Beam smoothing by introducing spatial dispersion for high-peak-power laser pulse compression

Xihang Yang; Xiaofeng Tang; Yanqi Liu; Jianhui Bin; Yuxin Leng; Yuxin Leng

doi:10.1364/OE.501490

1. Introduction

High-peak-power and high-energy petawatt (PW) laser facilities are key tools for exploring frontier ultrahigh-intensity physics, such as particle acceleration, nuclear physics, and strong-field quantum electrodynamics [1–3]. Since the advent of lasers in 1960 [4], enhancing the peak power of lasers has been one of the main goals of research. However, due to the power damage to amplifier materials, the peak power of lasers almost remained limited to gigawatts. Until the chirped pulse amplification technique was proposed in 1985 [5], the peak power of lasers had rapidly developed in the past three decades [6–8]. The present PW-class laser systems can be simply classified into three types: the neodymium-doped glass (Nd:glass) laser, the Ti:sapphire laser, and the optical parametric chirped pulse amplification (OPCPA) laser. To further increase the peak power of these lasers by energy boost, an obstacle occurs due to the size and laser damage threshold of the compressor diffraction gratings. The peak power of a laser pulse is proportional to its energy and inversely proportional to its duration. We can further increase the peak power of lasers by shortening their duration. This method is called post-compression [9,10], or thin film compression [11], which is characterized by high energy-transfer efficiency, low cost, and a stable and compact footprint. The output pulse durations of the Ti:sapphire laser and OPCPA laser are around 20 fs, which can easily achieve 2 times pulse compression. For hybrid Nd:glass laser, especially the output pulse duration at 150 fs level [12], which has great potential to compress the pulse duration to sub-100 fs with one- or two-stage post-compression.

The post-compression technology has undisputed merits and has been investigated in various ranges of energy and central wavelength [9,10], but there are still some problems hindering its implementation in high-peak-power laser systems. The spatial intensity profile of high-peak-power lasers is inhomogeneous due to the pump lasers, imperfect optical components, and dust in the optical layout. Spatial beam quality plays a critical role in post-compression, as nonlinear phase (B-integral) is proportional to intensity. The non-uniform spatial intensity makes the broadened spectrum inhomogeneous in space (spatial chirp) and leads to less enhancement of peak power in the post-compression of a long pulse. Besides, this inhomogeneity also induces wavefront distortion in the post-compression and ultimately decreases the Strehl ratio at the pulse maximum, which leads to less efficient focusing [13]. While the wavefront distortion can be eliminated by adaptive mirrors [14,15], when the B-integral exceeds 3, small-scale self-focusing (SSSF) leads to strong beam intensity modulation in the post-compression, which may damage optical elements and create obstacles to achieving high peak power enhancement [16]. To suppress SSSF, self-filtration was widely used in post-compression [17,18], experiments indicate that the B-integral exceeds 19 and there is no damage to the Kerr medium [19,20]. But for such a large value of B-integral, in the dispersion compensation stage, the laser-induced damage caused by some hot spots in the laser beam is also challenging for the dispersion compensation optics. Additionally, our previous research also indicates that spatial intensity homogeneity decreases after dispersion compensation. Therefore, to get high beam quality and peak power output, improving the beam quality before post-compression is necessary.

To improve beam quality, in recent research on post-compression, a spatial filter has introduced after the last amplifier [21]. And the results show that this method can effectively smooth the input beam and improve the spatial beam quality of the compressed pulse. It is important to note that in order to avoid air breakdown and energy loss caused by laser focusing at the focus position, the small aperture filter diaphragm of a spatial filter must work in a vacuum environment. Besides, the spatial filter is usually placed before the last amplifier, this makes the spatial filter cannot remove the high-frequency modulations caused by the rest reflective mirror or the diffraction grating in a femtosecond PW laser system. Except for this technique, a new method has been proposed to smooth the beam by introducing an adjustable spatial dispersion using prism pairs or asymmetric four-grating compressors (AFGC) in the concept of a multi-step pulse compressor, which can effectively remove the hot spots and improve the beam quality of the laser pulse [22–24]. Introducing spatial dispersion by using a prism pair before the compressor to improve the beam quality can prevent potential laser-induced damage to diffraction gratings and, in the meantime, make it simpler and cheaper than using a spatial filter. For the asymmetric four-grating compressor setup, the introduced spatial dispersion resulting in beam smoothing can effectively protect the last grating from laser-induced damage. What’s more, in this process, no extra optical components need to be added to this system to change the layout, which is a more reasonable method than others. The idea of using AFGC to smooth the beam and then using it for post-compression was also suggested in Ref. [25], but it was not deeply investigated, and the effects of the introduced spatial dispersion on post-compression were not discussed, such as peak power enhancement, spectral homogeneity, and spatio-temporal properties.

