Observation of the enhanced backscattering of light by the end of a tilted dielectric cylinder owing to the caustic merging transition

The scattering of light by obliquely illuminated circular dielectric cylinders was previously demonstrated to be enhanced by a merger of Airy caustics at a critical tilt angle. [Appl. Opt. 37, 1534 (1998)]. A related enhancement is demonstrated here for backward and near-backward scattering for cylinders cut with a flat end perpendicular to the cylinder's axis. It is expected that merged caustics will enhance the backscattering by clouds of randomly oriented circular cylinders that have appropriately flat ends.     

Scattering observations for tilted transparent fibers: evolution of airy caustics with cylinder tilt and the caustic merging transition

When a dielectric circular cylinder is obliquely illuminated, the scattering angle associated with the Airy caustics of the cylinder's primary rainbow depends on the tilt of the cylinder. We display records of the scattering pattern for a transparent poly(methyl methacrylate) fiber ranging from small values of tilt through values of tilt that are sufficiently large for the Airy caustics from both sides of the fiber to merge in a meridional plane containing the incident wave vector and the fiber's axis. The records are compared directly with the evolution of the caustic projected onto the observation plane, and certain qualitative features of the global evolution of the caustics are confirmed. Although the observations used laser illumination, they are relevant to anticipating the scattering by sunlit transparent tilted cylinders.     

Electromagnetic scattering by an infinite cylinder of material or metamaterial coating eccentrically a dielectric cylinder

The electromagnetic scattering by an infinite cylinder of dielectric material or metamaterial, coating eccentrically another infinite dielectric cylinder, is treated in this work. The problem is solved using classical separation of variables techniques. No use is made of the translational addition theorem. For small eccentricities h = d/a(? 1), where d is the distance between the axes of the cylinders and a the radius of the outer cylinder, we use instead the cosine and the sine laws to satisfy the boundary conditions at the surface of the outer cylinder. Keeping terms up to the order h2 we finally obtain exact, closed-form expressions for the expansion coefficients g(1) and g(2) in the relation S(h) = S(0)[1 + g(1)h + g(2)h2 + O(h3)], giving the scattered field and the scattering cross sections of the problem, where S(0) corresponds to the coaxial geometry, with h = 0 (d = 0). Both polarizations are considered for normal incidence. Numerical results are given for various values of the parameters, corresponding to materials or metamaterials. Our method is an alternative of the one using the translational addition theorem in the case of small eccentricities h.     

Modeling of the scattering of electromagnetic waves by a thin dielectric coating on a cylinder

Double-sided boundary conditions containing only tangential components of a diffracted field are used to model the interaction of electromagnetic waves with a cylinder of arbitrary cross section covered with a thin dielectric layer. The obtained boundary-value problem is reduced to a system of two singular integral equations of the second kind with kernels whose structure is similar to the kernels of integral equations of the first kind for a perfectly conducting scatterer. The numerical solution of the integral equations of the problem is obtained by the method of mechanical quadratures. The scattering properties of an elliptic cylinder with different dielectric coatings are studied in the superhigh-frequency band. It is shown that the coating strongly affects the diffraction properties of the cylinder. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 42, No. 1, pp. 96–104, January–February, 2006.     

Transverse electric scattering by a dielectric biconvex cylinder loaded with a shallow circular trough in a ground plane

The scattering problem of transverse electric wave from a dielectric biconvex cylinder buried in a shallow circular trough of a ground plane is investigated and a rigorous series solution is also derived. Based on the region-matching method, the analysed region is decomposed into two subregions by introducing a semi-circular auxiliary boundary. The magnetic field of each subregion is expressed in terms of cylindrical wave functions with unknown expansion coefficients. After imposing the matching conditions and the boundary condition on the trough surface with the aid of Graf's addition theorem, the unknown coefficients are determined. Comparisons with published data for a dielectric circular cylinder case show very good agreement. Visible effects of depth-to-half-width ratios of a dielectric biconvex cylinder on echo width, far- field pattern and near-field distribution are illustrated in graphical form.     

Model of scattering by a perturbed thin cylinder

A model of wave scattering by a perturbed thin cylinder is constructed. The model is based on the theory of self-adjoint operator extensions. A method is found for choosing a model operator ensuring that the model solution is identical to the leading term of the asymptotic expansion, in terms of the small diameter of the cylinder, of the real scattering problem. Pis’ma Zh. Tekh. Fiz. 25, 42–45 (March 26, 1999)     

Excitation of a dielectric cylinder by a point source of radiation

The excitation of a layered dielectric cylinder by a point source is investigated. A procedure is described for representing the solutions of diffraction problems in terms of fractional Bessel and related functions (so-called cylinder functions) suitable for numerical calculations. Far-field diffraction patterns are calculated for cylinders of large radius. Translated from Izmeritel'naya Tekhnika, No. 3, pp. 43–46, March, 1996.     

