Narrowing of transmittance band gaps in a multilayered microsphere with quasiperiodic left-handed stack

We studied the photon spectrum in coated microspheres with alternating quasiperiodic layers having left-handed (LH) materials included. It is found that the band gap (spectral zone of nearly zero transmittance) in such a system is strongly enhanced. At an increase of the quasiperiodicity parameter (QP), the boundaries of the spectral band gaps acquire intended shape. When QP exceeds the inverse golden mean value, a structure with extremely narrow separated resonant peaks with nearly complete transmittance arises. At increase QP such resonances migrate to the centre of the band gap. This effect allows creating optical filters with extremely narrow passbands.