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Abstract
A piecewise linear approximation is used to evaluate the propagation properties of TM modes in a planar optical waveguide with arbitrary index profile. This method is based on the vector wave equation and its solution can approach the exact solution by increasing the number of sublayers. The convergence properties of the propagation constant are examined numerically for two typical index profiles. The piecewise linear approximation is superior in convergence to the conventional step approximation method.
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