Band structure of absorptive two-dimensional photonic crystals

The band structure for an absorptive two-dimensional photonic crystal made from cylinders consisting of a Drude material is calculated. Absorption causes the spectrum to become complex and form islands in the negative complex half-plane. The boundaries of these islands are not always formed by the eigenvalues calculated for Bloch vectors on the characteristic path, and we find a hole in the spectrum. For realistic parameter values, the real part of the spectrum is hardly influenced by absorption, typically less than 0.25%. The employed method uses a Korringa-Kohn-Rostoker procedure together with analytical continuation. This results in an efficient approach that allows these band-structure calculations to be done on a Pentium III personal computer

Resonance-Induced Effects in Photonic Crystals

For the case of a simple face-centered-cubic photonic crystal of homogeneous dielectric spheres, we examine to what extent single-sphere Mie resonance frequencies are related to band gaps and whether the width of a gap can be enlarged due to nearby resonances. Contrary to some suggestions, no spectacular effects may be expected. When the dielectric constant of the spheres $\epsilon_s$ is greater than the dielectric constant $\epsilon_b$ of the background medium, then for any filling fraction $f$ there exists a critical $\epsilon_c$ above which the lowest lying Mie resonance frequency falls inside the lowest stop gap in the (111) crystal direction, close to its midgap frequency. If $\epsilon_s <\epsilon_b$, the correspondence between Mie resonances and both the (111) stop gap and a full gap does not follow such a regular pattern. If the Mie resonance frequency is close to a gap edge, one can observe a resonance-induced widening of a relative gap width by $\approx 5$.Comment: 14 pages, 3 figs., RevTex. For more info look at http://www.amolf.nl/external/wwwlab/atoms/theory/index.htm

Photon localization in disorder-induced periodic multilayers

We studied the influence of randomness on a periodic dielectric 1D stratified system. Numerical simulations are performed, and are compared to theoretical predictions. Non-analytic behaviour is found at the band edges. The anomalies that can arise in the middle of a band turn out to be far more pronounced than the ones in the Anderson-model.Nous avons examiné l'influence du désordre sur un système et stratifié et diélectrique, à une dimension. Le système est d'origine périodique. Des simulations numériques ont été effectuées et devraient être confrontées à des prédictions théoriques. L'exposant de Lyapunov est non analytique aux bords du spectre. Nous avons constaté que les anomalies qui pourraient se trouver au centre des bandes sont beaucoup plus nettes que celles dans le modèle d'Anderson