Asymmetry in Negative Refraction of Nonlinear Waves

Recently, inwardly propagating waves (called antiwaves, AWs) in nonlinear oscillatory systems have attracted much attention. An interesting negative refraction phenomenon has been observed in a bidomain system where one medium supports forwardly propagating waves (normal waves, NWs) and the other AWs. In this paper we find that negative refraction (NR) in nonlinear media has an asymmetric property, i.e., NR can be observed only by applying wave source withproper frequency to one medium, but not the other. Moreover, NR appears always when the incident waves are dense and the refractional waves are sparse. This asymmetry is a particular feature for nonlinear NR, which can neither be observed in linear refraction processes (both positive and negative refractions) nor in nonlinear positive refraction. The mechanism underlying the asymmetry of nonlinear NR are fully understood based on the competition of nonlinear waves.     

The phenomenon of conical refraction in a thin-layer periodic semiconductor-dielectric structure in a magnetic field

The propagation of electromagnetic waves along the optical axes of a thin-layer periodic semiconductor-dielectric structure in an external magnetic field (i.e., under conditions of external and internal conical refraction) has been investigated. It is shown that the conditions for conical refraction can be implemented in certain regions by changing the external magnetic field, wave frequency, and thickness of the layers forming the structure. By varying the above-mentioned characteristics, one can efficiently control the conical refraction parameters; in particular, the opening angles of the cone of internal and external conical refraction and the inclination of the optical axes with respect to the periodicity axis can be varied in a wide range. The results of this study may be useful for designing millimeter-wave, submillimeter-wave, and IR devices.     

Horizontal refraction of sound rays due to short-period internal waves in the ocean

The effect of a short-period internal wave measured in field conditions on the horizontal (side) refraction of sound rays is estimated. The angle of horizontal refraction, i.e., the angle between the direction of the signal arrival in the horizontal plane and the true direction to the sound source, is determined. The influence of various factors, such as the position of the receiving system in depth with respect to the layer of high sound velocity gradients, the rotation of the transmitter-receiver track with respect to the internal wave front, etc., on the horizontal refraction is estimated. Numerical calculations are carried out. Conclusions about the possible errors that arise in determining the azimuth direction to the sound source because of the effect of short-period internal waves are derived.     

Scroll-wave dynamics in the presence of ionic and conduction inhomogeneities in an anatomically realistic mathematical model for the pig heart

Nonlinear waves of the reaction–diffusion (RD) type occur in many biophysical systems, including the heart, where they initiate cardiac contraction. Such waves can form vortices called scroll waves, which result in the onset of life-threatening cardiac arrhythmias. The dynamics of scroll waves is affected by the presence of inhomogeneities, which, in a very general way, can be of (i) ionic type; i.e., they affect the reaction part, or (ii) conduction type, i.e., they affect the diffusion part of an RD-equation. We demonstrate, for the first time, by using a state-of-the-art, anatomically realistic model of the pig heart, how differences in the geometrical and biophysical nature of such inhomogeneities can influence scroll-wave dynamics in different ways. Our study reveals that conduction-type inhomogeneities become increasingly important at small length scales, i.e., in the case of multiple, randomly distributed, obstacles in space at the cellular scale (0.2–0.4 mm). Such configurations can lead to scroll-wave break up. In contrast, ionic inhomogeneities affect scroll-wave dynamics significantly at large length scales, when these inhomogeneities are localized in space at the tissue level (5–10 mm). In such configurations, these inhomogeneities can attract scroll waves, by pinning them to the heterogeneity, or lead to scroll-wave breakup.     

