Perturbation theory is used in order to calculate the effective-index distribution in dielectric waveguides that exhibit slow lateral variations. As an example, the method is employed to find the optical modes in diode lasers with lateral spatial variations in thickness. Very good agreement with experiment is obtained for the case of GaAlAs double heterostructure lasers with a crescent-shaped waveguide.
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Kapon et al. (1983) studied this question.