In this study, the beam uniformity is first improved by introducing spatial dispersion along one direction using AFGC or a prism pair. Besides, the circumstances of introducing spatial dispersion along two perpendicular directions using a prism pair together with an AFGC or two prism pairs are also discussed. And then the smoothed beam is used for post-compression, the effects of the introduced spatial dispersion on peak power enhancement, spectral homogeneity, and spatio-temporal properties are systematically studied.

2. Beam smoothing and post-compression

The scheme of beam smoothing and post-compression is shown in Fig. 1. The principle of beam smoothing is based on introducing spatial dispersion by AFGC or prism pairs. The introduced spatial dispersion redistributes the different spectral components of the laser beam in space, resulting in beam smoothing. The optical schemes of the AFGC, a prism pair, a prism pair together with an AFGC, and two prism pairs for beam smoothing are shown in Figs. 1(a), 1(b), 1(c), and 1(d), respectively. In high-peak-power laser systems, the compressor is based on four gold-coating reflect gratings with a symmetric configuration [26], where L₁ between G₁ and G₂ is equal to L₂ between G₃ and G₄. In the symmetric setup, the spatial dispersion introduced by the first two gratings is compensated by the last two gratings. For the asymmetric setup, where L₁≠L₂ and the spatial dispersion will be introduced. The amount of spatial dispersion width can be easily adjusted by changing the incident angle and the difference between L₁ and L₂. Which can be expressed as [22]

(1)$$d = (\tan {\theta _s} - \tan {\theta _l}) \times \cos \varphi \times ({L_2} - {L_1})$$

where d is the introduced spatial dispersion width, θ_s and θ_l represent the diffraction angels corresponding to the shortest and the longest wavelengths of the input laser pulse, φ is the incident angel on grating, L₁ and L₂ is the perpendicular distance between the two gratings.

Fig. 1. The scheme of beam smoothing and post-compression. (a) Optical setup of an AFGC, (b) a prism pair, (c) a prism pair together with an AFGC, and (d) two prism pairs for beam smoothing; (e) Optical setup of post-compression. G₁-G₄: grating, M: reflective mirror, CM: chirped mirror, FS: fused silica.

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Prism pairs are commonly used as dispersion optical elements to compensate for dispersion [27]. As shown in Fig. 1(b), when the pulse propagates through the prism, different wavelengths of light experience different refractive indices and refractive angles, leading to light redistribution in space and introducing spatial dispersion. The amount of spatial dispersion width can be achieved by changing the distance between the two prisms and the apex angle. Which can be described as [22,24]

(2)$$d = (\tan {\beta _s} - \tan {\beta _l}) \times \cos \alpha \times L$$

where α is the apex angel of the prism, L is the perpendicular distance between the two prisms, β_s and β_l are the refractive angles of the shortest and the longest wavelengths, respectively.

