Photonic crystals containing hyperbolic metamaterials

In this thesis, 1-D photonic crystals containing hyperbolical metamaterial (1-D PCCH), which obtained by combining the photonic crystals made by periodically arranged different dielectric materials and the hyperbolical metamaterial, are investigated. In this context, firstly, the concepts of photonic crystal structure and photonic band gap are briefly reviewed, after that, hyperbolical metamaterials and basic physical properties of them are explained in some detail. Transfer Matrix Method (TMM), used commonly in the photonic structure calculations, and also, Effective Medium Approximation (EMA), specially used in the determination of effective dielectric permittivity in metamaterials are explained. In the Results section, firstly, the Bragg mirror, being the simplest and well-known example for the one-dimensional photonic crystals, is discussed and basic optical properties and band gap structure of it are calculated. Later, on the purpose of clarify the fundamental properties of hyperbolical metamaterials and also understand that how change the properties of the hyperbolic metamaterials composed of different metal/dielectric materials with the filling factor, some calculations are performed in a set of different hyperbolic metamaterials. Finally, as an important stage of this thesis, 1-D PCCH structures (1-D Photonic Crystals Containing Hyperbolic metamaterial), which exhibited angle-insensitive spectral responses, are investigated and optical properties (reflectivity and absorption spectra) of these structures, designed in form of [(AB)nD]m are calculated. In this kind of structures, Ag (silver) and MgO (Magnesium Oxide) are employed as metal and dielectric materials, respectively. The dependencies of the obtained optical spectra upon the metamaterial fill factor and also, n and m period numbers, are analyzed. The relevant optical spectra are determined for both of the polarization states (TM and TE) and besides, the calculations are performed over the spectral range containing the visible region. For f = 0.5 fil factor value and also for the TM mode polarization, near the perfect angle-insensitive spectral responses are obtained.