A new identity is derived which relates the gain and the field distribution (or confinement factor) in a dielectric waveguide with complex refractive indices. This identity is valid for any guided mode of waveguides with an arbitrary cross section. It provides a new check of the accuracy of mode solvers. Also, it can be used in a variational approach to predict the gain or loss of a guided mode based on knowledge of confinement factors. It is shown that a previous analysis that is often used, is not correct. In addition, approximate expressions for the gain in slab waveguides are presented.

Abstract-We present a numerical optical model for calculating threshold material gain in vertical-cavity surface-emitting lasers. It is based on a vectorial solution of Maxwell's equations and therefore gives exact results where other approaches fail, e.g., in the case of oxide-confined devices, which have high lateral index contrasts. Results are given concerning the influence of oxide window thickness and position on threshold gain and modal stability. We also propose an intuitive plane-wave model to enhance the physical understanding of these effects.

Two exact expressions are derived for the effective mode indices of dielectric slab waveguides with complex refractive indices. One is for TE modes, the other for TM modes. The identities are valid for any guided mode of any dielectric slab waveguide and can be succesfully employed to check the accuracy of mode solvers. They explain why TE gain can be much greater than TM gain even when the confinement factors are comparable. Also, it is shown that an often used approximation for the TM gain is unreliable under practical conditions. A correct approximation is given.

No abstract