Exterior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder: semiclassical scattering theory analysis

We use the semiclassical limit of electromagnetic wave scattering theory to determine the properties of the exterior caustics of a diagonally incident plane wave scattered by an infinitely long homogeneous dielectric circular cylinder in both the near zone and the far zone. The transmission caustic has an exterior/interior cusp transition as the tilt angle of the incident beam is increased, and each of the rainbow caustics has a farzone rainbow/exterior cusp transition and an exterior/interior cusp transition as the incident beam tilt angle is increased. We experimentally observe and analyze both transitions of the first-order rainbow. We also compare the predictions of the semiclassical approximation with those of ray theory and exact electromagnetic wave scattering theory.     

Light scattering by a coated infinite cylinder in an absorbing medium

The scattering formulation for a coated infinite cylinder in an absorbing medium is presented in this paper. The cylinder is subjected to an arbitrarily polarized plane wave propagating in a general direction at the cylinder. The refractive index and magnetic permeability of the host medium, as well as those for the core and coating of the cylinder, can be real or complex. The scattering and extinction efficiencies and the scattering amplitudes are derived for both the near field and the far field. As the medium is absorbing, the "true" extinction and scattering efficiencies are derived based on the radiative energy outflow at the surface of the cylinder. The radiative efficiencies in the far field are denoted as "apparent" properties because they include absorption by the intervening medium. The influence of the refractive index and permeability of the host medium on the scattering properties of a coated cylinder is illustrated by numerical examples.     

Wave scattering by a circular cylinder half-immersed in water with an ice-cover

The problem of scattering of water waves obliquely incident on a fixed long circular cylinder half-immersed in deep water with an ice-cover is investigated here. The ice-cover is modelled as an elastic plate of very small thickness. The problem is formulated using the method of multipoles. This leads to an infinite system of linear equations which are solved numerically by truncation. The reflection and transmission coefficients are obtained and depicted graphically against the wave number for various values of the angle of incidence and flexural rigidity of the ice-cover to show the effect of the presence of ice-cover on these quantities. The effect of ice-cover is seen to increase the reflection coefficient and to decrease the transmission coefficient.     

Role of the tunneling ray in near-critical-angle scattering by a dielectric sphere

The scattering far zone for light transmitted through a sphere following p - 1 internal reflections by a family of near-grazing incident rays is subdivided into a lit region and a shadow region. The sharpness of the ray theory transition between the lit and the shadow regions is smoothed in wave theory by radiation shed by electromagnetic surface waves. It is shown that when higher-order terms in the physical optics approximation to the phase of the partial-wave scattering amplitudes are included, the transition between the lit and the shadow regions becomes a two-ray-to-zero-ray transition, called a superweak caustic in analogy to the more familiar scattering caustics and weak scattering caustics. One of the merged rays is a tunneling ray.     

Experimental observation of rainbow scattering by a coated cylinder: twin primary rainbows and thin-film interference

We experimentally examine the primary rainbow created by the illumination of a coated cylinder. We present a simple technique for varying the coating thickness over a wide range of values, and we see evidence for two different scattering regimes. In one, where the coating thickness is large, twin rainbows are produced. In the second, where the coating is thin enough to act as a thin film, a single rainbow is produced whose intensity varies periodically as the coating thickness varies. We find good agreement with previous theoretical predictions.     

Wave scattering by a horizontal circular cylinder in a two-layer fluid with an ice-cover

In a two-layer fluid wherein the upper layer is of finite depth and bounded above by a thin but uniform layer of ice-cover modelled as a thin elastic sheet and the lower layer is infinitely deep below the interface, time-harmonic waves with a given frequency can propagate with two different wavenumbers. The wave of smaller wavenumber propagates along the ice-cover while wave of higher wavenumber propagates along the interface. In this paper problems of wave scattering by a horizontal circular cylinder submerged in either the lower or in the upper layer due to obliquely as well as normally incident wave trains of both the wave numbers are investigated by using the method of multipole expansions. The effect of the presence of ice-cover on the various reflection and transmission coefficients due to incident waves at the ice-cover and the interface is depicted graphically in a number of figures.     