In high-peak-power laser system, AFGC can provide the same amount of spectral dispersion to compress the chirped pulses when L₁ + L₂ is equal to the typical four-grating compressor with a symmetric configuration; the spatial dispersion introduced by AFGC has no influence on the compressed pulse in time. Unlike the AFGC, the inserted prism pairs before the compressor, except for introducing spatial dispersion, also introduce spectral dispersion. The introduced spectral dispersion comes from material dispersion and angular dispersion, the material dispersion induces positive dispersion, and the angular dispersion induces negative dispersion. When the induced spatial dispersion is large, the total spectral dispersion is negative, the positive dispersion introduced by stretcher and material is pre-compensated [24]. Additionally, the prism pairs, combined with the AFGC, as shown in Fig. 1(c), can potentially fully compensate the third-order dispersion of the whole laser system to get short pulse duration output [28,29]. Due to the large beam size in high-peak power laser systems, the thickness of the prism is thick, but before the compressor diffraction gratings, the duration of the uncompressed pulse is generally at the nanosecond level, so the nonlinear effect can be neglected. In the beam smooth stage, a single prism pair, or AFGC, as shown in Figs. 1(a) and 1(b), just smooths the beam in one direction by introducing the spatial dispersion in the same direction. While two prism pairs in perpendicular directions or one prism pair together with an AFGC can smooth the beam in both vertical and horizontal directions, the optical setup is shown in Figs. 1(c) and 1(d).

The post-compression process consists of the nonlinear spectral broadening and dispersion compensation stages, as shown in Fig. 1(e). In the spectral broadening stage, the spectrum is broadened primarily via self-phase modulation (SPM) when the laser pulses free propagate through a Kerr nonlinear medium. In the dispersion compensation stage, the induced dispersion in the spectral broadening stage is compensated by dispersion optics, then the output pulses get a peak power enhancement and a shorter duration.

2.1 Theoretical model and parameters

In our simulation, the beam profile is assumed to be 10^th order super-Gaussian profile and beam diameter is 24 centimeters, the central wavelength is 1057 nm, the initial pulse duration is 150 fs, and the spectrum follows a Gaussian distribution. The pulse without smoothing, the pulse smoothed along the y direction, and the pulse smoothed in both x and y directions are investigated. Mathematically, the beam smoothing stage of introducing spatial dispersion along y direction can be expressed as [30]

(3)$$A(x,y,\omega ) = {A_0}\exp ( - 2\ln 2\frac{{{{(\omega - {\omega _0})}^2}}}{{\Delta {\omega ^2}}})\exp ( - \frac{{{{[{{x^2} + {{(y - \varepsilon (\omega - {\omega_0}))}^2}} ]}^n}}}{{{w^{2n}}}})$$

where A₀ is the electric field constant amplitude, ω₀ is the central frequency, ω is the frequency of laser pulse, Δω is the spectral full width at half maximum (FWHM) width, w is the beam size, ε is the spatial dispersion coefficient and is defined as the ratio between spatial dispersion width to the spectral FWHM width, and n is the laser pulse shape parameter. In the beam smoothing stage, 30 mm of spatial dispersion width is introduced to smooth the beam.

In the spectral broadening stage, the peak intensity of without beam smoothing laser pulse is 3 TW/ cm², 1 mm-thick fused silica is used as the nonlinear Kerr medium in our simulation, and the related nonlinear reflective index n₂ is 2.74 × 10⁻¹⁶ cm²/W [31]. The split-step Fourier method is used to solve the 3 + 1D (all three spatial dimensions and time) nonlinear Schrodinger equations of pulse propagation in the Kerr medium [32–34]. Diffraction, second-order dispersion, and third-order dispersion (TOD) of material, SPM, and self-steepening are taken into account in our simulation. In the spatio-temproal domain, nonlinear Schrodinger equations for the propagation of a laser pulse in a nonlinear medium can be approximately described by

(4)$$\frac{{\partial A}}{{\partial z}} = \frac{i}{{2{n_0}k}}\left( {\frac{{{\partial^2}}}{{\partial {x^2}}} + \frac{{{\partial^2}}}{{\partial {y^2}}}} \right)A - \left( {i\frac{{{\beta_2}}}{2}\frac{{{\partial^2}}}{{\partial {t^2}}} - \frac{{{\beta_3}}}{6}\frac{{{\partial^3}}}{{\partial {t^3}}}} \right)A + ik{n_2}\left( {{{|A |}^2} + \frac{i}{{{\omega_0}A}}\frac{{\partial ({{|A |}^2}A)}}{{\partial t}}} \right)A$$

where n₀ is refractive index of nonlinear medium, k is wavenumber, β₂ is second-order dispersion, and β₃ is TOD.

