Generalized optical theorem and integrated cross-sections

A new method so study the optical theorem when a Coulomb field is present is derived. Screening effects are present without having been explicitely introduced. For very heavy systems the determination of the reaction cross-section from elastic scattering data is shown to be feasible without the use of a model. Finally a digression towards elementary particle physics is given.     

Optical theorem detectors for active scatterers

We develop a new theory of the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. It applies to arbitrary lossless backgrounds and quite general probing fields. The derived formulation holds for arbitrary passive scatterers, which can be dissipative, as well as for the more general class of active scatterers which are composed of a (passive) scatterer component and an active, radiating (antenna) component. The generalization of the optical theorem to active scatterers is relevant to many applications such as surveillance of active targets including certain cloaks and invisible scatterers and wireless communications. The derived theoretical framework includes the familiar real power optical theorem describing power extinction due to both dissipation and scattering as well as a novel reactive optical theorem related to the reactive power changes. The developed approach naturally leads to three optical theorem indicators or statistics which can be used to detect changes or targets in unknown complex media. The paper includes numerical simulation results that illustrate the application of the derived optical theorem results to change detection in complex and random media.     

Generalized optical theorem to a multipole source excitation in the scattering theory

In the present paper, the Optical Theorem is generalized to the case of a penetrable obstacle excited by a multipole of arbitrary order in the presence of a transparent substrate. This generalization allows one to test computer modules when wave scattering by lossless penetrable obstacle is considered. Besides, it enables one to evaluate the absorption cross-section by subtracting the scattering cross-section from the extinction cross-section. This seems to be important because, in this particular case, the far field does not involve a Sommerfeld integral.     

Generalized ray-transfer matrix for an optical element having an arbitrary wavefront aberration

A generalized ray-transfer matrix for describing the action of an optical element having an arbitrary wavefront aberration is obtained. In this generalized ray-transfer matrix, the action of the aberrated optical element is represented by the product of radial ray-transfer matrices and tangential ray-transfer matrices. The refraction angle of an incident ray is calculated from the gradient of the wavefront aberration at the point of incidence, and the radial and tangential ray-transfer matrices directly use the gradient as a matrix component. To show the validity of the generalized ray-transfer matrix, intercept heights from a spot diagram are calculated with the generalized ray-transfer matrix and compared with those calculated with commercial ray-tracing software.     

An “optical” theorem for acoustic scattering by baffled flexible surfaces

The classical optical theorem for scattering by compact obstacles is a forward scattering theorem. That is, the total cross section of the obstacle is proportional to the imaginary part of the far field directivity factor evaluated in the forward scattering direction. An analogous theorem is derived in this paper for the scattering of acoustic waves by baffled membranes and plates. In this “optical” theorem the directivity factor is evaluated in the direction of the specularly reflected wave, so that it is a reflected scattering theorem.     

Adjoint modeling for acoustic inversion

The use of adjoint modeling for acoustic inversion is investigated. An adjoint model is derived from a linearized forward propagation model to propagate data-model misfit at the observation points back through the medium to the medium perturbations not being accounted for in the model. This adjoint model can be used to aid in inverting for these unaccounted medium perturbations. Adjoint methods are being applied to a variety of inversion problems, but have not drawn much attention from the underwater acoustic community. This paper presents an application of adjoint methods to acoustic inversion. Inversions are demonstrated in simulation for both range-independent and range-dependent sound speed profiles using the adjoint of a parabolic equation model. Sensitivity and error analyses are discussed showing how the adjoint model enables calculations to be performed in the space of observations, rather than the often much larger space of model parameters. Using an adjoint model enables directions of steepest descent in the model parameters (what we invert for) to be calculated using far fewer modeling runs than if a forward model only were used.     

Coherent backscattering of light by complex random media of spherical scatterers: numerical solution

Novel Monte Carlo techniques are described for the computation of reflection coefficient matrices for multiple scattering of light in plane-parallel random media of spherical scatterers. The present multiple scattering theory is composed of coherent backscattering and radiative transfer. In the radiative transfer part, the Stokes parameters of light escaping from the medium are updated at each scattering process in predefined angles of emergence. The scattering directions at each process are randomized using probability densities for the polar and azimuthal scattering angles: the former angle is generated using the single-scattering phase function, whereafter the latter follows from Kepler's equation. For spherical scatterers in the Rayleigh regime, randomization proceeds semi-analytically whereas, beyond that regime, cubic spline presentation of the scattering matrix is used for numerical computations. In the coherent backscattering part, the reciprocity of electromagnetic waves in the backscattering direction allows the renormalization of the reversely propagating waves, whereafter the scattering characteristics are computed in other directions. High orders of scattering (~10 000) can be treated because of the peculiar polarization characteristics of the reverse wave: after a number of scatterings, the polarization state of the reverse wave becomes independent of that of the incident wave, that is, it becomes fully dictated by the scatterings at the end of the reverse path. The coherent backscattering part depends on the single-scattering albedo in a non-monotonous way, the most pronounced signatures showing up for absorbing scatterers. The numerical results compare favourably to the literature results for nonabsorbing spherical scatterers both in and beyond the Rayleigh regime.     

Generalized regression theorem for open systems

A recently proposed method to treat open systems is applied to the evaluation of multitime correlation functions of operators of the open system itself. A general quantum-mechanical regression theorem is deduced, which holds also when the open system undergoes a non- markoffian motion. Such analysis extends the results previously obtained for singletime expectation values and further illustrates the advantages of the method.     

