Interaction of Counter-propagating Elliptically Polarized Light Waves in Isotropic Nonlinear Media

Abstract

The nonlinear interaction of elliptically polarized counter-propagating waves in an isotropic transparent medium is analysed. Self-induced changes in the polarization of the counter-propagating light waves, are described. Using these results, a new type of modulator giving self-induced rotation of the polarization ellipse (SIRPE) is studied. The transmission of counter-propagating waves in the SIRPE modulator is shown to exhibit saturation with increase in light intensity and to be a multiple-valued function of the light intensity.     

Exact Solution for Transverse Electric Polarized Nonlinear Guided Waves in Saturable Media

Abstract

The power dependent wave-vector and stationary field distributions for TE polarized nonlinear waves guided by an interface between a linear dielectric and a saturable nonlinear self-focusing medium characterized by the dielectric function ? = ?_c + α_c¦E¦² + β_c¦E¦⁴ are exactly calculated. Exact nonlinear wave solutions are also given for TE polarized nonlinear waves guided by dielectric or metallic films bounded on one side by a self-focusing saturable medium characterized by the above dielectric function. The stability on propagation of these nonlinear stationary wave solutions was investigated numerically.     

Solution of Maxwell's Equations Using the MQ Method

A meshless time domain numerical method based on the radial basis functions using multiquadrics (MQ) is employed to simulate electromagnetic field problems by directly solving the time-varying Maxwell's equations without transforming to simplified versions of the wave or Helmholtz equations. In contrast to the conventional numerical schemes used in the computational electromagnetism such as FDTD, FETD or BEM, the MQ method is a truly meshless method such that no mesh generation is required. It is also easy to deal with the appropriate partial derivatives, divergences, curls, gradients, or integrals like semi-analytic solutions. For illustration purposes, the MQ method is employed to calculate the propagations of the electric and magnetic waves in the homogeneous, isotropic, and non-lossy 2D rectangular waveguide as well as 3D cavity resonator. Good agreements are obtained as compared to analytical solutions. By directly solving the Maxwell's equations, the MQ scheme provides a very simple and effective numerical scheme for the computational electromagnetism.     

J-Integral of Dissimilar Anisotropic Media

The plane problem J - integral of an interfacial crack between dissimilar anisotropic materials is derived. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dissipation of Solitary Waves in Aluminum with Grain Boundary

The behaviour of passing solitary waves through the region of grain boundary has been investigated on the basis of the molecular dynamics method. It has been shown that solitary waves initiated by compression and shear loading have a different interaction with the grain boundary region. The possibilities of using solitary waves for nondestructive testing of materials, in particular, for testing the quality of coatings, for testing of accumulation of microdamages, etc. have been noted.     

Squeezing of Bound Solitary Waves in a Birefringent Optical Fibre

Abstract

The coupled nonlinear Schrödinger equations in a birefringent optical fibre are derived by means of the method of path integrals. The dependence of the squeezing effect on the coupled waves is obtained with a first-order perturbation approximation, considering zero-dispersion, normal and abnormal dispersion.     

Reaction Driven Elastic Waves in Solid Media

Chemical reactions and phase transformations couple in solid systems with the stress fields. When reaction rates become of the same order as the rate of relaxation of mechanical perturbations, the reactions can stabilize elastic waves in the system. Density varies with temperature and conversion and since the elastic waves are driven by the gradients in temperature and conversion, these source terms travel with the same speed as the reaction front. A model is presented for elastic waves in solid media, driven by a moving source term that is well approximated by a delta function. The propagation velocity of this source is constant, but it can propagate either subsonically or supersonically. The effects of precompressing the sample, applying a force at one boundary, and varying the strength of the source term with time are included in the discussion. The model is useful to study transformation reactions under shock-compression, ultrafast deflagrations, and detonations in the solid phase.     

In Situ Measurement of Thermal Diffusivity in Anisotropic Media

A knowledge of thermal conductivity/diffusivity is essential in several situations in engineering. This material property serves also as a measure of the quality of the manufactured materials. The thermal conductivity and diffusivity are measured by specialized labs using commercially available equipment. Even though both the number of such sites and the available measurement techniques are quite large, non-destructive, fast, and reliable techniques are still demanded. The developed technique, due to its rapidity and nondestructive character, can be embedded in a manufacturing process. As opposed to most methods, it does not require preparation of samples of a special shape (e.g., a small cylinder, a thin foil, cuboid). Moreover, one measurement cycle of the proposed technique yields two principal components of the diffusivities of orthotropic materials.     

Propagation of Electromagnetic Waves in Media Undergoing Complex Motions

Results of a theoretical and experimental investigation into new effects in moving-media optics are presented. An exact analytical solution is obtained for the trajectory of the wave vector of a monochromatic electromagnetic plane wave in a medium undergoing a complex motion. It is shown that the spatial dragging of the electromagnetic wave by the moving medium can be described correctly in the general case only if relativistic terms of order β² are taken into account. Also, in this investigation a spatial effect of the light drag was observed at a wavelength of λ =0· 63299 μm by means of an optical disk with a refractive index n=1· 4766, a radius of R ₀ =0· 06 m rotating at a frequency of ω =25 Hz. A relative shift of the interference pattern, monitored by the time of the interference band motion across the aperture of a photodetector for the disk rotating in the opposite directions, amounted to of the interference bandwidth. The results of theoretical calculations of the expected interference pattern shift on the basis of the total solution of the dispersion equation in the experiment are in agreement with the experimental results. Analysis of the results obtained suggests that the detected effects determine a wide class of observed phenomena, even when the velocities of moving media are non-relativistic.     

