Numerical Solutions of Maxwell's Equations to Calculate Waves Propagation in Dielectric Material using Finite Difference Time Domain (FDTD) Technique
Keywords:
: Maxwell’s curl equations, finite difference time domain (FDTD), one dimension (1-D), two dimensions (2-D) and transverse magnetic (TMz) wave.Abstract
This paper presents the numerical solutions of Maxwell's time dependent curl equations by using finite difference time domain (FDTD) technique for simulating the electromagnetic waves propagation in a dielectric medium designed in different shapes in two dimensional system. The waves propagated in the dielectric slab, which can be studied to show that for the example, a dielectric medium can use to guide the waves in a material. The results of the calculations indicated that the performance of a dielectric slab model acted as a guide of the signals. The impact of a dielectric slab orientation variation can be studied. The results demonstrated that each change in the shape structure of a dielectric could result into the different distributions, as an example two different distributions generated when the dielectric slabs oriented in the x-direction compared with y-direction. Moreover, the propagations of the waves can be studied when varying the phase. The first simulation the dielectric slabs placed in free space and the second the dielectric slab placed between two parallel strips made of the perfect electric conductors (PECs). The result of the first simulation demonstrated that the signal updated on the dielectric as well as free space while the result of the second simulation, the signal only updated in the dielectric slab between the strips. In one dimensional (1-D) as an example of the propagation of electromagnetic wave in a dielectric constant compared with PEC. The results have shown that it is possible to study two different types of materials in a one simulation. Therefore, the results obtained clearly demonstrated that electromagnetic wave completely reflected back into a domain when the pulse is striking with the PEC while in a region of dielectric, the pulse propagated in a dielectric constant and the other parts reflected back into a domain.
References
Hendi A., Alkallas F., Almoussa H., Alshahri H. and Almoneef M. (2020). Finite difference time domain method for simulating dielectric materials and metamaterials. Digest journal of nonomaterialand biostructures, 15, 3, 707-719.
Thomas V. and John R. Griffiths, (2012). RF coils for MRI, a John Wiley and Sons.
Yee, K. S. (1966). Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotopic Media. IEEE Transaction on Antenna Propagation, 14, 302-307.
Jackson J., (1998). Classical electrodynamics, United state America.
Taflove A. and Morris E. (1975). Numerical Solution of Steady State Electromagnetic Scattering Problems using the Time Dependent Maxwell’s Equations. IEEE Transaction on Microwave Theory and Techniques, 23, 623-630.
Arnold A., Y. Yue and Wang M. (2020). Non-Split Perfectly Matched Layer Boundary Condition for Numerical Solution of 2D Maxwell Equations, International Journal of Electromagnetic (IJLE), 3, 1, 1-9.
Emmanouil T., et al. (1998). FDTD characterization of waveguide probe structures. IEEE transactions on microwave theory and techniques, Vol. 46, 1452-1460.
Bojan D., et al. (2015). Optimization of excitation in FDTD method and corresponding source modelling. Radio engineering, 24, 10-16.
Otman S. and Ouaskit. S. (2017). FDTD Simulations of Surface Plasmon using the effective Permittivity applied to the dispersive Media. American Journal of Electromagnetic and Applications, 5, 14-19.
Mur G. (1981). Absorbing Boundary Conditions for the Finite Difference Approximation of the Time Domain Electromagnetic field equations. IEEE Transactions on Electromagnetic Compatibility, EMC-23, 377-382.
