Bessel–Gauss beam optical resonator

In a simple picture, a Bessel beam is viewed as a transverse standing wave formed in the interference region between incoming and outgoing conical waves. Based on this interpretation we propose an optical resonator that supports modes that are approximations to Bessel–Gauss beams. The Fox–Li algorithm in two transverse dimensions is applied to confirm the conclusion.     

Recovery of the free field in noisy environment by using the spherical wave superposition method

To remove the scattering effect of the disturbing sound on the target source when implementing nearfield acoustic holography in a non-free field, a free field recovery technique based on the spherical wave superposition method is proposed. In the method, the sound field separation technique based on the spherical wave superposition method is first used to separate the incoming and outgoing fields, and a further step for separating the radiated and scattered fields is performed by utilizing the surface admittance of the target source as the boundary condition. The technique makes it possible to correctly identify noise sources in a non-free sound field. The basic principle of the technique is described firstly, a method for choosing the optimal number of spherical wave expansion terms is given, and two numerical simulations are used to demonstrate the validity of this technique. It is shown that, for the lower frequency, the scattering effect can be neglected, and the radiated field of the target source can be obtained by the sound field separation technique, however, as the increasing of the frequency, the scattering effect cannot be neglected, and the free field recovery technique has to be used to obtain the radiated field of the target source.     

采用球面波叠加法还原自由声场的方法

为解决非自由声场中近场声全息重建时,干扰声在目标声源表面产生的散射影响,提出一种基于球面波叠加法的自由场还原技术。该技术首先采用基于球面波叠加法的声场分离技术获得向内和向外传播的声场,然后以目标声源的表面导纳作为边界条件,实现目标声源辐射声和散射声的分离,从而获得等效于自由声场的测量条件。该技术为准确实现非自由声场中的噪声源识别创造了条件。文中首先详细描述了该技术的基本原理,并提出一种最优球面波展开项数选取方法,最后通过数值仿真说明了该技术的有效性。结果表明:在频率较低时,散射声影响较小,采用声场分离技术和自由场还原技术效果相当;但随着频率升高,散射声影响逐步增强,必须采用自由场还原技术才能准确获得目标声源辐射声。      

Mixture of outgoing and incoming electromagnetic radiation. Change of mass of the source of radiation

In a previous paper the author, using a method of successive approximations, verified by means of the Einstein-Maxwell equations of general relativity the well-known result that outgoing electromagnetic radiation from a source conveys energy, so that the source loses gravitational mass corresponding to this energy. The purpose of this work is to show a similar result for the general case of any mixture of outgoing and incoming radiation.This work is included in a thesis submitted by the author (1964) to the University of London for the degree of Ph.D.     

Wronskian analysis of resonance tunnelling reactions

A Wronskian formalism is developed for resonance tunnelling reactions. It is shown how the S matrix can be written in terms of Wronskians between solutions of the Schrödinger equation representing incoming and outgoing waves. The method is an adaptation of the Jost function approach to elastic two-body scattering. Formal expressions are derived for the imaginary parts of the energy eigenvalues that arise from the application of complex boundary conditions used in a previous semiclassical analysis. When the imaginary parts are small, so that the resonance is sharp, the S matrix can be written in a Breit-Wigner resonance form. The theory unifies and extends the semiclassical analysis of resonance tunnelling reactions given previously.     

Polarization selection rules in scattering of cavity polaritons

We theoretically discuss scattering of polaritons in semiconductor microcavities by means of a microscopic model. Taking into account the composite character of excitons (formed by an electron and a hole), we analyze the relation between polarizations of incoming and outgoing polariton states under resonant excitation by linearly polarized laser beams with opposite in-plane momenta. In addition to these polarization selection rules, we investigate the nonlinear processes up to the sixth order and we show the origin of an induced anisotropy due to the excitation beams which is responsible for the operation of an optical gate based on polariton–polariton scattering in a microcavity.     

