Spherical Scatterers Research Articles

Быстрый метод анализа возмущения электромагнитного поля малыми сферическими рассеивателями

Быстрый метод анализа возмущения электромагнитного поля малыми сферическими рассеивателями

Invariance Principle for the Random Lorentz Gas\u2014Beyond the Boltzmann-Grad Limit

We prove the invariance principle for a random Lorentz-gas particle in 3 dimensions under the Boltzmann-Grad limit and simultaneous diffusive scaling. That is, for the trajectory of a point-like particle moving among infinite-mass, hard-core, spherical scatterers of radius r, placed according to a Poisson point process of density varrho , in the limit varrho rightarrow infty , rrightarrow 0, varrho r^{2}rightarrow 1 up to time scales of order T=o(r^{-2}left| {log r}right| ^{-2}). To our knowledge this represents the first significant progress towards solving rigorously this problem in classical nonequilibrium statistical physics, since the groundbreaking work of Gallavotti (Phys Rev 185:308–322, 1969, Nota Interna Univ di Roma 358, 1970, Statistical mechanics. A short treatise. Theoretical and mathematical physics series, Springer, Berlin, 1999), Spohn (Commun Math Phys 60:277–290, 1978, Rev Mod Phys 52:569–611, 1980) and Boldrighini–Bunimovich–Sinai (J Stat Phys 32:477–501, 1983). The novelty is that the diffusive scaling of particle trajectory and the kinetic (Boltzmann-Grad) limit are taken simultaneously. The main ingredients are a coupling of the mechanical trajectory with the Markovian random flight process, and probabilistic and geometric controls on the efficiency of this coupling. Similar results have been earlier obtained for the weak coupling limit of classical and quantum random Lorentz gas, by Komorowski–Ryzhik (Commun Math Phys 263:277–323, 2006), respectively, Erdős–Salmhofer–Yau (Acta Math 200:211–277, 2008, Commun Math Phys 271:1–53, 2007). However, the following are substantial differences between our work and these ones: (1) The physical setting is different: low density rather than weak coupling. (2) The method of approach is different: probabilistic coupling rather than analytic/perturbative. (3) Due to (2), the time scale of validity of our diffusive approximation—expressed in terms of the kinetic time scale—is much longer and fully explicit.

4D Optically Reconfigurable Volumetric Metamaterials

Metamaterials are artificially created media, which allow introducing additional degrees of freedom into electromagnetic design by controlling constitutive material parameters. Reconfigurable time‐dependent metamaterials can further enlarge those capabilities by introducing a temporal variable as an additional controllable parameter. Herein, a first‐of‐its‐kind reconfigurable volumetric metamaterial‐based scatterer is demonstrated, wherein the electromagnetic properties are controlled dynamically with light. In particular, hybridized resonances in arrays of split ring resonators give rise to a collective mode that presents properties of artificial high‐frequency magnetism for centimeter waves. Resonant behavior of each individual ring is controlled with a photocurrent, which allows the fast tuning of macroscopic effective permeability. Thus, the artificial gigahertz magnon resonant excitation within a subwavelength spherical scatterer is governed by light intensity. 4D control over electromagnetic scattering in both space and time opens new avenues for modern applications, including wireless communications and automotive radars to name just a few.

Minimalist Mie coefficient model.

When considering light scattering from a sphere, the ratios between the expansion coefficients of the scattered and the incident field in a spherical basis are known as the Mie coefficients. Generally, Mie coefficients depend on many degrees of freedom, including the dimensions and electromagnetic properties of the spherical object. However, for fundamental research, it is important to have easy expressions for all possible values of Mie coefficients within the existing physical constraints and which depend on the least number of degrees of freedom. While such expressions are known for spheres made from non-absorbing materials, we present here, for the first time to our knowledge, corresponding expressions for spheres made from absorbing materials. To illustrate the usefulness of these expressions, we investigate the upper bound for the absorption cross section of a trimer made from electric dipolar spheres. Given the results, we have designed a dipolar ITO trimer that offers a maximal absorption cross section. Our approach is not limited to dipolar terms, but indeed, as demonstrated in the manuscript, can be applied to higher order terms as well. Using our model, one can scan the entire accessible parameter space of spheres for specific functionalities in systems made from spherical scatterers.

