A unified optical theorem for scalar and vectorial wave fields

The generalized optical theorem is an integral relation for the angle-dependent scattering amplitude of an inhomogeneous scattering object embedded in a homogeneous background. It has been derived separately for several scalar and vectorial wave phenomena. Here a unified optical theorem is derived that encompasses the separate versions for scalar and vectorial waves. Moreover, this unified theorem also holds for scattering by anisotropic elastic and piezoelectric scatterers as well as bianisotropic (non-reciprocal) EM scatterers.     

Enhanced scattering from a thin film with one-dimensional disorder

This paper deals with a TE plane wave scattering from a thin film with one-dimensional disorder by means of the stochastic functional approach. The thin film is one-dimensionally inhomogeneous in the horizontal direction with infinite extent, and is homogeneous in the vertical direction with finite thickness. Based on an approximate wavefield representation in terms of a Wiener–Hermite expansion in a preceding paper (Tamura et al., 2004, Waves in Random Media, 14, 435–465), the first- and second-order incoherent scattering cross-sections are presented in explicit forms and scattering properties are discussed. The scattering properties vary entirely with the film thickness. In a case where the thickness is smaller than a few wavelengths in the thin film, enhanced scattering and associated enhanced scattering may appear as sharp peaks or dips on the second-order incoherent scattering distribution if the thin film has guided wave modes. When the thickness becomes sufficiently larger than the wavelength inside the film, a new enhanced scattering phenomenon appears as gentle peaks on the second-order incoherent scattering distribution in four special directions. Such four directions are the directions of forward scattering, specular reflection, backscattering, and the symmetrical direction of forward scattering with respect to the normal of the film surface.The first-order incoherent scattering occurs distinctly in four such directions. Such enhanced scattering is independent of the existence of the guided wave modes inside the thin film, and deeply relates to the structure of the thin film with one-dimensional disorder that has infinite correlation in the vertical direction. For SiC and glass thin films having one-dimensional disorder with a Gaussian correlation and three types of exponential correlation, the first- and second-order incoherent scattering cross-sections are illustrated in figures. The narrow enhanced scattering peaks appear for the glass film in a thin case. The gentle enhanced peaks turn up for both the SiC and glass films in a thick case. Furthermore, the optical theorem is calculated for several cases. It is then found that the error of the optical theorem decreases and the performance of the wavefield is improved by taking into account the second-order incoherent scattering.     

Probing of Ehrlich ascites carcinoma cell using in situ aggregates of Au-NPs as SERS label created by plasmon exciting hybrid-TEM*11 laser mode

Apart from commonly employed target-specific labeling/adsorption of antibodies over Au-NPs surface for the creation of localized aggregates, an alternative approach using optical tweezers (OT) driven by hybrid-TEM*₁₁ mode has been devised and exploited for in vitro detection of Ehrlich ascites carcinoma cells (EAC) relying on enhanced scattering. Intra-cavity generated spatially featured asymmetric (SFA) laser beam (λ = 532 nm) has effected simultaneous trapping of mice-EAC cells and in-situ crowd/assembly of incubated Au-NPs/small gold nano-aggregates (created from two or more individual Au-NPs). Relatively larger focus spot created by tightly focused SFA beam than frequently employed Gaussian-mode in OT has offered an extended working area and hence dilute heating has taken care of EAC cells. GNA improves significantly the sensitivity of diagnostics relying on scattered light and the safety and efficacy of therapeutic nanotechnologies for the diseases of cancer and vascular system in medicine.     

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.     

Methodological challenges of optical tweezers‐based X‐ray fluorescence imaging of biological model organisms at synchrotron facilities

Recently, a radically new synchrotron radiation‐based elemental imaging approach for the analysis of biological model organisms and single cells in their natural in vivo state was introduced. The methodology combines optical tweezers (OT) technology for non‐contact laser‐based sample manipulation with synchrotron radiation confocal X‐ray fluorescence (XRF) microimaging for the first time at ESRF‐ID13. The optical manipulation possibilities and limitations of biological model organisms, the OT setup developments for XRF imaging and the confocal XRF‐related challenges are reported. In general, the applicability of the OT‐based setup is extended with the aim of introducing the OT XRF methodology in all research fields where highly sensitive in vivo multi‐elemental analysis is of relevance at the (sub)micrometre spatial resolution level.     

Scattering from anisotropic particles: A challenge for the optical theorem?

