Search

In this work, we obtain closed expressions for the transfer matrix and the transmittance of electromagnetic waves propagating in finite one-dimensional anisotropic periodic stratified media with an arbitrary number of cells. By invoking the Cayley–Hamilton theorem on the transfer matrix for the electromagnetic field in a periodic stratified media formed by N cells, we obtain a fourth-order recursive relation for the matrix coefficients that defines the so-called Tetranacci polynomials (TPs). In the symmetric case, corresponding to a unit-cell transfer matrix with a characteristic polynomial where the coefficients of the linear and cubic terms are equal, closed expressions for the solutions to the recursive relation, known as symmetric TPs, have recently been derived, allowing us to write the transfer matrix and transmittance in a closed form. We show as sufficient conditions that the 4 × 4 differential propagation matrix of each layer in the binary unit cell, Δ , a) has eigenvalues of the form ± p 1 , ± p 2 , with p 1 ≠ p 2 , and b) its off-diagonal 2 × 2 block matrices possess the same symmetric structure in both layers. Otherwise, the recursive relations are still solvable for any 4 × 4 matrix and provide an algorithm to compute the N th power of the transfer matrix without carrying out explicitly the matrix multiplication of N matrices. We obtain analytical expressions for the dispersion relation and transmittance, in closed form, for two finite periodic systems: the first one consists of two birefringent uniaxial media with their optical axis perpendicular to the z -axis, and the second consists of two isotropic media subject to an external magnetic field oriented along the z -axis and exhibiting the Faraday effect. Our formalism applies also to lossy media, magnetic anisotropy or optical activity. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we explain why beyond a certain critical frequency the extreme ends of a beam under flexural oscillations remain sometimes plane and in other cases become warped. We have seen this to be the case when the flexural oscillations of a beam are studied experimentally. Using the plane stress elastodynamic theory as well as a more precise calculation based on a 3D finite element method, we show for the first time that when the transverse displacement has a derivative equal to zero near the beam extremes, the ends can indeed become warped. In addition it is shown, from an energetic point of view, that warped modes result from a constructive spatial interference of the two components of flexural oscillations while flat modes result from a destructive interference of these two components. [ABSTRACT FROM AUTHOR]

In a previous paper (2012) we presented experimental results proving that the critical frequency f C predicted by Timoshenko beam theory indeed exists. We also showed that for frequencies f smaller than f C the spectrum is formed by almost equally spaced levels whereas for f > f C the spectrum consists of pairs of eigenvalues very close to each other as predicted by numerical solutions of Timoshenko׳s equation: we shall refer to them as Timoshenko doublets. In this work we measure for the first time experimental dispersion relations. For this purpose it was necessary to obtain normal-mode amplitudes with a high precision, which was done with a new experimental setup developed by us. We found that experimental dispersion relations coincide very well with theoretical predictions. Furthermore, we provide an explanation of Timoshenko doublets. [ABSTRACT FROM AUTHOR]

Three classical systems formed by the pairs of coupled resonators are analyzed, including a system of elastically coupled masses, a system of rigid rods separated by a notch, and an optical system made by a pair of dielectric films separated by a thin metallic layer. We show numerically that these systems are analogous to each other. For the latter two systems, the theoretical results are confirmed experimentally. This study allows us to discuss in classical systems properties that typically are only described quantum mechanically, such as the avoided crossing theorem, the strength function phenomenon, and the effect of the coupling element. [ABSTRACT FROM AUTHOR]

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]

Two elastic systems are considered in this work: A special linear chain of harmonic oscillators and a quasi one-dimensional vibrating rod. Starting in both cases with a locally periodic system formed by unit cells with a single element, these cells are converted into binary cells. The acoustic and optical bands then appear. For the vibrating rod experimental values are compared with theoretical results; in particular, the normal-mode amplitudes are obtained and the agreement is excellent. [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: 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]

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]

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]

Abstract: We studied the photon spectrum in coated microspheres with alternating quasiperiodic layers having left-handed (LH) materials included. It is found that the band gap (spectral zone of nearly zero transmittancy) in such a system is strongly enhanced. At an increase of the quasiperiodicity parameter γ, the boundaries of the spectral band gaps acquire the intended shape. When γ exceeds the inverse golden mean value, a structure with extremely narrow separated resonant peaks with nearly complete transmittance arises. At increased γ, such resonances migrate to the center of the band gap. This effect allows creating optical filters with extremely narrow passbands. [Copyright &y& Elsevier]

Abstract: We studied the field radiation of disordered optical nanoemitters incorporated into three-dimensional (3D) spanning cluster in a percolation material. In supercritical state, the field intensity is large enough to produce a dynamic high-density coherent field. The resulting state becomes different for lossless and lossy mediums. For material with small losses the long-term coherence arises in the supercritical area close to the percolation threshold. As a result, the dynamic non-monotonic behavior of the field order parameter raises that allows to reach the optimal field intensity. This effect can allow optimization of the disordered optical nanostructures with incorporated radiating nanoemitters in various applications of information technology. [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]

We report the experimental observation of doorway states phenomenon for acoustic waves in porous silicon structures. We designed and fabricated a structure capable to exhibit the acoustic doorway states phenomenon around 1 GHZ. The structure consists of two porous silicon layers, one with low porosity and another with higher porosity and smaller thickness, followed by a much more thicker layer of crystalline silicon. We study the doorway state phenomenon in the frequency and in the time domain. To do this, we measured the acoustic transmission spectra in the frequency domain, and by using the Fourier transform, we obtain the transmission in the time domain. The transmission spectrum of the fabricated sample shows acoustic doorway states in frequencies around 1 GHz. The experimental results are in good agreement with the transfer matrix calculations. [ABSTRACT FROM AUTHOR]

In this work, we demonstrate, analytically and numerically, that degenerate states of a beam with free ends, with anti-symmetrical transverse mode shape and occurring in the first-degeneracy points above the cutoff frequency, tend asymptotically to the thickness-shear mode in the infinitely long beam limit, which has not been previously reported. We compare our numerical results, obtained using a Timoshenko–Ehrenfest beam theory of second order, with those obtained with the Finite Element method and plane stress elastodynamics theory, obtaining an excellent agreement. We show that anti-symmetric states within the vicinity of these first-degeneracy states are very similar and closely resemble the so-called thickness-shear mode but for a finite beam with free ends under flexural vibrations. • Mode shapes of degenerate states are studied in Timoshenko–Ehrenfest beams. • First-degeneracy asymmetric states turn out very similar to the thickness-shear mode. • Instead, it is shown that transverse oscillations of the cutoff states are non-negligible. • Results for a beam with free ends are corroborated with the Finite Element method. • It is demonstrated that analogs to the thickness-shear mode exist for finite beams. [ABSTRACT FROM AUTHOR]

In a previous work an elastic bar with a groove or notch that presents a doorway state was studied when the system was excited with 20 cycles of harmonic signals. The strength function had a Lorentzian width Γd = 1/πτd, where τd is the decay time of the prompt response. In the present paper, the doorway-state phenomenon is analyzed again for the same harmonic signals but for a very large number of cycles. The strength-function phenomenon is once more obtained, but now with a Lorentzian width Γ' which is larger than Γd. A qualitative and numerical explanation of this fact is given, leading therefore to further understanding of doorway states in elastic systems. The numerical results show a very good agreement with the values measured in the laboratory. [ABSTRACT FROM AUTHOR]