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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]

We studied numerically the frequency spectrum of photons in a multilayered microsphere coated by a quasiperiodic (Pascal) dielectric stack. It is found that the transmittancy spectrum of such a stack consists of quasiband gaps and narrow resonances caused by re-relection of optical waves. When the number (Pascal order) of layers increases, the band gaps and resonances split, and the structure of the frequency spectrum acquires a fractal form. Some parts of the spectrum show the self-similarity in the diferent frequency scales. [ABSTRACT FROM AUTHOR]

Abstract: We study numerically the frequency spectrum of light propagating through a multilayered micro-sphere coated by an alternating sub-wavelength photonic bandgap stack with an embedded defect. We found the formation of an extremely narrow resonant peak with nearly complete transmission in the area of the band gap. The spectral evolution of such a resonance at the change of a defect layer is investigated in details. It is found the confinement of the defect photon mode that results in the formation of strong field oscillations in the vicinity of the defect layer. The influence of a random deviation in the width of the spherical layers is also discussed. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]