A new improved WKB solution of the symmetrical multiple quantum wells planar waveguide

Abstract

Based on the Helmholtz's equation and energy conservation law for the travelling wave field, the actual wave function for the TE travelling wave in the inhomogeneous dielectric is recommended, the original field distribution functions of the TE mode in symmetrical planar waveguide core layer and cladding layers are suggested. Moreover, the virgin phase shift for total reflection effect at the turning point is proposed, the eigen equation of a new improved WKB method for the symmetrical planar waveguide is given. As the concept of phase delay for optical wave in the dielectric and the new improved WKB method are engaged, the multiple quantum wells planar waveguide is considered as an equivalent of the triplex layer waveguide, a new method for analyzing the symmetrical multiple quantum wells planar waveguide is put forward. Several approximate formulas for computing the effective refractive index, the normalized frequency and mode field distribution are presented. Then, found on the maximal matching efficiency method for the mode field distributions, the expression of Gaussian approximation for the mode field distribution of single mode symmetrical multiple quantum wells planar waveguide is present. As an example, the normalized field distributions of GaAs/GaAlAs symmetrical multiple quantum wells planar waveguide is referred.