Effects induced by Mie resonance in two-dimensional photonic crystals

The effects of Mie resonance on the photonic band-gap structure of two-dimensional photonic crystals are investigated in detail. Firstly, we demonstrate the correlation between the band-gap structure and Mie resonance, such as the midgap frequency and the changes in gap width with different cylinder radii. We find that the midgap frequency and the gap width increase linearly and then saturate, before and after the Mie resonance frequency crosses the midgap frequency. The radius value at the crossing point between the midgap frequency and the Mie resonance frequency becomes smaller with the increase in the refractive contrast. For large radius, all the Mie resonance frequencies fall into the corresponding bands. Secondly, the changes in the gap width are studied with increasing index of the cylinders. Changing rules of the gap width are found depending on the position of the Mie resonance frequency. For example, when the Mie resonance falls inside the gap the gap width increases most rapidly and reaches its maximum value when the Mie resonance is leaving the gap range (around the lower edge of the gap). After that the gap width decreases very steeply with increase in the refractive contrast. Thirdly, we investigate the effect of Mie resonance on the band width for the 'heavy-photon band', which is the third band of our system. We find that, quite different from other bands, the band widths of such bands are determined by the overlapping integral of the Mie resonance states. All these results can be explained by the Mie resonance based on two physical pictures, i.e. the scattering picture and the hopping picture. According to these analyses and results, we may understand more clearly how the Mie resonances influence the formation of the band-gap structure. The Mie resonance effects on photonic band-gap structure presented in this paper would be valuable in designing various kinds of photonic crystals.