A Finite Difference Frequency Domain Based Full Vectorial Transverse Modesolver for Anisotropic Waveguides with Arbitrary Permittivity and Permeability Tensors

In this work a Yee's mesh based full vectorial transverse finite difference frequency (FDFD) modesolver has been derived from discretized Maxwell's equations in Matrix form for anisotropic waveguides with arbitrary permittivity and permeability tensors. This work incorporates arbitrary permittivity and permeability simultaneously into matrix equations of Yee's mesh based modesolver, which previous works have not done. For benchmarking the Python implementation of these matrix equations, cross section of Yittrium Iron Garnate (YIG) channel waveguide has been taken as first one of the three test structures. Numerical result from this work has been compared with that from previous work on YIG channel waveguide and is found to be in good agreement. Further, for benchmarking the effective index values of waveguides having both permittivity and permeability anisotropic simultaneously, a finite element based commercial software (COMSOL) has been used, the values of effective indexes from solver presented in this work and commercial software have been compared, and are also found to be in good agreement.