Abstract
To develop a sound base on which to design efficient lightguides, it is necessary to understand the physics of the propagating modes of this transmission medium. In this paper, we examine the properties of the scalar modes in an infinite lens-like medium and the vector modes in a self-focusing fiber with an infinite homogeneous cladding for a hyperbolic secant index distribution. We find that only the meridional rays are equalized and that this only occurs when there is no material dispersion.
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