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A new two-dimensional root-finding algorithm is proposed for studying multilayer waveguides. This algorithm uses a convergent circle chain in the complex plane to approach the two-dimensional root and is especially suitable for finding roots of complicated and rapidly oscillatory functions for which conventional methods do not converge. The attenuation constants of typical slab waveguides with multilayer coatings were calculated by using this method under double precision. The results are compared with those given by other approximate methods.
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Sun et al. (1991) studied this question.
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