Difference between TE and TM modal gain in amplifying waveguides: analysis and assessment of two perturbation approaches |
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Authors: | Haes J. Demeulenaere B. Baets R. Lenstra D. Visser T.D. Blok H. |
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Affiliation: | (1) Department of Information Technology (INTEC), University of Gent-IMEC, St-Pietersnieuwstraat 41, 9000 Gent, Belgium;(2) Department of Physics and Astronomy, Free University, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands;(3) Department of Electrical Engineering, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands |
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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. This revised version was published online in November 2006 with corrections to the Cover Date. |
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