A theory is presented for the DISPERSION relations of the nonlinear phononpolaritons arising when phonons are coupled to the electromagnetic waves in multilayered structures of nonlinear materials. The calculations are applied to a multilayered structure consisting of a thin film surrounded by semi-infinite bounding MEDIA where each layer may have a frequency dependent dielectric function and KERR-TYPE nonlinearity. At least one of the MEDIA is an ionic crystal supporting optical phonon modes. The resulting analytic and numerical solutions for the DISPERSION relations of phonon-polaritons with s-polarization are considered for several cases. We find that the presence of nonlinearities leads to multiple branches in the DISPERSION relation. The results are plotted as frequency versus wave vector and frequency versus nonlinearity for different phononpolariton modes. The parameters that modify the modes correspond to the inplane wave vector, the thickness of the film, the phonon frequencies and the nonlinearity of each layer.

DISPERSION, as the characteristic variation of refractive index with wavelength, is more pronounced, where the wavelength is approaching to the absorption band. In ultra-optical glasses, the nonlinear refractive index, concerning to the light intensity dependent phenomenon, becomes considerable. Here, two ultra-optical property glass systems; TiO2-Bi2O3-PbO (TBP) and Ga2O3-Bi2O3-PbO (GBP), which exhibited the most refractive indices, were selected. Their refractive index and DISPERSION measurements were done by `Minimum angle of deviation in a prism` method employing a spectrometer under different light spectra transmission. The corresponding nonlinear refractive indices of glasses were calculated by the Weber, et al., and Boling, et al., formulae and were analysed. The minimum refractive index in very long waves (infra-red), `n∞ ` and λ s were estimated by `Kordes semi-empirical formula` and the DISPERSION curve fit method. Results suggested that the both glass systems could be good candidates for use in nonlinear optical applications, e. g. switches in all-optical telecommunications.

Photonic crystal fibers (PCFs) as waveguides with low DISPERSION, low confinement loss, and low nonlinearity can be used in optical telecommunication systems. In this paper, a hexagonal-circular photonic crystal fiber is proposed. In the first design, we present a hexagonal PCF with 70 ps/nm.km DISPERSION at 1550 nm wavelength. The confinement loss and nonlinearity of this structure are respectively obtained as 0.6´10-12dB/cm and 8.988 W-1km-1. In the second design, by improving th e primary structure as hexagonal-circular PCF, the nearly zero DISPERSION is obtained. The simulation results show that the confinement loss and nonlinearity of the improved structure are 8´10-11 dB/cm and 7.956 W-1km-1, respectively.

In this study, the nonlinear free vibration of conservative two degrees of freedom systems is analyzed using the homotopy analysis method (HAM). The mathematical model of such systems is described by two second-order coupled differential equations with cubic nonlinearities. First, novel approximate analytical solutions for displacements and frequencies are established using HAM. Then, the homotopy Padeacute technique is applied to accelerate the convergence rate of the solutions. Comparison between the obtained results and those available in the literature shows that the first-order approximation of homotopy Padeacute technique leads to accurate solutions with a maximum relative error less than 0.068 percent for all the considered cases. 

this empirical analysis endeavors to trace out the causal nexus between core inflation and economic growth from the perspective of twenty worlds’ leading economy with the help of the nonlinear Granger causality approach by using time series data from 1981 to 2016. Based on nonlinear Granger causality results, it has been found that there is unidirectional casualty running from core inflation to economic growth in Belgium, Denmark, Franc, Greece, India, Norway, and Portugal as well as Sweden. In these countries, core inflation is causing economic growth. As per as Australia, Canada, Germany, Greece, Japan, New Zealand, Portugal, Sweden, Switzerland, and the United Kingdom is concerned the outcome of causality analysis documents that there is unidirectional causality running from economic growth towards the core inflation. Finally, the analysis also manifests that there is no causality running from core inflation towards the economic growth and vice-versa in Ireland, Israel, Netherlands, and Spain.

In this paper, we report the simulation results for impact of nonlinear KERR effect on band structures of a two dimensional photonic crystal (2D-PhC) with no defect, a PhC based W1-waveguide (W1W), and also Coupled-Cavity Waveguides (CCWs). All PhC structures are assumed to a square lattice of constant a made of GaAs rods of radius r=0.2a, in an air background. The numerical simulation was performed using the nonlinear finite difference time domain (NFDTD) technique. In doing so, we have normalized the electric field and the electric flux density vectors, and used a multi probe procedure. These have resulted in very accurate DISPERSION relations that, in turn, have enabled us to make some novel observations. For instance, simulations show that with an increase in the input light intensity (in the nonlinear regime) the band edges for all three PhC structures experience some red shifts. The red shifts observed for CCWs are, of course, larger than the red shifts experienced by other two structures. Furthermore, the numerical results for CCWs also show that the larger the light input intensity, the smaller the corresponding maximum light group velocity becomes. To the best of our knowledge, this is the first instance that such observations on the impact of the nonlinear KERR effect on the band diagram of 2D-PhC waveguides are reported.

In this paper, a Hamiltonian model, which includes the interaction of two two-level atoms with a codirectional KERR nonlinear coupler via the Raman non-degenerate two-photon transition, is introduced. The atomic interaction is assumed to be in the dipole-dipole form, and the total system is also in thermal equilibrium with the environment. The total excitation number operator, as the constant of the motion of the system, provides a decomposition of the Hilbert space of system into direct sums of invariant subspaces. As a result, the representation of the Hamiltonian becomes a block-diagonal matrix. By diagonalizing each of the blocks, we obtain eigenvalues and the corresponding eigenstates of the Hamiltonian. Then we obtain the thermal state of the system in the whole Hilbert space and within its excitation subspaces. We quantify the thermal entanglement between the atoms in the Hilbert space of the system and within its excitation subspaces using the measure of the concurrence. Finally, the effect of temperature and system parameters on the degree of thermal entanglement is investigated. The results show that in the subspaces with an odd excitation number, the atomic thermal entanglement is thermally robust and remains constant.