  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.
