Generation of a High-Intensity Temporal Step Waveform Based on Stimulated Brillouin Scattering

Abstract

This paper proposes a method based on stimulated Brillouin scattering (SBS) for reshaping a temporal Gaussian waveform into a temporal high-intensity step waveform. The theoretical analysis showed that the reshaped temporal waveform depended on the phonon lifetime, the Brillouin gain coefficient, the interaction length between the Stokes and the pump pulse, and the pump energy. It further showed the dynamic evolution of the reshaped temporal waveform with these four parameters. By optimizing these parameters, a temporal step waveform with an intensity of 36.92 MW/cm² was obtained in the experiment.

1. Introduction

The generation of a high-intensity temporal step waveform pulse has attracted increasing interest due to its wide applications in laser ignition [1,2,3], laser lidar [4], and laser machining [5]. In an optical parametric oscillator (OPO), the high-energy temporal step waveform pulse contributes to increasing the pump-to-signal conversion efficiency [6,7,8]. In addition, it can also improve the compression ratio of stimulated Brillouin scattering (SBS) pulse compression [9,10]. An arbitrary waveform generator (AWG) combined with an acousto-optic modulator is currently the preferred method to directly produce the temporal step waveform at a low pulse energy (less than 1 μJ) and a low pulse intensity (less than 0.1 kW/cm²) [11,12,13,14,15]. Alternatively, a Pockels cell can be used for reshaping a high-energy temporal Gaussian waveform [16,17]; however, this method is no longer effective when the rise-time of the leading edge reaches picoseconds. Obtaining temporal waveforms with high intensity and a leading-edge time resolution of picoseconds through these shaping methods is highly challenging.

Hasi et al. proposed a temporal pulse-shaping technique based on SBS optical limiting, and obtained a temporal flat-top waveform pulse by controlling the SBS residual pump pulse [18]. Although this technique had a high-energy load, it had limitations due to its uncontrollable pulse duration and energy. Subsequently, Zhao-Hong et al. presented a method of generating a temporal flat-top waveform pulse based on SBS amplification [19]. They obtained a temporal flat-top pulse with a duration ranging from 9.1 to 13.3 ns and continuously adjustable energy ranging from 90 to 210 mJ by injecting a small Stokes seed into the Brillouin amplifier. In research on laser pulse compression, Zhao-Hong et al. obtained a temporal step waveform pulse based on SBS [9]. No detailed study on the relevant parameters affecting the temporal waveform of step pulse was carried out, and the temporal step waveform was obtained only under the specific conditions. In addition, the energy of the temporal step waveform was only about 30 mJ and nonadjustable. The waveform shaping based on SBS is advantageous due to its high energy, high time resolution, and simple structure. However, controllably generating a high-intensity temporal step waveform through SBS waveform shaping is still a challenge.

This paper proposes a novel waveform-shaping method based on the SBS compression principle. Furthermore, the phonon lifetime, the Brillouin gain coefficient, the interaction length between the Stokes and the pump, and the pump energy were identified as the key factors that affected the output temporal waveform. Through theoretical analysis and parameter optimization, the dynamic process of outputting a Stokes temporal waveform was demonstrated. In addition, the optimum conditions for obtaining a temporal step waveform were identified. In the experiment, a high-intensity temporal step waveform pulse with an energy of 65 mJ and an efficiency of 36.92 MW/cm² was achieved.

2. Theoretical Simulation

To explore the feasibility of obtaining a high-energy temporal step waveform based on SBS compression and to analyze the key factors affecting the output temporal waveform, a theoretical model of Stokes temporal waveform evolution was established based on the SBS-coupled wave equations [20,21]. The pump and Stokes fields are represented by E_L and E_S, and Q is the acoustic field. The coupled wave equation is:

$$\frac{\partial {\mathrm{E}}_{\mathrm{L}}}{\partial \mathrm{z}}-\frac{\mathrm{n}\partial {\mathrm{E}}_{\mathrm{L}}}{\mathrm{c}\partial \mathrm{t}}-\frac{\mathsf{\alpha }}{2}{\mathrm{E}}_{\mathrm{L}}=-\mathrm{i}{\mathrm{g}}_{\mathrm{L}}\mathrm{Q}{\mathrm{E}}_{\mathrm{S}}$$

