Evidences of evanescent Bloch waves in Phononic Crystals

We show both experimentally and theoretically the evanescent behaviour of modes in the Band Gap (BG) of finite Phononic Crystal (PC). Based on experimental and numerical data we obtain the imaginary part of the wave vector in good agreement with the complex band structures obtained by the Extended Plane Wave Expansion (EPWE). The calculated and measured acoustic field of a localized mode out of the point defect inside the PC presents also evanescent behaviour. The correct understanding of evanescent modes is fundamental for designing narrow filters and wave guides based on Phononic Crystals with defects.Comment: 8 pages, 3 figure

Quantum mechanism of light transmission by the intermediate filaments in some specialized optically transparent cells

Some very transparent cells in the optical tract of vertebrates, such as the lens fiber cells, possess certain types of specialized intermediate filaments (IFs) that have essential significance for their transparency. The exact mechanism describing why the IFs are so important for transparency is unknown. Recently, transparency was described also in the retinal Muller cells (MCs). We report that the main processes of the MCs contain bundles of long specialized IFs, each about 10 nm in diameter; most likely, these filaments are the channels providing light transmission to the photoreceptor cells in mammalian and avian retinas. We interpret the transmission of light in such channels using the notions of quantum confinement, describing energy transport in structures with electroconductive walls and diameter much smaller than the wavelength of the respective photons. Model calculations produce photon transmission efficiency in such channels exceeding 0.8, in optimized geometry. We infer that protein molecules make up the channels, proposing a qualitative mechanism of light transmission by such structures. The developed model may be used to describe light transmission by the IFs in any transparent cells. (C) 2016 Society of Photo-Optical Instrumentation Engineers (SPIE)PR NASA EPSCoR (NASA) [NNX13AB22A]; NIH [G12 MD007583]; Russian Science Foundation [16-14-10159]info:eu-repo/semantics/publishedVersio

Function Photonic Crystals

In the paper, we present a new kind of function photonic crystals, which refractive index is a function of space position. Unlike conventional PCs, which structure grow from two materials, A and B, with different dielectric constants $\epsilon_{A}$ and $\epsilon_{B}$. By Fermat principle, we give the motion equations of light in one-dimensional, two-dimensional and three-dimensional function photonic crystals. For one-dimensional function photonic crystals, we study the dispersion relation, band gap structure and transmissivity, and compare them with conventional photonic crystals. By choosing various refractive index distribution function $n(z)$, we can obtain more width or more narrow band gap structure than conventional photonic crystals.Comment: 15 pages, 8 figures. arXiv admin note: text overlap with arXiv:1001.3793 by other authors; and text overlap with arXiv:1003.3524, arXiv:physics/0104088 by other authors without attributio

Band structure and reflectance for a nonlinear one-dimensional photonic crystal

We consider a model for a one-dimensional photonic crystal formed by a succession of Kerr-type equidistant spaceless interfaces immersed in a linear medium. We calculate the band structure and reflectance of this structure as a function of the incident wave intensity, and find two main behaviors: the appearance of prohibited bands, and the separation and narrowing of these bands. A system with these features is obtained by alternating very thin slabs of a soft matter material with thicker solid films, which can be used to design a device to control light propagation for specific wavelength intervals and light intensities.Comment: 6 pages, 6 figure

Nonlinear Schrodinger equations with multiple-well potential

We consider the stationary solutions for a class of Schrodinger equations with a N-well potential and a nonlinear perturbation. By means of semiclassical techniques we prove that the dominant term of the ground state solutions is described by a N-dimensional Hamiltonian system, where the coupling term among the coordinates is a tridiagonal Toeplitz matrix. In particular we consider the case of N=4 wells, where we show the occurrence of spontaneous symmetry-breaking bifurcation effect. In particular, in the limit of large focusing nonlinearity we prove that the ground state stationary solutions consist of N wavefunctions localized on a single well.Comment: Accepted on Physica D - Keywords: Nonlinear dynamics, Bifurcation, Semiclassical limit, Bose-Einstein condensates in lattice

Propagating and evanescent properties of duble-point defect in sonic crystals

Complex band structures and multiple scattering theory have been used in this paper to analyze the overlapping of the evanescent waves localized in point defects in sonic crystals (SCs). The extended plane wave expansion (EPWE) with supercell approximation gives the imaginary part of the Bloch vectors that produces the decay of the localized modes inside the periodic system. Double cavities can present a coupling between the evanescent modes localized in the defect, showing a symmetric or antisymmetric mode. When point defects are close, the complex band structures reveal a splitting of the frequencies of the localized modes. Both the real part and the imaginary values of k of the localized modes in the cavities present different values for each localized mode, which gives different properties for each mode. The novel measurements, in very good agreement with analytical data, show experimental evidence of the symmetric and antisymmetric localized modes for a double-point defect in SCs. The investigation of the localization phenomena and the coupling between defects in periodic systems has fundamental importance in both pure and applied physics.This work was supported by MEC (the Spanish Government) and FEDER funds through grants MAT2009-09438 and MTM2009-14483-C02-02.Romero García, V.; Sánchez Pérez, JV.; García-Raffi, LM. (2010). Propagating and evanescent properties of duble-point defect in sonic crystals. New Journal of Physics. 12:1-14. doi:10.1088/1367-2630/12/8/083024S1141