A time-symmetric classical electrodynamics

In this theory, both the advanced and retarded Liénard-Wiechert potentials are used to compute the fields of a charged point particle. The incoming radiation from the advanced fields balances the outgoing radiation of the retarded fields, and we assume that there are no radiation reaction terms in the equations of motion of the particles. We further assume that only retarded fields act on particles through the Lorentz force, and that advanced fields act on antiparticles. This is a theory that is symmetric under time reflection (reversal of the direction of motion plus charge conjugation).     

Physical symmetries in a theory of several scalar real fields

Let us consider a theory ofn scalar, real, local, Poincaré covariant quantum fields forming an irreducible set and giving rise to one particle states belonging to the same mass different from zero. The vacuum is unique. It is shown under fairly weak assumptions that every Poincaré and TCP invariant symmetry of the theory, implemented unitarily, which mapps localized elements of the field algebra into operators almost local with respect to the former (such a symmetry we call a physical one) can be defined uniquely in terms of the incoming or outgoing fields and ann-dimensional (real) orthogonal matrix. The symmetry commutes with the scattering matrix. Incidentally we show also that the symmetry groups are compact. A special case of these symmetries are the internal symmetries and symmetries induced by locally conserved currents local with respect to the basic fields and transforming under the same representation of the Poincaré group. We may make linear combinations out the original fields resulting in complex fields and its complex conjugate in a suitable way. The inspection of the representations of the groupsSO(n) and their subgroups sheds some light on the s.c. generalized Carruthers Theorem concerning the self- and pair-conjugate multiplets.     

EIKONAL-BORN EXPANSION AND ITS APPLICATION IN LARGE-ANGLE SCATTERING

In this paper, the scattering amplitude is expanded by two eikonal wave functions which propagate along the incoming and outgoing directions respectively to replace the distorted wave functions in DWBA. Then, we obtain a method to calculate the non-relativistic large angle scattering. This method can be easily generalized to relativistically phenomenological dynamical equation.     

Theory on the optical-phonon Raman scattering in GaAs/AlAs heterostructures

A microscopic theory of Raman scattering by optical phonons in GaAs/GaAlAs heterostructures is worked out systematically, on the basis of recent advances in our knowledge of the electronic structure and the optical-phonon modes in superlattices and quantum wells. Theories have shown that specific features of the intermediate states are of special importance for a quantitative theory. Thus, the heavy and light hole mixing effect, and the angular momentum state of the four-component excitons, can play a decisive role in determining the predominant scattering channels. Special attention has been paid to the Frolich-interaction induced scattering, which is dipole forbidden in bulk materials but allowed in multiple quantum wells owing to the barrier penetration and the hole mixing. Based on the microscopic theory, explanations are provided for such experimental facts as the asymmetry between the incoming and the outgoing resonance, the line shape of Raman spectra and the features of two-phonon Raman scattering in quantum well systems.     

Independent waves in complex source point theory

The full-wave generalization of the scalar Gaussian paraxial beam is determined by an analytical continuation of the field of a point source for the Helmholtz equation. The regions of validity of the analytically continued fields are investigated for the outgoing and the incoming waves. The two independent wave functions valid for the two half-spaces separating the secondary source plane are deduced.     

Collision theory for massless Fermions

Starting from the basic postulates of local relativistic quantum theory, the asymptotic incoming and outgoing collision states of massless Fermions are constructed. The corresponding Hilbert spaces have Fock structure and thus allow the usual definition of anS-matrix. In contrast to the massive case, there are geometric relations between the local nets of the underlying field algebra and the asymptotic fields.     

Anisotropy and interference in wave transport: an analytic theory

A theory is presented which incorporates the effect of dielectric anisotropy in random multiple scattering media. It predicts anisotropic diffusion, and a deflection of the diffuse energy flow in anisotropic slabs in the direction parallel to the slab. The transmittance integrated over all incoming and outgoing directions scales with the transport mean free path along the surface normal. The escape function in anisotropic dielectrics is no longer bell shaped. In this model anisotropy facilitates Anderson localization.     