(1)

$$\frac{\partial {\mathrm{E}}_{\mathrm{S}}}{\partial \mathrm{z}}+\frac{\mathrm{n}\partial {\mathrm{E}}_{\mathrm{S}}}{\mathrm{c}\partial \mathrm{t}}+\frac{\mathsf{\alpha }}{2}=\mathrm{i}{\mathrm{g}}_{\mathrm{S}}{\mathrm{Q}}^{*}{\mathrm{E}}_{\mathrm{L}}$$

(2)

$$\frac{\partial \mathrm{Q}}{\partial \mathrm{z}}+{\mathsf{\Gamma }}_{\mathrm{B}}\mathrm{Q}=\mathrm{i}{\mathrm{g}}_{\mathrm{a}}{\mathrm{E}}_{\mathrm{L}}{\mathrm{E}}_{\mathrm{S}}^{*}$$

(3)

where c is the speed of light, n is the refractive index of the medium, α is the absorption coefficient, Γ_B is the Brillouin linewidth, Γ_B = 1/(2τ_B), τ_B is the phonon lifetime, and * is for conjugation. g_L = γ_eω_L/(2ncρ₀), g_S = γ_eω_S/(2ncρ₀) and g_a = γ_e${\mathrm{q}}_{\mathrm{E}}^2$/(2ncρ₀) represent the photon—phonon coupling constants, where γe is the electrostrictive coefficient, ρ₀ is the nonperturbation density, and q_B = k_L − k_S is the acoustic wavevector; k_L and k_S are the wavevector of the laser field and Stokes field, respectively; and ω_L and ω_S are the frequencies of the laser field and Stokes field, respectively. Meanwhile, Ω_B denotes the acoustic frequency that satisfies the energy conservation law Ω_B = ω_L − ω_S. In addition, there is the relation Ω_B = q_Bv, where v is the propagation speed of a sound wave in the medium.

Next, Fourier-transformed Equation (3) to obtain:

$$\mathrm{i}\mathsf{\omega }\mathrm{Q}(\mathsf{\omega })+{\mathsf{\Gamma }}_{\mathrm{B}}\mathrm{Q}(\mathsf{\omega })=\mathrm{i}{\mathrm{g}}_{\mathrm{a}}\mathrm{F}[{\mathrm{E}}_{\mathrm{L}}{\mathrm{E}}_{\mathrm{S}}^{*}]$$

(4)

where F[E_L${\mathrm{E}}_{\mathrm{S}}^{*}$] is the Fourier transform of E_L${\mathrm{E}}_{\mathrm{S}}^{*}$. Next, the inverse Fourier transform of Equation (4) is carried out to obtain:

$$\mathrm{Q}={\mathrm{g}}_{\mathrm{a}}{\displaystyle {\int }_0^{\mathrm{t}}{\mathrm{E}}_{\mathrm{L}}{\mathrm{E}}_{\mathrm{S}}^{*}}{\mathrm{e}}^{-{\mathsf{\Gamma }}_{\mathrm{B}}(\mathrm{t}-\mathsf{\tau })}\mathrm{d}\mathsf{\tau }$$

(5)

Then, discretize Equation (5), which can be expressed as:

$${\mathrm{Q}}^{\mathrm{m}+1}={\mathrm{g}}_{\mathrm{a}}\frac{\Delta \mathrm{t}}{2}({\mathrm{p}}^{\mathrm{m}}+{\mathrm{E}}_{\mathrm{L}}^{\mathrm{m}+1}{\mathrm{E}}_{\mathrm{L}}^{\mathrm{m}+1*})$$

(6)

where

$${\mathrm{p}}^{\mathrm{m}+1}={\mathrm{e}}^{-{\mathsf{\Gamma }}_{\mathrm{B}}\Delta \mathrm{t}}({\mathrm{p}}^{\mathrm{m}}+2{\mathrm{E}}_{\mathrm{L}}^{\mathrm{m}+1}{\mathrm{E}}_{\mathrm{S}}^{\mathrm{m}+1*})$$

(7)

$${\mathrm{p}}^0={\mathrm{e}}^{-{\mathsf{\Gamma }}_{\mathrm{B}}\Delta \mathrm{t}}{\mathrm{E}}_{\mathrm{L}}^0{\mathrm{E}}_{\mathrm{S}}^{0*}$$

(8)