Applying time domain physical optics to acoustic wave backscattering problem

The interest in transient analysis of acoustic waves has been growing in recent years, due to the advance of wide-band sonars. In this paper, a transient analysis method for acoustic backscattering signals is proposed based on the time domain physical optics (TDPO). TDPO is formulated via a theoretical inverse Fourier transform of the conventional physical optics formula used in the frequency domain wave scattering analyses. A hidden surface removal algorithm using an adaptive triangular beam method and a virtual surface concept are adopted to explain shadow effects and multiple reflections among elements, respectively. Numerical analyses are carried out for two kinds of underwater targets: a submarine pressure hull and an idealized submarine, in order to validate the proposed method. The result of the submarine pressure hull shows good agreements between the proposed method and conventional physical optics based on inverse fast Fourier transform. Additionally, the result of the idealized submarine shows that the proposed method is efficient for finding highlights including their contribution to the whole backscattering signal.     

Exact solution for coherent backscattering of polarized light from a random medium of Rayleigh scatterers

We discuss a rigorous vectorial theory as a model to represent the enhanced backscattering of polarized light from a random medium. The theory is based on the well known relation between the contributions of the ladder and cyclical diagrams to the intensity which allows to express these contributions in terms of radiative transfer theory. The tensor transfer equation for the electromagnetic field in a half-space occupied by point-like scatterers is explicitly solved with the aid of the Wiener-Hopf method. For the case of normal incidence the angular distribution of the backscattered intensity and the enhancement factor are found for arbitrary angles between the incident and detected linear polarizations and the scanning plane. To describe spatial anisotropy of the backscattering cone the half width at half maximum of the intensity is calculated as a function of these angles. Coherent backscattering of circularly polarized light is also considered.     

Generalized virial theorem for the Klein-Gordon equation

The virial theorem for the Klein-Gordon equation has been generalized with respect to non-integrable scale-invariant probe functions. Ground-state energies as well as certain upper bounds on the coupling constants have been established. For definiteness several kinds of attractive power potentials have been considered.     

Reduction theory for symmetry breaking with applications to nematic systems

We formulate Euler–Poincaré and Lagrange–Poincaré equations for systems with broken symmetry. We specialize the general theory to present explicit equations of motion for nematic systems, ranging from single nematic molecules to biaxial liquid crystals. The geometric construction applies to order parameter spaces consisting of either unsigned unit vectors (directors) or symmetric matrices (alignment tensors). On the Hamiltonian side, we provide the corresponding Poisson brackets in both Lie–Poisson and Hamilton–Poincaré formulations. The explicit form of the helicity invariant for uniaxial nematics is also presented, together with a whole class of invariant quantities (Casimirs) for two-dimensional incompressible flows.     

Narrowband optical filter design for DWDM communication applications based on Generalized Aperiodic Thue-Morse structures

We present here a novel proposal for multichannel narrowband DWDM filter design, based on Generalized Aperiodic Thue-Morse (GATM) multilayer structures. Transmission spectra of light propagation through these structures are studied in this article. Numerical simulations in this research show an ultra high efficiency and a very low crosstalk for this filter so that the total transmission of filter output channels is up to 100% and the range of output wavelength is 1550 nm which is suitable for DWDM communication systems. By studying the effects of parameters of GATM structure, we realized that by varying parameters such as number of layers, distance between layers, refractive index of layers, etc., a suitable DWDM filter can be accomplished, which is in accordance with the communication ITU-T standard. This narrowband DWDM filter has capability of changing the number of channels and the bandwidth of each channel, at the special wavelength. By changing the thickness of each layer, the transmittance wavelength of the filter will change. The main advantage of the Thue-Morse structure is the numbers of selective layers, which in our designed structure, we choose GATM(3,2) where m = 3 and n = 2 in B^mAⁿ, and for the first time we change both m and n simultaneously in the proposed structure to control optical properties of the introduced filter.     

An extinction theorem for optical scattering

From a many-body theory of optical scattering we derive a relation for the collective behaviour of incoherently scattered light emerging from a molecular fluid. The relation involves a surface integral and has precisely the mathematical form of the Ewald-Oseen extinction theorem; it is exact in the sense of that theorem. We prove from the relation that scattered radiation is refracted and reflected at the surface of the scattering medium according to rules inferred from macroscopic optics. The relation provides a construction of contributions to the scattering with any number of internal reflections; it applies also to scattering restricted by stops. Explicit expressions for the surface dependent scattering in terms of a Fresnel transmissivity correct a previously reported theory of bulk scattering.     

Wave scattering from a random rough surface: reciprocal theorem and backscattering enhancement

The present paper gives a more complete treatment of the scattering from a two-dimensional random surface than previous works. Reciprocal theorems for the stochastic wave field and the incoherent scattering distribution (bistatic cross section) are derived and the presence of backscattering enhancement in the case of a slightly random Neumann surface is demonstrated. A physical interpretation of the backscattering enhancement associated with the presence of anomalous scattering on a slightly random Neumann surface is given. Some numerical calculations are performed to show the incoherent scattering distribution and the backscattering enhancement.     

Generalized renormalization group equation for systems of arbitrary symmetry

An exact renormalization group equation for the Ginzburg-Landau-Wilson functional of an arbitrary symmetry is obtained. The equation derived does not contain redundant operators which must be transformed away.     

Superconductivity without inversion symmetry: MnSi versus CePt3Si

Superconductivity in materials without spatial inversion symmetry is studied. We show that in contrast to common belief, spin-triplet pairing is not entirely excluded in such systems. Moreover, paramagnetic limiting is analyzed for both spin-singlet and -triplet pairing. The lack of inversion symmetry reduces the effect of the paramagnetic limiting for spin-singlet pairing. These results are applied to MnSi and CePt3Si.     

The Van Cittert-Zernike theorem for optical fibres

The Van Cittert-Zernike theorem determines the degree of coherence γ of light from a source radiating in a uniform medium in terms of the angular size α of the source. For the fields within an optical fibre far from the source, γ is found by replacing α by the critical angle for total internal reflection.