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Trajectory in the optical wave

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Abstract

A trajectory in the optical wave is presented. The trajectory is an extension of the geometrical ray and runs wherever the wave exists. The optical wave is solved for the composite of the system’s continuously varying index of refraction. The wave equation is assumed to be separable into variables, and the constants of separation are the mode parameters specifying the wave. A trajectory for the system in which the plane wave is incident upon an interface of two homogeneous media with different indices of refraction is illustrated. The trajectory runs to and fro across the interface. Shifts of the reflected and transmitted points from the incident point on the interface occur in addition to the Goos–Hänchen shift for the incident angle greater than the critical angle. A trajectory through the cylindrical Luneburg lens is shown. It passes through the lens without any reflection, as does the corresponding ray. It is deflected attractively or repulsively according to the value of the parameter. It approaches the ray in the short-wavelength limit.

© 1995 Optical Society of America

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