Analytical and numerical studies of wave propagation in waveguides filled with graded metamaterial structures
Time: Thu 2025-12-18 09.00
Location: H1, Teknikringen 33, Stockholm
Language: English
Subject area: Electrical Engineering
Doctoral student: Balwan Rana , Elektromagnetism och fusionsfysik
Opponent: Professor Ari Sihvola, Aalto University
Supervisor: Universitetslektor Mariana Dalarsson, Elektromagnetism och fusionsfysik; Professor Martin Norgren, Elektromagnetism och fusionsfysik
QC 20251124
Abstract
This thesis investigates wave propagation in waveguides with different cross-sectional geometries, filled with graded metamaterial structures. The growing interest in graded metamaterials in electromagnetic applications and models is motivated by their realism, mathematical simplicity, and versatility, compared to the conventional materials that are in use today. The majority of the research community resorts to the use of numerical implementations and solvers for obtaining a solution for the field distribution and propagation characteristics. However, these methods do not provide explicit physical insight into the connection between the steepness of the graded-index profiles and their respective field solutions. Thus, the motivation for the research in this thesis is to focus on analytically solving the wave equation for several graded-index profiles to gain physical insight into the field solutions and what phenomena may be predicted from these results.
The research in this thesis focuses on the graded impedance-matched RHM-LHM profile, which is a composite material involving an impedance-matched transition from a right-handed material to a left-handed material. The profile possesses a variable transition steepness of the relative material parameter values and dispersive characteristics. These variable properties act as degrees of freedom, thereby introducing a high degree of modeling flexibility and allowing for the study of wave propagation under more general conditions. Both non-periodic and periodic impedance-matched RHM-LHM transition profiles have been theoretically studied here using analytical functions. It is of interest to study these RHM-LHM composite materials, as the interaction between a regular material and a metamaterial may lead to newly discovered phenomena, novel analytical expressions of electromagnetic fields, and provide a deeper understanding of the underlying principles at the interface between such media.
The solution method is based on describing these graded metamaterial structures by their relative permittivity and permeability functions, where either one or both of these properties have a graded transition profile. The wave equation for each metamaterial structure is derived using Maxwell's equations and solved using the boundary conditions imposed by the waveguide geometry. The field distribution and propagation characteristics for a given electromagnetic mode are analytically expressed and visualized using the numerical software tool MATLAB. Furthermore, numerical results are obtained using the numerical software tool COMSOL Multiphysics, which are then compared with the analytical results to validate the analytical expressions derived from the wave equation.