Multilayered Sphere Research Articles

Electromagnetic scattering by multi-layered spheres in a 2-D Gaussian beam

Based on formula of vector wave functions in spherical and cylindrical coordinates and their transformation relations，a new method to solve beam coefficients of a two dimensions (2-D) on-axis Gaussian beam is provided. An analyzical expansion of beam coefficients is obtained. With the help of generalized Lorentz Mie theory，electromagnetic scattering by multi-layered spheres in a 2-D Gaussian beam is deduced. Distribution of scattering intensity changing with scattering angle are simulated. A comparison of scattering intensity with results of incident plane wave is given.

Transparency Effect Induced by Elastic Metamaterials

In the quasi-static limit, it is shown that the neutral inclusion concept can be applied to predict the transparency phenomenon. The transparency designs for a coated ellip- soid for electromagnetic wave and a multilayered sphere for acoustic wave with metamaterials have been proposed. In this paper, we will show how to cloak a solid object with elastic wave metamaterial, where the shear wave in the system is nontrivial. Based on the Mie theory, it is shown that the efiective bulk modulus, mass density, and shear modulus of the assemblage made of the coated spheres dominate the zero, the flrst and the second order scattering coe-cients of one coated sphere, respectively. So letting the flrst three scattering coe-cients vanish, the isotropic coated metamaterial can be determined in order to make a spherical object transparent for elastic wave, this again corresponds to the neutral inclusion concept.

Modified Spherical Wave Functions With Anisotropy Ratio: Application to the Analysis of Scattering by Multilayered Anisotropic Shells

We describe a novel and rigorous vector eigenfunction expansion of electric-type Green's dyadics for radially multi- layered uniaxial anisotropic media in terms of the modified spherical vector wave functions, which can take into account the effects of anisotropy ratio systematically. In each layer, the material constitutions e and epsiv macrmu macr are tensors and distribution of sources is arbitrary. Both the unbounded and scattering dyadic Green's functions (DGFs) for rotationally uniaxial anisotropic media are derived in spherical coordinates (r, thetas, phi). The coefficients of scattering DGFs, based on the coupling recursive algorithm satisfied by the coefficient matrix, are derived and expressed in a compact form. With these DGFs obtained, the electromagnetic fields in each layer are straightforward once the current source is known. A specific model is proposed for the scattering and absorption characteristics of multilayered uniaxial anisotropic spheres, and some novel performance regarding anisotropy effects is revealed.

Multilayered Nanocrystalline SnO2 Hollow Microspheres Synthesized by Chemically Induced Self-Assembly in the Hydrothermal Environment

Multilayered nanocrystalline SnO2 hollow microspheres (HS−SnO2) were synthesized by chemically induced self-assembly in the hydrothermal environment. First, multilayered spherical SnO2−C composite was produced through a condensation polymerization and carbonization of sucrose accompanied by hydrolysis of SnCl4 in the hydrothermal reaction. Then, the HS−SnO2were obtained by removal of carbon via calcination. The as-prepared HS−SnO2 exhibit good electrochemical performance as the anode material in lithium ion batteries. Since this synthetic route is simple, convenient, and “green”, it is possible to extend this synthetic method to preparation of a wide range of the multilayered hollow spheres of metal oxides for functional material applications.

Debye series for Gaussian beam scattering by a multilayered sphere

The Debye series has been a key tool for the understanding of light scattering features, and it is also a convenient method for understanding and improving the design of optical instruments aimed at optical particle sizing. Gouesbet has derived the Debye series formulation for generalized Lorenz-Mie theory (GLMT). However, the scattering object is a homogeneous sphere, and no numerical result is provided. The Debye series formula for plane-wave scattering by multilayered spheres has been derived before. We have devoted our work to the Debye series of Gaussian beam scattering by multilayered spheres. The integral localized approximation is employed in the calculation of beam-shape coefficients (BSCs) and allows the study of the scattering characteristics of particles illuminated by the strongly focused beams. The formula and code are verified by the comparison with the results produced by GLMT and also by the comparison with the result for the case of plane-wave incidence. The formula is also employed in the simulation of the first rainbow by illuminating the particle with one or several narrow beams.

