Stimulated rotational Raman scattering of arbitrarily polarized broadband light

Laser plasma instabilities are problematic for inertial confinement fusion because they can spoil illumination uniformity, reduce laser-target coupling, and create unwanted fast electrons. Recent experiments and simulations have shown that self-seeded stimulated rotational Raman scattering (SRRS) in air might achieve enough spectral broadening to mitigate these instabilities with only moderate unwanted broadening of the focal spot. The theoretical model for the simulations included chaotic broadband and spatially multimode light, but was a scalar formulation suitable for only linear polarization, where the SRRS gains and spectral broadening are limited by Stokes--anti-Stokes coupling. This paper derives a tensor formulation of SRRS theory suitable for modeling spectral broadening of arbitrarily polarized spatially and temporally incoherent light; it then describes the algorithms used to simulate the theory and provides some preliminary results that compare linear and elliptical polarizations. It begins with a paraxial wave equation for an arbitrarily polarized optical field envelope, which is phase modulated by a term proportional to a Raman driven molecular polarizability tensor. Treating the air molecules as rigid rotators, it uses a quantum treatment to derive a driven harmonic oscillator equation for that polarizability, then expresses these vector and tensor equations in terms of the field's right- and left-handed circular polarization components to derive the final coupled equations for arbitrary polarization. The formulation includes possible ac Stark shift contributions, but shows that they are negligible for intensities below $10\phantom{\rule{0.16em}{0ex}}\mathrm{GW}/{\mathrm{cm}}^{2}$. It then describes the algorithms used in the simulation code and the numerical model of the chaotic light, whose initial spectral bandwidth is broad enough to self-seed the SRRS. In this algorithm, the SRRS process accurately conserves the total energy at each axial plane along the propagation path. Finally, it compares simulations of power spectra and far-field profiles for elliptical vs linear polarization, which show that elliptically polarized light produces significantly more broadening of both profiles than linear polarization. For linear polarization, the SRRS process reduces the incident coherence time from 0.54 to 0.27 ps; for elliptical polarization, it reduces to 0.19 ps. The theory and simulation algorithms presented here provide a framework for evaluating techniques that combine beams of alternating circular polarizations with different spectra and angular divergences to improve SRRS spectral broadening without excessive focal spot broadening.