The use of transverse circular representation in circular cylinder coordinate system provides an alternative approach to the solution for vector Helmholtz partial differential equations (VH-PDE) of electromagnetics. After separation, VH-PDE for electric (magnetic) field splits into a set of three ordinary differential (Bessel) equations for two opposite transverse circular polarizations (TCP) and the axial component. The approach is suitable for solving the problem of cylindrical waveguides and cavities starting from the transverse fields. The coupling between TCP fields via the axial component affects nonreciprocal propagation in waveguides. The procedure is illustrated on a dielectric waveguide. It may be extended to the media with circular eigen polarizations including those displaying magnetooptical Faraday effect or optical activity.
2. Marcuse, D., Light Transmission Optics, Chap. 8, Van Nostrand Reinhold Company, 1972.
3. Marcuse, D., Theory of Dielectric Optical Waveguides, Chap. 1, Academic Press, 1974.
4. Snyder, A. W. and J. D. Love, Optical Waveguide Theory, Chapman and Hall, 1991.
5. Kong, J. A., Electromagnetic Wave Theory, Chap. 3, EMW Publishing, Cambridge, Massachusets, USA, 2000.
6. Goell, J. E., "A circular-harmonic computer analysis of rectangular dielectric waveguide," Bell Syst. Tech. J., Vol. 48, No. 9, 2133-2160, 1969.
7. Poladian, L., M. Straton, A. Docherty, and A. Argyros, "Pure chiral optical fibres," Opt. Express, Vol. 19, No. 2, 968-980, 2011.
8. Zhang, Z., J. Gan, X. Heng, Y. Wu, Q. Li, Q. Qian, D. Chen, and Z. Yang, "Optical fiber design with orbital angular momentum light purity higher than 99.9%," Opt. Express, Vol. 23, No. 23, 29331-29341, 2015.
9. Gloge, D., "Weakly guiding fibers," Appl. Opt., Vol. 10, No. 10, 2252-2258, 1971.
10. Snyder, A. W., "Understanding monomode optical fibers," Proc. IEEE, Vol. 69, No. 1, 6-13, 1981.
11. Chew, W. C., Waves and Fields in Inhomogeneous Media, Chap. 3, IEEE Press Series on Electromagnetic Waves, 1995.
12. Yoshino, T., "Theory for the Faraday effect in optical fiber," J. Opt. Soc. Am. B, Vol. 22, No. 9, 1856-1860, 2005.