Difference between TE and TM modal gain in amplifying waveguides: analysis and assessment of two perturbation approaches.

Abstract

The commonly used confinement factor-based formula for modal gain in amplifying waveguides – gmod=Γgmat, with Γ a confinement factor – is well established and accurate for TE modes. The TM case is rarely, and sometimes erroneously, described in the literature. Using a variational formulation the fundamental difference between TE and TM modal gain is illustrated. An accurate expression, correct up to first order, for the TM modal gain is then derived from a known general perturbation formula. However, as this does not lead to a true confinement factor formulation, some approximations are introduced, leading to a unified formulation of both TE and TM modal gain. A second method to calculate the modal gain, based on the analyticity of the dispersion equation, is also discussed. Simulation and comparison with modal gain values from a complex mode solver will finally illustrate the validity of the different approaches.