Thermal Noise in Dissipative Media

To account for the spontaneous thermal fluctuations in a general dissipative medium, a current-source term may be introduced into Maxwell's equations. The dyadic correlation function of the source term is evaluated for a uniform medium at uniform temperature in which the driving field Ē and driven-current density J̄d are related by differential equations in time and space variables. In those cases in which a simple tensor relation exists between the Fourier components of Ē and J̄d at a particular frequency, the result is generalized to nonuniform media. A similar generalization is achieved only under some restrictive assumptions for media characterized by differential equations in the space variables. The results obtained may be applied to the computation of thermal noise radiated from a medium at nonuniform temperature, and can serve as an aid toward understanding of noise mechanisms. The source term is also evaluated for a thin plasma from simple physical reasoning and is found to check with the result derived from the general theory.