Fabrication of Hollow Hybrid Microspheres Coated with Silica/Titania via Sol−Gel Process and Enhanced Photocatalytic Activities

In this paper, we reported a facile and effective approach for fabrication of polystyrene (PS)/silica/titania hybrid microspheres and their resultant hollow double shell hybrid spheres with a smooth and uniform shell of SiO2/TiO2. In this approach, the cationic polystyrene spheres were first synthesized by emulsifier-free emulsion polymerization using the cationic initiator. Subsequently, the PS/SiO2/TiO2 multilayer hybrid spheres were successfully formed by two-step sol−gel methods. The as-prepared hybrid spheres were characterized by scanning electron microscopy, transmission electron microscopy, X-ray diffraction, energy dispersive X-ray spectroscopy (EDS), thermogravimetric analysis, ζ potential measurement, and N2 adsorption/desorption isotherm analysis. The effects of the titanium tetrabutoxide content, surfactant content, and the midlayer of silica on the morphology, porosity and mean pore size, specific surface area, and thermal property of the obtained hybrid spheres were systematically evaluated...

Acoustic wave transparency for a multilayered sphere with acoustic metamaterials

By analogy with the electromagnetic wave, the acoustic transparency phenomenon is analyzed for a multilayered sphere with acoustic metamaterials. The neutral-inclusion concept is used to predict the transparency conditions in the quasistatic case, which are further confirmed by a full-wave analysis. The mechanism of the transparency is based on lowering the total-scattering cross section of the composite sphere. It is found that, to improve the transparency, the angle-dependent scattering cross section must also be minimized for all directions.

Propagator-matrix Technique for the Viscoelastic Response of a Multi-layered Sphere to Surface Toroidal Traction

Propagator-matrix Technique for the Viscoelastic Response of a Multi-layered Sphere to Surface Toroidal Traction

Preparation of PS-Cores/Au Nanoparticles and Polyaniline-Shells Sub-Microspheres via Layer-by-Layer Method

Functional multi-layers containing polyaniline (PANI) /gold nanoparticles have been successfully decorated on the substrate of polystyrene (PS) latex spheres via layer-by-layer method. Gold nanoparticles were assembled on the surface of PS latex spheres via their consecutive electrostatic adsorption from solution, followed by the formation of polyaniline layer to obtain the PS-cores/ conductive polymer and Au-shells multi-layer spheres. FTIR spectroscopy, scanning electron microscopy (SEM) and transmission electron microscopy (TEM) confirmed the growth of gold nanoparticles and PANI layer on the PS colloidal particles.

Biosensing potential of silica/gold nanoshells: Sensitivity of plasmon resonance to the local dielectric environment

The sensitivity of the gold nanoshell localized plasmon resonance (LPR) to the local dielectric environment is studied in terms of a multilayered sphere with a silica core, gold nanoshell, and two dielectric layers modeling the primary functionalization of gold surface and the secondary binding of target biomolecules. The adsorption-induced changes in the extinction and scattering spectra are analyzed by the dipolar Rayleigh approximation and multilayered Mie codes for gold shell diameters of 20–160 nm and (gold shell thickness)/(gold shell diameter) ratios of 0.025–0.75. To calculate the optical polarizability of a multilayered particle, we develop a simple analytical method based on the dipole equivalency principle as applied to a multilayered conjugate and its homogeneous counterpart. This is used to derive simple relations between the local dielectric environment parameters and the gold nanoshell structure. Our analysis predicts greater sensitivity of nanoshell's LPR to the local dielectric environment compared to the solid gold spheres, whereas the absolute changes in spectral maxima are less than those for the equivolume spheres. By contrast, the differential extinction and scattering spectra of gold nanoshells can be used as a sensitive tool for optical monitoring of biomolecular binding onto nanoshell surface. The maximal local-environment sensitivity has been found for the gold (shell/radius) ratios within the range 0.2–0.4.

