Abstract
Abstract Field distributions and propagation constants of modes in weakly guiding circularly symmetric optical waveguides having arbitrary radial refractive index distribution are determinable from a variational analysis, which uses the solution of the scalar wave equation for the infinitely extended parabolic refractive index profile as a reference (Laguerre-Gaussian functions). The power coupling coefficients of the power, which is transferred from a focused Gaussian beam to an LPvp-mode, depend on frequency and on four normalized launching parameters. Once the field-describing matrix equation has been solved numerically, closed-form expressions are obtained. The condition for optimal matching of the fundamental mode is given, and it is found that the maximum power excitation coefficient may be close to 100% even for substantially disturbed profiles.
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