Integral equation model of light scattering by an oriented monodisperse system of triaxial dielectric ellipsoids: application in ectacytometry

A novel mathematical model of light scattering by an oriented monodisperse system of triaxial dielectric ellipsoids of complex index of refraction is presented. It is based on an integral equation solution to the scattering of a plane electromagnetic wave by a single triaxial dielectric ellipsoid. Both the position and the orientation of a single representative scatterer in a given coordinate system are considered arbitrary. A Monte Carlo simulation is developed to reproduce the diffraction pattern of a population of aligned ellipsoids. As an example of practical importance, light scattering by a population of erythrocytes subjected to intense shear stress is modeled. Agreement with experimental observations and the anomalous diffraction theory is illustrated. Thus a novel check of the electromagnetic basis of ektacytometry is provided. Furthermore, the versatility of the integral equation method, particularly in the advent of parallel processing systems, is demonstrated.     

Change of ultra-short laser pulse shape after scattering by a nanosphere in a dielectric matrix

The scattering of ultra-short laser pulses by a metallic nanosphere embedded in a dielectric matrix was studied theoretically in the frame of the dipole approximation. Calculations were performed for the corrected Gaussian shape of the incident laser pulse, which enabled us to consider both multi-cycle and sub-cycle pulses. Analysis of the influence of the scattering process on the shape of scattered pulse is made for various durations and carrier frequencies of the incident pulses.     

Scale transformation of Maxwell's equations and scattering by an elliptic cylinder

A scale transformation that converts an ellipse into a circle has been suggested in the literature as a method for eliminating the need to evaluate the conventional Mathieu function solution for scattering by an elliptic cylinder. This suggestion is tested by examining the wave equation in the scaled coordinate system and by evaluating the scattering from a thin ellipse for conditions where it is expected that an approximate solution can be obtained using the scalar theory single-slit approximation. It is found that, for a plane electromagnetic wave normally incident on a thin perfectly conducting ellipse, the position of the first minimum in the diffraction pattern, relative to the central axis, differs by approximately a factor of 7 between the single-slit and the scaled theory approach to the problem. The examination of the scaled wave equation and the scattering calculation suggests that, because the scale transformation generates an anisotropic medium, the use of a uniform medium solution in the scaled coordinate system is not appropriate.     

Polarized light scattering by microroughness and small defects in dielectric layers

The polarization of light scattered by the surface of a material contains information that can be used to identify the sources of that scatter. Theories for light scattering from interfacial roughness of a dielectric layer and from defects in that dielectric layer are reviewed. Methods for calculating the Mueller matrix or the Stokes vector for scatter from multiple sources and for decomposing a Stokes vector into contributions from two nondepolarizing scattering sources are derived. The theories are evaluated for a specific sample and geometry. Results show that some incident polarizations are more effective than others at discriminating among scattering sources, with s-polarized light being least effective. The polarization of light scattered from interfacial roughness depends upon the relative roughness of the two interfaces and the degree of correlation between the two interfaces. The scattering from defects in the film depends on the depth of the defect and differs from that from any one of the cases of interfacial roughness. The scattering from defects randomly distributed in the film and for small dielectric permittivity variations in the film is also calculated. Experimental results are presented for a 52-nm SiO2 film thermally grown on microrough silicon.     

Single-Gaussian-beam interaction with a dielectric microsphere: radiation forces, multiple internal reflections, and caustic structures

We analyze the generation of radiation forces in the various internal reflections that occur when a tightly focused, unpolarized Gaussian beam interacts with a dielectric microsphere. The Euler transformation is used to compute the relevant axial-force vectors that are associated with the internal reflections rapidly. The net force is computed as the average of the forces generated by the s- and p-polarization components of the electric-field vector. The force characteristics are strongly dependent on the algebraic value of the index mismatch Δn at the sphere interface. For the two cases of Δn = 0.65, 0.32 with a sphere index n(2) = 1.65, the inclusion of the contributions from the second and third internal reflections after the magnitude of the effective force by at least 10%. For Δn < 0, the individual force contributions from internal reflections beyond the first are at least 4 orders of magnitude less than those of the first interaction. The caustic structures produced by the internal reflections are also profiled for both cases of Δn = ±0.32.     

Extinction and scattering of a guided beam in a hollow dielectric waveguide.

We present a theoretical approach to the problem of mode scattering by a spherical object that is placed inside a circular dielectric waveguide. This approach is based on the separation-of-variables method for each subsystem, namely, the spherical inclusion and the circular dielectric cylinder, and on the concept of the generalized recursive T-matrix algorithm for multilayered structures. We apply the technique to the backward and the forward scattering of a quasi-optical beam in the form of the fundamental HE11 mode by a sphere inside a circular hollow dielectric waveguide. The results calculated for the perfectly conducting spherical objects inside the circular hollow dielectric waveguide are compared with corresponding measured data of the backward-and the forward-scattering characteristics at the 4-mm wave band.