Browsing by Author "Hermann, Christian"

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Open Access
Three dimensional finite difference time domain simulations of photonic crystals
(2004) Hermann, Christian; Hess, Ortwin (Prof. Dr.)
In this work fundamental optical properties of various photonic crystal structures are analysed numerically within the framework of three dimensional finite-difference time-domain (FDTD) simulations. After a discussion of the underlying physical and mathematical principles from electrodynamics and solid state physics leading to the formation of a photonic bandgaps, two important example systems are discussed in detail. First, we study two-dimensionally patterned layer-by-layer systems. These system are promising with respect to applications in integrated optics, but suffer severely from out-of-plane radiation losses. With fully three dimensional simulations we analyse this loss mechanism for several vertical layer-setups, obtaining new and important results regarding the understanding of the interaction of in-plane structure and surrounding. E.g. we describe for the first time the existence of cladding modes in complicated layer-by-layer structures. Second, we analyse the strong space-, frequency- and polarisation dependance of spontaneous emission within the weak coupling limit in an three-dimensionally structured inverted opal crystallite of finite size. The inverted opal, exhibiting a complete bandgap, shows (beside the supression of emission for bandgap frequencies) strong enhancement for emitters placed on dielectric interfaces. These results are important for interpretating luminescence experiments of inhomogeneously infiltrated dye molecules. In the last part of the work we discuss the numerical method itself with special focus on the necessary adaptations for the treatment of photonic crystal structures.