Analytical expression for mode-coherence coefficient of a uniformly-distributed wave propagating in different homogeneous media

Presented is a derivation of an analytical expression for the mode-coherence coefficients of uniformdistributed wave propagating within different homogeneous media—as in the case of hyperbolic Gaussian beams—and a simple method involving the superposition of two such beams is proposed. The results obtained from this work are very applicable to study and analysis of Hermite-Gaussian beam propagation, especially in the problems of radiation-matter interaction, and laser beam propagation such as employed in free-space and fiber optical communications.