Light scattering by optically anisotropic scatterers: T-matrix theory for radial and uniform anisotropies

Material- and shape-dependent optical modes of hyperbolic spheroidal nano-resonators

Hyperbolic nanoresonators, composed of anisotropic materials with opposite signs of permittivity, have unique optical properties due to a large degree of freedom that hyperbolic dispersion provides in designing their response. Here, we focus on uniaxial hyperbolic nanoresonators composed of a model silver-silica multilayer in the form of spheroids with a broad aspect ratio encompassing both prolate and oblate particles. The origin and evolution of the optical response and mode coupling are investigated using both numerical (T-matrix and FDTD) and theoretical methods. We show the tunability of the optical resonances and the interplay of the shape and material anisotropy in determining the spectral response. Depending on the illumination conditions as well as shape and material anisotropy, a single hyperbolic spheroid can show a dominant electric resonance, behaving as a pure metallic nanoparticle, or a strong dipolar magnetic resonance even in the quasistatic regime. The quasistatic magnetic response of indicates a material-dependent origin of the mode, which is obtained due to coupling of the magnetic and electric multipoles. Such coupling characteristics can be employed in various modern applications based on metasurfaces.

Light scattering of a uniform uniaxial anisotropic sphere by an on-axis high-order Bessel vortex beam

Analytical solutions to the scattering of a uniform uniaxial anisotropic sphere illuminated by an on-axis high-order Bessel vortex beam (HOBVB) are investigated. Using the vector wave theory, the expansion coefficients of the incident HOBVB in terms of the spherical vector wave functions (SVWFs) are obtained. According to the orthogonality of the associated Legendre function and exponential function, more concise expressions of the expansion coefficients are derived. It can reinterpret the incident HOBVB faster compared with the expansion coefficients of double integral forms. The internal fields of a uniform uniaxial anisotropic sphere are proposed in the integrating form of the SVWFs by introducing the Fourier transform. The differences of scattering characteristics of a uniaxial anisotropic sphere illuminated by a zero-order Bessel beam, Gaussian beam, and HOBVB are exhibited. Influences of the topological charge, conical angle, and particle size parameters on the angle distributions of the radar cross section are analyzed in detail. The scattering and extinction efficiencies varied with the particle radius, conical angle, permeability, and dielectric anisotropy are also discussed. The results provide insights into the scattering and light-matter interactions and may find important applications in optical propagation and optical micromanipulation of biological and anisotropic complex particles.

Optical properties of spherulite opals

Spherulites are birefringent structures with spherical symmetry, typically observed in crystallized polymers. We compute the band structure of opals made of close-packed assemblies of highly birefringent spherulites. We demonstrate that spherulitic birefringence of constituent spheres does not affect the symmetries of an opal, yet significantly affects the dispersion of eigenmodes, leading to new pseudogaps in sections of the band structure and, consequently, enhanced reflectivity.

Light guiding and switching using eccentric core-shell geometries

High Refractive Index (HRI) dielectric nanoparticles have been proposed as an alternative to metallic ones due to their low absorption and magnetodielectric response in the VIS and NIR ranges. For the latter, important scattering directionality effects can be obtained. Also, systems constituted by dimers of HRI dielectric nanoparticles have shown to produce switching effects by playing with the polarization, frequency or intensity of the incident radiation. Here, we show that scattering directionality effects can be achieved with a single eccentric metallo-HRI dielectric core-shell nanoparticle. As an example, the effect of the metallic core displacements for a single Ag-Si core-shell nanoparticle has been analyzed. We report rotation of the main scattering lobe either clockwise or counterclockwise depending on the polarization of the incident radiation leading to new scattering configurations for switching purposes. Also, the efficiency of the scattering directionality can be enhanced. Finally, chains of these scattering units have shown good radiation guiding effects, and for 1D periodic arrays, redirection of diffracted intensity can be observed as a consequence of blazing effects. The proposed scattering units constitute new blocks for building systems for optical communications, solar energy harvesting devices and light guiding at the nanoscale level.

