Dielectric Sphere Research Articles

Interaction of Two Charged Dielectric Spheres with a Point Charge

Interaction of Two Charged Dielectric Spheres with a Point Charge

Experimental evaluation of Luneburg lens using radial holes for relative permittivity distribution

In this paper, we describe a novel 3-D Luneburg lens using radial holes. A Luneburg lens can suppress the side lobe of the antenna and increase the gain. The prototype Luneburg lens was fabricated using a 30mm radius dielectric sphere with uniform permittivity by 2.1 and many holes by 1mm radius, called radial holes drilled vertically on the sphere surface. The relative permittivity distribution of the Luneburg lens is realized by changing the number and depth of five types of holes. To confirm the effectiveness of the fabricated Luneburg lens, the far-field radiation pattern at 25GHz was measured using a flanged rectangular waveguide as a wave source. It achieved a high gain of 22.4dBi. The measured radiation pattern generally agreed well with the theoretical radiation pattern of the Luneburg lens, and the validity of the Luneburg lens with radial holes at the quasi-millimeter wave was confirmed. It can be used for beam steering in 5G/6G base stations.

Space-resolved chemical information from infrared extinction spectra

A new method is presented for the extraction of the complex index of refraction from the extinction efficiency, Q_{ext} {({tilde{nu }})}, of homogeneous and layered dielectric spheres that simultaneously removes scattering effects and corrects measured extinction spectra for systematic experimental errors such as baseline shifts, tilts, curvature, and scaling. No reference spectrum is required and fit functions may be used that automatically satisfy the Kramers–Kronig relations. Thus, the method yields the complex refractive index of a sample for unambiguous interpretation of the chemical information of the sample. In the case of homogeneous spheres, the method also determines the radius of the sphere. In the case of layered spheres, the method determines the substances within each layer. Only a single-element detector is required. Using numerically computed Q_{ext}({tilde{nu }}) data of polymethyl-methacrylate and polystyrene homogeneous and layered spheres, we show that the new reconstruction algorithm is accurate and reliable. Reconstructing the complex refractive index from a published, experimentally measured raw absorbance spectrum shows that the new method simultaneously corrects spectra for scattering effects and, given shape information, corrects raw spectra for systematic errors that result in spectral distortions such as baseline shifts, tilts, curvature, and scaling.

Terahertz Microjets as Realizations of Subwavelength Focusing in the Terahertz Spectrum

In this article, we recognize the growing interest to realize terahertz (THz) spectroscopy on the submillimetre scale and target its fundamental challenge—in the need for subwavelength focusing. The challenge is addressed here by way of the THz microjet. We show that THz microjets can be formed as intense focal spots with subwavelength sizes by focusing THz radiation through engineered dielectric spheres. The dielectric spheres are analyzed via the electromagnetic (Mie) theory and effective medium (Bruggeman) theory, and then implemented out of microcomposite material with the requisite (optimal) refractive indices and (minimal) extinction coefficients for the targeted 0.3–0.7-THz spectrum. Ultimately, the dielectric spheres are tested and found to realize THz microjets as intense focal spots with the desired subwavelength sizes.

Mathematical Analysis of Conducting and Dielectric Sphere in Fractional Space

This paper presents an analytical analysis of a sphere placed in fractional dimensional space. The Laplacian Equation in fractional space describes physics as a complex phenomenon. The general solution of the Laplacian equation in fractional space is obtained by the separable variable technique. We have investigated a close form solution for conducting sphere and dielectric sphere. Further, the electric potential and charge density, induced due to a point charge is calculated in fractional space, and also the energy radiated by the sphere is determined. The results are compared with the classical results by setting the fractional parameter α = 3 which normally lies in the limit 2 < α ≤ 3.

Unraveling Dipolar Regime and Kerker Conditions in Mid‐Index Mesoscale Dielectric Materials

AbstractNanophotonic phenomena, such as zero optical back scattering, nonradiating anapole states, etc. are related to the excitation of single dipolar modes—hence so far, they have only been observed within a few relatively high‐index dielectric materials (refractive index, n > 3.5) in the nanoscale regime at the optical frequencies. Here, dipolar regime is unraveled, close‐to‐zero backscattering is demonstrated, and optical anapoles are excited in mid‐index dielectric spheres (titanium di‐oxide, TiO2; n ≈ 2.6) at the mesoscale regime (particle diameter, d ≈ incident wavelength, λ) under illumination with tightly focused Gaussian beams (TFGBs). Successive scattering minima associated with dipolar excitation are observed satisfying the first Kerker condition in the scattering spectra of single TiO2 spheres with diameters in the micrometer range. Moreover, at specific wavelengths, the electric and magnetic dipolar scattering amplitudes of the dielectric microspheres simultaneously go close‐to‐zero, leading to the excitation of hybrid optical anapoles with a total scattering intensity ≈ 5 times weaker for TFGB illumination with numerical aperture, NA ≈ 0.95 compared to NA ≈ 0.1. The result pushes the boundary of the observation of nanophotonic phenomena to a new regime with regards to type and size of the materials.