The optical theorem is a very general law of scattering theory that has been discussed almost exclusively for spherically symmetric scatterers. In this work we present the extension to the case of anisotropic scatterers, by treating explicitly the problem within the Rayleigh-Gans approximation. Working formulas for the fluctuating components of the forward-scattering amplitude S _VV(0) and S _VH(0) are given, and a paradox concerning the applicability of the optical theorem is solved. While the S _VH(0) cannot interfere with the incoming vertical polarized beam, we show that S _VV(0) fluctuates around a non-zero average so to compensate at any instant for the integrated scattered intensity at both polarizations. The results are relevant for the design and interpretation of experiments of dynamic depolarized light scattering in the forward direction.     

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.     

Quantum 1/f noise associated with ionized impurity scattering and electron-phonon scattering in condensed matter

Scattering of charged particles is accompanied by the emission of soft photons. Handel's theory of 1/f noise, based on the infrared quasi-divergent coupling of the system to the electromagnetic field, indicates that the current associated with a beam of scattered particles will exhibit 1/f noise. His derivation is valid in a vacuum. Here we extend his results and obtain the fluctuation spectrum for the fluctuations in cross-section and for the scattering rates w _kk′ in k-space, using the Born approximation. Next we consider mobility fluctuations due to these scattering rates, employing the relaxation time solutions of the Boltzmann transport equation, valid in non-degenerate semiconductors. Explicit results are obtained for the mobility-fluctuation noise caused by ionized impurity scattering, acoustic phonon scattering, optical phonon scattering, polar optical phonon scattering, and intervalley scattering. We derive Hooge's law, and the Hooge parameters for the above-mentioned processes are obtained in detail. This is then applied to n-type silicon and n-type gallium arsenide; the overall Hooge parameter, which is a weighted average of the partial α-parameters, is computed as a function of temperature and compared with experiment. For silicon, good agreement is obtained with available data. As a byproduct we also find the mobilities as function of temperature for these materials. Excellent agreement with the well-known experimental data is observed.

We still note that this is the first theoretical derivation of Hooge's law and that the magnitude of the noise is obtained in detail without adjustable parameters. We believe that quantum 1/f noise gives the limiting value of 1/f noise that can be observed.     

On shell,subtracted dispersion relations and low energy theorems from current algebra

A method discussed in an earlier paper is applied to the case of ππ and πN scattering and to electroproduction. As an example we derive for the ππ scattering amplitude a subtracted, covariant on-shell dispersion relation in which the subtraction polynomial is determined by the corresponding low energy theorem plus possibly small corrections. We also show how this same method may be applied to the derivation of low energy theorems.     

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 theorems for the reconstruction of Green's function of an inhomogeneous elastic medium

This paper investigates the reconstruction of elastic Green's function from the cross-correlation of waves excited by random noise in the context of scattering theory. Using a general operator equation-the resolvent formula-Green's function reconstruction is established when the noise sources satisfy an equipartition condition. In an inhomogeneous medium, the operator formalism leads to generalized forms of optical theorem involving the off-shell T-matrix of elastic waves, which describes scattering in the near-field. The role of temporal absorption in the formulation of the theorem is discussed. Previously established symmetry and reciprocity relations involving the on-shell T-matrix are recovered in the usual far-field and infinitesimal absorption limits. The theory is applied to a point scattering model for elastic waves. The T-matrix of the point scatterer incorporating all recurrent scattering loops is obtained by a regularization procedure. The physical significance of the point scatterer is discussed. In particular this model satisfies the off-shell version of the generalized optical theorem. The link between equipartition and Green's function reconstruction in a scattering medium is discussed.     

Fluorescent optical tomography with large data sets

In recent years, optical tomography (OT) of highly scattering biological samples has increasingly relied on noncontact CCD-based imaging devices that can record extremely large data sets, with up to 10(9) independent measurements per sample. Reconstruction of such data sets requires fast algorithms. The latter have been developed and applied experimentally in our previous work to imaging of the intrinsic absorption coefficient of highly scattering media. However, it is widely recognized that the use of fluorescent contrast agents in OT has the potential to significantly enhance the technique. We show that the algorithms previously developed by us can be modified to reconstruct the concentration of fluorescent contrast agents.     

How to measure the optical thickness of scattering particles from the phase delay of scattered waves: application to turbid samples

We present a method based on the optical theorem that yields absolute, calibration free estimates of the optical thickness of scattering particles. The thickness is determined from the phase delay of the zero angle scattered wave. It uses a heterodyne scattering scheme operating in the Raman-Nath approximation. The phase is determined by the position of Talbot-like modulations in the two dimensional power spectrum S(qx, qy) of the transmitted beam intensity distribution. The method is quite insensitive to multiple scattering. It is successfully tested to provide quantitative verification of the optical theorem. Exploratory tests on soft matter samples are reported to suggest its wide applicability to turbid samples.     

