Eur. Phys. J. Plus (2020) 135: 59
https://doi.org/10.1140/epjp/s13360-019-00089-w

Regular Article

Computation of shift in oscillation frequency in the cavity resonator caused by anisotropicity and inhomogeneity of the permittivity

Netaji Subhas Institute of Technology, New Delhi, India

^* e-mail: pragya.shilpi4@gmail.com

Received: 22 May 2019
Accepted: 28 December 2019
Published online: 13 January 2020

Abstract

Shift in oscillation frequency in cavity resonator caused by anisotropicity and inhomogeneity of permittivity utilizing perturbation method is formulated in this paper. Permittivity of medium is a tensor quantity with anisotropicity only in x–y plane assumed. For this problem, governing Maxwell equations are decomposed into linear combination of two equations, i.e., perpendicular (x–y) plane and z direction. By cavity perturbation method applied to combination of linear equations, shift in oscillation frequency is computed. The same cavity resonator is simulated on HFSS software for vacuum and a simple anisotropic medium, and results are cross-verified. Error in oscillation frequency is calculated for small inclusion of anisotropicity in vacuum. Perturbations are of the order to , thus satisfying the necessity for employing numerical perturbation method. Oscillation frequencies in media having permittivity tensor with continuous inhomogeneous functions are also evaluated, which is superior to the theory of finite element method. Permittivity tensor with complex diagonal entries is also tackled in this paper but cannot be consummated on HFSS (high-frequency simulation software).