Leng, and R. Li, “In-house beam-splitting pulse compressor for high-energy petawatt lasers,” Opt. Express 28(15), 22978–22991 (2020). [CrossRef]

45. J. Liu, X. Shen, S. Du, and R. Li, “Multistep pulse compressor for 10s to 100s PW lasers,” Opt. Express 29(11), 17140–17158 (2021). [CrossRef]

46. Z. Zang, S. Peng, W. Jin, Y. Zuo, G. Steinmeyer, Y. Dai, and D. Liu, “In-situ measurement and compensation of complex spatio-temporal couplings in ultra-intense lasers,” Opt. Lasers Eng. 160, 107239 (2023). [CrossRef]

47. J. Bromage, C. Dorrer, and R. K. Jungquist, “Temporal contrast degradation at the focus of ultrafast pulses from high-frequency spectral phase modulation,” J. Opt. Soc. Am. B 29(5), 1125–1135 (2012). [CrossRef]

48. Z. Li, N. Miyanaga, and J. Kawanaka, “Theoretical comparison of spatiotemporal contrasts of pulsed beams in unfocusing, 1D-focusing, and 2D-focusing fields and enhancement of the on-axis temporal contrast at the focus,” J. Opt. Soc. Am. B 35(8), 1861–1870 (2018). [CrossRef]

49. X. Shen, S. Du, W. Liang, P. Wang, J. Liu, and R. Li, “Two-step pulse compressor based on asymmetric four-grating compressor for femtosecond petawatt lasers,” Appl. Phys. B 128(8), 159 (2022). [CrossRef]

Simulating spatiotemporal dynamics of ultra-intense ultrashort lasers through imperfect grating compressors

Abstract

1. Introduction

2. Improved model and simulation parameter

2.1 Single-pass double-pair grating compressor

2.2 Single-pass single-pair grating compressor

2.3 Electric field in space-time

2.4 Simulation parameter

3. Distortion in (2 + 1) D space-time

4. Distortion in single-pass double-pair grating compressor

5. Distortion in single-pass single-pair grating compressor

6. On-target intensity comparison

7. Discussion

8. Conclusion

Funding

Acknowledgments

Disclosures

Data availability

References

Data availability

Cited By

Figures (10)

Equations (15)

Optics Express