In the pulse dispersion compensation stage, the introduced group delay dispersion (GDD) in the spectral broadening stage is compensated by chirped mirrors. This procedure can be expressed as

(5)$${A_c}(x,y,t) = {F^{ - 1}}\left[ {F({A_{out}}(x,y,t))\exp ( - i\frac{{\beta {{(\omega - {\omega_0})}^2}}}{2})} \right]$$

where A_out(x,y,t) is the complex amplitude after the laser pulse propagates through the nonlinear medium, A_c(x,y,t) is the complex amplitude of the compressed pulse; F and F^-1 are the direct and inverse Fourier transforms in time and frequency, respectively; β is the introduced GDD value of chirped mirrors.

2.2 Beam smoothing

In high-peak-power laser systems, the laser pulse is highly spatial intensity modulated, and the output pulse generally has many hot spots. Thus, when hot spots are added to the beam, the spatial intensity profile of the non-smoothed pulse is shown in Fig. 2(a), with a related peak-average of 1.4 and spatial intensity homogeneity of 0.75. Figure 2(b) shows the spatial intensity profile of the beam with 30 mm of spatial dispersion width introduced to smooth it along the y direction, resulting in a beam size expansion of up to 26 cm in the y direction, a peak-average of 1.3, and a spatial intensity homogeneity of 0.78. The spatial intensity homogeneity seems unchanged due to the beam expansion. Figure 2(c) shows the spatial intensity profile of the beam smoothed both in the y and x directions, with a peak average of 1.4 and spatial intensity homogeneity of 0.75. After beam smoothing, the maximum peak intensity of the pulse smoothed just along the y axis is 2.67 TW/cm², and the pulse smoothed in both horizontal and vertical directions is 2.65 TW/cm². In the beam smoothing stage, the hot spots are removed and spatial intensity homogeneity in the central region has improved, as shown in Figs. 2(d) and 2(c), further combination with the self-filtration technique, which has the potential to dramatically decrease the SSSF in the spectral broadening stage and avoid beam breaks into multiple filaments and the creation of hot spots.

Fig. 2. Spatial intensity profile of (a) the non-smoothed beam; (b) the beam smoothed in the y direction; (c) the beam smoothed in both y and x axes; (d) the horizontal spatial intensity distributions, and (e) the vertical spatial intensity distributions of the non-smoothed beam, the beam smoothed in the y direction, and the beam smoothed in both y and x axes.

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The spatio-spectral profile and spectrum intensity profile of just introduced spatial dispersion in one direction are shown in Figs. 3(a) and 3(b), respectively. The introduced spatial dispersion leads to a narrow spectrum at the edge of the beam, and the related pulse duration is wider than the central position. The pulse duration map and spectrum half-bandwidth map are shown in Figs. 4(a) and 4(b), respectively. The spectrum bandwidth map is non-homogeneous in the central area due to spectrum redistribution and overlap, which leads to spectrum shape changes and no longer a strict Gaussian shape, as shown in Fig. 4(c). Although the spectrum shape slightly changes, the pulse duration map is homogeneous in the central area. The spatial spectrum and spectral shape of spatial dispersion introduced in both y and x directions are shown in Figs. 3(e) and 3(f). Comparing the laser pulse smoothed in just one direction to the laser pulse smoothed in both directions, the latter exhibits a large area of inhomogeneous spectrum in space. The spatio-temporal profile and temporal shape indicate the beam is uniform in the central region, and the pulse duration map and half-bandwidth spectrum map also demonstrate this, as shown in Figs. 4(d) and 4(e). The top-right blue region in Fig. 4(e) represents the short-wavelength part of the spectrum, the bottom-left blue region represents the long-wavelength part of the spectrum. Although the introduced spatial dispersion leads to intensity redistribution in space, the intensity in the edge part of the beam is low, and the impacts on the near-field of the laser pulse can be almost negligible, as shown in Figs. 2(d) and 2(e). However, the effect of the introduced spatial dispersion on the laser pulse in the spectral and time domains cannot be neglected and plays a critical role in post-compression.

Fig. 3. (a), (b), (c), and (d) show the normalized spatio-spectral profile, spectrum intensity at different positions, the normalized temporal profile, and the temporal intensity at different positions along the dashed line in Fig. 2(b); (e), (f), (g), and (h) show the normalized spatio-spectral profile, spectrum intensity at different positions, the normalized temporal profile, and the temporal intensity at different positions along the dashed line in Fig. 2(c).

