A rigorous boundary value solution for the lateral modes of stripe geometry injection lasers

Abstract
A new mathematical model useful for analyzing lateral modes of stripe geometry lasers is presented. The oxide stripe laser is modeled as a three-layer waveguide in which the dielectric constant of the active layer varies only along the lateral direction; the dielectric constant of the surrounding passive layers is assumed to be position independent. The solution technique affords a rigorous matching of the fields of the active layer with those of the surrounding passive layers. To illustrate the model, the modes of a waveguide with parabolic dielectric variation along the lateral direction are investigated. The fields are written as a linear combination of Hermite-Gaussian (H-G) functions; heretofore, fields have been described with a single H-G function. Fundamental mode spread (spot size at halfpower) is calculated and related to the gain distribution. (Previous estimates of the lateral field spread of the fundamental mode using a single H-G function not rigorously matched at the boundaries can yield spot sizes as much as 30 percent different from results calculated from linear combinations of H-G functions.) In addition, the peak gain fields are determined at threshold for various waveguide geometries.