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The mutual relation between transverse and longitudinal electromagnetic field components in a curved optical fiber is derived. The wave equations for transverse fields much simpler than those for longitudinal fields are obtained in the first-order perturbation. The wave equations for a radially inhomogeneous fiber derived in a toroidal coordinate system are equivalent to those derived from a straight waveguide approximation with an effective index profile incorporated with the curvature effect. Linearly polarized mode representation holds exactly only for the fundamental mode.
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Sakai et al. (1981) studied this question.
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