Abstract

A small-wavelength, quasi-geometric optics is developed. The approach is based on an amplitude wave function that represents both the probability amplitude of the geometrical rays and the physical-optics disturbance. All ray paths contribute phases to the amplitude function proportional to their optical paths, measured in units of normalized wavelength. However, the dominant contributions are due to those rays that satisfy Fermat’s principle. This formulation leads to an integral equation for the wave-amplitude function with a kernel function that is a path integral. The integral equation reduces, in weakly focusing paraxial media, to a solution of a Schrödinger type of partial differential equation. The classical ray variables are operators with expectation values satisfying the geometric-optics equations. The second moments of the ray operators, with minimum-uncertainty initial wave packet, define second-order optical parameters. A special case of the quasi-geometric-optics integral equation is the quasi-optical laser-mode equation, allowing the interpretation of the stationary modes as probability amplitudes. For media with arbitrary inhomogeneous index of refraction, a matrix wave equation with a two-component wave function is derived. The matrix ray operators also satisfy a correspondence principle. A physical interpretation of the new wave function is presented.

PDF Article

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription