Fig. 1. Properties of a sunlight-like laser pulse with a flat-top frequency spectrum and bandwidth Δω/ω₀ = 1%. The sunlight-like laser is modeled by Eqs. (1)–(3), where the central frequency ω₀ = 2πc/λ with λ = 351 nm. (a) and (b) Electric field components E_y and E_z, respectively, where the time-averaged electric field amplitude E0=〈Ey2(t)〉=〈Ez2(t)〉. (c) Amplitude frequency spectrum f(ω) and phase frequency spectrum ϕ(ω) of E_y. (d) Stokes parameters of the sunlight-like laser pulse, where I denotes the intensity regardless of polarization, Q the linear polarization along the y (+) or z (−) axis, U the linear polarization at + 45° (+) or −45° (−) from the y axis, and V the right-handed (+) or left-handed (−) circular polarization.³⁸

Fig. 2. Properties of temporal speckles in a sunlight-like laser pulse. (a) Electric fields of two typical adjacent speckles (denoted by “S1” and “S2”) corresponding to E_y within 0.3–0.7 ps in Fig. 1(a). (b) Amplitude spectra f_S1(ω) and f_S2(ω) of these two speckles, showing the obvious frequency shift δω between them. (c) Statistical mean frequency shift 〈δω〉 between the central frequencies of two adjacent speckles as a function of bandwidth. (d) Statistical mean duration 〈δt〉 of a single speckle as a function of bandwidth. The statistical analyses in (c) and (d) are performed over all adjacent speckles for 〈δω〉 and over all speckles for 〈δt〉, with 100 independent broadband laser beams for each bandwidth. The statistical results under different spectral resolutions are compared by using three different laser pulse durations: 6000T₀ (7.02 ps), 12 000T₀ (14.04 ps), and 18 000T₀ (21.06 ps).

Fig. 3. (a) Average SRS reflectivity within 6000λ/c obtained from 1D PIC simulations as a function of laser intensity for a monochromatic laser (MCL), a broadband laser (BBL) with bandwidths Δω/ω₀ = 1% and 2%, and a sunlight-like laser (SLL) with bandwidth Δω/ω₀ = 1%, respectively. The purple dashed line indicates R_SRS = 1%. (b) First saturation time of the backward-reflected light as a function of laser intensity for the three different kinds of laser beams. (c) Time evolution of the electric field of the backward laser light, where all incident lasers have the same intensity of I₀ = 3 × 10¹⁵ W/cm², and both the broadband laser and sunlight-like laser have a bandwidth Δω/ω₀ = 1%. (d) Electron energy spectra for the monochromatic laser, broadband laser, and sunlight-like laser at the final simulation time of 6000λ/c. (e) and (f) Time evolution of |E_x| for the broadband laser and sunlight-like laser, respectively. In (b) and (d), all lasers have the same intensity I₀ = 1.4 × 10¹⁵ W/cm², and the broadband laser and sunlight-like laser have the same bandwidth Δω/ω₀ = 1%.

Fig. 4. Wave-vector distributions of the plasma wave field E_x at 1500T₀ found from 2D PIC simulations for (a) a monochromatic laser (MCL), (b) a broadband laser (BBL), and (c) a sunlight-like laser (SLL). All possible plasma wave vectors are distributed around the theoretical dashed circles owing to the wave-vector and frequency matching conditions: k₀ = k_s + k_p, ω₀ = ω_s + ω_p, where the subscripts 0, s, and p refer to the incident, scattered, and plasma waves, respectively. (d) Corresponding electron energy spectra at the final time of 1500T₀. All the lasers have the same intensity I₀ = 1.4 × 10¹⁵ W/cm², and the broadband laser and sunlight-like laser have the same bandwidth Δω/ω₀ = 1%. For simplicity, the laser intensity is assumed to be uniform in the y direction.