Optical waveguide dispersion characteristics from the scalar wave equation

The electric and magnetic fields of an optical waveguide are well represented as derivatives of a linearly polarized vector potential. This vector potential obeys a scalar wave equation. Through the use of a variational principle one may obtain good approximations to the dispersion relation, however, without resolution of the birefringence. A simple perturbational approach yields the birefringence. Universal plots may be obtained in this way for TE and TM modes for rectangular channel waveguides with small index discontinuities.