A theory is presented of the refractive-index distribution which produces a prescribed two-dimensional ray path. When two inhomogeneous media give the same paraxial ray equation with respect to a prescribed path, they are referred to as the paraxially equivalent media. Various types of the equivalent media pertaining to a circular ray path are discussed, and numerical examples of the paraxial ray paths are given. Furthermore, a mechanical model of a ray is used to clarify the physical meaning of the condition imposed on the index profile to produce a prescribed ray path.
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Nemoto et al. (1979) studied this question.
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