Abstract
For planar multilayer waveguides with multiple quantum wells (MQW), integral formulas for the optimal refractive index when the MQW are replaced by a single uniform layer are derived by considering linear perturbations of the fields and propagation constants for solutions of the wave equation. These integral formulas simplify to familiar discrete averages if the spatial variations of the fields over a period of the MQW are small. The discrete average result for TE modes is applied to a waveguide with a single MQW guiding region and the relative magnitude of the errors in the power distribution and propagation constant for symmetric and antisymmetric modes are explained.
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