Modified Airy function solutions to optical waveguide problems

Abstract

Modified Airy function (MAF) method gives an approximate solution of the wave equation for planar waveguides with an arbitrary refractive index distribution. Unlike WKB method, the MAF solution does not diverge at the turning points and there is no need of connection formulae. Comparison with exact results for practical wave guides show that the errors in MAF solutions are small. Use of a first order perturbation theory together with the MAF solution reduces very much the error in the eigenvalues. It has been shown that an improvement of the method gives almost exact eigenvalues and the eigenfunctions. Though the method will be illustrated with examples of optical wave-guides, it is equally applicable to problems in quantum mechanics and other areas of physics and engineering.