Transport of broadband radiation through a nonlinear dispersive medium

Abstract

Analytical and numerical solutions are presented to elucidate the important physical aspects of the incoherent nonlinear interaction and propagation of high-intensity radiation in an absorbing (or amplifying) medium. The properties of radiation-driven one-dimensional density discontinuities or wave fronts are examined for monochromatic and broadband radiation sources, and for a nonlinear absorbing medium characterized by a spectral absorption cross section that is square, Gaussian, or Lorentzian. The effect of the angular distribution of the radiation source is considered in detail. The results of the analysis show that the propagation behavior of the radiation-driven wave front depends strongly on the spectral dependence of the absorption cross section. The wave front propagates with a constant shape and at a constant velocity ${v}_{b}$ only for monochromatic radiation or a square absorption cross section. For a Lorentzian, ${v}_{b}\ensuremath{\sim}{x}^{\frac{1}{2}}$ at large values of the propagation distance $x$. The absorption of intense radiation in a medium generally causes local heating, which can introduce hydrodynamic disturbances that propagate behind, along with, or ahead of the radiation-driven wave front. Conditions are derived for the amount of heat addition that is required to produce these disturbances for a given velocity of the wave front.