A New Class of Nonlinear Guided Waves

Abstract

We consider a planar structure consisting of a linear film and adjacent substrate and cladding having unequal refractive indices and nonlinear coefficients. We show that a new class of waves exists in this structure. We analyse it and present its characteristics. In a symmetric waveguide, some branches reduce to well-known dispersion curves, but there are also unusual degenerate states which can have various applications.     

各向异性椭圆方程的多重网格局部Fourier分析

Fourier光滑分析和Fourier二网格分析是研究多重网格收敛性和误差估计的基础。本文主要针对各向异性椭圆方程,研究多重网格方法中的Fourier分析方法。将研究各向异性椭圆方程在采用不同的离散和光滑时,光滑因子以及二网格因子的计算方法,并给出利用程序计算所得的结果。这将是对偏微分方程数值分析方法的新的重要尝试。     

Self-phase Modulation in Quadratically Nonlinear Media

Abstract

We discuss self-phase modulations and related transverse effects accompanying interaction of a light beam with a second harmonic radiation generated by it. Some experimental observations are explained by a simple perturbative approach. Numerical simulations provide a further insight into the nature of transverse self-effects in quadratically nonlinear media. An effective x ⁽³⁾-like behaviour of dispersive quadratically nonlinear media is discussed. Such feature may lead to important consequences for measurements of the x ⁽³⁾ tensor in complex nonlinear media.     

Nonlinear Interaction of Electromagnetic Waves in a Dense Plasma

Technical Physics Letters - We discuss the nonlinear phenomena caused by the quadratic interaction of electromagnetic waves in a dense charged medium (Coulomb systems and plasma), including the...     

Electro-magneto-thermo-visco-elastic Plane Waves in Rotating Media with Thermal Relaxation

A study is made of the propagation of plane electro-magneto-thermo-visco-elastic harmonic waves in an unbounded isotropic conducting visco-elastic medium of Kelvin–Voigt type permeated by a primary uniform magnetic field when the entire medium rotates with a uniform angular velocity. The thermal relaxation time of heat conduction, the electric displacement current, the coupling between heat flow density and current density, and that between the temperature gradient and the electric current are included in the analysis. A more general dispersion relation is obtained to determine the effects of rotation, thermal relaxation time, visco-elastic parameters, and the external magnetic field on the phase velocity of the waves. Perturbation techniques are used to study the influence of small magneto-elastic and thermo-elastic couplings on the phase velocity of the waves. Cases of low and high frequencies are also analyzed to determine the effect of rotation, visco-elastic parameters, thermo elastic and magneto-elastic coupling, as well as thermal relaxation time of heat conduction on the waves.     

Propagation of Thermoelastic Waves in Micropolar Mixture of Porous Media

The theory of coupled thermoelasticity for a micropolar mixture of porous media (Eringen AC, J Appl Phys 94:909, 2003) is generalized in the context of Lord and Shulman and Green and Lindsay theories of generalized thermoelasticity. The governing equations of generalized thermoelasticity of a micropolar mixture of porous media are solved to show the existence of three coupled longitudinal displacement waves, two coupled longitudinal microrotational waves, and six coupled transverse waves, which attenuate and are dispersive in nature.     

Polarization Vectors of Acoustic Phonons Propagating in Mechanically Stable Anisotropic Media

We consider properties of long wavelength acoustic phonons propagating in anisotropic elastic media. For cubic media we found three subregions of mechanical stability region in which polarization properties of modes are anomalous. To achieve the detailed specification of this unusual behavior we performed vast numerical calculations and devised new characteristics, namely surfaces of polarization angles and maps of polarization enhancement factors.     

Nonlinear Second Sound Waves in Superfluid Helium in a Resonator

No Heading We communicate the results of numerical studies of acoustic turbulence in a system of nonlinear second sound waves in superfluid He-II in a resonator. It is shown that at sufficiently high amplitude of the external driving force the power-like energy distribution over frequency is formed in the system of second sound waves. This distribution is attributed to formation of the acoustic turbulence regime in the system. The energy distribution inside this interval is close to E ~ ^–2 and it does not depend on the sign of the coefficient, i.e. the coherent structures (shock waves) do not contribute into statistical properties of the second sound distribution in the turbulent state.PACS: 67.40.Pm, 67.60.Fp     

A Polarized Transfer Matrix for Electromagnetic Waves in Structured Media

Abstract

The study of electromagnetic systems with dielectric or magnetic properties that vary spatially on or below the scale set by the wavelength of the radiation considered is of interest both in the field of photonic band gap materials and in that of random multiple scattering media. A key calculation technique in both areas is the transfer matrix. We derive a new transfer matrix, written in the language of scattering between transverse polarized wave states. This could be used in either photonic band calculations or in disordered media calculations. We demonstrate the use of the new transfer matrix to describe transport through a layered random dielectric in the Rayleigh scattering regime. This problem has considerable similarities to that of non-interacting electrons in a one-dimensional random potential. A complete solution for one polarization can be given by the use of group theoretical results. The other polarization exhibits pronounced dipole effects which can easily be calculated to lowest order.