Let g_L ≈ g_S = g₁, g_a = g₂, g = 2g₁g₂/Γ_B, where g is the Brillouin gain coefficient. Discretize Equations (1) and (2) and bring Equation (6) into them. Consider the change of section σ, then Equations (1) and (2) can be expressed as:

$${\mathrm{E}}_{\mathrm{L}\mathrm{j}+1}^{\mathrm{m}+1}-{\mathrm{E}}_{\mathrm{L}\mathrm{j}}^{\mathrm{m}+1}-\frac{\mathrm{n}\Delta \mathrm{z}}{\mathrm{c}\Delta \mathrm{t}}({\mathrm{E}}_{\mathrm{L}\mathrm{j}}^{\mathrm{m}+1}-{\mathrm{E}}_{\mathrm{L}\mathrm{j}}^{\mathrm{m}})-\frac{\mathsf{\alpha }\Delta \mathrm{z}}{2}{\mathrm{E}}_{\mathrm{L}\mathrm{j}}^{\mathrm{m}+1}=\frac{{\mathsf{\Gamma }}_{\mathrm{B}}\Delta \mathrm{z}}{2\mathsf{\sigma }(\mathrm{z})}\mathrm{g}{\mathrm{E}}_{\mathrm{S}\mathrm{j}}^{\mathrm{m}+1}\frac{\Delta \mathrm{t}}{2}({\mathrm{p}}_{\mathrm{j}}^{\mathrm{m}}+{\mathrm{E}}_{\mathrm{L}\mathrm{j}}^{\mathrm{m}+1}{\mathrm{E}}_{\mathrm{S}\mathrm{j}}^{\mathrm{m}+1*})$$

(9)

$${\mathrm{E}}_{\mathrm{S}\mathrm{j}+1}^{\mathrm{m}+1}-{\mathrm{E}}_{\mathrm{S}\mathrm{j}}^{\mathrm{m}+1}+\frac{\mathrm{n}\Delta \mathrm{z}}{\mathrm{c}\Delta \mathrm{t}}({\mathrm{E}}_{\mathrm{S}\mathrm{j}}^{\mathrm{m}+1}-{\mathrm{E}}_{\mathrm{S}\mathrm{j}}^{\mathrm{m}})+\frac{\mathsf{\alpha }\Delta \mathrm{z}}{2}{\mathrm{E}}_{\mathrm{S}\mathrm{j}}^{\mathrm{m}+1}=\frac{{\mathsf{\Gamma }}_{\mathrm{B}}\Delta \mathrm{z}}{2\mathsf{\sigma }(\mathrm{z})}\mathrm{g}{\mathrm{E}}_{\mathrm{L}\mathrm{j}}^{\mathrm{m}+1}\frac{\Delta \mathrm{t}}{2}({\mathrm{p}}_{\mathrm{j}}^{\mathrm{m}}+{\mathrm{E}}_{\mathrm{L}\mathrm{j}}^{\mathrm{m}+1*}{\mathrm{E}}_{\mathrm{S}\mathrm{j}}^{\mathrm{m}+1})$$

(10)

where σ(z) = π${\mathrm{w}}_0^2$[1 + (z − z₀)²/${\mathrm{z}}_{\mathrm{r}}^2$] is the section, w₀ = 1/2θ_pf is the waist radius, z₀ is the waist position, z_r = π${\mathrm{w}}_0^2$/λ is the common focus parameters of the pump, θ_p is the divergence angle, f is the focal length of the lens, and λ is the wavelength of the pump.

Let r_b = nΔz/(cΔt), G = gΓ_BΔtΔz/[4σ(z)], and then Equations (9) and (10) can be expressed as:

$${\mathrm{E}}_{\mathrm{L}\mathrm{j}}^{\mathrm{m}+1}=\frac{{\mathrm{E}}_{\mathrm{L}\mathrm{j}+1}^{\mathrm{m}+1}+{\mathrm{r}}_{\mathrm{b}}{\mathrm{E}}_{\mathrm{L}\mathrm{j}}^{\mathrm{m}}-{\mathrm{G}}_{\mathrm{j}}{\mathrm{p}}_{\mathrm{j}}^{\mathrm{m}}{\mathrm{E}}_{\mathrm{S}\mathrm{j}}^{\mathrm{m}+1}}{1+{\mathrm{r}}_{\mathrm{b}}+{\mathrm{G}}_{\mathrm{j}}{\left|{\mathrm{E}}_{\mathrm{L}\mathrm{j}}^{\mathrm{m}}\right|}^2+\frac{1}{2}\mathsf{\alpha }\Delta \mathrm{z}}$$

