This paper investigates guided and leaky modes in four-layer waveguides with sixteen different index cross sections, including theS-shaped refractive index distribution. TheS-form waveguides may result from introduced absorption losses in the outer layer or quasi-single-mode operation with absorption losses of higher-order unwanted modes. Also, the higher value of outer layer index as compared with the core can produce quasi-single-mode operation with radiation losses of higher-order unwanted leaky modes.
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Cherny et al. (1979) studied this question.
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