‘Killing Mie Softly’: Analytic Integrals for Complex Resonant States

Summary We consider integrals of products of Bessel functions and of spherical Bessel functions, combined with a Gaussian factor guaranteeing convergence at infinity. These integrals arise in wave and quantum mechanical scattering problems of open systems containing cylindrical or spherical scatterers, particularly when those problems are considered in the framework of complex resonant modes. Explicit representations are obtained for the integrals, building on those in the 1992 paper by McPhedran, Dawes and Scott. Attention is paid to those sums with a distributive part arising as the Gaussian tends towards the unit function. In this limit, orthogonality and normalisability of complex modes are investigated.

Scattering Into Guided Modes Due to Imperfect Graded-Index Structure in Polymer Optical Fibers

Rayleigh scattering in graded-index polymer optical fibers (GI-POF) is studied under the assumption that spherical scatterers are uniformly distributed within the layers of concentric ring structure. This approximation allows to describe typical imperfections occurring during the fabrication of GI-POFs. For the purpose of experimental characterization by side illumination, an analytical model of the light conversion into waveguide modes has been developed. This model describes the mode excitation by a multiplicative contribution of three different physical mechanisms. The corresponding experimental analysis of the light scattering has been performed and compared with numerical simulation results for the fibers with single-ring and multi-ring structures. Besides the application to GI-POFs, this article can be also applied to multi-step index fibers.

Efficient computation of arbitrary beam scattering on a sphere

Electromagnetic scattering on a sphere is one of the most fundamental problems, which has a closed form analytical solution in the form of Mie series. Being initially formulated for a plane incident wave, the formalism can be extended to more complex forms of incident illumination. Here we present a fast calculation approach to address the scattering problem in the case of arbitrary illumination, incident on a spherical scatterer. This method is based on the plane wave decomposition of the incident illumination and weighted integration of Mie solutions, rotated to a global coordinate system. Tabulated solutions, sampled with an accurately level of sparsity, and efficient rotational transformations allow performing fast calculations on electrically large structures, outperforming capabilities relatively to other numerical techniques. Our approach is appropriate for real-time analysis of electromagnetic scattering from electrically large objects, which is essential for monitoring and control applications, such as optomechanical manipulation, scanning microscopy, and fast optimization algorithms.

Characteristic Mueller matrices for direct assessment of the breaking of symmetries.

Mueller polarimetry is a powerful optical technique in the analysis of micro-structural properties of optical samples. However, there is no explicit relationship between individual Mueller matrix elements and the physical properties of the sample. Several matrix decomposition algorithms corresponding to specific optical models have been proposed, which extract the physical information from measured Mueller matrices. Nevertheless, we still need a prior assessment method to decide which model is more suitable for the experimental data. In this Letter, we propose a set of characteristic Mueller matrices that allows us to obtain information about the breaking of rotation, mirror, and reciprocal symmetry properties in the sample by direct inspection of several elements of the Mueller matrix. By further analyzing the possible origin of symmetry breaking, we can learn the type and mixing status of anisotropies in the measured sample. We have verified our theory with Monte Carlo simulations of polarized light scattering in an isotropic or anisotropic medium containing different configurations of spherical and cylindrical scatterers. This study may help experimenters choose more suitable Mueller matrix decomposition methods.

Analysis of tissue microstructure with Mueller microscopy: logarithmic decomposition and Monte Carlo modeling.

