The first analytic solution for guiding a circularly symmetric TM wave along a solid lossless dielectric cylinder was obtained by Hondros and Debye in 1910 [1]. Until 1936, there was no complete mathematical analysis for this problem which was carried out by Carson et al. [2]. They were the first to show that to satisfy all the boundary conditions, a hybrid wave (i.e., the coexistence of longitudinal electric and magnetic fields) must be present. In other words, asymmetric TE and TM modes were inextricably coupled to each other along a circular dielectric rod. They also showed that (1) pure TE and TM waves could only exist in the circularly symmetric case, and (2) there existed one and only one mode, namely the lowest order hybrid wave called the HE11 mode, which possessed no cutoff frequency and could propagate at all frequencies. All other circularly symmetric or nonsymmetric modes had cutoff frequencies. The dispersion relations of these modes were also obtained in their paper, but no numerical results were given.
In 1961, Snitzer [10] rederived the analytic results originally given by Carson et al. and applied them specifically to the optical fiber problem. The purpose of this chapter is to provide the analytic approach and results for the problem of wave propagation along a solid circular cylindrical waveguide and its variations, layered radially inhomogeneous dielectric cylinders, hollow cylinders, etc.
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(2008). Circular Dielectric Waveguides. In: The Essence of Dielectric Waveguides. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-49799-0_5
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