Arbitrary-Shape Dielectric Particles Interacting in the Linearized Poisson-Boltzmann Framework: An Analytical Treatment.

This work considers the interaction of two dielectric particles of arbitrary shape immersed into a solvent containing a dissociated salt and assuming that the linearized Poisson-Boltzmann equation holds. We establish a new general spherical re-expansion result which relies neither on the conventional condition that particle radii are small with respect to the characteristic separating distance between particles nor on any symmetry assumption. This is instrumental in calculating suitable expansion coefficients for the electrostatic potential inside and outside the objects and in constructing small-parameter asymptotic expansions for the potential, the total electrostatic energy, and forces in ascending order of Debye screening. This generalizes a recent result for the case of dielectric spheres to particles of arbitrary shape and builds for the first time a rigorous (exact at the Debye-Hückel level) analytical theory of electrostatic interactions of such particles at arbitrary distances. Numerical tests confirm that the proposed theory may also become especially useful in developing a new class of grid-free, fast, highly scalable solvers.

Polarizabilities and electric field-induced forces in periodic two-component linear dielectric sphere chains

Idealized single-stranded linear chains of dielectric spheres in a dielectric medium can be used as a model system for electric field-induced particle chaining in complex systems, such as electrorheological fluids. The polarizability of the spheres in the chains and the interparticle (bonding) forces between them determine the macroscopic (e.g. dielectric, rheological) behavior of the bulk. We have derived new analytical equations for the bonding forces in a linear, bidisperse chain, where two components with different sizes form a periodic structure. The force equations were obtained on the basis of local field strength at the particle sites by taking into account the interactions beyond the nearest neighbors within the chain. The dependence of the bonding force and the local field strength on the ratio of particle sizes was investigated. As an application the dielectric permittivity of a bulk model system with bidisperse chains was calculated using the Clausius–Mossotti equation.

Comparison of Electromagnetic Forces Evaluated in Yee-Lattice Finite-Difference Time-Domain and Lattice-Boltzmann Method

Electrodynamic simulations in the Yee-lattice finite-difference time-domain method (YL-FDTDM) require half-unit-cell and half-time-unit offsets between electric and magnetic field components. To evaluate energy, momentum, and force in the YL-FDTDM, electric and magnetic fields must be colocated in both space and time. Colocation operations can be computationally intensive while introducing implementation complexity and numerical error. As an alternative to the YL-FDTDM, the Hauser and Verhey electrodynamic lattice-Boltzmann method (HV ELBM) is implemented on a single lattice representing electric and magnetic fields at the same location and time. Since colocation is not required on a single lattice, its central differences are simpler to implement and more accurate. Continuous plane-wave scattering of electric and magnetic fields from a nondispersive dielectric sphere is solved using the YL-FDTDM, the HV ELBM, and Mie scattering analysis. The YL-FDTDM and HV ELBM are compared in terms of numerical error and computational time representing the analytical Mie solution for the Einstein and Laub time-averaged force density. The HV ELBM requires less computational time to evaluate a time-averaged force density with half the error of the YL-FDTDM. At a similar absolute error, the HV ELBM evaluates a time-averaged force density in less than 10% of the computational time.

Scattering by circularly symmetric structured optical fields in stratified media

Structured optical fields (SOFs) with spatially inhomogeneous phase, amplitude, or polarization can excite substantially different optical responses in nanoscale scattering particles. Inhibition of low-order multipolar resonances, excitation of dark modes and anapoles, and spin and orbital angular momenta dichroism have been demonstrated, broadening the scope of nanoscale manipulations of optical resonances by using these engineered external SOFs. However, studying scattering effects illuminated by SOFs is more complicated than conventional plane wave illuminations, and the difficulty increases for scattering particles on a substrate. In this paper, we present explicit expressions of SOFs propagating through stratified media, or multilayered systems, and provide their beam-shape coefficients. Specifically, simple analytic expressions are provided for circularly symmetric Bessel beams passing through an interface. Then, scattering calculations for a dielectric sphere on a substrate illuminated by an evanescent optical vortex are performed via the $T$-matrix method, which yields accurate and efficient results as compared with finite element analysis. This paper will find practical applications in modeling SOFs for realistic configurations of scattering of particles on a substrate at nonplanar nonparaxial external light source illuminations.

