Correction to the effective refractive index and the confinement factor in waveguide modeling for quantum cascade lasers

The equations for the effective medium refractive index and for the confinement factor in the waveguide design for quantum cascade lasers are derived. Compared to equations used in prior literature, by applying rigorous perturbation theory and including the effect of the anisotropic optical gain and non-Hermitian properties of the waveguide structure and materials, a few percent correction should be made to the confinement factor and the effective gain. This result can easily be generalized to any optical devices with a layered structure.