Fig. 1. Linear theory of the SRS growth rate for a two-color laser. (a) Distribution of SRS growth rate Γ calculated according to Eq. (1) with a₀ = 0.02 and n₀ = 0.128n_c. Here, Δk=(kx−k0)2+ky2−ksr and θ = 180° − arctan[k_y/(k_x − k₀)]. The resonance point k_sr is defined by the wave vector and frequency matching conditions of a monochromatic laser beam. (b) Region for Γ > 0 as a function of scattering angle (θ) for two individual laser beams at frequencies ω₀ ± 0.5δω, denoted by the red and blue regions, respectively. Here, δω/ω₀ = 1.2%, and a_1,2 = 0.0141. The solid red and blue lines are the resonance points calculated using Eq. (3), and the width of each instability region is calculated using Eq. (2). (c) Growth rate as a function of scattering angle calculated using Eq. (5) for two-color laser light with δω/ω₀ = 1.2%. (d) Coupling threshold angle θ_th as a function of the frequency difference δω between two individual monochromatic laser beams.

Fig. 2. SRS in the cases of monochromatic and two-color lasers with S-polarization. (a) Spatial distribution of E_x at 800T₀. (b) Wave-vector distribution of E_x integrated over 0 ≤ t ≤ 1500T₀ for monochromatic laser with S-polarization. Here, a₀ = 0.02, w₀ = 10λ, and n₀ = 0.128n_c. (c) and (d) Integrated wave-vector distributions for E_x (S-polarized laser) before 1500T₀ in cases with two different laser frequencies, δω/ω₀ = 0.6% and δω/ω₀ = 1.2%, respectively. The amplitudes of the two beamlets are a₁ = 0.0141 and a₂ = 0.0141.

Fig. 3. SRS in the cases of monochromatic and two-color lasers with P-polarization: integrated wave-vector distributions for E_x (P-polarized laser) over 0 ≤ t ≤ 1500 T₀ in the case of (a) a monochromatic laser and (b) a two-color laser with δω/ω₀ = 1.2%.

Fig. 4. SRS generated by a broadband laser. (a) Integrated wave-vector distribution for E_x over 0 ≤ t ≤ 1500T₀ for the case of an S-polarized broadband laser with Δω/ω₀ = 2.6%. (b) Scattering angle θ with the maximum amplitude as a function of bandwidth. (c) Average reflectivity and transmittivity and (d) electron energy spectrum at 2500T₀ for broadband lasers with different bandwidths and polarizations.

Fig. 5. Hot electron generation with a broadband laser: p_x–p_y phase distributions [(a) and (c)] and energy–angle distributions [(b) and (d)] of hot electrons with kinetic energy E_k > 30 keV at t = 2500 T₀ obtained from 2D PIC simulation for the cases of monochromatic laser light [(a) and (b)] and broadband laser light with Δω/ω₀ = 2.6% [(c) and (d)]. Here, φ_i = arctan(p_iy/p_ix), and i labels the individual electrons. The other simulation parameters were the same as those in Fig. 4(a).

Fig. 6. Model of a broadband laser. (a) The temporal evolution of the electric field obtained from Eq. (B3) for a broadband laser beam with a relative bandwidth Δω/ω₀ = 4.0%. (b) Corresponding frequency spectrum and random phase spectrum obtained by Fourier transformation of the electric field in (a). (c) Spatial–temporal distribution of the electric field given by Eq. (B4) for a broadband laser beam with a relative bandwidth Δω/ω₀ = 4.0% and a spot size w₀ = 10λ.