Photonic band mixing in linear chains of optically coupled microspheres

The paper deals with optical excitations arising in a one-dimensional chain of identical spheres due to optical coupling of whispering gallery modes (WGM). The band structure of these excitations depends significantly on the intermixing between WGMs characterized by different values of angular quantum number, l. We develop a general theory of the photonic band structure of these excitations taking these effects into account and applied it to several cases of recent experimental interest. In the case of bands originating from WGMs with the angular quantum number of the same parity, the calculated dispersion laws are in good qualitative agreement with recent experiment results. Bands resulting from hybridization of excitations resulting from whispering gallery modes with different parity of l exhibits anomalous dispersion properties characterized by a gap in the allowed values of wave numbers and divergence of group velocity.