Remarks on the radiative transfer approach to scattering of electromagnetic waves in layered random media

The radiative transfer (RT) approach is widely used in applications involving scattering from layered random media with rough interfaces. Although it has been successful in several applications in various disciplines it is well known that this approach involves certain approximations. In this paper these assumptions and approximations are reexamined. To enable this a statistical wave approach is employed to this problem and the governing equations for the first and second moments of the wave functions are derived. A transition is hence made to arrive at a system of equations corresponding to that of the RT approach. It is hence found that more conditions are implicitly involved in the RT approach than generally believed to be sufficient.     

Ray splitting in the reflection and refraction of surface acoustic waves in anisotropic solids

This paper examines the conditions for, and provides examples of, ray splitting in the reflection and refraction of surface acoustic waves (SAW) in elastically anisotropic solids at straight obstacles such as edges, surface breaking cracks, and interfaces between different solids. The concern here is not with the partial scattering of an incident SAW's energy into bulk waves, but with the occurrence of more than one SAW ray in the reflected and/or transmitted wave fields, by analogy with birefringence in optics and mode conversion of bulk elastic waves at interfaces. SAW ray splitting is dependent on the SAW slowness curve possessing concave regions, which within the constraint of wave vector conservation parallel to the obstacle allows multiple outgoing SAW modes for certain directions of incidence and orientation of obstacle. The existence of pseudo-SAW for a given surface provides a further channel for ray splitting. This paper discusses some typical material configurations for which SAW ray splitting occurs. An example is provided of mode conversion entailing backward reflection or negative refraction. Experimental demonstration of ray splitting in the reflection of a laser generated SAW in GaAs(111) is provided. The calculation of SAW mode conversion amplitudes lies outside the scope of this paper.     

An equivalent source method for recovering and reconstructing the target sound field in a non-free field

In a non-free field,the existence of disturbing sources would destroy the free-field condition required by near-field acoustic holography,and confuse the identification of target source due to the scattering effect caused by disturbing sound falling on the target source.To totally remove the influence of disturbing source,a method for recovering and reconstructing the target sound field in a non-free field was proposed based on the equivalent source method and the pressure-velocity measurement.In the proposed method,the sound field separation technique was firstly used to separate the mixed sound field into the outgoing field coming from the target source and the incoming field coming from the disturbing source.Then the scattered component contained in the outgoing field was calculated by using the disturbing sound and the surface impedance of the target source.Finally,the sound field radiated by the target source in a free field was obtained by subtracting the scattered component from the outgoing field and was further used to reconstruct the sound field of the target source.The proposed method was numerically and experimentally testified and the results of both the simulation and the experiment demonstrated the validity of the proposed method.     

非自由声场中目标声场还原与重建的等效源方法

为消除在非自由声场中重建声场时干扰声源对重建效果的影响,提出一种采用单个测量面上的声压和质点振速作为输入、等效源法作为分离和重建算法的非自由声场中目标声场还原与重建方法。该方法首先利用单面声压-质点振速测量和基于等效源法的声场分离技术将测量的混合声场分离为来自目标声源的向外传播的声场和来自干扰声源的向内传播的声场,然后利用向内传播的声场和目标声源的边界条件计算出干扰声在目标声源表面产生的散射声场,并将其从向外传播的声场中去除,还原出目标声源在自由声场条件下的辐射声场,最后利用还原的声场实现目标声场重建。通过数值仿真和实验检验了该方法的有效性和必要性。仿真和实验的结果表明,该方法可以在非自由声场的测量条件下,有效地去除干扰声的影响,实现目标声场的准确重建。      

Quantum theory of transverse galvano-magnetic phenomena

A quantum theory of electrical conduction in crosfsed electric and magnetic fields is given for the limit of very weak scattering. A density matrix formulation of the problem is used, and an arbitrary scattering mechanism is considered. The theory is found to be completely equivalent to theories given earlier by and by and .

Formulae are given for the resistivity in the quantum limit for both longitudinal and transverse orientations of electric field, for degenerate and non-degenerate statistics, and for several different scattering mechanisms. The oscillatory conductivity is calculated for acoustical and ionized-impurity scattering mechanisms. Formulae obtained for the quantum transport effects are in disagreement with the formulae of and of . The discrepancy is attributed to unwarranted approximations in those authors' treatments of scattering.