Green's function for coupled optical modes

Abstract

The problem of obtaining the correlation functions for the photons of a laser emitting into two coupled modes can be simplified by using thermodynamic Green's Functions. The coupling is such that an electron which emits a photon into one mode can influence another electron emitting into another mode. These photons are therefore cross-correlated. The atomic currents due to the transitions of the radiating electrons are also correlated because of the coupling or interaction potential. The atomic current correlation functions are not measured, information on them is obtained by measuring the photon correlation functions. This means coupled differential equations for the time-dependent amplitudes of the oscillators (photons) must be solved. Thermodynamic Green's functions are used, which contain the stimulation parameters. These are proportional to the absolute square of the matrix element for the stimulated transition. It is found that the cross-stimulation parameter is added to the stimulation parameter of both modes in the expression for the amplitudes of the modes, and subtracted from the stimulated parameters in the expressions for the line widths. This has the effect of increasing the amplitudes and the linewidths of both modes. These increases will not in general be equal because the stimulation parameters of both modes in general are not equal.