Wave dynamics in random, absorptive or laseractive media

Abstract

We consider the behavior of light propagating in dielectrically disordered and energetically nonconservative material. Disorder and energy nonconservation can be dealt with via the use of the mathematical formalism commonly known as the Keldysh technique. We derive in the Keldysh formalism a field theory of light propagation in disordered, nonconservative media. This field theoretical formulation is commonly known as the nonlinear sigma model. We also show how to calculate physical quantities like correlation functions from the sigma model, and how a source term can be included in the action of the field theory. We apply the derived field theory to the calculation of full counting statistics. We derive a generating functional for the cumulants of energy transmitted through a weakly nonconservative one-dimensional disordered system. We find fluctuations of transmittance which is in accordance to Dorokhov’s distribution of transmission coefficients. Our numerical results also agree quantitatively with previous diagrammatic results of low order cumulants. We apply the field theoretical formalism to random lasing. We calculate the photonic distribution function. We find that the distribution function obeys a nonlocal Fisher equation. Finally we consider the effect of the vector nature of light on wave properties, specifically whether polarization increases or decreases the propensity of light waves in disordered dielectric media to become localized (Anderson localization).We map the light polarization to a “pseudospin” degree of freedom which we then treat with techniques adapted from classical studies of electronic spin. We find that the polarization of light waves does in fact contribution to a diminished probability of return to the origin, the value of which determines of course the ease for the occurrence of Anderson localization.