Modeling electromagnetic wave propagation through time - varying medium using the finite-difference time-domain (FDTD) method

Abstract

Electromagnetic waves play a central role in modern communication, sensing, and space-based systems. Technologies such as satellite communication, radar, and remote sensing depend on the reliable transmission of electromagnetic signals over wide frequency ranges. The performance of these systems is strongly influenced by the characteristics of the propagation medium. Therefore, accurate numerical modeling of electromagnetic wave behavior is essential for reliable system design and analysis. In many classical electromagnetic models, material properties such as electric permittivity (ε) and magnetic permeability (μ) are assumed to be constant in time. This assumption simplifies the mathematical formulation but limits the applicability of the models. In reality, many propagation environments exhibit time-dependent behavior. Such environments include plasma media, the upper atmosphere, and artificially engineered materials. Temporal variations in material parameters can significantly modify wave propagation by altering amplitude, phase, period, and frequency content. The ionosphere is a well-known natural example of a time-varying electromagnetic medium. Extending from approximately 60 km to 1000 km above the Earth's surface, the ionosphere is continuously influenced by solar radiation, geomagnetic activity, and seasonal effects. These processes cause time-dependent changes in electron density and, consequently, in the electromagnetic properties of the medium. As a result, electromagnetic waves propagating through the ionosphere may experience refraction, absorption, delay, and frequency shifts. Accurate modeling of such effects requires numerical methods that explicitly account for temporal variations. This thesis investigates electromagnetic wave propagation in time-varying media using the Finite-Difference Time-Domain (FDTD) method. The FDTD technique directly solves Maxwell's equations by discretizing both space and time. Electric and magnetic field components are updated sequentially using an explicit time-stepping scheme. This structure allows transient wave behavior to be observed naturally and enables the inclusion of material properties that vary with time. All numerical simulations are implemented in the MATLAB environment. The primary application considered in this study is a plasma medium with time-dependent electromagnetic parameters. The standard FDTD update equations are modified so that the permittivity ε(t) and permeability μ(t) can change at each time step. Simulations are carried out on a three-dimensional staggered grid based on the Yee lattice. The results demonstrate that temporal increases in permittivity lead to a measurable rise in wave frequency and a corresponding reduction in the wave period. These observations indicate strong interaction and energy exchange between the electromagnetic field and the evolving medium. In addition to plasma modeling, the thesis examines electromagnetic wave propagation in complex media and nonlinear dielectric media. In these engineered materials, electromagnetic properties can be intentionally designed and externally modulated. By comparing the simulation results obtained from plasma and complex media, the study highlights the differences between naturally occurring and artificially controlled time-varying media. The comparison shows that while both environments produce frequency shifts and phase modulation, the underlying physical mechanisms differ. The results of this work emphasize the importance of incorporating time-dependent material parameters into electromagnetic simulations. Models that neglect temporal variations may fail to predict critical propagation effects in dynamic environments. The numerical framework developed in this thesis provides a reliable tool for analyzing wave behavior in time-varying plasmas and engineered materials. The findings are directly relevant to satellite communication systems, radar applications, remote sensing technologies, and the design of advanced electromagnetic materials. Overall, this study contributes to a deeper understanding of electromagnetic wave propagation in nonstationary media and offers a robust computational approach for future research in time-varying electromagnetic systems.