Asymptotic evaluation of the normalised cut-off frequencies of an optical waveguide with quadratic index variation

Asymptotic expressions for normalised cut-off frequencies of modes having large meridional order n and small azimuthal order m are obtained for an inhomogeneous waveguide having quadratic index variation. A fractional integral technique is used to construct solutions directly from the differential equation in the form of an integral representation, which is expanded by the steepest-descent procedure.