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Fig. 4. (a) The pulse duration map, (b) the spectrum bandwidth map, and (c) the spectrum intensity at different positions along the x-axis after introducing spatial dispersion along the y-axis; (d) the pulse duration map, (e) the spectrum bandwidth map, and (f) the spectrum intensity at different positions along the x-axis after introducing spatial dispersion along both the x and y axes.

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2.3 Post-compression

The spatial spectrum of the broadened pulse is shown in Figs. 5. Figures 5(a) and 5(b) show the spatio-spectral profile along the y and x directions of the non-smoothed pulse. According to the spatio-spectral profile, we analyzed the spectral homogeneity (red line in the right panel of every spatio-spectral profile), which quantified the spectral overlap of any location in the beam and the beam center, as defined in Ref. [35]. Besides, the spectral homogeneity was also weighted with the beam profile, which was calculated by integrating the spatio-spectral profile along the wavelength axis (blue line in the right panel of every spatio-spectral profile). The spectrum homogeneity is correlational to the spatial intensity, and in the central region, the spatial spectrum homogeneity is over 93%. Figures 5(c) and 5(d) show the spatial spectrum of the laser pulse smoothed along the y direction. Due to the introduced spatial dispersion in the beam smoothing stage, the broadened spectrum along the y direction is also inhomogeneous. Figures 5(e) and 5(f) show the spatial spectrum of the laser pulse smoothed in both the y and x directions, the uniformity of the spectrum is less than 50% in the central region. Comparing the non-smoothed beam, the smoothed one-direction beam, and the smoothed in both directions beam, the simulation results indicate the laser pulse smoothed in both directions has the worst spatial spectrum uniformity due to the introduced spatial dispersion, leading to a decrease in spectral broadening at the edge of the beam.

Fig. 5. (a) and (b) the spatio-spectral profile along the y and x directions corresponding to a non-smoothed pulse; (c) and (d) show the spatio-spectral profile along the y and x directions of the laser pulse smoothed along the y direction; (e) and (f) show the spatio-spectral profile of the laser pulse smoothed along the y and x directions. Right: spatio-spectral map integrated along the wavelength axis (blue line) and corresponding spectral homogeneity (red line).

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The accumulated B-integral maps in the Kerr medium of the pulse without beam smoothing, the pulse smoothed along one direction, and the pulse smoothed in both directions, as shown in Figs. 6(a-1), 6(a-2) and 6(a-3), respectively, and the related maximum B-integral values are 4.87, 4.34, and 4.31. Figures 6(b-1)-(b-3) show the pulse duration maps of compressed pulse, and the minimum pulse durations are 42.4 fs, 45.4 fs, and 46.8 fs, corresponding to the pulse without beam smoothing, the pulse smoothed along one direction, and the pulse smoothed in both directions, respectively. The pulse duration map of the compressed pulse is non-uniform due to the inhomogeneous spectral broadening. Besides, the introduced spatial dispersion leads to inhomogeneous spectral distribution and intensity decreases, ultimately aggravating inhomogeneous spectral broadening and degrading peak power enhancement. Figures 6(c-1)-(c-3) show the spatial intensity profiles of the pulse without beam smoothing, the pulse smoothed along one direction, and the pulse smoothed in both directions, the corresponding peak intensities are 9.6 TW/cm², 7.97 TW/cm², and 7.82 TW/cm², respectively. After dispersion compensation, the smoothed laser pulse exhibits a lower peak intensity, which can effectively avoid laser-induced damage to the optical elements, such as reflect optical elements and focusing elements.

Fig. 6. (a-1)–(a-4) The accumulated B-integral maps corresponding to the laser pulse without beam smoothing, beam smoothed along the y-axis and beam smoothed along both x and y axes; (b-1)-(b-4) the related pulse duration map; (c-1)-(c-4) the related spatial intensity profile after dispersion compensation.

