Supervisors info:
Κοσμάς Τσακμακίδης, Επίκουρος Καθηγητής, Τμήμα Φυσικής, ΕΚΠΑ
Summary:
The current research was carried out as a graduate assignment for the department of Physics of the National and Kapodistrian University of Athens, in the field of Condensed Matter Physics, under the supervision of Professor Kosmas L. Tsakmakidis. The study thoroughly examines the materials which present dispersion and metamaterials, with the use of simulation models in 1 and 2 dimensions using the Finite Difference Time Domain – FDTD method. The whole study including the programming codes for the modelisation of the problems have been carried out solely by the writer. The Matlab Mathwork program was used for the graphic illustrations and simulations. Initially, a brief reference to the theory is presented, which is necessary for the understanding of electromagnetism and Maxwell’s equations, which are used in the FDTD method. Next, a detailed analysis of the FDTD method and the Yee algorithm is presented, which is the core of the method and analytical deduction of the algorithm needed for the study of electromagnetic problems. There is a brief analysis of the materials and how they are categorized according to the properties they present. Then, the computational methods that are used for solving the problems are analyzed. The study of the materials with dispersion (dispersive materials) begins with dimension 1. Specifically, the free space and simple problems are studied in order to understand the FDTD method and then the Drude, Debye and Lorentz materials are studied, in conjunction with a comparison of results of the 3 computational methods that are used. The same study is carried out on dimensions 2, after a thorough discussion of the extraction of the algorithm for the study of two-dimensional materials. Finally, there is a theoretical and computational study of metamaterials in 2 dimensions. Furthermore, every study and simulation for each material is followed by an analytical discussion and conclusion for the validity of the FDTD method and the extent to which the results of the simulations in relation to the theory is analyzed separately in each case.
Keywords:
Dispersive materials, materials, simulations, matlab, metamaterials, electromagnetism, computational physics
