Calculation of Propagation Constants in Circular Gyrotropic Optical Fibers

Circular optical fibers are dielectric waveguides allowing for electromagnetic wave propagation in the region of the core, if the former has a greater refractive index than the cladding. In this work, we extend the study from circular isotropic optical fibers to circular gyrotropic ones, for the full-wave calculation of the propagation constants. In particular, the circular core can be anisotropic, either gyroelectric or gyromagnetic, while the cladding is isotropic and infinitely extended. To construct the determinantal equation, also known as the characteristic equation, to calculate the propagation constants, the electromagnetic field in the gyrotropic core is expressed analytically in terms of a superpotential. These analytical expressions involve the elements of the gyrotropic permittivity and permeability in the tangential components of the fields. In the cladding, the fields are expressed in Hertz potentials with appropriate decaying cylindrical wavefunctions. Satisfying the interface conditions at the core-cladding interface, we obtain a homogeneous linear system whose determinantal equation yields the propagation constants of the hybrid modes. The solution is fully validated for isotropic core-cladding optical fibers by comparing the extracted propagation constants with those from the well-known separation of variables solution. For gyrotropic cores, we employ COMSOL Multiphysics to verify the correctness of our results. Numerical results are given for various values of the parameters.