Destabilization of TAE modes by particle anisotropy

Plasmas heated by ICRF produce energetic particle distribution functions which are sharply peaked in pitch-angle. At moderate toroidal mode numbers, this anisotropy is the dominant instability drive when compared with the universal instability drive due to the spatial gradient. The universal drive, acting alone, destabilizes only co-propagating waves (i.e., waves propagating in the same toroidal direction as the diamagnetic flow of the energetic particles), but stabilizes counter-propagating waves (i.e., waves propagating in the toroidal direction opposite to that of the diamagnetic flow of the energetic particles). Nonetheless, in a tokamak, it is possible that particle anisotropy can produce a larger linear growth rate for counter-propagating waves, and provide a mechanism for preferred destabilization of the counter-propagating TAE modes that are sometimes experimentally observed.     

Reflection and refraction of elastic wave at VTI-TTI media interface

We explore the physical phenomenon of acoustic waves induced at the interface between two different anisotropic rock media.Specifically,one medium is a transversely isotropic medium with a vertical axis of symmetry(VTI medium)and the other one is a transversely isotropic medium with a tilt axis of symmetry(TTI medium).By solving the Kelvin-Christoffel equation,an eighth-order polynomial is established for reflection and refraction angles,which is confirmed from SnelFs law.Three types of analytical expressions of the polarization coefficients of the induced waves are obtained corresponding to different incident angle regions.An effective algorithm has been developed for numerical analysis of the polarization coefficients.Applying characteristic anisotropic parameters reported in the literature,the influencing factors on reflection and refraction coefficients are analyzed,e.g.,the anisotropy,the tilt-angle of rock-layer,and the incident-angle.The calculated reflection and refraction coefficients have been rechecked for energy conservation.     

Using streamlines to visualize acoustic energy flow across boundaries

For spherical waves that radiate from a point source in a homogeneous fluid and propagate across a plane boundary into a dissimilar homogeneous fluid, the acoustic field may differ significantly from the geometric acoustic approximation if either the source or receiver is near the interface (in acoustic wavelengths) or if the stationary phase path is near the critical angle. In such cases, the entire acoustic field must be considered, including inhomogeneous waves associated with diffraction (i.e., those components that vanish with increasing frequency). The energy flow from a continuous-wave monopole point source across the boundary is visualized by tracing acoustic streamlines: those curves whose tangent at every point is parallel to the local acoustic intensity vector, averaged over a wave cycle. It is seen that the acoustic energy flow is not always in line with the "Snell's law" or stationary phase path. Also, plots of acoustic energy streamlines do not display unusual behavior in the vicinity of the critical angle. Finally, it is shown that there exists a law of refraction of acoustic energy streamlines at boundaries with density discontinuities analogous to Snell's law of refraction of ray paths across sound speed discontinuities. Examples include water-to-seabed transmission and water-to-air transmission.     

Wave refraction in negative-index media: always positive and very inhomogeneous

We present the first treatment of the refraction of physical electromagnetic waves in newly developed negative index media (NIM), also known as left-handed media (LHM). The NIM dispersion relation implies that group fronts refract positively even when phase fronts refract negatively. This difference results in rapidly dispersing, very inhomogeneous waves. In fact, causality and finite signal speed always prevent negative wave signal (not phase) refraction. Earlier interpretations of phase refraction as "negative light refraction" and "light focusing by plane slabs" are therefore incorrect, and published NIM experiments can be explained without invoking negative signal refraction.     

Scattering phenomenon of qP wave at the interface of FGPM and piezoelectric medium

The present paper aims to investigate the reflection and refraction of quasi-longitudinal (qP) waves at the welded interface between rotating piezoelectric and FGPM half-spaces. The equation of motion and constitutive relations for both the media have been used to derive the expressions for reflection and refraction coefficients for various reflected and transmitted waves. Also, the energy ratios (dependent on incident angle) are calculated. Moreover, the sum of all energy ratios is approximately unity at each value of incident angle which ensures that the law of energy conservation at the interface. Moreover, it is observed that the reflection and refraction coefficients of various reflected and transmitted waves depend not only on the incident angle but also on the material constants of the medium, parameters of the electric potential, initial stress as well as rotation parameters of the two media. A particular case has been deduced to validate the present study. This investigation may have possible applications in the areas of signal processing, transduction, frequency shifting (a change in the velocity of surface waves and controlling the selectivity of a filter compensation) of individual devices.     

