WKB approximation for optical guide modes in a medium with exponentially varying index

Abstract

Although the WKB has been shown to be a good approximation in situations where a medium with exponentially varying index of refraction supports more than one optical mode, it might be expected to be poor near cutoff. There the index difference between the surface and interior that supports guiding has decreased by the factor 1/e at a depth that may be as small as a fraction of a wavelength. We show that, despite this, the WKB does provide a good approximation near cutoff.