Recursive T matrix algorithm for resonant multiple scattering: applications to localized plasmon excitations

A matrix balanced version of the recursive centered T matrix algorithm applicable to systems possessing resonant interparticle couplings is presented. Possible domains of application include systems containing interacting localized plasmon resonances, surface resonances, and photonic jet phenomena. This method is of particular interest when considering modifications to complex systems. The numerical accuracy of this technique is demonstrated in a study of particles with strongly interacting localized plasmon resonances.     

Mie scattering by an anisotropic object. Part I. Homogeneous sphere

Establishing a vector spherical harmonic expansion of the electromagnetic field propagating inside an arbitrary anisotropic medium, we extend Mie theory to the diffraction by an anisotropic sphere, with or without losses. The particular case of a uniaxial material leads to a simpler analysis. This work opens the way to the construction of a differential theory of diffraction by a three-dimensional object with arbitrary shape, filled by an arbitrary anisotropic material.     

On the validity of soft particle approximations for the light scattering by a homogeneous dielectric sphere

Abstract

The validity of various soft particle approximations has been examined for the scattering of light by a homogeneous dielectric sphere. A scalar analogue of the S-approximation has been presented. It is shown that this much simpler approximation could be nearly as good as the sophisticated S-approximation itself. Numerical results for the extinction and the scattered intensities are examined over a wide refracted index and size parameter domain. The anomalous diffraction approximation has also been included in numerical comparisons.     

Application of semiclassical and geometrical optics theories to resonant modes of a coated sphere

This work deals with some aspects of the resonant scattering of electromagnetic waves by a metallic sphere covered by a dielectric layer, in the weak-absorption approximation. We carry out a geometrical optics treatment of the scattering and develop semiclassical formulas to determine the positions and widths of the system resonances. In addition, we show that the mean lifetime of broad resonances is strongly dependent on the polarization of the incident light.     

Time-resolved transmission through homogeneous scattering media: time-response effects

An analytical expression has been obtained that describes the time variation of time-resolved signals transmitted through or reflected by a homogeneous scattering slab as measured with a detection system having a square-impulse response. This expression can be used to improve the match between theoretical and experimental time-resolved signals measured with a system having a finite response time. It can also be used to assess the effect of a finite detection response time on the time-domain characterization of a turbid medium. The expression can be adapted to detection systems that are not time invariant.     

Computations of the Mueller matrix elements for scattering from layered structures with rough surfaces, with applications to optical detection

A full-wave method is used to evaluate the Mueller matrix elements for scattering from layered structures with random rough surfaces. These provide a database for applications in optical detection over a broad range of rough surface statistical parameters. They can be used to determine the optimal frequencies and incident angles that provide most reliable measurements for optical detection. The elements of the Mueller matrix that are most sensitive to medium parameters of the layered structures can also be identified. Contributions from individual terms of the full-wave solutions are shown to have distinct physical interpretations.     

Construction of anisotropic polyconvex energies and applications to thin shells

In computer simulations where constitutive equations are considered anisotropic polyconvex energies can preferably be used because the existence of minimizers is then automatically guaranteed. In this work we investigate the capability to simulate anisotropy effects of anisotropic thin shells using polyconvex anisotropic energies. The construction of the considered polyconvex transversely isotropic energy is based on specific structural tensors. The iterative enforcement of the zero normal stress condition at the integration points allows the consideration of arbitrary three-dimensional constitutive equations. As a representative example we compare results for isotropic and anisotropic plates.     

Dynamic elastic constants of anisotropic materials by resonant ultrasound spectroscopy

Resonant ultrasound spectroscopy (RUS) has been applied to the anisotropic elastic stiffness determination of SiC/Al composites and highly textured Zr-2.5 Nb alloys. To determine the elastic stiffness of anisotropic materials, the resonant frequencies of a rectangular parallelepiped specimen were measured and compared with the calculated frequencies based on the input data of the estimated stiffness, dimensions, and density. The initial estimates of the elastic stiffness of SiC/Al composites were calculated using the Mori-Tananka (MT) theory and the concept of effective aspect ratio of reinforcements. For highly textured Zr-2.5 Nb alloy, the initial estimates were obtained from its orientation distribution function, determined by X-ray diffraction, and the reported elastic stiffness of a single crystal zirconium. Through a comparison of calculated frequencies with those measured by RUS, elastic stiffness values have been determined very accurately by iteration and convergence processes.     

