Optical properties and Poincaré mapping in spherical multilayered systems: periodic, quasiperiodic, and disordered.

We systematically studied the optical properties (narrows peaks position) of the transmission spectra for microspheres coated by a multilayered stack. Three different sequences of spherical stack-periodic, quasiperiodic, and disordered-are studied by the transfer matrix approach. Dependence of the number of resonances in the transmission spectrum as function of number of layers in the stack is numerically investigated with details. It is shown that characteristic shape of the recursive return map forms well-defined ordered spectrum in the state space. The shape of such structures is different for different frequency ranges and various spherical quantum numbers. For quasiperiodic case, the latter leads to a specific signature of studied sequences and generates the self-similarity in the transmittance spectra. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]