Abstract
The algebraic formulas for calculating modes and propagation constants in waveguides with an arbitrary index profile are derived with the use of hypervirial theorems (HVT) and Hellmann-Feynman theorem (HFT). Formulas and numerical results for a gaussian index profile are obtained and compared with those obtained by WKB or ray technique and earlier perturbation approaches. The method is simple to apply, and the results are very accurate.
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