Periodic Stratified Structure Research Articles

Periodic homogenization of elliptic systems with stratified structure

This paper concerns with the quantitative homogenization of second-order elliptic systems with periodic stratified structure in Lipschitz domains. Under the symmetry assumption on coefficient matrix, the sharp \begin{document}$ O(\varepsilon) $\end{document} -convergence rate in \begin{document}$ L^{p_0}(\Omega) $\end{document} with \begin{document}$ p_0 = \frac{2d}{d-1} $\end{document} is obtained based on detailed discussions on stratified functions. Without the symmetry assumption, an \begin{document}$ O(\varepsilon^\sigma) $\end{document} -convergence rate is also derived for some \begin{document}$ \sigma by the Meyers estimate. Based on this convergence rate, we establish the uniform interior Lipschitz estimate. The uniform interior \begin{document}$ W^{1, p} $\end{document} and Holder estimates are also obtained by the real variable method.

Studies on the mechanism of acoustic pulse train and full transmission

Critical phenomenon in a one-dimensional periodic stratified structure with time-varying elastic modulus functions is found out for acoustic waves. By using the classical separation of variables method to solve the one-dimensional wave equation, and taking the time-varying elastic modulus functions into consideration, a critical value can be found of the varying amplitude of the time-varying elastic modulus functions. Near the critical value, due to the alternation of the characteristic exponent, the reflectivity of the one-dimensional periodic stratified structure changes in essence. Below or at the critical value, the incident wave can be converted into a periodic and millisecond pulse train, particularly when the varying amplitude is at the critical value. In addition, the layer number can be up to 16. Under these circumstances, complete pulse train of 0 or 1 is generated with respect to time; in the end, when above the critical value, the reflectivity decreases rapidly to 0 within 50 milliseconds, indicating that, at one moment, the incident wave can be totally transferred through the structure as if the stratified structure becomes transparent, which means a modulational transparency. In conclusion, by altering the varying amplitude of the time-varying elastic modulus functions, three different phenomena are generated. These excellent properties could find potential applications of one-dimensional periodic stratified structure in the acoustic transducer and the control of the acoustic wave.

Coherent X-rays excited by a relativistic electron crossing a periodic stratified structure in Bragg scattering geometry

The dynamic theory of coherent X-rays excited by a relativistic electron crossing an artificial periodic stratified structure in Bragg scattering geometry has been developed for the general case of asymmetric reflection. Expressions describing the spectral-angular characteristics of radiation have been derived and investigated.

Modulational transparency and femtosecond pulse train in Bragg reflectors with time-varying dielectric constant

A theoretical study is conducted to investigate the nonlinear properties of a one-dimensional (1D) periodic stratified structure with time-varying dielectric constants. When the dielectric constant is modulated temporally, the distributed Bragg reflector exhibits different throughputs depending on the modulation amplitude. Below or at the critical value, a periodic and stable femtosecond pulse train is generated; above this critical value, the modulational transparency is observed, as the reflectivity decreases rapidly, so that all incident radiation is completely transferred through the layered media. When the layer number is up to 15, the pulse train generated at the critical value is periodic with perfect reflectivity and zero rejection. These excellent optical properties may enhance the potential applications of the 1D periodic stratified structure in optical switches and laser optics.

Radiation emitted by an oscillating dipole embedded in a periodic stratified structure: A direct matrix analysis

The Abeles matrix formalism is combined with the plane-wave expansion method to calculate the radiation emitted by an oscillating dipole embedded within a periodic multilayer planar structure. This approach is implemented to account for the soft-x-ray Kossel structures recently observed with W/C multilayers [P. Jonnard et al., Phys. Rev. A 68, 032505 (2003)].

Exact analytic expressions for electromagnetic propagation and optical nonlinear generation in finite one-dimensional periodic multilayers

The translation matrix formalism has been used to find an exact analytic solution for linear light propagation in a finite one-dimensional periodic stratified structure. This modal approach allows us to derive a closed formula for the electric field in every point of the structure, by simply imposing a convenient form for the boundary conditions. We show how to apply this result to second-harmonic generation in the undepleted pump regime.

Limit analysis of the diffraction of a plane wave by a one-dimensional periodic medium

In this paper we address the problem of the reflection coefficient limit in a periodic stratified structure when the number of periods tends to infinity. We show that the graph of the reflected energy admits a superior envelope and we exhibit an explicit formula.

Periodic stratified structure in a multilayer planar optical waveguide

The contribution of a periodic stratified structure to the optical guiding properties of a multilayer planar waveguide is analyzed. We present an equivalent-layer method for the periodic stratified structure in a multiplayer waveguide that not only allows the whole periodic stratified structure to be treated as a single layer but offers exact solutions for the propagation constant of the waveguide and the power-confinement factor within the periodic stratified structure in a multilayer waveguide. This method is applied to study the optical guiding characteristics of multiquantum-well waveguides, such as the propagation constant, the field distribution, the power-confinement factor, and the group refractive index. The effective indices and the confinement factors of several practical GaInAsP/InP multiquantum-well lasers are calculated and analyzed.

Application of neutron diffraction to the study of interface magnetization on thin films with artificial superlattices

We have elucidated the studies on the interface magnetization applying the simple kinematical theory of neutron diffraction for the periodic stratified structure. In order to realize the principle we made an artificial superstructure film consisting bilayers of ferromagnetic versus non magnetic materials. The present paper is devoted to a discussion of the principle of the application of neutron diffraction, the experiments and the results. We also compare the results with the depth profile analysis of Mössbauer spectroscopy.