Effects induced by Mie resonance in two-dimensional photonic crystals

Abstract

The effects of Mie resonance on the photonic band-gap structure of two-dimensionalphotonic crystals are investigated in detail. Firstly, we demonstrate the correlation betweenthe band-gap structure and Mie resonance, such as the midgap frequency and the changesin gap width with different cylinder radii. We find that the midgap frequencyand the gap width increase linearly and then saturate, before and after the Mieresonance frequency crosses the midgap frequency. The radius value at the crossingpoint between the midgap frequency and the Mie resonance frequency becomessmaller with the increase in the refractive contrast. For large radius, all the Mieresonance frequencies fall into the corresponding bands. Secondly, the changesin the gap width are studied with increasing index of the cylinders. Changingrules of the gap width are found depending on the position of the Mie resonancefrequency. For example, when the Mie resonance falls inside the gap the gap widthincreases most rapidly and reaches its maximum value when the Mie resonance isleaving the gap range (around the lower edge of the gap). After that the gapwidth decreases very steeply with increase in the refractive contrast. Thirdly, weinvestigate the effect of Mie resonance on the band width for the ‘heavy-photonband’, which is the third band of our system. We find that, quite different fromother bands, the band widths of such bands are determined by the overlappingintegral of the Mie resonance states. All these results can be explained by theMie resonance based on two physical pictures, i.e. the scattering picture and thehopping picture. According to these analyses and results, we may understandmore clearly how the Mie resonances influence the formation of the band-gapstructure. The Mie resonance effects on photonic band-gap structure presented inthis paper would be valuable in designing various kinds of photonic crystals.