Resonance-induced effects in photonic crystals

For the case of a simple face-centred-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 spectac ular effects may be expected. When the dielectric constant of the spheres e psilon(s) is greater than the dielectric constant epsilon(b) of the backgro und medium, then for any filling fraction f there exists a critical epsilon (c) above which the lowest-lying Mie resonance frequency falls inside the l owest stop gap in the (111) crystal direction, close to its midgap frequenc y. If epsilon(s) < epsilon(b), the correspondence between Mie resonances an d both the (Ill)stop gap and a full gap does not follow such a regular patt ern. If the Mie resonance frequency is close to a gap edge, one can observe a resonance-induced widening of a relative gap width by approximate to 5%.