(11)

$${\mathrm{E}}_{\mathrm{S}\mathrm{j}+1}^{\mathrm{m}+1}={\mathrm{r}}_{\mathrm{b}}{\mathrm{E}}_{\mathrm{S}\mathrm{j}}^{\mathrm{m}}+{\mathrm{G}}_{\mathrm{j}}{\mathrm{p}}_{\mathrm{j}}^{\mathrm{m}*}{\mathrm{E}}_{\mathrm{L}\mathrm{j}}^{\mathrm{m}+1}+(1-{\mathrm{r}}_{\mathrm{b}}+{\mathrm{G}}_{\mathrm{j}}{\left|{\mathrm{E}}_{\mathrm{L}\mathrm{j}}^{\mathrm{m}+1}\right|}^2-\frac{1}{2}\mathsf{\alpha }\Delta \mathrm{z}){\mathrm{E}}_{\mathrm{S}\mathrm{j}}^{\mathrm{m}+1}$$

(12)

According to the above theoretical model, the phonon lifetime, the Brillouin gain coefficient, the interaction length between the Stokes and the pump, and the pump energy were the key factors for determining the output temporal waveform. The pulse width of the Gaussian pump at 1064 nm was set at 9 ns. The crucial parameters of phonon lifetime, Brillouin gain coefficient, interaction length between the Stokes and the pump, and pump energy are shown in

Table 1. Changes in four key parameters: phonon lifetime, Brillouin gain coefficient, the interaction length between the Stokes and the pump, and pump energy.

Phonon Lifetime (ns)	0.1 to 2.1
Brillouin gain coefficient (cm/GW)	0.1 to 0.5
Interaction length between the Stokes and the pump (cm)	5 to 45
Pump energy (J)	0.5 to 1.3

:

The essence of the Stokes waveform evolution is the change in the extraction degree of the pump pulse energy by the Stokes leading edge. Overextraction leads to a low trailing-edge energy. The evolution of a Stokes temporal waveform can be divided into the following three cases, as shown in Figure 1. Figure 1a demonstrates the ideal temporal step waveform, which has a high-power steep leading edge with low energy and a low-power stable trailing edge with high energy. When the trailing-edge energy is negligible, as shown in Figure 1b, the characteristic the waveform exhibits is more like a steep-front waveform than a step waveform. The waveform presents a bimodal waveform, as shown in Figure 1c, when the trailing edge has excessive energy. To further quantitatively analyze the evolution of the Stokes temporal waveform, the energy ratio of the trailing-edge energy is studied from the minimum or inflection point to the final energy. Mathematically, the definition of inflection point is the point that changes the upward or downward direction of the curve; that is, the concave and convex dividing point of the curve [22]. When the ratio of the trailing-edge energy to the entire waveform energy (R) was less than 50%, the waveform is not a temporal step. If the ratio of the trailing-edge energy to the entire waveform energy was higher than 90% and the minimum point was less than 82% of the maximum point; that is, y₁ < 0.82y₂, according to Rayleigh criterion [23], the waveform was bimodal. When the ratio of the trailing-edge energy to the entire waveform energy was between 50% and 90%, it was a step waveform of the trailing-edge step energy that varies with parameters.

The simulation results are shown in Figure 2. The simulation results of the effect of the phonon lifetime on the Stokes temporal waveform can be seen in Figure 2a. When the phonon lifetime was 0.2 ns (red line), the Stokes trailing edge was a stable step, and the ratio of the trailing-edge energy to the entire waveform energy was 59%, which was an ideal temporal step waveform. As the phonon lifetime decreased from 0.5 ns to 0.1 ns, the Stokes trailing edge gradually rose to a bimodal waveform, and the trailing-edge energy ratio increased from 32% to 91%. Shorter phonons indicated the rapid decay of the acoustic field. Under certain pump parameters, the Stokes leading edge could not extract enough pump energy, and a large amount of energy was transferred to the Stokes trailing edge, resulting in a bimodal waveform. Consequently, the phonon lifetime of the SBS medium played a crucial role in obtaining the temporal step waveform. Therefore, in the experiments, the phonon lifetime was maintained between 0.1 ns and 0.3 ns.

With the phonon lifetime fixed at 0.2 ns, the relationship between the SBS medium Brillouin gain coefficient and the Stokes temporal waveforms is noted in Figure 2b. With an increase in the Brillouin gain coefficient, the trailing edge rose gradually. When the Brillouin gain coefficient was 0.2 cm/GW (red line), the trailing edge formed a step. Essentially, with a larger Brillouin gain coefficient, the Stokes leading edge could extract more energy from the pump. Therefore, it was essential to control the Brillouin gain coefficient, which was maintained between 0.2 cm/GW to 0.4 cm/GW in the experiments, as described in Figure 2b.

