Abstract

A theoretical discussion is given of some of the properties of the mode of minimum diffraction loss propagating between two apertures in a general inhomogeneous medium. This mode is a useful wave analog of the geometrical-optics ray between two points. The aperture illuminations that yield this particular mode are the solutions of an eigenvalue problem. The eigenvalue equations are derivable from a variational principle that seeks the illuminations yielding the maximum power transfer between the apertures. The same eigenvalue equations result from the variational principle that seeks the illuminations giving stationary phase shift during transmission. Hence the optimum wave analog of an isolated ray automatically satisfies phase stationarity. When these concepts are applied to refraction and reflection, the phase-variational principle is analogous to Fermat’s principle for the same phenomena.

© 1965 Optical Society of America

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