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 spectacular effects may be expected. When the dielectric constant of the spheres ^es is greater than the dielectric constant ^eb of the background medium, then for any filling fraction f there exists a critical ^ec 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 ^es<eb, 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 ^»5%.