Another determining factor that influenced the Stokes temporal waveform was the interaction length between the Stokes and the pump. With the phonon lifetime and Brillouin gain coefficient set as 0.2 ns and 0.2 cm/GW, respectively, Figure 2c illustrates the variation in the Stokes temporal waveform with the interaction length between the Stokes and the pump. The Stokes trailing edge was a stable step, and the ratio of the trailing-edge energy to the entire waveform energy was 59% at an interaction length of 15 cm (blue line). With an increase in the interaction length, more energy was extracted by the Stokes leading edge and the extraction by the trailing edge is weaker; therefore, the step disappeared gradually. Consequently, a temporal step waveform could be obtained by maintaining the interaction length between the Stokes and the pump between 5 cm and 20 cm, as shown in Figure 2c.

In addition, the pump energy was also a considerable parameter that affected the Stokes temporal waveform. As shown in Figure 2d, when the pump energy was 0.9 J (blue line), the Stokes temporal waveform was an ideal step waveform, and the trailing-edge energy accounted for about 59% of the entire waveform energy. As the pump energy increased from 0.5 J to 1.3 J, the trailing edge of the Stokes gradually rose and became a bimodal waveform, and the trailing-edge energy ratio increased from 31% to 83%. The smaller pump energy could be fully extracted by the leading edge of the Stokes, and the trailing edge could not be effectively raised, representing an SBS compression process. With a continuous increase in the pump energy, the Stokes leading edge could not extract the pump energy completely, and the remaining excessive pump energy was extracted by the Stokes trailing edge, which was gradually raised to form a bimodal waveform. Therefore, in the experiment, we could regulate the extraction degree of the Stokes trailing edge by adjusting the pump energy. As shown in Figure 2d, when the medium parameters were ideal and the interaction length between the Stokes and the pump was optimal, the pump energy was preferably around 0.9 J.

Based on the above conclusions, the ideal SBS medium parameters for generating the temporal step waveform were a phonon lifetime of 0.2 ns and a Brillouin gain coefficient of 0.2 cm/GW. The best interaction length and pump energy were 15 cm and 900 mJ, respectively. However, there is no ideal medium among the SBS media that have been studied and applied at present. We found media with a gain coefficient close to 0.2 cm/GW and a phonon lifetime close to 0.2 ns [9,24,25,26]. The parameters were as shown in

Table 2. Phonon lifetimes and Brillouin gain coefficients of different SBS media: FC-70, HS-260, D03, and FC-40.

SBS Medium	Phonon Lifetime (ns)	Brillouin Gain Coefficient (cm/GW)
FC-70	0.1	0.2
HS-260	0.1	0.4
D03	0.2	1.3
FC-40	0.2	1.8

:

Based on the above results, at a pump energy of 900 mJ and an interaction length of 15 cm, the four media could not achieve the output of a temporal step waveform, and the output Stokes temporal waveforms were all bimodal waveforms. The problem to be solved was the excessive extraction of pump energy from the Stokes trailing edge. It can be seen in Figure 2d that the reduction in pump energy could effectively inhibit the extraction of the pump energy by the Stokes trailing edge. Therefore, we simulated the change in the Stokes temporal waveform with the decrease in energy using the SBS media of FC-70, HS-260, D03, and FC-40.

The simulation results are shown in Figure 3. With the decline in pump energy, the extraction degree of the pump from the trailing edge decreased continuously. When the pump energy was reduced to a certain value, all four SBS media could realize the output of a temporal step waveform. However, the pump energies of the four SBS media when obtaining the temporal step waveform were different. When the pump energy was 100 mJ, a temporal step waveform with an energy of 77 mJ and a ratio of the trailing edge energy to the entire waveform energy (R) of 62.45% was obtained for FC-70. As shown in Figure 3, when the pump energy was reduced to 100 mJ, the temporal step waveform still could not be obtained by the other three media, and the ratios of the trailing edge energy to the entire waveform energy were more than 79%. For HS-260, D03, and FC-40, when the temporal step waveform was obtained, the pump energy was 70 mJ, 50 mJ and 40 mJ, respectively. Moreover, the energies of the temporal step waveforms they obtained were not as high as that obtained for FC-70. Therefore, FC-70 was the most suitable medium for generating a temporal step waveform based on SBS among the media found so far.