.Significance: Definitive diagnostics of many diseases is based on the histological analysis of thin tissue cuts with optical white light microscopy. Extra information on tissue structural properties obtained with polarized light would help the pathologist to improve the accuracy of his diagnosis.Aim: We report on using Mueller matrix microscopy data, logarithmic decomposition, and polarized Monte Carlo (MC) modeling for qualitative and quantitative analysis of thin tissue cuts to extract the information on tissue microstructure that is not available with a conventional white light microscopy.Approach: Unstained cuts of human skin equivalents were measured with a custom-built liquid-crystal-based Mueller microscope in transmission configuration. To interpret experimental data, we performed the simulations with a polarized MC algorithm for scattering anisotropic media. Several optical models of tissue (spherical scatterers within birefringent host medium, and combination of spherical and cylindrical scatterers within either isotropic or birefringent host medium) were tested.Results: A set of rotation invariants for the logarithmic decomposition of a Mueller matrix was derived to rule out the impact of sample orientation. These invariants were calculated for both simulated and measured Mueller matrices of the dermal layer of skin equivalents. We demonstrated that only the simulations with a model combining both spherical and cylindrical scatterers within birefringent host medium reproduced the experimental trends in optical properties of the dermal layer (linear retardance, linear dichroism, and anisotropic linear depolarization) with layer thickness.Conclusions: Our studies prove that Mueller polarimetry provides relevant information not only on a size of dominant scatterers (e.g., cell nuclei versus subwavelength organelles) but also on its shape (e.g., cells versus collagen fibers). The latter is directly related to the state of extracellular collagen matrix, which is often affected by early pathology. Hence, using polarimetric data can help to increase the accuracy of diagnosis.

Quasi-rayleigh polarization leap of monodisperse spherical particle as a tool to detect particle radius

When the size of scattering particle is increased to be comparable with wavelength, Rayleigh approximation becomes not valid. In polarization scattering pattern this quasi-rayleigh behavior manifests itself as a sharp drop of the degree of linear polarization to the negative values. In this paper, we studied the properties and features of this quasi-rayleigh polarization leap for monodisperse spherical scatterers. The main regularities that determine the wavelength position of the quasi-rayleigh polarization leap are established depending on the phase angle, refractive index and size parameter of the scatterers. A method is suggested for determining the radius of spherical scattering particles of the polystyrene beads in Earth's atmosphere. A simple interpolation formula is given, which allows, based on observational data, such as phase angle and the wavelength at which the quasi-rayleigh polarization leap is observed, to calculate the particle radius.

Robust inverse-design of scattering spectrum in core-shell structure using modified denoising autoencoder neural network

Neural network-based inverse design of nanophotonic device network is computationally and time efficient, but in general suffers the problems of robustness and stability against variation of the input target electromagnetic response. The inverse design network is required to be robust against the input electromagnetic response and to be capable of approximating the given electromagnetic response, even under the circumstances that the exact target response may not exist. We introduce a modified denoising autoencoder network to ensure the robustness of neural network-based inverse design, which consists of (1) a pre-trained network as a substitute of numerical simulation and (2) an inverse design network. We further purposely train the network with certain random disturbances added to the training dataset generated by the pre-trained network. Consequently, our modified denoising autoencoder network is more robust and more accurate than the conventional fully connected neural network. The strength and flexibility of our proposed network is illustrated via three concrete examples of achieving the desired scattering spectra of layered spherical scatterers.

Tunneling optical resonances in light-droplet interactions: simulations of spaceborne cloud droplet observations.