Efficient Full-Wave Modeling of Microwave Components With Interval-Valued Electromagnetic Parameters by Polynomial Chaos Expansion-Based DGTD Method

An efficient polynomial chaos expansion (PCE)-based discontinuous Galerkin time-domain (DGTD) method is proposed to analyze microwave components with interval-valued electromagnetic (EM) parameters. The proposed method retains the flexibility of the conventional DGTD method in the element-level domain decomposition and parallel computing. Numerical examples with the interval-valued electron density of plasma and permittivity of a dielectric block are presented to demonstrate the accuracy and capability of the proposed method. The scattering from a dielectric sphere with an interval-valued permittivity is evaluated to verify the applicability of the proposed method in unbounded scattering analysis. Numerical results illustrate that the proposed PCE-based DGTD method has great superiority in computational accuracy and efficiency over the Gaussian process (GP) technique and the Monte Carlo (MC) method in both deterministic and stochastic analyses with the interval-valued parameters, and it requires only a single simulation to obtain all results in the high-dimensional interval domains.

Purcell-induced suppression of superradiance for molecular overlayers on noble atom surfaces.

We study the impact of an environment on the electromagnetic responses of a molecule in the presence of a dielectric medium. By applying the dipole-dipole coupling between the molecule's and the environment's degrees of freedom, we can reduce the complex system into its components and predict excitation lifetimes of single and few molecules attached to a dielectric surface by knowing the entire quantum-mechanical properties of the molecules, such as transition energies and dipole moments. The derived theory allows for the description of superradiance between two molecules depending on the geometric arrangement between both concerning their separation and orientation with respect to each other. We analyze the possibility of superradiance between two molecules bound to a dielectric sphere and determine a change in the relevant length scale where the usually considered wavelength in free space is replaced with the binding distance, drastically reducing the length scales at which collective effects can take place.

Optical radiation force on a dielectric sphere by a polarized Airy beam.

The optical radiation force acting on a homogeneous and lossless dielectric spherical particle by a polarized Airy beam is analyzed in terms of the generalized Lorenz-Mie theory. The transverse and longitudinal radiation force components are theoretically evaluated and numerically simulated, emphasizing the transverse scale ω0, attenuation parameter γ, and polarization of the incident Airy beam versus the size parameter ka of the sphere. These results reveal that a polarized Airy beam can trap the dielectric sphere in its main caustic or sidelobes of the beam by the optical transverse force and be guided along the parabolic trajectory of the longitudinal optical force. Moreover, γ and ω0 of the Airy beams and ka of the dielectric sphere can affect the amplitude and distribution of the optical force components. This research may be helpful for the development of Airy optical tweezers in applications involving particle manipulation, optical levitation, particle sorting, and other emergent areas.

Optical Force of Bessel Pincer Light-Sheets Beam on a Dielectric Sphere of Arbitrary Size.

In the framework of Generalized Lorenz-Mie theory (GLMT), based on the expansion results of electromagnetic field radiation components of Bessel pincer light sheets beam acting on dielectric particles of arbitrary size, the expression of radiation force components in a Cartesian coordinate system is obtained by using the Maxwell stress tensor method. On the one hand, the effects of the refractive index and the equivalent radius of spherical particles on the distribution of radiation force are discussed; On the other hand, the influence of beam scaling parameter and beam order of Bessel pincer light sheets beam on the distribution of radiation force are investigated. The results indicate that the changes of particle's refractive index and effective radius only affect the distribution of radiation force. However, the beam scaling parameter and beam order of Bessel pincer light sheets beam have a very sharp impact on the convergence position, distribution range and bending degree far away from the wave source of the radiation force. Single-beam optical tweezers using the self-focusing and self-bending Bessel pincer light-sheets beam are crucial for applications such as single molecule biophysics, optical manipulation and particle separation/clearing.

Comparison of 2.5D finite element formulations with perfectly matched layers for solving open axisymmetric electromagnetic cavity problems

AbstractAxial symmetry in time‐harmonic electromagnetic wave problems can be exploited by considering a Fourier expansion along the angular direction, reducing fully three‐dimensional computations to two‐dimensional ones on an azimuthal cross section. While this transition leads to a significant decrease in computational effort, it introduces additional difficulties, which necessitate appropriate finite element (FE) formulations. By combining the latter with perfectly matched layers (PML), open problems can be considered. In this work, we compare and discuss the performance of different combinations of axisymmetric FE formulations and PMLs, using a dielectric sphere in open space as a test case. As an application example, a superconducting Fabry–Pérot photon trap is considered.

