Weakly focusing transparent media provide possible means for guided transmission of coherent light beams with relatively small loss. The scalar wave equation for the eigenmodes of propagation in such a medium is formally identical with Schroedinger's wave equation. Hence, the methods used in the solution of quantum-mechanical problems, such as the Wentzel-Kramers-Brillouin (WKB) approximation, are immediately applicable to this problem. Solutions for the eigenmodes and eigenvalues in the case of focusing in one dimension are given, and the Pöschl-Teller medium, whose index varies as n = n0[1 − (α/2) tan2ηx] is discussed in some detail. In addition, the relationship between the wave solutions and geometrical (ray) optics is examined.
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J. P. Gordon (1966) studied this question.
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