Constitutive relations and the electromagnetic spectrum in a fluctuating medium

A two-parameter susceptibility function χ(t;τ) is introduced, to characterize the local macroscopic properties of a linear isotropic dielectric, whose behavior may change in time. χ(t;τ) generally is a stochastic variable with respect to its first argument. An expression is derived for the spectral density of the induced polarization in terms of the spectral densities of the fluctuations of χ and of the electric field. In general, this relationship is not a simple convolution. In the special case when the incident electric field is monochromatic, the induced polarization has the usual Brilouin-type spectrum.