Debye Series Analysis of Forward Scattering by a Multi-layered Sphere

A formula of Debye series for forward scattering by a multi-layered sphere is presented. The Debye series expansion allows for the decomposition of the global scattering process in a series of local interactions, and clarifies the physical origins of many effects that occur in electromagnetic scattering. The forward-scattering pattern contains many information about the properties, and the method is widely used for determining such properties on the basis of forward-scattering pattern. In the paper, the Debye series is employed to the study of forward scattering by a multi-layered sphere, which is of great importance to the study of characteristics of particles. DOI: 10.2529/PIERS060906223536 For many practical applications such as combustion, environmental control, fluid mechanics, and chemical reaction, we need to measure the properties of particles such as size and refractive indextemperature ratio quickly and precisely. The forward-scattering pattern contains many information about the properties, and it is widely used for determining such properties on the basis of forwardscattering pattern. The scattering of a plane electromagnetic wave by a single multilayered spherical particle has been extensively discussed within a theoretical framework similar to the Lorenz-Mie Theory (LMT) in many areas of theoretical and applied research, such as combustion, chemical engineering, remote sensing, communication, biology, and medicine [1]. The Mie theory is a rigorous solution of the Maxwell equations and contains all effects that contribute to the scattering [2, 3]. But it gives few clues to the various physical processes that are responsible for the scattering [2–4]. Full geometrical optics theory can be used with reasonable accuracy for forward direction light scattering computations related to particle sizing and characterization [5], and has been extended to forward scattering by coated particles [6]. But as soon as the scatters are complicated, for instance multi-layered sphere, the construction of the geometrical optics approximation formula is very difficult. The Debye series writes each term of the Mie series as another infinite series, and clarifies the physical origins of many effect that occur in electromagnetic scattering [2, 3], which is of great importance in the study of characteristics of electromagnetic scattering. The Debye series was originally formulated for scattering of a normally incident plane wave by a cylinder [7] and has been subsequently extended to scattering by a sphere [8, 9], the internal fields [10], scattering by a coated sphere [11], scattering of a plane wave diagonally incident on a cylinder [12], and scattering by a multilayered sphere [2] and a spherical Bragg grating [13]. We consider an l-layered dielectric sphere whose refractive index of any layer j is mj (region j) and whose radius a is embedded in a dielectric medium of refractive index ml+1 (region l + 1), as shown in Fig. 1. When the sphere is illuminated by a monochromatic plane wave of wavelength λ, the classic Mie coefficients an and b l n can be expanded in the Debye series [2] an bn }

Design for electromagnetic wave transparency with metamaterials

With the help of the "neutral inclusion" concept, the conditions of electromagnetic wave transparency for multilayered spheres, coated spheroids, and general particulate composites are analytically derived in the quasistatic case. The basic idea is to make the effective material property of a composite region equal to that of the surrounding medium. The general full-wave analysis shows that the obtained quasistatic conditions are useful in designing the electromagnetically transparent materials.

Optical trapping of a spherically symmetric sphere in the ray-optics regime: a model for optical tweezers upon cells

Since their invention in 1986, optical tweezers have become a popular manipulation and force measurement tool in cellular and molecular biology. However, until recently there has not been a sophisticated model for optical tweezers on trapping cells in the ray-optics regime. We present a model for optical tweezers to calculate the optical force upon a spherically symmetric multilayer sphere representing a common biological cell. A numerical simulation of this model shows that not only is the magnitude of the optical force upon a Chinese hamster ovary cell significantly three times smaller than that upon a polystyrene bead of the same size, but the distribution of the optical force upon a cell is also much different from that upon a uniform particle, and there is a 30% difference in the optical trapping stiffness of these two cases. Furthermore, under a small variant condition for the refractive indices of any adjacent layers of the sphere, this model provides a simple approximation to calculate the optical force and the stiffness of an optical tweezers system.

Theory of light emission in sonoluminescence as thermal radiation

Based on the model proposed by Hilgenfeldt [Nature (London) 398, 401 (1999)], we present here a comprehensive theory of thermal radiation in single-bubble sonoluminescence (SBSL). We first invoke the generalized Kirchhoff's law to obtain the thermal emissivity from the absorption cross section of a multilayered sphere (MLS). A sonoluminescing bubble, whose internal structure is determined from hydrodynamic simulations, is then modeled as a MLS and in turn the thermal radiation is evaluated. Numerical results obtained from simulations for argon bubbles show that our theory successfully captures the major features observed in SBSL experiments.