A fruitful approach for light-droplet interaction in atmospheric optics, the quantum optical analogy combined with partial wave analysis, is used to characterize (location, width) very sharp tunneling optical resonances (TORs). For this purpose, a fast and flexible technique of computation, the transfer matrix method, has been developed; it is described herein. This paper proposes explicit calculations of TORs, considering isolated droplets and a droplet population, and so goes further than earlier studies. Applied in the context of POLDER observations, from the visible to the near infrared, it is shown that TORs enhance cross sections with respect to Mie's theory as currently computed in atmospheric optics. Precisely, for a typical warm cloud droplet population, this enhancement can reach almost 30% in the case of absorption. Scattering and extinction cross sections are also higher than those of Mie's theory, but to a lesser extent. As a conclusion, it is suggested that tunneling should be taken into account more explicitly when addressing light scattering by droplets. No scattering inversion technique is investigated in this paper, but for the time being, the results presented can be used as look-up tables (at least orders of magnitude) for practical computations in atmospheric remote sensing. Finally, the approach presented herein is proposed as a perspective to be used in different situations involving other spherical (or almost spherical) scatterers that otherwise should be addressed approximately.

Validation of differences in backscatter coefficients among four ultrasound scanners with different beamforming methods.

The backscatter coefficient (BSC) indicates the absolute scatterer property of a material, independently of clinicians and system settings. Our study verified that the BSC differed among the scanners, transducers, and beamforming methods used for quantitative ultrasound analyses of biological tissues. Measurements were performed on four tissue-mimicking homogeneous phantoms containing spherical scatterers with mean diameters of 20 and 30µm prepared at concentrations of 0.5 and 2.0 wt%, respectively. The BSCs in the different systems were compared using ultrasound scanners with two single-element transducers and five linear high- or low-frequency probes. The beamforming methods were line-by-line formation using focused imaging (FI) and parallel beam formation using plane wave imaging (PWI). The BSC of each system was calculated by the reference phantom method. The mean deviation from the theoretical BSC computed by the Faran model was analyzed as the benchmark validation of the calculated BSC. The BSCs calculated in systems with different properties and beamforming methods well concurred with the theoretical BSC. The mean deviation was below ± 2.8dB on average, and within the approximate standard deviation (± 2.2dB at most) in all cases. These variations agreed with a previous study in which the largest error among four different scanners with FI beamforming was 3.5dB. The BSC in PWI was equivalent to those in the other systems and to those of FI beamforming. This result indicates the possibility of ultra-high frame-rate BSC analysis using PWI.

Electromagnetic Scattering in Curvilinear Coordinates Using a Generalized Functions Method

AbstractA system of equations for calculating the electric field in curvilinear coordinates without imposing external boundary conditions is proposed. First, the system of equations is derived using generalized functions, without imposing external boundary conditions or a coordinate system. Then, in order to demonstrate the use of the system of equations, the derived system is applied to the case of a spherical scatterer, which is then narrowed to the case of a perfect electrically conducting (PEC) sphere. It is shown that for the particular case of a PEC sphere, the resulting field expression agrees with the Stratton‐Chu solution for the Maxwell's equations, confirming that the proposed method can be used to reach a general solution for the electromagnetic field scattered by a PEC sphere, which allows for the calculation of its cross section.

Learning and teaching acoustics through bubbles

By a lark, I started my acoustics career as a graduate student studying a single big bubble in the form of the combustive sound source. By at least the luck of being in a certain place at a certain time, I finished my graduate education by studying bubbles in the form of the acoustics of bubbly liquids. It turns out that the subject of bubbles provides an excellent lens through which to learn and teach acoustics. One starts with lumped element approximations which lead to simple harmonic oscillators and resonance. You can study the bubble oscillator as linear system and encounter increasingly complex nonlinear behavior at comparatively low amplitudes. A bubble is a source of sound initially modeled as a simple spherical source and can of course behave as a spherical scatterer. Add one or many bubbles and one can study more complex scattering and propagation that includes dispersion and loss. Along the way one encounters effective medium theories of varying complexity and statistical descriptions of acoustic phenomena. There are also applications that require inference and inverse techniques. You can even apply a model of a single bubble to study the expansion and contraction of the universe. Examples of these including demos and videos will be presented.By a lark, I started my acoustics career as a graduate student studying a single big bubble in the form of the combustive sound source. By at least the luck of being in a certain place at a certain time, I finished my graduate education by studying bubbles in the form of the acoustics of bubbly liquids. It turns out that the subject of bubbles provides an excellent lens through which to learn and teach acoustics. One starts with lumped element approximations which lead to simple harmonic oscillators and resonance. You can study the bubble oscillator as linear system and encounter increasingly complex nonlinear behavior at comparatively low amplitudes. A bubble is a source of sound initially modeled as a simple spherical source and can of course behave as a spherical scatterer. Add one or many bubbles and one can study more complex scattering and propagation that includes dispersion and loss. Along the way one encounters effective medium theories of varying complexity and statistical descriptions of acoust...