Relative index theorems and supersymmetric scattering theory

We discuss supersymmetric scattering theory and employ Krein's theory of spectral shift functions to investigate supersymmetric scattering systems. This is the basis for the derivation of relative index theorems on some classes of open manifolds. As an example we discuss the de Rham complex for obstacles in ^N and asymptotically flat manifolds. It is shown that the absolute or relative Euler characteristic of an obstacle in ^N may be obtained from scattering data for the Laplace operator on forms with absolute or relative boundary conditions respectively. In the case of asymptotically flat manifolds we obtain the Chern-Gauss-Bonnet theorem for theL ²-Euler characteristic.On leave of absence from Institute of Physics, Leningrad State University, Leningrad     

A Microscopic Derivation of the Quantum Mechanical Formal Scattering Cross Section

We prove that the empirical distribution of crossings of a “detector” surface by scattered particles converges in appropriate limits to the scattering cross section computed by stationary scattering theory. Our result, which is based on Bohmian mechanics and the flux-across-surfaces theorem, is the first derivation of the cross section starting from first microscopic principles.     

Anomalous scattering factors of some rare earth elements evaluated using photon interaction cross-sections

The real and imaginary parts,f’(E) and”(E) of the dispersion corrections to the forward Rayleigh scattering amplitude (also called anomalous scattering factors) for the elements La, Ce, Pr, Nd, Sm, Gd, Dy, Ho and Er, have been determined by a numerical evaluation of the dispersion integral that relates them through the optical theorem to the photoeffect cross-sections. The photoeffect cross-sections are derived from the total attenuation cross-section data set experimentally determined using high resolution high purity germanium detector in a narrow beam good geometry set-up for these elements in the photon energy range 5 to 1332 keV and reported earlier by the authors. Below 5 keV, Scofield’s photoeffect cross-sections compiled in XCOM program have been interpolated and used. Simple formulae forf” in terms of atomic number and energy have also been obtained. The data cover the energy region from 6 to 85 keV and atomic numberZ from 57–68. The results obtained are found to agree fairly well with the other available data.     

Transport properties of the Anderson lattice

Transport properties including electrical resistivity, thermoelectric power, Lorenz number and a.c. conductivity are evaluated in an approximate fashion for the Anderson lattice model for six-fold degenerate Ce ions. Coherence (Bloch's theorem) is explicitly included while the effects of intersite interactions which may be responsible for magnetic and superconducting instabilities are neglected. The calculations utilize the AverageT-matrix Approximation (ATA) with the self-consistent Non-Crossing Approximation (NCA) perturbation theory employed to give the single siteT-matrix estimate. The resistivity peaks near the characteristic Kondo temperatureT ₀, with high temperature logarithmic decrease and low temperatureT ² behavior. The thermoelectric power is positive and similar to the impurity result except for low temperatures; sign changes in the thermopower are in principle possible with momentum dependent hybridization. Frequency and temperature dependent optical conductivity calculations are in qualitative agreement with experimental data, although a suitably defined optical effective mass and scattering rate do not agree at least for large orbital degeneracy. The behavior of these latter quantities is qualitatively different for twofold degeneracy. Unanswered questions arising from the experimental literature are summarized.     

The local field correction to the optical potential at high energy

A key assumption in the derivation of the optical potential for high energy hadron-nucleus scattering is that no target nucleon is struck more than once. The local field (rescattering) amplitude gives the probability for the projectile to strike a target nucleon twice with an intermediate interaction with another nucleon. This rescattering amplitude generates a correction to the basic high energy optical potential, and it must be small for the above assumption to be valid. We evaluate the local field correction to the optical potential using the formalism of Foldy and Walecka. The projectile-nucleon potential is assumed to have a finite range, and the target nucleons are kept sufficiently far apart by a hard core correlation function that there is no overlap between target particles, and all off-energy-shell effects vanish. With a specific form for the high energy behavior of the on-shell projectile-nucleon scattering amplitude, we find that the local field correction vanishes rapidly at high energy.     

Spatial coherence properties of light from optical fibres

The mutual intensity of the optical field in the Fraunhofer diffraction region produced from the end of an optical fibre under illumination of a coherent beam, is theoretically analysed by using an optical fibre-end source model. In this source model, the optical field at the end of the fibre is expressed as an aggregation of independent plane waves with random directions and phases, because the guided modes propagating through the fibre may be regarded as a stochastic process. It is found that the optical field in the diffraction region from the multimode optical fibre is not homogeneous butquasi homogeneous in a statistical sense. The spatial coherence properties in the field are discussed in connection with theV number (the normalized frequency) of the fibre and in comparison with those in the field produced from an incoherent source obeying the van Cittert-Zernike theorem.