By solving the scalar wave equation for modes of a circularly bent homogeneous single-mode fiber, using the conformal mapping and variational methods, for which various Gaussian-based trial fields are used to represent the fundamental HE11 mode, and through quantitative and qualitative analysis, the transverse field profile of the fundamental mode on such waveguiding structures is investigated. The results obtained are compared to those obtained numerically and in the existing literature. The combined methods used here present certain advantages over a number of existing methods insofar as it provides more accurate results than those obtained previously, especially those obtained using the simple Gaussian approximation.


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