Reflexion und Brechung des Lichtes an einer anisotropen Schicht

Reflection and Refraction of Light by an Anisotropic Layer The linear problem of reflection and refraction of plane monochromatic electromagnetic waves by a plane-parallel homogeneous anisotropic layer between (in general different) homogeneous optically isotropic semiinfinite media is treated on the basis of MAXWELL 's equations and the boundary conditions following from them. The permittivity tensor of the anisotropic layer is assumed to be widely arbitrary and therefore asymmetric, neglecting only the spatial dispersion, i. e., the dependence on the wave vector. The electrical fields of reflected, refracted, and transmitted waves are calculated in dependence on the electric field of the incident wave. The conditions for waveguide modes of the layer in the absence of incident waves are obtained from the vanishing of a determinant. The general formulae are specialized to the cases of normal incidence and also of perpendicular and parallel polarisation, relatively to the plane of incidence, of the refracted partial waves in the anisotropic layer thus obtaining simplifications in these cases. The interesting cases of uniaxial layers, when the optic axis lies either parallel or perpendicular to the plane of incidence, belong to the last mentioned special cases of perpendicular and parallel polarisation relatively to the plane of incidence.     

Optical bulk and surface waves with negative refraction

In materials with negative refraction, the direction of wave propagation is opposite to the direction of the wave vector. Using an approach that characterizes the optical response of a medium totally by a generalized dielectric permittivity, , we discuss the possibility of seeing negative refraction for optical waves in a number of nonmagnetic media. These include bulk waves in organic materials and in gyrotropic materials where additional exciton–polariton waves can have a negative group velocity. It is known that dispersion of surface waves can be engineered by tailoring a surface transition layer. We show how this effect can be used to obtain surface waves with negative refraction.     

Reflection and refraction of waves in oscillatory media

This paper uses the two-dimensional Brusselator model to study reflection and refraction of chemical waves. It presents some boundary conditions of chemical waves, with which occurence of observed phenomena at interface as refraction and reflection of chemical waves can be interpreted. Moreover, the angle of reflection may be calculated by using the boundary conditions. It finds that reflection and refraction of chemical waves can occur simultaneously even if plane wave goes from a medium with higher speed to a medium with lower speed, provided the incident angle is larger than the critical angle.     

Total reflection of waves propagating from an isotropic medium to an anisotropic medium

We examine the value n(i)/n(eff)(theta(t)) , the ratio of the indices of refraction for waves transmitted from an isotropic medium to an anisotropic medium. It is found that total reflection can occur in the case of propagation from a rarer medium to a denser medium.     

原子光纤中物质波演化的唯象描述

最近,Luo等人在实验上实现了所谓的原子光纤技术(原子物质波沿着一个25μm长的螺旋型波导走完了完整的两圈路径)。本文替该弯曲原子光纤中物质波的时间演化量子力学过程提供了一个唯象描述,主要讨论了三个相关问题：(i)原子物质波与弯曲波导相互作用的有效哈密顿量的构造;(ii)获得描述弯曲原子光纤中物质波的波函数;(iii)证明该物质波波函数恰好是原子动量算符的本征态,表明该唯象描述是自洽的。我们认为本文的唯象模型对于所谓的“原子光学”(atom optics)的研究是有一定意义的。     

Index of refraction of GaAsAlxGa1−xAs superlattices and multiple quantum wells

Recent research of superlattices and multiple quantum wells has generated considerable interest in the optical waveguiding properties of these structures for optoelectronic applications. As a result we present a theoretical study of the index of refraction of superlattices and determine its variation as a function of frequency and the superlattice parameters, i.e., layer width and AlAs composition. Γ-region exciton and valence-band mixing effects are included in the model. It is found that these two effects have an important influence on the value of the index of refraction and that superstructure effects rapidly decrease for energies greater than the superlattice potential barriers. Because of the quasi-two-dimensional character of the Γ-region excitons, our results indicate that the superlattice index of refraction can vary by ∼ 2% at the quantized, bound-exciton, transition energies. Overall, the theoretical results are in good agreement with the experimental data.     