Debye series for light scattering by a multilayered sphere

We have derived the formula for the Debye-series decomposition for light scattering by a multilayered sphere. This formulism permits the mechanism of light scattering to be studied. An efficient algorithm is introduced that permits stable calculation for a large sphere with many layers. The formation of triple first-order rainbows by a three-layered sphere and single-order rainbows and the interference of different-order rainbows by a sphere with a gradient refractive index, are then studied by use of the Debye model and Mie calculation. The possibility of taking only one single mode or several modes for each layer is shown to be useful in the study of the scattering characteristics of a multilayered sphere and in the measurement of the sizes and refractive indices of particles.

Debye series analysis of scattering of a plane wave by a spherical Bragg grating

The Debye series decomposition of the partial-wave scattering amplitudes of a multilayer sphere is derived. The partial-wave transmission and reflection terms appearing in the Debye series are multiple-scattering amplitudes written in terms of four basic quantities and combined together layer by layer in an identical way. The resulting expressions are then used to calculate the scattered intensity of a spherical Bragg grating covering a dielectric core particle and to analyze a number of new structures appearing in the scattered intensity.

Multilayered metal core-shell nanostructures for inducing a large and tunable local optical field

We examine the near-field optical properties of multilayered metal core-shell sphere nanostructures by extending the Mie theory, and demonstrate that the local-field enhancement can be increased by adding new metal shells. A local intensity enhancement of more than 10(5) times can be obtained in the cavity between the Ag core and the innermost Ag shell for proper configurations of multilayered Ag core-shell spheres. The high enhancement can be tuned from the red to the infrared region by varying the configurations of the core-shell nanostructures.

Melting Behavior of Copper Nanocrystals Encapsulated in Onion-like Carbon Cages

Nanoparticulate materials are promising objects for studying the processes that triggermelting of solids. On a pyrolytic route, we successfully encapsulated 20–60 nm diameter Cu nanocrystals within multilayer graphitic carbon spheres. In situ electron microscope observations of the melting and displacement of the encapsulated Cu nanocrystals at temperatures up to 1175 K have provided clear evidence of the process of surface melting and its dependence on the quality of the metal/carbon interface. Detection of crystal defects inside the Cu particles during melting and vaporization has proved that the metal phase maintains its solid crystalline state in the particle center. Indications of the influence of surface anisotropy on the melting behavior were obtained. The carbon cages as a whole remained unchanged during the observations.

Multishell bimetallic AuAg nanoparticles: synthesis, structure and optical properties

Core–shell and multishell bimetallic AuAg nanoparticles have been synthesized by successive reduction of metal salts with ascorbic acid on pre-made seeds in the presence of a cationic surfactant, cetyltrimethylammonium bromide (CTAB). The coverage of the seeds is extremely uniform, although in some cases deviations from a spherical shape are observed with the formation of nanorods or nanoprisms. The evolution of the optical properties as further metal layers are deposited is very dramatic and can be modelled using Mie theory for multilayer spheres. However, preliminary results using high-resolution STEM-XEDS elemental mapping suggest that the actual distribution of the two metals within the multilayer spheres may involve (partial) alloying of the metals.

Modelling the optical properties of composite and porous interstellar grains

There are indications that interstellar and interplanetary dust grains have an inhomogeneous and fluffy structure. We investigate different methods to describe light scattering by such composite particles. Both a model of layered particles and discrete dipole calculations for particles with Rayleigh and non-Rayleigh inclusions are used. The calculations demonstrate that porosity is a key parameter for determining light scattering. We find that the optical properties of the layered particles depend on the number and position of layers if the number of layers is small ($\la 15$). For a larger number of layers the scattering characteristics become independent of the layer sequence. The optical properties of particles with inclusions depend on the size of inclusions provided the porosity is large. The scattering characteristics of very porous particles with inclusions of different sizes are found to be close to those of multi-layered spheres. We compare the results of these calculations with the predictions of the effective medium theories (EMT) which are often used in astronomy as a tool to calculate the optical properties of composite particles. The results of our analysis show that the internal structure of grains (layers versus inclusions) only slightly affects the optics of particles provided the porosity does not exceed 50%. It is also demonstrated that in this case the optical properties of composite grains calculated with EMT agree with the results of the exact method for layered particles. For larger porosity, the standard EMT rules (i.e., Garnett and Bruggeman rules) give reliable results for particles with Rayleigh inclusions only.