DIFFERENCE BETWEEN TE AND TM MODAL GAIN IN AMPLIFYING WAVE-GUIDES - ANALYSIS AND ASSESSMENT OF 2 PERTURBATION APPROACHES

The commonly used confinement factor-based formula for modal gain in a mplifying waveguides - g(mod) = Gamma g(mat), with Gamma a confinement factor - is well established and accurate for TE modes. The TM case i s rarely, and sometimes erroneously, described in the literature. Usin g a variational formulation the fundamental difference between TE and TM modal gain is illustrated. An accurate expression, correct up to fi rst order, for the TM modal gain is then derived from a known general perturbation formula. However, as this does not lead to a true confine ment factor formulation, some approximations are introduced, leading t o a unified formulation of both if and TM modal gain. A second method to calculate the modal gain, based on the analyticity of the dispersio n equation, is also discussed. Simulation and comparison with modal ga in values from a complex mode solver will finally illustrate the valid ity of the different approaches.