Fresnel problem and surface waves

The similarity and difference between the Fresnel problem, i.e., the problem of electromagnetic wave reflection and refraction, including that at the Brewster angle, and the problem of surface electromagnetic wave (SEW) excitation on a plane surface of a conducting medium is studied.     

凝聚炸药爆轰波在高声速材料界面上的折射现象分析

凝聚炸药爆轰在边界高声速材料约束下传播时,爆轰波会在约束材料界面上产生复杂的折射现象.本文针对凝聚炸药爆轰波在高声速材料界面上的折射现象展开理论和数值模拟分析.首先通过建立在爆轰ZND模型上的改进爆轰波极曲线理论给出爆轰波折射类型,然后发展一种求解爆轰反应流动方程的基于特征理论的二阶单元中心型Lagrange计算方法来数值模拟典型的爆轰波折射过程.从改进爆轰波极曲线理论和二阶Lagrange方法数值模拟给出的结果看出,凝聚炸药爆轰波在高声速材料界面上的折射类型有四种:反射冲击波的正规折射、带束缚前驱波的非正规折射、带双Mach反射的非正规折射、带λ波结构的非正规折射.     

Strongly frequency-dependent negative refraction of a two-dimensional sonic crystal wedge

Negative refraction of a two-dimensional sonic crystal prism has been numerically demonstrated by finite-difference time-domain (FDTD) simulations. It is shown that both positive refraction and negative refraction can be predominant corresponding to different frequencies in the second band. The equifrequency surfaces and some expansion coefficients have also been calculated by the plane-wave expansion method to help understand the FDTD results. These frequency-dependent properties of negative refraction are attributed to the coupling between higher-order Bragg waves inside the sonic crystals and the waves in the homogeneous medium.     

De Broglie's wave particle duality in the stochastic interpretation of quantum mechanics: A testable physical assumption

If one starts from de Broglie's basic relativistic assumptions, i.e., that all particles have an intrinsic real internal vibration in their rest frame, i.e., hv ₀ =m ₀ c ² ; that when they are at any one point in space-time the phase of this vibration cannot depend on the choice of the reference frame, then, one can show (following Mackinnon ⁽¹⁾ ) that there exists a nondispersive wave packet of de Broglie's waves which can be assimilated to the nonlinear soliton wave U ₀ introduced by him in his double solution model of wave mechanics. ⁽²⁾ Since de Broglie's linear pilot waves can be considered to be real waves propagating as collective motions on a covariant subquantum chaotic aether, ⁽³⁾ these new solition waves can be considered as describing the particle's immediate neighborhood, i.e., the aether's reaction to the particle's motion in the stochastic interpretation of quantum mechanics. The existence of such a physical aether (which provides a perfectly causal interpretation of the action-a-distance implied by the Einstein-Podolsky-Rosen experiments) can now be proved by establishing the reality of de Broglie's waves in realizable experiments.     

Wave propagation in an anisotropic metamaterial with single-sheeted hyperboloid dispersion relation

We investigate the wave propagation in an anisotropic metamaterial with single-sheeted hyperboloid dispersion relation. Based on boundary conditions and dispersion relations, we find that the opposite amphoteric refraction, such that E (or H)-polarized waves are positively refracted whereas H (or E)-polarized waves are negatively refracted, can occur at the interface associated with the anisotropic metamaterial. Under a certain condition, both E- and H-polarized waves can exhibit the same single-sheeted hyperboloid or straight line dispersion relation, while the two polarized waves exhibit different propagation characteristics. We expect some potential device applications can be derived based on the unique amphoteric refraction properties. PACS 78.20.Ci; 41.20.Jb; 42.25.Gy