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Due to the inhomogeneous spatial intensity, the B-integral is also inhomogeneous in space, resulting in different values of the optimum compensated dispersion for every point in space. In the pulse dispersion compensation stage, the global (whole beam) optimum value of the compensated dispersion must be considered. Figures 7(a) and 7(c) show the factor of peak power enhancement variation with the amount of compensated dispersion corresponding to 20 mm and 30 mm of spatial dispersion width introduced in the beam smoothing stage, respectively. The optimum values of the compensated dispersion and the factor of peak power enhancement of the non-smoothed pulse are -1500 fs² and 2.74, respectively. For the laser pulse with 20 mm of spatial dispersion width introduced in one direction and both directions, the corresponding optimum values of the compensated dispersion and the factor of peak power enhancement are -1552 fs², -1595 fs² and 2.5, 2.4, respectively. For the laser pulse with 30 mm of spatial dispersion width introduced in one direction and both directions, the corresponding optimum values of the compensated dispersion and the factor of peak power enhancement are -1601 fs², -1686 fs², and 2.4, 2.2, respectively.

Fig. 7. (a) Peak power enhancement factor (PF) variation with the compensated GDD. (b) The compressed pulse temporal intensity shape at the central position of the beam; black line (without beam smoothing); green line (beam smoothed along the y direction); blue line (beam smoothed both the x and y directions); the dotted lines are the related phases. Bottom (c) and (d), corresponding to the laser pulse that introduced 30 mm spatial dispersion width in the beam smoothing stage.

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The beam smoothed in both directions, with the lowest peak power enhancement due to the beam size expansion and a large area of inhomogeneous spectrum compared to the beam smoothed in just one direction. Comparing the pulse smoothed in one direction with 30 mm of spatial dispersion width to the pulse smoothed in both directions with 20 mm of spatial dispersion width, the factor of peak power enhancement is close. For a high spatial intensity modulated pulse, the beam homogeneity can be easily improved by introducing small spatial dispersion, but it's harder to improve the beam homogeneity of a lower spatial intensity modulated pulse by introducing spatial dispersion [22–24]. In high-peak power laser systems, where the modulation is significant, it is a good choice to smooth the laser pulse in both directions with a small spatial dispersion. The peak intensities of the smoothed pulse and compressed pulse with different spatial dispersion width introduced are shown in Table 1. The introduced spatial dispersion can effectively remove these hot spots, but at the sacrifice of degrading peak power enhancement. From the simulation result, high uniformity and high peak power enhancement cannot be achieved simultaneously. Thus, in the beam smoothing stage, the value of the introduced spatial dispersion needs to be carefully considered to remove the hot spots while ensuring minimal effect on the factor of peak power enhancement. After removing the hot spots by adjusting spatial dispersion, high peak power enhancement can also be achieved by increasing the thickness of Kerr medium (B-integral) in a single stage post-compression.

Table 1. peak intensities of smoothed pulse and compressed pulse

View Table

The wavefront distortion is introduced in the spectrum broadening stage due to the inhomogeneous spatial intensity. This wavefront distortion can result in self-focusing and may damage the optical elements. Additionally, the degradation of beam quality can lead to a decrease in focused laser intensity [13–15]. Figure 8 shows the spatio-temporal profile of the compressed pulse, and due to the inhomogeneous spatial intensity of the laser pulse, the compressed pulse in space is unsteady in time, as shown in Figs. 8(a-1) and 8(b-1), which will lead to less efficient focusing. The results show that the pulse smoothed in both horizontal and vertical directions, with less unsteadiness in time in the central position. The pulse smoothed in one direction shows more steadiness in time along the non-smoothed and smoothed directions than the non-smoothed pulse, but due to the inhomogeneous spectral distribution in the edges, the pulse duration is longer than the central position, and the effect of introduced spatial dispersion during the beam smoothing stage on focusing intensity needs further investigation, both numerically and experimentally.

Fig. 8. (a-1)–(a-3) Spatio-temporal profile of compressed pulse along the x direction corresponding to without beam smoothing, beam smoothed along the y direction, and beam smoothed in both directions; (b-1)–(b-3) spatio-temporal profile of compressed pulse along the y direction corresponding to without beam smoothing, beam smoothed along the y direction, and beam smoothed in both directions.

