光盘光学系统的矢量衍射理论分析

本文以完整的矢量衍射理论分析了光盘光学系统。首先将入射的聚焦光束分解为平面波谱 ,得到每个平面波的振幅矢量 ;然后计算光盘对每个平面波的衍射 ,得到衍射波的振幅矢量 ,从而得到了整个衍射波场的空间频谱 ;最后计算物镜光瞳上的能通量 ,得到光盘系统的读出信号。在衍射计算中 ,光盘被定义为二维金属光栅 ,根据信息符的不同模型 ,选用坐标变换方法、耦合波方法或模态方法。对于典型的 DVD光学系统来说 ,矢量理论的结论与标量理论相差甚远 ,要得到正确的结果就必须采用矢量衍射理论     

Electromagnetic wave refraction on the interface of absorptive and transparent isotropic media and non-resonant excitation of surface waves

New formulae for the angles of refraction at the interface of the absorbing/transparent isotropic media are derived from Maxwell's equations. Using the time-averaged Poynting vector for the direction of the beam of light, the noncoincidence of incidence and refraction planes is predicted for the mixed polarization of incident wave. The angle between the refracted beam and incidence plane is especially large for the condition of non-resonant excitation of surface electromagnetic waves at a flat interface of absorptive-transparent media.     

轴锥镜光强分布的角谱衍射数值分析法

针对理论上推导轴锥镜的衍射光场分布解析式较为困难,且用菲涅耳衍射理论分析时存在近轴近似及不能适用于近场衍射光场分析的问题,采用了严格遵从标量衍射亥姆霍兹方程的角谱衍射波前重建方法,对轴锥镜在单色和准单色高斯光波照射下的横向和轴向衍射光强分布特性,以及在单色均匀平面光波照射下的轴向衍射光强分布进行了数值计算和分析。结果表明,轴锥镜后单色光衍射光强分布在几何光束重叠的菱形区域内为近似无衍射贝塞尔光强分布,轴上光强沿光轴方向呈振荡变化,轴上光强分布规律与入射光波的垂轴横向光强分布有关;入射光的准单色性使得贝塞尔衍射条纹对比度略下降、轴上光强沿光轴方向振荡程度减小,但分布规律与单色光一致。     

Cross-frequency correlation of intensity fluctuations for a deeply modulated phase screen

We consider the intensity fluctuation patterns produced beyond a deeply modulated phase changing screen when two plane waves, each with a different frequency, are incident on the same screen. The spatial frequency spectrum corresponding to the cross-correlation between these two different intensity fluctuation patterns is derived. This spectrum has two distinct regions, one of low spatial frequencies which is independent of the incident wave frequencies, and another at high spatial frequencies which is wave frequency dependent. As the difference between the incident wave frequencies increases the upper cut-off spatial frequency of the spectrum decreases. The corresponding cross-scintillation index is also considered and it is shown that this is independent of the incident wave frequencies close to the phase screen and including the focal region where there is a peak in the index. In the far field the scintillation index approaches unity as the distance from the screen increases in the monochromatic case. However, for different incident wave frequencies the far-field scintillation index falls off both with distance from screen and with increasing wave frequency difference.     

Reflexion und Brechung des Lichtes an der Grenzebene zwischen zwei anisotropen Medien

Reflection and Refraction of Light at the Boundary Plane between Two Anisotropic Media Relations for the amplitudes in the case of reflection and refraction of plane monochromatic waves at the boundary plane between two arbitrarily anisotropic media are derived from Maxwell equations with invariant methods. Solutions are represented with use of the refraction vectors and of the polarization vectors for the electric field. From the general solution of the problem the following essentially more simple special cases are obtained: 1. normal incidence, 2. optic axis in direction of the incident or reflected wave, 3. parallel and normal polarization of the partial waves in both media relatively to the plane of incidence.     

A theory of a receiving antenna in a moving isotropic plasma

We analyze the response of a dipole antenna to the noise-like and/or regular (quasimonochromatic) plasma oscillations and waves. The antenna is immersed in an isotropic plasma moving with velocity greater than the electron thermal velocity. In the case of a noise field, we calculate the squared spectral power density of the noise voltage at the input of a receiving antenna for frequencies close to the electron plasma frequency. It is shown that the main contribution to the noise is made by the radiation due to the excitation of waves at anomalous Doppler frequencies. In the case of an incident monochromatic wave, the mean square voltage at the antenna input is calculated as a function of the wave frequency and angle of arrival. It is shown that the effective antenna length can differ strongly from the geometrical length of the dipole. This fact results from the dispersion of longitudinal waves ensuring that many plane waves (a continuum, in the limiting case) contribute to the re-radiated field for a given direction of propagation of the radiation energy.     

