The symmetrical Epstein refractive index profile (with free space conditions on each side of the transition) is generalized to a non-symmetrical form including both a barrier and a well by the discovery of a profile that cannot be obtained from the standard Epstein profile merely by adjusting the parameters. The analytical evaluation of the reflexion and transmission properties of the model is more complicated than that which occurs in the study of the Epstein profile.
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J. Heading (1967) studied this question.
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