Refractive index approximations from linear perturbation theory for planar MQW waveguides

The mode powers and propagation constants for planar multilayer waveguides formed with multiple quantum well (MQW) materials and with the MQW layers replaced by a single uniform layer are compared. By considering linear perturbations of the solutions of the wave equation, the optimal choice of average for the dielectric constant of the substituted single layer is determined. For the case of TE modes, minimal error in the propagation constant is predicted if a weighted average of the dielectric constants of the MQW materials is used. For the case of TM modes, using a weighted average of the reciprocal of the dielectric constants is predicted to yield the minimum error. Numerical results confirm these predictions