Light scattering by slightly nonspherical particles on surfaces

We investigate the shape dependence of the scattering by dielectric and metallic particles on surfaces by considering particles whose free-space scattering properties are nearly identical. The scattering by metallic particles is strongly dependent on the shape of the particle in the region near where the particle touches the surface. The scattering by dielectric particles displays a weaker, but nonetheless significant, dependence on particle shape. These results have a significant effect on the use of light scattering to size and identify particles on surfaces.     

Electromagnetic scattering by nonspherical particles: Recent advances

This note gives a short introduction to the reprint of the article “Numerical methods in electromagnetic scattering theory” by Kahnert, M (JQSRT 2003;79-80:775-824). Some of the most important developments in the field since the publication of this article are briefly reviewed. A list of typos that have been identified in the original article is given in the appendix.     

Detecting submerged objects by Brillouin scattering

The principle of detecting submerged objects by Brillouin scattering is analyzed. It is based on testing the frequency shift rather than the intensity of the scattered signal. Experiments based on the principle are carried out. An actual detecting system for practical applications is designed, and the experimental results obtained by using the system are given. The experimental results show that the method of Brillouin scattering possesses several advantages compared to the method of testing the signal intensity. The conclusion is that Brillouin scattering is a good method for detecting submerged objects. PACS 42.68.Wt; 42.79.Qx; 78.35.+c     

Quantum irregular scattering induced by tunneling

Irregular behavior in a simple two-dimensional scattering model is investigated in the quantum domain. The scattering potential is composed from Dirac deltas on a stadium shaped curve. The unusual feature of the model is that the irregular patterns disappear in the classical limit because the main mechanism leading to resonances in the cross section data is the quantum tunneling. Calculations for the standard characteristics such as nearest-neighbor distribution of eigenphases of the S-matrix, the distribution of the S-matrix elements and the correlation function of the total cross section are performed. Deviations from the usual predictions for irregular scattering have been found in certain regions, which can be traced back to the fact that the model does not have such a characteristic time like the classical escape rate, which survives the classical limit.     

Radiation force caused by scattering, absorption, and emission of light by nonspherical particles

General formulas for computing the radiation force exerted on arbitrarily oriented and arbitrarily shaped nonspherical particles due to scattering, absorption, and emission of electromagnetic radiation are derived. For randomly oriented particles with a plane of symmetry, the formula for the average radiation force caused by the particle response to external illumination reduces to the standard Debye formula derived from the Lorenz–Mie theory, whereas the average radiation force caused by emission vanishes.     

Quantum experiments with macroscopic mechanical objects

Recent achievements in the isolation of macroscopic mechanical objects from a heat bath make it possible to implement quantum measurements with such systems. In this case, either a free mass or an oscillator can be used as a test object. The advantage of the first variant is in significantly longer relaxation times achieved for free masses. The advantage of the second variant is in the absence of restrictions on the limiting measurement accuracy associated with internal losses in the meter. This restriction can be bypassed, retaining a long relaxation time typical of free masses, if a test oscillator with a ponderomotive electromagnetic rigidity is used. Estimates show that the potential sensitivity of this test body for the modern level of technology may be considerably higher than the standard quantum limit.     

Small-angle neutron scattering at fractal objects

The calculation of the correlation function of an isotropic fractal particle with the finite size ξ and the dimension D is presented. It is shown that the correlation function γ(r) of volume and surface fractals is described by a generalized expression and is proportional to the Macdonald function (D–3)/2 of the second order multiplied by the power function r ^(D–3)/2. For volume and surface fractals, the asymptotics of the correlation function at the limit r/ξ < 1 coincides with the corresponding correlation functions of unlimited fractals. The one-dimensional correlation function G(z), which, for an isotropic fractal particle, is described by an analogous expression with a shift of the index of the Macdonald function and the exponent of the power function by 1/2, is measured using spin-echo small-angle neutron scattering. The boundary case of the transition from a volume to a surface fractal corresponding to the cubic dependence of the neutron scattering cross section Q ^?3 leads to an exact analytical expression for the one-dimensional correlation function G(z) = exp(?z/ξ), and the asymptotics of the correlation function in the range of fractal behavior for r/ξ < 1 is proportional to ln(ξ/r). This corresponds to a special type of self-similarity with the additive law of scaling rather than the multiplicative one, as in the case of a volume fractal.     

Near- and far-field light scattering by nonspherical particles: Applicability of methods that involve a spherical basis

The separation of variables method for coordinate system, the extended boundary condition method, and the point-matching method that are used to solve the problem of light scattering by nonspherical particles are considered from a unified viewpoint. It is shown that, if the mathematical correctness condition (the Rayleigh hypothesis) holds, these methods are interrelated and are equivalent. The applicability ranges of the methods in the near- and far-field zones are analyzed, discussed, and compared on both analytical (based on analytical investigations) and practical (based on numerical calculations) grounds.     

Application of spheroidal functions in theory of light scattering by nonspherical particles: Separation of variables method

The separation of variables method (SVM), which uses a spheroidal basis, is proposed. According to this method, fields are presented in the form of expansion in terms of spheroidal functions. The previously conducted analysis of various methods using a spherical basis showed that the SVM is applicable in a broader area for numerical calculations, while the proposed approach using a spheroidal basis yields reliable results in the case of spheroids with a high degree of asphericity where other methods and approaches cannot be used. Importantly, the method includes an SVM that uses a spherical basis as the limiting case. Thus, the proposed method has all chances of being highly efficient for calculation of optical characteristics of various nonspherical particles in a wide range of parameters of the formulated problem.     

Quantum imaging and inverse scattering

We consider the inverse scattering problem that arises in two-photon quantum imaging with interferometric measurements. We show that the two-point correlation function of the field contains information about the scattering medium at a spatial frequency of twice the Rayleigh bandwidth. The linearized inverse problem, however, yields reconstructions with a resolution of λ/2, where λ is the wavelength of light.     

Mean-field T-matrix approach to elastic wave scattering by small and point-like objects

The T-matrix of a small inclusion embedded in a homogeneous matrix is calculated for vector elastic waves. The theory relies on an approximation of the local stress and momentum inside the inclusion by volumetric averages, which allows the summation of the full multiple-scattering series. The limiting case of a point scatterer is discussed. The mean-field T-matrix and its point limit both satisfy the elastodynamic version of the optical theorem. The accuracy of the results is discussed by comparison with some exact solutions for spheres. In particular, the mean-field T-matrix allows the approximate modeling of low-frequency resonances by small, high-contrast objects. The present theory could be applied to the multiple scattering of elastic waves by a collection of small or fuzzy resonant scatterers.     

Average values of the invariant polarization parameters for scattering by compound objects

The problem of analytical calculation of average values of the invariant polarization electromagnetic field parameters is considered for scattering by a compound object comprising an artificial small-sized object and underlying surface with a considerable number of centers of secondary scattering. The main difference of this work from the results obtained by W. Boerner, E. Pottier, and S. Cloude [1–3] and other researchers is efficient application of polarization invariants of radar objects that can be measured in real time and displayed on a radar monitor. The application of these invariants allows the radar image contrast to be improved significantly and the probability of detection of small-sized objects against the underlying surface background to be increased.