Asymptotic fourier analysis of a “sawtooth like” wave for dual frequency source excitation

An exact weak shock zone solution was found previously for Burgers' equation for plane waves. An approximate solution for spherical waves also was obtained. Both of these solutions held for dual frequency excitation at the source. In the work reported in the present paper, an asymptotic formula was derived which yields harmonic amplitudes at a point beyond the “sawtooth like” zone. The formula's predicted harmonic amplitudes have been found to agree well with numerical results for a specific dual frequency case. Excellent agreement also was obtained with the well-known solution for a monochromatic source. The new formula predicts that for certain frequency ratios of the primary signals the amplitude of the parametrically generated difference signal will exceed that of a directly projected signal at the same frequency and with the same total input power. This result holds for infinite planar and spherical source geometries.The formula should be useful in estimating beam axis values of the harmonic amplitudes for practical source geometries by applying the plane wave version in the near field and the spherical version in the far field. Such information can be of value to those who are constructing mathematical models of parametric array behavior.     

A General Spectral-Domain Formulation of the Electromagnetic Scattering by a Perfectly Conducting Circular Cylinder

A full-wave method for the two-dimensional scattering problem by a perfectly conducting circular cylinder is presented, providing an exact solution for the Helmholtz equation in very general cases. The method is based on the Fourier series expression of the boundary conditions (Dirichlet and Neumann) generated by an arbitrary, finite-power, incident beam, and the analysis is performed in the complex plane of the analytic continuation of a space spectral variable. This approach allows us to define an analytic continuation for cylindrical wave expansions, working with lossy propagation media and with a full incident spectrum, including inhomogeneous waves, both in E and in H polarization. Convergence of the modal expansion is investigated, to verify that very weak hypotheses are needed, and no geometrical or paraxial approximation is required. Extact expressions for the expansion coefficients are given, in terms of complex intergrations involving the Fourier spectrum of the incident beam.     

Experimental study of ultrasonic beam sectors for energy conversion into Lamb waves and Rayleigh waves

When a bounded beam is incident on an immersed plate Lamb waves or Rayleigh waves can be generated. Because the amplitude of a bounded beam is not constant along its wave front, a specific beam profile is formed that influences the local efficiency of energy conversion of incident sound into Lamb waves or Rayleigh waves. Understanding this phenomenon is important for ultrasonic immersion experiments of objects because the quality of such experiments highly depends on the amount of energy transmitted into the object. This paper shows by means of experiments based on monochromatic Schlieren photography that the area within the bounded beam responsible for Lamb wave generation differs from that responsible for Rayleigh wave generation. Furthermore it provides experimental verification of an earlier numerical study concerning Rayleigh wave generation.     

Superimposed volume holograms for measuring the phase and degree of mutual coherence of a light wave

Superimposed volume holograms, which make it possible to determine the phase and degree of mutual coherence of a stationary light wave consisting of partially coherent plane components incident on the holograms at different angles are proposed. To find these parameters of the light wave, the intensities of the waves reconstructed by the holograms are measured in the case of amplitude and phase modulation of the wave incident on the holograms. The phases and degrees of mutual coherence of the components of the wave incident on the holograms are found from the measured data. The holograms are studied based on the modal theory of superimposed volume holograms.     

New method of spatial superposition of attenuated waves for ultrasound field modelling

The objective of this work is the contrary issues of ultrasonic diagnostics in medicine when modern requirements for resolution are in conflict with strict safety issues. There is only one way to make progress by starting to take into account the attenuation in biological tissues and the wave diffraction phenomena. The aim of this work is to develop the flexible ultrasound field model implemented in routine algorithms of digital signal processing. The method consists of the calculation of plane wave propagation and the calculation of an ultrasound signal field. On the basis of the spatial impulse response of an aperture for calculation of space-spread ultrasound signals and the spectrum decomposition method for modelling plane wave propagation in lossy media, the modified method of spatial superposition of attenuated waves was developed. Using the method of equidistant line calculation the time and frequency features of the ultrasound signal field caused by the geometry and dynamics of the aperture, the attenuation and velocity dispersion in the medium are determined. The method was successfully applied to the investigation of the system for intracranial media monitoring, where a new measurement channel based on the changes of attenuation and dispersion in intracranial medium has been implemented.     