Electromechanical Modeling of Rolling Spherical Triboelectric Nanogenerators Considering Nonlinear Effects

AbstractIn this study, electromechanical coupling modeling and analysis of the rolling spherical triboelectric nanogenerators (RS‐TENG) considering nonlinear effects are conducted. After a brief review of the power generation mechanism, a capacitance‐fitting model of the RS‐TENG spherical electrode is proposed. By using the energy principle and differential equations of equivalent circuits, an electromechanical coupling model is established by considering the nonlinear variation in the dielectric sphere rolling angle. Using the harmonic balance method (HBM), the dynamic output characteristics of the RS‐TENG are analytically solved. Numerical integration and dynamic tests are used to verify the accuracy of HBM results. By comparing the changes in the RS‐TENG output performance with and without the nonlinear effect, it is shown that the model proposed in this study can effectively avoid the underestimation of the operation bandwidth (a relative increment of 43%) and overestimation of the maximum power density (a relative decrement of 32%), and significantly improve the accuracy of the RS‐TENG performance estimation. The influence of design parameters on the dynamic output characteristics of the system is discussed. The fitting coefficients obtained from the parameter influence discussion can be used as the basis for the RS‐TENG output performance design.

Near-field analysis of electromagnetic chirality in the Mie scattering by a dielectric sphere

We revisit the Mie scattering in view of electromagnetic chirality, especially in the near field of a scattering sphere. To this goal, we take the simplest two-dielectric system where both an embedding medium and an embedded sphere are loss-free, non-magnetic, and dielectric. For a given linearly polarized incident wave, the net chirality should vanish when integrated over the whole space. The reactive chirality indicating the divergence-full spin angular momentum density shows an analogous behavior. Meanwhile, the electromagnetic chirality obtained in response to a circularly polarized incident wave exhibits distinct super-chiral behaviors. In addition, we examined key bilinear parameters for another incident wave, where two orthogonal linearly polarized waves are combined without a phase delay.

Colored passive daytime radiative cooling coatings based on dielectric and plasmonic spheres

Passive daytime radiative cooling (PDRC) is a promising alternative to current compression-based cooling systems, which can directly radiate energy into outer space with a high thermal emittance (ε¯LWIR) in the long-wavelength infrared atmospheric transmission window. It’s critical to enhance solar reflectance (R¯solar) to avoid solar heating in the daytime. Meanwhile, the super-­white color is generally not desirable due to aesthetics. Here, we design a bilayer coating that simultaneously achieves colored PDRC by using the optimized SiO2 microspheres for PDRC in the underlayer and intrinsic narrow absorption of plasmonic nanospheres for color in the thin top layer. Experimental results indicate that R¯solar and ε¯LWIR of the white SiO2 coating can be optimized as: R¯solar = 0.942 and ε¯LWIR = 0.931. Furthermore, R¯solar of the colored PDRC coating with the Au layer would weaken slightly to be 0.859, ε¯LWIR still maintains as 0.933. Note that both of them are higher than that of the commercial coatings (R¯solar = 0.836, ε¯LWIR = 0.925). Under the direct sunlight of ∼881 W/m2, the white PDRC coating achieves a temperature decrease of up to 10.9 °C, which is 7.5 °C (with Au layer) and 5.1 °C (with an Ag layer) for colored PDRC coatings. In addition, the PDRC coating has great storage stability, excellent water repellency, substrate adaptability, and fire resistance, allowing it suitable and practical for large-scale commercial and sustainability applications.

Effects of the coupling of dielectric spherical particles on signatures in infrared microspectroscopy

Infrared microspectroscopy is a powerful tool in the analysis of biological samples. However, strong electromagnetic scattering may occur since the wavelength of the incident radiation and the samples may be of comparable size. Based on the Mie theory of single spheres, correction algorithms have been developed to retrieve pure absorbance spectra. Studies of the scattering characteristics of samples of different types, obtained by microspectroscopy, have been performed. However, the detailed, microscopic effects of the coupling of the samples on signatures in spectra, obtained by infrared microspectroscopy, are still not clear. The aim of this paper is to investigate how the coupling of spherical samples influences the spectra. Applying the surface integral equation (SIE) method, we simulate small dielectric spheres, arranged as double-spheres or small arrays of spheres. We find that the coupling of the spheres hardly influences the broad oscillations observed in infrared spectra (the Mie wiggles) unless the radii of the spheres are different or the angle between the direction of the incident radiation and the normal of the plane where the spheres are located is large. Sharp resonance features in the spectra (the Mie ripples) are affected by the coupling of the spheres and this effect depends on the polarization of the incident wave. Experiments are performed to verify our conclusions.

Optical Phenomena in Dielectric Spheres Several Light Wavelengths in Size: A Review

Optical Phenomena in Dielectric Spheres Several Light Wavelengths in Size: A Review