Optical trapping of the anisotropic crystal nanorod

We observed in the optical tweezers experiment that some anisotropic nanorod was stably trapped in an orientation tiled to the beam axis. We explain this trapping with the T-matrix calculation. As the vector spherical wave functions do not individually satisfy the anisotropic vector wave equation, we expand the incident and scattered fields in the isotropic buffer in terms of E→, and the internal field in the anisotropic nanoparticle in terms of D→, and use the boundary condition for the normal components of D→ to compute the T-matrix. We found that when the optical axes of an anisotropic nanorod are not aligned to the nanorod axis, the nanorod may be trapped stably at a tilted angle, under which the lateral torque equals to zero and the derivative of the torque is negative.

SCATTERING FROM SINGLE NANOPARTICLES: MIE THEORY REVISITED

Recent intense interest in nanoparticle materials and nanoparticle-based contrast enhancement agents for biophysical applications gives new relevance to Mie scattering theory in its original context of application. The Mie theory still provides the most exact treatment of scattering from single nanoparticles of the noble metals. When recast in terms of modern electrodynamic formalism, the theory provides a concise closed-form representation for the scattered fields and also serves as a vehicle to elaborate the formal electrodynamic technique. The behavior of the Debye truncation condition for the multipole expansion is illustrated with numerical examples, clearly showing the features of the transition between the Rayleigh, dipole and higher order multipole approximations for the scattered fields. The classical Mie theory is an approximation in that only the transverse field components are included in the calculation. Extensions to the classical theory which include the effects of longitudinal fields are discussed and illustrated numerically. The example of scattering from multilayer composite particles is used to examine the feasibility of engineering spectral features of the scattering cross-section to target the requirements of specific applications.

Opening up complete photonic bandgaps in three-dimensional photonic crystals consisting of biaxial dielectric spheres

In this paper, the scattering matrix of sphere with dielectric biaxial anisotropy is obtained exactly within the framework of the extended Mie theory. By incorporating the scattering matrix into the multiple scattering method, we study theoretically the photonic band structure of three dimensional photonic crystals consisting of biaxial dielectric spheres. Our results demonstrate that complete photonic bandgaps can be found in both fcc and sc lattice structures, which are absent in photonic crystals composed of isotropic dielectric spheres. Moreover we have compared our results with those coming from the photonic crystals consisting of the uniaxially birefringent dielectric spheres. It is found that because of the enhancement of the anisotropy, the degeneracy is lifted further, resulting in two neighboring photonic bandgaps, the lower one is complete while the upper one is partial existing only in some special regions of the first Brillouin zone.

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.

Mie scattering by an anisotropic object. Part II. Arbitrary-shaped object: differential theory

The differential theory of diffraction by an arbitrary-shaped body made of arbitrary anisotropic material is developed. The electromagnetic field is expanded on the basis of vector spherical harmonics, and the Maxwell equations in spherical coordinates are reduced to a first-order differential set. When discontinuities of permittivity exist, we apply the fast numerical factorization to find the link between the electric field vector and the vector of electric induction, developed in a truncated basis. The diffraction problem is reduced to a boundary-value problem by using a shooting method combined with the S-matrix propagation algorithm, formulated for the field components instead of the amplitudes.

Electromagnetic scattering by optically anisotropic magnetic particle

The Mie theory for electromagnetic scattering by spherical particle is extended to the case of magnetic particle with gyromagnetic type of permeability. Specifically, we first construct for the magnetic induction B(I) inside the particle a new set of vector basis functions, which are the solution of the wave equation for B(I) and expanded in terms of the usual vector spherical wave functions (VSWF's) with different values of wave vector k(l). The relationship between k(l) and the frequency is obtained as the eigenvalues of an eigensystem determined by the permeability tensor. The incident and scattered fields are expanded as usual in terms of the VSWF's. By matching the boundary conditions, a linear set of coupled equations for the expansion coefficients are obtained and then solved for the solution to the scattering problem. Preliminary numerical results are presented for the case in which the scattering is due solely to the optical anisotropy within the particle. The scattering efficiency is found to exhibit miscellaneous dependence on the incident angle, the polarization, the degree of anisotropy, as well as the size parameter. In addition, the possibility of the photonic Hall effect for one Mie scatterer is confirmed.