One dimensional randomly located crystal structures: annular designs, genetic algorithm implementations and photonic band gap calculations

E. Yablonovich and S. John's pioneeringstudies about Photonic Crystals (PCs) have gathered the interest of researchers around world since the time that the idea was proposed in 1987. . The term "photonic" describes operations related to photons within a medium that is composed of periodically genereted dielectric structures with different refractive indices. Such materials are designed to manipulate the photons propagation and they are called Photonic Crystals. In fact, fundamentals of the photonic crystal structure is based on quantum mechanics. Similar to electrons movement under the presence of periodically varying potential in a semi-conducting crystal, photons in periodic dielectric structures behave like electrons in many ways. If lattice potential of the crystal structure is high enough electron propagation in any direction is forbidden. For example, electrons which have insufficent energies, with respect to valance band and conduction band energy differences, can not propagate in semi conductor materials, similarly PC lattice may generate a complete Photonic Band Gap (PBG) in which no photon is allowed to propagate. Due to this unique feature of the PC's, they are investigated in many different studies. One strcuture that is heavily explored is the one dimensional nanobeam waveguide structures. Mainly, this kind of structures transmits photons in allowed statesand there may appear a broad PBG; however, if there is a defect in the periodically modulated refractive index variation, a transmission of photons for defect states in the PBG region can occur. This usually results in trapping of electromagnetic (EM) wave in the defect region. The defect mode with Q-value consumes it in time by propagating in the waveguide (Qw) and by leakages to the surrounding dielectric metarial (Qa). In this work, properties of the 1D cavity structures are investigated in the case of the 1D PCs composed of randomly located air holes. Besides, cavity resonance frequency overlapping for the EM waves in different polarizations is investigated. In other words, polarization independent cavity structure is achieved. Besides, Q factor enhancement for 1D PC structures with genetic algorithm implementation and analytic PBG calculation of the structures are important explorations performed in the presented thesis.