Scattering matrix approach to the resonant states and Q values of microdisk lasing cavities

We develop a scattering matrix approach for the numerical calculation of resonant states and Q values of a nonideal optical disk cavity with an arbitrary shape and with an arbitrary varying refraction index. The developed method is applied to study the effect of surface roughness and inhomogeneity of the refraction index on Q values of microdisk cavities for lasing applications. We demonstrate that even small surface roughness (deltar < or approximately equal to lambda/50) can lead to a drastic degradation of high-Q cavity modes by many orders of magnitude. The results of the numerical simulation are analyzed and explained in terms of wave reflection at a curved dielectric interface, combined with an examination of Poincaré surfaces of section and of Husimi distributions.     

Algorithm for calculating the complex scattering function of a metal sphere

A simple recurrent algorithm for calculating the complex scattering function of a metal sphere is proposed. The speed with which this function can be calculated by means of this algorithm is considered and it is shown that it is best to use cubic spline-interpolation of the complex scattering function of a spherical reflector to calibrate the high-frequency channel during measurements. Translated from Izmeritel'naya Tekhnika, No. 7, pp. 49–54, July, 1996.     

Response matrix of an extended Bonner sphere system

We have developed a system of Bonner spheres designed for use around high-energy accelerators. The upper energy limit of the system was extended using a lead radiator, which acts as an energy converter via the (n,xn) reaction. In addition, we use ¹¹C activation as an additional component integrated into the system and the spectra unfolding process. In the first version of the system, the lead radiator was present in only one sphere with diameter of 30.48 cm. The object of the present work was to investigate the geometry of the lead radiator and its use in moderators of several different sizes. As a result, we have developed a modular design and calculated the response matrix of the new system.     

Scattering of a plane wave by an anisotropic ferrite-coated conducting sphere

On the basis of the three-dimensional spherical vector wave functions in ferrite anisotropic media, and the fact that the first and second spherical vector wave functions in ferrite anisotropic media satisfy the same differential equations, the electromagnetic fields in homogeneous ferrite anisotropic media can be expressed as the addition of the first and second spherical vector wave functions in ferrite anisotropic media. Applying the continue boundary condition of the tangential component of electromagnetic fields in the interface between the ferrite anisotropic medium and free space, and the tangential electric field vanishing in the interface of the conducting sphere, the expansion coefficients of electromagnetic fields in terms of spherical vector wave function in ferrite medium and the scattering fields in free space can be derived. The theoretical analysis and numerical result show that when the radius of a conducting sphere approaches zero, the present method can be reduced to that of the homogeneous ferrite anisotropic sphere. The present method can be applied to the analyses of related microwave devices, antennas and the character of radar targets.     

Parameter identification of the homogeneous anisotropic hardening model using the virtual fields method

In this paper, the virtual fields method is applied to identify the constitutive parameters of the homogeneous yield function-based anisotropic hardening model. The procedure, previously developed for isotropic hardening law, is extended to the anisotropic case in this study. For validation purpose, a finite element model is developed to check the feasibility of the proposed methodology in retrieving the target constitutive parameters. The identification results are critically discussed. The suitability of this finite element model is also assessed with a view to future experiments.     

