Vol. 59

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Helmholtz Equation in Transverse Circular Representation

By Stefan Visnovsky
Progress In Electromagnetics Research M, Vol. 59, 161-170, 2017


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.


Stefan Visnovsky, "Helmholtz Equation in Transverse Circular Representation," Progress In Electromagnetics Research M, Vol. 59, 161-170, 2017.


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