Scattering of a spheroidal particle illuminated by a gaussian beam

An approach to expanding a Gaussian beam in terms of the spheroidal wave functions in spheroidal coordinates is presented. The beam-shape coefficients of the Gaussian beam in spheroidal coordinates can be computed conveniently by use of the known expression for beam-shape coefficients, g(n), in spherical coordinates. The unknown expansion coefficients of scattered and internal electromagnetic fields are determined by a system of equations derived from the boundary conditions for continuity of the tangential components of the electric and magnetic vectors across the surface of the spheroid. A solution to the problem of scattering of a Gaussian beam by a homogeneous prolate (or oblate) spheroidal particle is obtained. The numerical values of the expansion coefficients and the scattered intensity distribution for incidence of an on-axis Gaussian beam are given.     

Scattering of a tightly focused beam by an optically trapped particle

Near-forward scattering of an optically trapped 5-mum-radius polystyrene latex sphere by the trapping beam was examined both theoretically and experimentally. Since the trapping beam is tightly focused, the beam fields superpose and interfere with the scattered fields in the forward hemisphere. The observed light intensity consists of a series of concentric bright and dark fringes centered about the forward-scattering direction. Both the number of fringes and their contrast depend on the position of the trapping beam focal waist with respect to the sphere. The fringes are caused by diffraction that is due to the truncation of the tail of the trapping beam as the beam is transmitted through the sphere.     

Far-field scattering of a non-Gaussian off-axis axisymmetric laser beam by a spherical particle

Experimental laser beam profiles often deviate somewhat from the ideal Gaussian shape of the axisymmetric TEM(00) laser mode. To take these deviations into account when calculating light scattering of an off-axis beam by a spherical particle, we use our phase-modeling method to approximate the beam-shape coefficients in the partial wave expansion of an experimental laser beam. We then use these beam-shape coefficients to compute the near-forward direction scattering of the off-axis beam by the particle. Our results are compared with laboratory data, and we give a physical interpretation of the various features observed in the angular scattering patterns.     

Scattering of SH waves by a spherical layer

In the frame work of the theory of classical elasticity we study the interaction of spherical elastic SH waves of harmonic type with a spherical layer when the source is placed outside the layer. The exact solution of this scattering problem is investigated in detail after a generalized Debye's expansion is established. The presence of the spherical layer is evident from the second term of this development. The interpretations obtained for a one-sphere model remain valid. However, among the differences we note that the surface waves created on the outer face of the layer rise or die out according to an angle which depends on the mechanical and geometrical features of the layer.     

Far-field scattering of an axisymmetric laser beam of arbitrary profile by an on-axis spherical particle

Experimental laser beam profiles often deviate somewhat from the ideal Gaussian shape of the TEM(00) laser mode. In order to take these deviations into account when calculating light scattering, we propose a method for approximating the beam shape coefficients in the partial wave expansion of an experimental laser beam. We then compute scattering by a single dielectric spherical particle placed on the beam's axis using this method and compare our results to laboratory data. Our model calculations fit the laboratory data well.     

Scattering of a Gaussian beam by an impedance half-plane

The diffraction of a Gaussian beam by an impedance half-plane is studied through the method of the modified theory of physical optics. An electric line source, which is defined in the complex space, is used to represent the Gaussian beam. The uniform evaluation of the diffraction integral is performed and the scattering patterns of the field are investigated for various numerical parameters of the incident wave.     

Scattering of electromagnetic spherical waves by a buried spheroidal perfect conductor

We examine the electromagnetic scattering of spherical waves by a buried spheroidal perfect conductor. The proposed analysis is based on the integral equation formalism of the problem and focuses on the establishment of a multiparametric model describing analytically the scattering process under consideration. Both the theoretical and the numerical treatment are presented. The outcome of the analysis is the determination of the scattered field in the observation environment along with its multivariable on several physical and geometric parameters of the system.     

Stokes resistance of a porous spherical particle in a spherical cavity

The boundary effect on the asymmetrical motion of a porous spherical particle in an eccentricspherical cavity is investigated in the quasi-steady limit under creeping flow conditions. The porous particletranslates and rotates in the viscous fluid, located within the spherical cavity, normal to the line connectingtheir centers. The fluid inside the porous particle is governed by the Brinkman equation. A tangential stressjump condition at the interface between the fluid and the porous particle is applied. A semi-analytical approachbased on a collocation technique is used. Due to the linearity of the present problem, the flow variables for theclear fluid region are constructed by superposing basic solutions of two problems: the first one is the regularsolution inside the cavity region in the absence of the porous particle where a first system of coordinates has itsorigin at the center of the cavity, while the second problem is the regular solution in the infinite region outsidethe spherical porous particle where a second coordinate system with its origin at the center of the porousparticle is used. Numerical results displaying the resistance coefficients acting on the particle are obtainedwith good convergence for various values of the physical parameters of the problem. The results are tabulatedand represented graphically. The findings demonstrate that the collocation results of the resistance coefficientsare in good agreement with the corresponding results for the impermeable solid particle.     

Scattering of a Hermite-Gaussian beam field by a chiral sphere.

