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We present here a simple matrix method for obtaining propagation characteristics, including losses for various modes of an arbitrarily graded planar waveguide structure which may have media of complex refractive indices. We show the applicability of the method for obtaining leakage losses and absorption losses, as well as for calculating beat length in directional couplers. The method involves straightforward 2 × 2 matrix multiplications, and does not require the solutions of any transcendental or differential equations.
Date of Publication: May 1987