Abstract

A procedure is described for calculating the power coupled between collimated, partially coherent vector fields that are in different states of coherence. This topic is of considerable importance in designing submillimeter-wave optical systems for astronomy. It is shown that if the incoming field $\mathcal{S}$ has coherence matrix A, and the outgoing field $\mathcal{D}$ has coherence matrix B, then the power coupled is simply $\mathit{Ps}=\mathrm{Tr}({\mathbf{ATBT}}^{†}),$ where the elements of T project the basis functions of B onto those of A. A similar technique can be used to calculate the power coupled from the background of $\mathcal{S}$ to $\mathcal{D}$. The scheme is illustrated by calculating the power coupled between two scalar, Gaussian Schell-model beams. The procedure can be incorporated into optical design software.

© 2001 Optical Society of America

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