Scattering of a Hermite-Gaussian beam field by a chiral sphere is analyzed. A Hermite-Gaussian beam field is expressed as a superposition of multipole fields at complex-source points. Electromagnetic fields are expanded in terms of the spherical vector wave functions. The unknown expansion coefficients for the scattered field and the internal field are determined by the boundary conditions. As numerical examples, the scattered near fields of the beam incidence are calculated, and the effects of the chirality and the radius of the chiral sphere on the fields are examined. The results for a Gaussian beam incidence are also compared with those of a plane-wave incidence.     

Heating of a massive spherical particle by radiation and convection

An approximate analytical solution of the nonlinear problem of heating of a spherical body by radiation and convection is obtained.     

Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. I. By a spherical particle

The geometrical-optics approximation of light scattering by a transparent or absorbing spherical particle is extended from plane wave to Gaussian beam incidence. The formulas for the calculation of the phase of each ray and the divergence factor are revised, and the interference of all the emerging rays is taken into account. The extended geometrical-optics approximation (EGOA) permits one to calculate the scattering diagram in all directions from 0 degrees to 180 degrees. The intensities of the scattered field calculated by the EGOA are compared with those calculated by the generalized Lorenz-Mie theory, and good agreement is found. The surface wave effect in Gaussian beam scattering is also qualitatively analyzed by introducing a flux ratio factor. The approach proposed is particularly important to the further extension of the geometrical-optics approximation to the scattering of large spheroidal particles.     

Scattering of a pulsed wave by a sphere with an eccentric spherical inclusion

A dielectric sphere with an eccentric spherical dielectric inclusion and an incident amplitude-modulated plane electromagnetic wave constitute an exterior radiation problem, which is solved in this paper. A solution is obtained by combined use of the Fourier transform and the indirect-mode-matching method. The analysis yields a set of linear equations for the wave amplitudes of the frequency-domain expansion of the electric-field intensity within and outside the externally spherical inhomogeneous body; that set is solved by truncation and matrix inversion. The shape of the backscattered pulse in the time domain is determined by application of the inverse fast Fourier transform. Numerical results are shown for a pulse backscattered by an acrylic sphere that contains an eccentric spherical cavity. The effects of cavity position and size on pulse spreading and delay are discussed.     

Wall effects on a spherical particle

The motion of a solid spherical particle at the instant it passes the centre of a spheroidal container has been investigated using the no-slip condition at the surfaces. The shape of this spheroidal container is assumed to deviate slightly from that of a sphere at the surface. An expression for the stream function describing the flow field has been obtained to the first order in the parameter characterizing the deviation and this in turn has been utilized to evaluate the drag on the particle. Wall effects are then examined and special cases deduced.     

Mie scattering by a spherical particle in an absorbing medium

We show that the large-size parameter limit of the scattering efficiency of a spherical particle of relative refractive index m(r) embedded in an absorbing medium is equal to [m(r) - 1[2/]m(r) + 1]2 and not to zero as has been claimed in a recent article [J. Appl. Opt. 40, 1354-1361 (2001)].     

Scattering of torsional waves by a spherical cavity in a long circular elastic cylinder

Summary. The axisymmetric wave equation is solved for the problem of torsional elastic waves scattered by a spherical cavity located symmetrically in an infinitely long circular cylinder. Using Fourier transforms, the problem is reduced to the solution of an infinite system of simultaneous equations, which is suitable for the numerical solution. The numerical results on the transmission and reflection coefficients are shown for various values of sphere radius and frequency. Equation of energy conservation is utilized to check the numerical procedure.     

Thermal stressed state of a transversely isotropic spherical shell with round hole

On the basis of the generalized theory of shells constructed by the method of expansion of unknown functions in Fourier series in the Legendre polynomials of the thickness coordinate, we study the problem of thermal stressed state of a gently sloping transversely isotropic spherical shell with round hole. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 6, pp. 23–29, November–December, 2008.     

Mass transfer in a reactive spherical particle

A macrokinetic model is presented for the solid-phase transformation of a particle under arbitrary relationships between the sorption-desorption, dissolution, and diffusion rates of the initial and final products.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 48, No. 5, pp. 796–803, May, 1985.     

Scattering in twin-cavity narrow-band interference filters illuminated by a monochromatic beam

The scattering behavior of the all-dielectric twin-cavity narrow-band interference filter is studied both in theory and in experiment in two cases, l(1) = l(2) and l (1) not equal l(2), where l(1) and l(2) are the optical thicknesses of the two cavities. It has been shown that the scattering properties are determined mainly by the spacers in which the electric-field intensities are large because of the presence of large standing-wave fields. The scattered light cones are found on both sides of the filter illuminated by a monochromatic light of which the wavelength (lambda(L)) is shorter than the peak wavelength (lambda(0)?) of the filter. The scattering angle of each cone is equal to the tilted angle of the filter when the peak wavelength of the filter shifts to the illumination wavelength. For the case l(1) not equal l(2), the distributions of the scattered light on both sides of the filter are quite different. The analytical calculations are in good agreement with experimental results. The possible applications of scattering in the twin-cavity filter in determining the bandwidth of the peak transmittance and the optical thicknesses of two spacers are addressed.