3. Experiments and Discussion

The optical layout is shown in Figure 4. A custom Nd:YAG laser was operated in a single longitudinal mode. The laser could supply an output energy of 200 mJ in a 9 ns pulse with a 1064 nm wavelength. A Faraday rotator (FR) and two polarizers (P₁, P₂) composed an isolator that prevented the backward laser from entering the laser resonator. A half-wave plate λ/2 and a polarizer P₃ were used together as a variable attenuator to adjust the energy of the pump. An SBS single-cell compressor was adopted in this experiment. The pump, which was circularly polarized by a quarter-wave plate λ/4, was focused by lens L into the SBS cell with a length of 120 cm. The backward Stokes became linearly polarized light through the quarter-wave plate λ/4 and was reflected by the polarizer P₃.

Based on the above simulation results, FC-70 with a 0.1 ns phonon lifetime and a 0.2 cm/GW Brillouin gain coefficient was selected as the SBS medium. In practice, the interaction length between the Stokes and the pump was adjusted by adjusting the focal length of the lens. The pump energy and pulse width were fixed at 115 mJ and 9 ns, respectively, as shown in Figure 5a. The evolution of the Stokes temporal waveform, as well as the change in the energy ratio of the trailing edge step as the interaction length between the Stokes and the pump varied from 5 cm to 25 cm, are demonstrated in Figure 5b. With an increase in the interaction length, the trailing edge step gradually decreased, and the ratio of the trailing-edge energy to the entire waveform energy decreased from 86% to 70%. When the interaction length was too short, the Stokes front was not fully amplified before leaving the medium, and the pump energy was mainly transferred to the trailing edge. The trailing edge was overamplified, and a bimodal waveform appeared. By further increasing the interaction length, the leading and trailing edges were uniformly amplified. When the interaction length was 15 cm, an ideal temporal step waveform with an energy of 65 mJ and an intensity of 36.92 MW/cm² was obtained. Further increasing the interaction length resulted in the leading edge gaining more energy and finally forming a steep-front waveform. Therefore, by controlling the interaction length, the ratio of the trailing-edge energy to the entire waveform energy could be adjusted to obtain the desired waveform.

Meanwhile, the energies of the input pump and output-step waveform were detected. The trend of the output-step waveform energy and pump-to-step waveform energy efficiency on the interaction length between the Stokes and the pump is illustrated in Figure 6a. Notably, the step waveform energy decreased from 89 mJ to 43 mJ, and the pump-to-step waveform energy efficiency decreased from 77.39% to 37.39% as the interaction length between the Stokes and the pump increased from 5 cm to 25 cm at a pump energy of 115 mJ. The pulse width and intensity of the output temporal step are depicted in Figure 6b. Evidently, the output pulse width gradually declined from 7.87 ns to 4.76 ns with an increase in the interaction length, and the intensity also declined from 40.01 MW/cm² to 31.97 MW/cm². With an increase in the focal length of the lens, the amplification of the leading edge was enhanced, whereas the amplification of the trailing edge was limited; thus, the output energy and pulse width were gradually reduced. When the pump energy was fixed, a longer interaction length resulted in a weaker focus intensity and a lower output efficiency, as shown in Figure 6a. This was also the reason for the slight change in pulse width. Furthermore, the decreasing output efficiency also led to the continuous reduction in output intensity. An ideal temporal step waveform with an intensity of 36.92 MW/cm² was obtained at the interaction length between the Stokes and the pump of 15 cm, as shown in Figure 6b.

The above results present the waveform-shaping method of a temporal step waveform based on Brillouin compression; however, the pulse intensity needs to be further increased for application in high-energy physics. A higher-energy pump intensity can be utilized to achieve effective operation in the saturated gain region. In addition, the optical elements used in the experiment were uncoated. Using well-coated devices could further improve output efficiency.

4. Conclusions

A method based on stimulated Brillouin scattering (SBS) compression for reshaping a temporal Gaussian waveform into a temporal step waveform has been demonstrated. The theoretical analysis showed that the reshaped temporal waveform depended on the phonon lifetime, the Brillouin gain coefficient, the interaction length between the Stokes and the pump pulse, and the pump energy. The dynamic evolution of the reshaped temporal waveform using these four parameters was shown. By optimizing these parameters, a temporal step waveform with an intensity of 36.92 MW/cm² was obtained in the experiment.