Combined complex-source beam and spherical-multipole analysis for the electromagnetic probing of conical structures

The paper addresses the combination of the spherical-multipole analysis in sphero-conal coordinates with a uniform complex-source beam (CSB) in order to analyze the scattering of a localized electromagnetic plane wave by any desired part of a perfectly conducting elliptic cone. The concept of uniform CSB is introduced and rigorously applied to the diffraction by a semi-infinite elliptic cone. The analysis takes into account the fact that the incident CSB does not satisfy the radiation condition. A new modal form of the Green's function for the elliptic cone is derived based on the principle that there is no energy loss to infinity. The numerical evaluation includes the scattered far fields of a CSB incident on the corner of a plane angular sector with different opening angles.     

Interference of plane light waves with different polarizations and the Jones matrix formalism

A new method is developed to solve the interference problem that involves two plane monochromatic waves of equal frequency provided these waves, in general, have different polarizations and their wave vectors are arbitrarily oriented. Using a three-dimensional generalized Jones vector, we find analytical solutions for the spatial-intensity distribution of the total wave and (at certain orientations of the wave vectors) for the parameters characterizing its polarization state. The results of the work are applied to wide variety of interference problems.     

Phase relations for a sound wave at its reflection and transmission through a plane layer

A property never considered before in acoustics is established: in the case of a sound wave incidence on a plane layer bordered by two liquid media with identical elastic properties, the phase difference between the reflected and transmitted waves is equal to π/2 irrespective of the physical constants of the layer and the media contacting it, as well as of the frequency of the incident wave.     

Reflection–refraction of attenuated waves at the interface between a thermo-poroelastic medium and a thermoelastic medium

Phenomenon of reflection and refraction is considered at the plane interface between a thermoelastic medium and thermo-poroelastic medium. Both the media are isotropic and behave dissipative to wave propagation. Incident wave in thermo-poroelastic medium is considered inhomogeneous with deviation allowed between the directions of propagation and maximum attenuation. For this incidence, four attenuated waves reflect back in thermo-poroelastic medium and three waves refract to the continuing thermoelastic medium. Each of these reflected/refracted waves is inhomogeneous and propagates with a phase shift. The propagation characteristics (velocity, attenuation, inhomogeneity, phase shift, amplitude, energy) of reflected and refracted waves are calculated as functions of propagation direction and inhomogeneity of the incident wave. Variations in these propagation characteristics with the incident direction are illustrated through a numerical example.     

On the interaction of a shear wave with a moving domain wall in a nonlinear response of the spin subsystem

A solution of the problem of parametric interaction between a plane monochromatic shear wave and a uniformly moving 180°-domain wall of a garnet-ferrite crystal is obtained in the exchangeless magnetostatic approximation by using the perturbation method under the conditions of a nonlinear response of the spin subsystem. It is shown that in a ferromagnetic resonance with magnetostatic oscillation of stray fields, the nonlinearity of the spin subsystem leads to the excitation of shear waves of triple frequency, which may have amplitudes comparable with that of the incident wave for oscillations doubly localized by a domain wall.     

Parametric Doppler effect in the case of oblique incidence in a medium with a plasma dispersion law

The parametric Doppler effect that occurs upon reflection of a plane monochromatic wave obliquely incident on an inhomogeneity of the refractive index moving in a medium with a frequency dispersion (homogeneous wave regimes) is analyzed. For a plasma-type frequency dispersion, the dependences of the frequency and angle of reflection on the frequency of the incident wave and on the angle of incidence are found.     

X-ray Laue diffraction with allowance for two-dimensional curvature of the wavefront: The concept a locally plane wave

Symmetrical Laue diffraction in a perfect crystal with a plane entance surface is considered. The two dimensional curvature of the wave front of the incident beam is taken into account. Using the corresponding Green function, a general expression for the amplitude of diffracted wave in the crystal is presented. Based on this expression, the concept of a locally plane wave is analyzed taking into account two-dimensional curvature of the wave front. This concept is used for obtaining the rocking curves depending on the angles of deviation from the chosen exact Bragg direction in both the diffraction plane and in perpendicular direction. The obtained result is compared with the result of the standard dynamical diffraction theory.     

Two-dimensional coupled mode equation for grating waveguide excitation by a focused beam

The problem of grating coupling of a focused incident beam under non-normal incidence into a slab waveguide is given a complete three-dimensional (3D) solution. The diffracted field is expressed as the Fourier integral of a regular part and of a singular part resulting from the existence of the coupled guided mode. A suitable expression of the field in the neighborhood of the pole and a rigorous definition of the modal field lead to a generalized coupled mode equation relating the incident field and the two-dimensional (2D) modal field propagating in the plane of the slab waveguide. The phenomenological parameters involved in the coupled wave equation: the propagation constant, the radiation coefficient as well as the modal field shape are derived from the exact treatment of plane wave diffraction in the same structure. The solution of the complete coupling problem is given in the particular case of a Gaussian incident beam, and of a high index step-index waveguide.