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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]

Abstract: The theory of flexural vibrations proposed by Timoshenko almost 90 years ago has been the subject of several recent papers. In the Timoshenko beam theory a critical frequency is expected and for frequencies f larger than , some authors argue that a second spectrum exists. This is still the matter of much debate. In order to settle this question we have performed experimental measurements of flexural normal-mode frequencies and amplitudes which are much more precise than what has been obtained up to now. For some purposes cylindrical rods are more convenient, whereas in other cases rectangular beams are easier to deal with, so we analyze rods and beams of different shapes and sizes. We show that, below , all observed resonant peaks can be associated with one of the compressional, torsional or Timoshenko resonances and that no resonant peaks are left undetected. The validity of Timoshenko beam theory below and that only one spectrum appears in this regime is therefore proved. The comparison between theory and experiment for rectangular beams also shows that our experimental setup is appropriate, so we can use it confidently for . The measurements we report here in this regime show the existence of a second spectrum, at least for free–free boundary conditions. [Copyright &y& Elsevier]

We numerically investigate the optical transmission through a compound spherical stack with conventional and metamaterial (MM) layers and also embedded MM defect. A formation of extremely narrow resonant peak with nearly complete transmittance in area of a band gap is found. We demonstrate that photon fields of certain frequencies can be strongly confined by a left-handed (LH) defect. The influence of a random deviation in the width of compound spherical layers as well the transit to the whispering gallery mode (WGM) is also discussed. [ABSTRACT FROM AUTHOR]