Generalized optical theorem for scatterers having inversion symmetry: applications to acoustic backscattering

The far-field acoustic scattering amplitudes for the scattering of plane waves by targets having inversion symmetry obey a generalized optical theorem in the absence of dissipation. The theorem allows a component of the complex scattering amplitude in an arbitrary direction to be expressed in terms of an angular integration involving scattering amplitudes evaluated at different angles. The result reduces to the usual optical theorem in the case of forward scattering. The theorem is applied to the backscattering by a perfectly soft sphere as a numerical example. The relevant integrand is shown to be oscillatory. Some potential applications to inverse problems, multiple scattering, and the verification of numerical algorithms are noted.     

Optical potential of a disordered array of scatterers

We study the propagation of scalar waves in a disordered array of static scatters. We derive a cluster expansion for the optical potential in analogy to that for the dielectric constant of a polarizable suspension. It is shown that the long range of the free space Green function leads to divergence of the cluster integrals at low energy. The divergences are removed by a resummation procedure analogous to the resummation of Mayer cluster integrals in the theory of electrolytes. We derive expressions for the most important contributions to the optical potential.     

Optical metrology for massive detectors of gravitational waves

The high level reached in the stability of laser sources and in the quality of optical components makes interferometric metrology appealing to those involved in the search for detection of gravitational waves (GWs). In this paper we present a readout for massive detectors of GWs, based on laser interferometry with high finesse Fabry–Pérot cavities, and describe the frequency stability of the laser source. The achievable sensitivity at the quantum limit level inherent to this technique requires a careful design, in order to reduce other sources of extra noise. In particular, we focus on the local effects of thermal and radiation pressure fluctuations and present an optical configuration that can reduce these effects below the quantum limit level.     

Optical theorem and Aharonov-Bohm scattering

A rigorous derivation of the optical theorem (OT) from the conservation of probability flux (CPF) is presented for scattering on an arbitrary spherically symmetric potential inN-spatial dimensions (ND). The constructed expression for the OT is found to yield the corresponding well-known results for two- and three-dimensional cases in a rather natural way. The Aharonov-Bohm (AB) effect is considered as a scattering event of an electron by a magnetic field confined in an infinitely long shielded solenoid and a similar derivation is attempted for an appropriate optical theorem. Our current understanding of the scattering theory is found to be inadequate for the purpose. The reason for this is discussed in some detail.     

Optical techniques for active integratedantenna circuits

This paper reviews some of the recent efforts in the area of microwave–optical interactions applied to active integrated antennas and arrays. Two optical–microwave techniques and examples of their application are presented. First, antenna remoting via optical means is discussed. Second, optical control of microwave devices in active antenna circuits is demonstrated.     

Optical theorem for multipole sources in wave diffraction theory

The optical theorem is generalized to the case of local body excitation by multipole sources. It is found that, to calculate the extinction cross section, it is sufficient to calculate the scattered field derivatives at a single point. It is shown that the Purcell factor, which is a rather important parameter, can be represented in analytic form. The result is generalized to the case of a local scatterer incorporated in a homogeneous halfspace.     

Optical detectors on GaSe and InSe layered crystals

Fast uncooled GaSe and InSe detectors that can record ultrashort (10^?12–10^?9 s) laser pulses in the visual and near-IR ranges are developed. The quick response of the detectors is due to rapid recombination channels with a high capture cross section present in the crystals.     

Rayleigh approximation for axisymmetric scatterers

The Rayleigh approximation is known to be designed only for small ellipsoidal scatterers. We suggest an approach that allows one to find a simple, often analytical, long-wavelength approximation for nonellipsoidal particles. We apply the approach to axisymmetric scatterers and utilize Chebyshev particles to study the main properties of the obtained approximation. To a certain degree, it can be considered as an extension of the Rayleigh approximation to nonspheroidal scatterers.     

Optical rigidity in signal-recycled configurations of laser gravitational-wave detectors

We analyze laser gravitational-wave interferometers with additional mirror in signal port (signal-recycled configurations) which use the optical rigidity both for the Advanced LIGO (Fabry–Perot/Michelson) and GEO-600 (pure Michelson) topologies. We found a set of parameters to obtain better than Standard Quantum Limit (SQL) sensitivity without increasing laser pumping. The gain in sensitivity is inversely proportional to the bandwidth inside which this gain is achieved. By varying parameters one can change the shape of sensitivity curve from a single minimum curve to a double minimum curve through different regimes. This gives an additional possibility to increase the bandwidth but at the sacrifice of sensitivity. We also show that our “narrow band” regimes provide the gain in signal to noise ratio even for signals with wide spectrum.     

Optical theorem in curved space-time quantum field theory

A structural analysis is given of the optical theorem in theS-matrix approach to mutually interacting quantum fields in classical Robertson-Walker universes. As a case study, theφψ ²-interaction of conformally coupled massive (φ) and massless (φ) Klein-Gordon particles is studied. Based on the outgoing massless particles as indicator configuration, the physical interpretation is reduced to the corresponding added-up probabilities. Several examples are discussed in an in-in scheme which has the advantage that only a few non-Minkowskian in-in Feynman diagrams are involved.     

