Control of Stimulated Raman Scattering in the Strongly Nonlinear and Kinetic Regime Using Spike Trains of Uneven Duration and Delay

Stimulated Raman scattering (SRS) in its strongly nonlinear, kinetic regime is controlled by a technique of deterministic, strong temporal modulation and spatial scrambling of laser speckle patterns, called spike trains of uneven duration and delay (STUD) pulses [B. Afeyan and S. Hüller (unpublished)]. Kinetic simulations show that the proper use of STUD pulses decreases SRS reflectivity by more than an order of magnitude over random-phase-plate or induced-spatial-incoherence beams of the same average intensity and comparable bandwidth.

Figure 1

$E_y$ (left) and corresponding instantaneous back-scattered Poynting flux $\max (-E_y{B}_z,0)$ (right) over the two-dimensional simulation volume for cases: (a) an RPP laser beam at average laser intensity $⟨I⟩=5\times 10^{14}\mathrm{W}/{\mathrm{cm}}^2$ (top), (b) a $5000\times 1$, $1:0.5:0.5$ STUD pulse beam at time-averaged incident laser intensity $⟨I⟩=5\times 10^{14}\mathrm{W}/{\mathrm{cm}}^2$ (center); and, (c) the same STUD pulse beam, but with $⟨I⟩=3.2\times 10^{14}\mathrm{W}/{\mathrm{cm}}^2$ (bottom) (note logarithmic scale on Poynting flux). The center panels are $E_x^2$ for the leftmost $80\mu \mathrm{m}$ of each simulation, showing EPW wave amplitude correlated with instantaneous SRS backscattered Poynting flux. The inset is reflectivity vs time for cases (a) (black) and (b) (blue); (c) (red) evinces negligible backscatter. The times shown are 1.6 ps (a) and 3.6 ps (b),(c), chosen when large, bursts of SRS backscatter were present in (a) and (b).

Figure 2

Hot electron flux per unit length $\mathrm{\Phi }$ vs electron energy ($E_K$) for the three simulations in Fig. 1. Shown are trapped particle fluxes, obtained by subtracting contributions from a Maxwellian (time-averaged over the duration of the simulation). Fluxes are measured on boundary regions, as indicated by the colors (c.f. the simulation box above, drawn to scale): $z=\pm 40\mu \mathrm{m}$, $0<x<250\mu \mathrm{m}$ (black); $z=\pm 40\mu \mathrm{m}$, $250<x<500\mu \mathrm{m}$ (red) and $x=500\mu \mathrm{m}$ (blue).

Figure 3

Angular distribution of the time-averaged backscattered light power for cases (a) (black, dashed), (b) (dot-dashed, blue), and (c) (red) as in Figs. 1 and 2. The spectra for (b) and (c) evince lower backscattered light power, but finite angle with respect to the incident laser (cone angle $|\theta |<1/2f$, shown by the vertical lines).

Figure 4

SRS reflectivity vs average incident intensity (left) and linear gain (right) for RPP and a variety of STUD-pulse beams. The black (△) are for RPP. Red (▫) and blue (∘) curves are for STUD pulses with $5000\times 1$, $1:0.5:0.5$ and $5000\times 1$, $1:0.5:1$ (i.e., twice the “on” time) for the latter density profile. The magenta points labeled “ISI” are for STUD pulses with $8000\times 1$, $1:0.5:0.5$ (left) and $9500\times 1$, $1:0.5:0.5$ (right) and indicate little advantage over RPP for the conditions shown. The green (△) is for STUD pulses with $5000\times 4$, $1:0.5:0.5$, i.e., scrambling every four pulses. The ($+$) is for $2000\times 1$, $1:0.5:0.5$.