Μελέτη συντονιζόμενων διατάξεων διδιάστατων φωτονικών κρυστάλλων με διήθηση νηματικών υγρών κρυστάλλων
Authors: Κοσμίδου Ελισσάβετ 
Published: January 2014

The scope of this doctoral thesis is the computational study of various tunable devices based on two-dimensional photonic crystal lattices where nematic liquid crystal materials are infiltrated. The analysis accounts for the effect of the director orientation profile on the spectral properties of the structures under investigation. The first chapter contains a thorough bibliographical survey with reference to the basic evolutionary stages of the research area of photonic crystals. Special emphasis is given on the idea of liquid crystal infiltration. In the second chapter the principal properties of two-dimensional photonic crystal lattices and liquid crystal materials are summarized. A brief review of the utilized computational methods is the subject of the third chapter. An anisotropic FDTD scheme and the ADE technique for the simulation of liquid crystals and metals, respectively, are briefly described. Additionally, a PML technique suitable for the termination of photonic crystal waveguides which comprise anisotropic materials is presented. Based on Βloch’ s theorem two novel alternative algorithms are developed, which are appropriate for the computation of TE and TM dispersion diagrams of structures based on two-dimensional square and triangular lattices which contain liquid crystals or metallic elements. The fourth chapter is devoted to the analysis of one-dimensional photonic crystal cavities infiltrated with nematic liquid crystals. The considered geometries are realized on a triangular lattice of air voids in silicon. The nematic material is inserted either into properly selected voids or as a layer interposed between two blocks of the periodic lattice. In the first case it is assumed that an external static electric field changes the uniform alignment of the nematic director, thus controlling the spectral properties of the cavity. On the other hand, when the defect consists of a liquid crystal layer, tuning is achieved by a voltage which is applied between two ITO films surrounding the layer and formulates the nematic director profile and consequently the resonant frequencies. Various geometries are examined in order to determine the influence of specific geometrical parameters on the resonant frequencies, as well as on their tunability. Overall, wide tuning ranges and narrow linewidths are achieved. The study of tunable devices is continued in the fifth chapter, where photonic crystal directional couplers are analyzed. In this case the nematic material is inserted into the waveguides or in the coupling region either by filling certain air voids or as a layer. The analysis aims to find coupler structures with tunable dispersion diagrams that support only two supermodes in a wide area inside the bandgap. The optimal coupler geometry results from the insertion of the nematic material into the air voids of properly designed waveguides. It is ascertained that the respective dispersion diagram is strongly affected by the molecular orientation. Moreover, very small coupling lengths are computed even when the coupling region is expanded. The coupler’s capability to operate as a channel interleaver is also investigated. The analysis is extended in the sixth chapter by considering various molecular orientation profiles for liquid crystals inserted into the air voids of a triangular lattice. Specifically, the infiltrated periodic lattice, as well as indicative cavities, waveguides and directional couplers are investigated, taking into account different anchoring conditions (homeotropic/tangential - strong/weak) and electric fields of various characteristics. It is revealed that the orientation profile of the nematic director can strongly affect the operation of the analyzed structures. Therefore, the exact knowledge of the anchoring conditions is very important in order to conduct accurate experimental studies and theoretical calculations. In the final chapter the main conclusions of the presented study are summarized and potential extensions for future research are suggested.