Concentric layered Hermite scatterers

The long wavelength limit of scattering from spheres has a rich history in optics, electromagnetics, and acoustics. Recently it was shown that a common integral kernel pertains to formulations of weak spherical scatterers in both acoustics and electromagnetic regimes. Furthermore, the relationship between backscattered amplitude and wavenumber k was shown to follow power laws higher than the Rayleigh scattering $k^2$ power law, when the inhomogeneity had a material composition that conformed to a Gaussian weighted Hermite polynomial. Although this class of scatterers, called Hermite scatterers, are plausible, it may be simpler to manufacture scatterers with a core surrounded by one or more layers. In this case the inhomogeneous material property conforms to a piecewise continuous constant function. We demonstrate that the necessary and sufficient conditions for supra-Rayleigh scattering power laws in this case can be stated simply by considering moments of the inhomogeneous function and its spatial transform. This development opens an additional path for construction of, and use of scatterers with unique power law behavior.     

Diffusion approximation for billiards with totally accommodating scatterers

We study the 2D motion of independent point particles colliding with a periodic array of circular obstacles. The interaction between the particles and the obstacles is described by a total accommodation reflection law. Assuming that the array of scatterers has finite horizon, the density of particles is approximated by the solution of a diffusion equation in the long-time and large-scale regime. The proof relies on a multiscale asymptotics and gives the order of approximation.     

Interaction of acoustic scatterers

The interaction of scatterers under steady-state acoustic irradiation is studied for the case of scatterers in the form of elliptic cylinders taken as an example. The angular scattering characteristics of two interacting cylinders are calculated and compared with the angular characteristics of a single cylinder in a wide frequency band and in a wide angular range of irradiation. The parameters of interacting bodies (the angle of irradiation, the size with respect to the wavelength, and the distance between the bodies) at which the interaction is negligibly small are determined.     

采用凝视器件的搜索跟踪系统中的扫描补偿光学技术

为了充分发挥器件的性能,采用凝视探测器件的搜索跟踪系统需要特殊的光学结构补偿搜索跟踪时产生的扫描效应。给出了物方和像方扫描补偿光路的形式和构成,分析了平行和会聚光路两种不同补偿结构的特点,论述了扫描补偿引入的光学问题以及相应解决途径,提出了扫描补偿引入的最大光学原理性误差小于1/3~1/4像素的观点。     

Ultrasound speckle and equivalent scatterers

B-mode ultrasound images are characterised by the speckle artefact, which introduces fine-false structures whose apparent resolution is beyond the imaging system capabilities. Speckle presence is due to interference effects between overlapping echoes and its occurrence is related to a great number of randomly distributed structure scatterers within a resolution cell. Basing our analysis on linear system theory, we show that a dense random set of scatterers can be substituted by an equivalent one with a much smaller number of periodic scatterers. This new structure with regularly distributed scatterers is able to give rise to the same B-mode image and the same speckle pattern, for a given ultrasound pulse. This new approach helps the understanding of the deterministic nature of speckle and may reduce drastically the computing time in numerical simulations. Additionally, it can contribute to periodicity analysis used in tissue characterisation.     

Optical design and active optics methods in astronomy

Optical designs for astronomy involve implementation of active optics and adaptive optics from X-ray to the infrared. Developments and results of active optics methods for telescopes, spectrographs and coronagraph planet finders are presented. The high accuracy and remarkable smoothness of surfaces generated by active optics methods also allow elaborating new optical design types with high aspheric and/or non-axisymmetric surfaces. Depending on the goal and performance requested for a deformable optical surface analytical investigations are carried out with one of the various facets of elasticity theory: small deformation thin plate theory, large deformation thin plate theory, shallow spherical shell theory, weakly conical shell theory. The resulting thickness distribution and associated bending force boundaries can be refined further with finite element analysis.     

Optical nonreciprocity in a magnetically active isotropic medium

The complex permittivity tensor of a magnetically active isotropic medium is expanded, to third-order accuracy, in terms of a small parameter equal to the ratio of the mean distance between the atoms of the medium to the wavelength of an electromagnetic wave. A dispersion equation is constructed. On the basis of this equation, the refractive indices of the medium for normal waves are obtained when a longitudinal magnetic field is applied to the medium. It is shown that calculations to third-order accuracy yield different values for the velocities of all four normal waves that propagate in the medium in forward and backward directions. Calculations are carried out for the experiment conducted with the use of a ring laser for measuring the expansion coefficients of the complex permittivity tensor that are responsible for the small difference between the velocities of the normal waves propagating in forward and backward directions. It is shown that, in the case of an isotropic optically nonactive medium, the third-order expansion coefficients can be measured by means of a ring laser with an absolute accuracy on the order of 10^?14.     

Analysis of the time-reversal operator for scatterers of finite size

Recently, it was shown that the time-reversal operator for a single, small spherical scatterer could have up to four distinguishable eigenstates [Chambers and Gautesen, J. Acoust. Soc. Am. 109, 2616-2624 (2001)]. In this paper, that analysis is generalized for scatterers of arbitrary shape and larger size. It is shown that the time-reversal operator may have an indefinitely large number of distinguishable eigenstates, with the exact number depending on the nature of the scatterer and the geometry of the time-reversal mirror. In addition, the case of a multiple number of well-separated scatterers is investigated, with the result that the total spectrum is the direct combination of the eigenstates associated with each scatterer. As an example, the singular value spectrum of the time-reversal operator for a linear array is calculated explicitly for bubbles and hard rubber spheres of finite size. Both resonance peaks and apparent crossing points can be observed in the spectrum as the size of the scatterer increases.