Optical fields in a multilayered microsphere with a quasiperiodic spherical stack

We studied the frequency spectrum of photons in a multilayered microsphere coated by a quasiperiodic (Fibonacci) dielectric stack numerically. We found that the transmittancy spectrum of such a stack consists of quasiband gaps and narrow resonances caused by re-reflection of optical waves. When the number (Fibonacci order) of layers increases, the band gaps and resonances split, and the structure of the frequency spectrum acquires a fractal form. We found the self-similarity of the frequency spectrum and evaluated the fractal dimension both for lossless and dissipative cases. The influence of a weak random deviation of spherical layers width is also discussed.