Two-stream theory of light propagation in amplifying media

Abstract

The two-stream approximation to the radiative transport equation (RTE) is a convenient exactly solvable model that allows one to analyze propagation of light in amplifying media. In spite of neglecting the phase and the interference effects, this model describes the same phenomena as Maxwell’s equation: electromagnetic resonances, onset of lasing, and onset of instabilities. An important added bonus of the RTE description is that it provides for a simple and unambiguous test of physicality of stationary solutions. In the case of Maxwell’s equations, it is not always obvious or easy to determine whether certain stationary (in particular, monochromatic) solutions are physical. In the case of RTE, the specific intensity of unphysical stationary solutions becomes negative for some subset of its arguments. In the paper, stationary and time-dependent solutions to the two-stream model are analyzed. It is shown that the conditions for stationary lasing and for emergence of instabilities depend only on the geometry of the sample and the strength of amplification but not on the intensity of incident light.