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3. Discussion and conclusion

The factors affecting the focus intensity in the post-compression of high-peak power laser systems mainly contain the limited peak power enhancement factor in the signal post-compression stage due to the SSSF; the inhomogeneous spectral broadening in the edge of beam; the wavefront distortions introduced in the spectral broadening stage due to the inhomogeneous spatial intensity. In this study, the introduced spatial dispersion can alleviate the influence of wavefront distortions and suppress the SSSF. Although the introduced spatial dispersion aggravates the inhomogeneous spectral broadening, high peak power enhancement and high focus intensity also can be achieved, there are three reasons.

First, in our simulation, hot spots are artificially added to the laser pulse, but in a real laser system, the spatial intensity is highly modulated and hot spots with different diameters are irregularly distributed in space. In the beam smoothing stage, just a small value of spatial dispersion can effectively smooth the high-peak-power laser pulse [22,25]. Thus, the introduced spatial dispersion contributes less to the inhomogeneous spectral broadening than the result in this paper.

Second, unlike the self-filtration technique, which is used to suppress SSSF by removing the dangerous noise sources. In the beam smoothing stage, the beam homogeneity has improved, and in the meantime, the spatial noise intensity has decreased. However, spatial noise isn’t removed in this process. It is better to combine the beam smoothing technique and the self-filtration technique to suppress the SSSF in post-compression. In this case, a large value of the B-integral in a single post-compression stage is allowed, ultimately leading to a higher peak power enhancement.

Third, the beam quality is first improved in the beam smoothing stage, and as a result, wavefront distortions are reduced in the post-compression stage, which allows for a higher focus intensity than the non-smoothed pulse. In addition, the spatio-temporal focusing technique can be employed to eliminate the effect of spatial dispersion on focus intensity [30,36], and deformable mirrors can be used to compensate the wavefront distortions between the edge and central regions of the laser pulse, which leads to more efficient focusing [14,15].

In conclusion, to avoid damage to optical elements and achieve a high peak power enhancement in the post-compression of high-peak-power laser pulses, we propose to smooth the laser pulse by introducing spatial dispersion using prism pairs or AFGC before post-compression. We have numerically studied the spatio-temporal properties, spatial spectrum, and spatial intensity properties of the pulse without beam smoothing, the pulse smoothed in one direction, and the pulse smoothed in both x and y directions. The results show that the introduced spatial dispersion can effectively remove hot spots, especially when the pulse is smoothed in both y and x directions. Although the introduced spatial dispersion during the beam smoothing stage may decrease peak power enhancement, it can effectively reduce wavefront distortions and prevent damage to optical elements. Besides, after smoothing the beam, the effect of the introduced spatial dispersion on peak power enhancement can be reduced by increasing the thickness of the Kerr medium, ultimately achieving a high peak power enhancement. We believe that the method proposed in this paper is an efficient way to suppress SSSF and can achieve a high focus intensity. As the focusing intensity plays a critical role in laser-material interaction, the focusing field of the laser pulse with spatial dispersion, wavefront distortions and spectral phase will be researched in our next-step work.

Funding

State Key Laboratory of High Field Laser Physics.

Acknowledgments

The authors thank Dr. Shu-Man Du and Dr. Wen-Hai Liang for their fruitful discussions and support.

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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	20 mm spatial dispersion width		30 mm spatial dispersion width
	Smoothed pulse	Compressed pulse	Smoothed pulse	Compressed pulse
Beam 1^a	/	9.6 TW/cm²	/	9.6 TW/cm²
Beam 2^a	2.74 TW/cm²	8.36 TW/cm²	2.67 TW/cm²	7.97 TW/cm²
Beam 3^a	2.71 TW/cm²	8.17 TW/cm²	2.65 TW/cm²	7.82 TW/cm²

Beam smoothing by introducing spatial dispersion for high-peak-power laser pulse compression

Abstract

1. Introduction

2. Beam smoothing and post-compression

2.1 Theoretical model and parameters

2.2 Beam smoothing

2.3 Post-compression

3. Discussion and conclusion

Funding

Acknowledgments

Disclosures

Data availability

References

Data availability

Cited By

Figures (8)

Tables (1)

Equations (5)

Optics Express