Analysis of electromagnetic scattering by uniaxial anisotropic bispheres

Based on the generalized multiparticle Mie theory and the Fourier transformation approach, electromagnetic (EM) scattering of two interacting homogeneous uniaxial anisotropic spheres with parallel primary optical axes is investigated. By introducing the Fourier transformation, the EM fields in the uniaxial anisotropic spheres are expanded in terms of the spherical vector wave functions. The interactive scattering coefficients and the expansion coefficients of the internal fields are derived through the continuous boundary conditions on which the interaction of the bispheres is considered. Some selected calculations on the effects of the size parameter, the uniaxial anisotropic absorbing dielectric, and the sphere separation distance are described. The backward radar cross section of two uniaxial anisotropic spheres with a complex permittivity tensor changing with the sphere separation distance is numerically studied. The authors are hopeful that the work in this paper will help provide an effective calibration for further research on the scattering characteristic of an aggregate of anisotropic spheres or other shaped anisotropic particles.     

Collisional rates for the inelastic Maxwell model: application to the divergence of anisotropic high-order velocity moments in the homogeneous cooling state

The collisional rates associated with the isotropic velocity moments ${\langle V^{2r}\rangle}$ and the anisotropic moments ${\langle V^{2r}V_i\rangle}$ and ${\langle V^{2r}(V_iV_j-d^{-1}V^2\delta_{ij})\rangle}$ are exactly derived in the case of the inelastic Maxwell model as functions of the exponent r, the coefficient of restitution ??, and the dimensionality d. The results are applied to the evolution of the moments in the homogeneous free cooling state. It is found that, at a given value of ??, not only the isotropic moments of a degree higher than a certain value diverge but also the anisotropic moments do. This implies that, while the scaled distribution function has been proven in the literature to converge to the isotropic self-similar solution in well-defined mathematical terms, nonzero initial anisotropic moments do not decay with time. On the other hand, our results show that the ratio between an anisotropic moment and the isotropic moment of the same degree tends to zero.     

On the Rayleigh surface waves on an anisotropic homogeneous thermoelastic half space

In this paper, we consider the propagation of surface waves in half spaces made of anisotropic homogeneous thermoelastic materials. When the thermal dissipative properties of a half space are taken into consideration, the undamped characteristic features of Rayleigh waves do not remain valid. Then, the process is irreversible and the Rayleigh waves are damped in time and dispersive. Here, we show that the Stroh formulation of the problem leads to a first-order linear partial differential system with constant coefficients. The associated characteristic equation (the propagation condition) is an eight degree equation with complex coefficients and, therefore, its solutions are complex numbers. Consequently, the secular equation results to be with complex coefficients, and therefore, the surface wave is damped in time and dispersed. The results are illustrated for the case of an orthotropic homogeneous thermoelastic half space, when an explicit bicubic form of the characteristic equation with complex coefficients is obtained. The analysis of these Rayleigh waves in a homogeneous orthotropic half space is numerically exemplified. Further, in the case of an isotropic homogeneous thermoelastic material, the characteristic equation is solved exactly and the general solution of the first-order differential system follows. On this basis, the Rayleigh-type surface waves are studied, and the dispersion condition is found.     

Analysis of the resonant scattering of light by cylinders at oblique incidence

We study the resonant scattering of light at oblique incidence by dielectric uncoated and coated cylinders. We develop a stable algorithm that permits us to calculate the resonances of a single dielectric cylinder as the tilting angle varies. This algorithm is based on semiclassical formulas for the distance between resonances. Results show that the resonances and the resonant electromagnetic energy flux near and internal to the cylindrical surface are highly sensitive to variations in the tilting angle. In addition, the coating effects are studied for scattering of light at oblique incidence by an infinite, perfect cylindrical conductor coated by a dielectric layer. In this case the resonance calculations show a peculiar similarity between this light scattering and atomic-molecular scattering. A physical interpretation for these effects is given, based on an analogy of optics and quantum mechanics.     

The radiation of an isothermal sphere with consideration of scattering

We have solved the problem of the radiation from an isothermal sphere with a spherical scattering indicatrix. We demonstrate that the emissivity of the sphere and of the plane layer, with consideration of scattering, can be approximately presented by a single function of the product resulting from the multiplication of the attenuation factor by the geometric characteristic of the radiating volume.