The eigenvalue equations of N-parallel graded-index waveguides are derived in a recursive form for the first time by using the WKB method and the transfer matrix method. For the derivation, trial solutions are defined which not only converge at turning points but also approximate the conventional WKB solutions. It is confirmed through the computer simulation that the results of the derived WKB eigenvalue equations are in good agreement with those of the finite-difference method in the well-guided regions.
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Kim et al. (1997) studied this question.
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