Characterization of siloxane-infiltrated ceramics microstructure by spectral scattering in the near infrared

The spectral scattering technique is considered to estimate the scatterers (pores) size distribution. It is based on the fitting of spectral scattering coefficients determined by Mie theory and radiative transfer inverse problem solution. The previously proposed method was improved for multiphase system analysis. The spectral directional-hemispherical reflectances of slabs of not less than two different geometrical thicknesses are used for inverse radiative transfer problem solution. Semitransparent ceramics with less than 10–15% of total porosity, that contains homogeneously distributed close to solid sphere scatterers, is the application object of the proposed technique. General expressions for multiphase systems were simplified to three-phase ones to reduce the number of optimization variables and adapted to the evaluation of semitransparent ceramics infiltrated by the polymer.The proposed technique was implemented for the evaluation of silica ceramics with 10% porosity before and after the infiltration by the methyl-phenyl-spirocyclosiloxanol followed by the polyfunctional condensation to obtain the polymethyl-phenyl-spirocyclosiloxane. Two techniques of ceramics infiltration with the low-molecular polymer viz by the solution and by the melt were compared. Size distributions of the polymer-filled pores was shown to be affected by the infiltration procedure and polymerization regime. It was shown that less than 25% of the initial pore volume appears to be polymer-filled in the case of ceramics infiltration by the solution. Infiltration from the melt fills not less than 80% of the pore volume. The mean pore diameter of air-filled pores was estimated by gas/mercury porometry and spectral scattering technique. Both methods are shown to be in a rather good agreement. By these techniques air-filled pores mean diameters were shown to be 0.37 and 0.44 µm respectively for ceramics before the infiltration and 0.54 and 0.55 µm for the ceramics infiltrated through the solution. The spectral scattering technique shows mean diameter of polymer-filled pores to be 0.11–0.17 and 0.49 µm in the cases of ceramics infiltration by the solution and by the melt respectively. Thus, sizes of polymer-filled pores are shown to be shifted to the higher values because of infiltration by the melt. The obtained data on polymer-filled pores sizes may be useful for the analysis of ceramics strengthening by the polymer infiltration and infiltration procedure optimization.

Shapes and distributions of soft tissue scatterers

What causes scattering of ultrasound from normal soft tissues such as the liver, thyroid, and prostate? Commonly, the answer is formulated around the properties of spherical scatterers, related to cellular shapes and sizes. However, an alternative view is that the closely packed cells forming the tissue parenchyma create the reference media, and the long cylindrical-shaped fluid vessels serve as the scattering sites. Under a weak scattering or Born approximation for the extracellular fluid in the vessels, and assuming an isotropic distribution of cylindrical channels across a wide range of diameters, consistent with a fractal branching pattern, some simple predictions can be made about the nature of backscatter as a function of frequency in soft tissues. Specifically, a number of plausible shapes would predict that backscatter increases as a power law of frequency, where the power law is determined by the function governing the number density of the vessels versus diameter. These results are compared with some historical models developed over the last 100 years in scattering theory and point to the need for higher spatial resolution and higher bandwidths to obtain more precise measures of the key parameters in normal tissues, and to better identify the dominant structures responsible for backscatter in everyday clinical imaging.

Maximal quantum scattering by homogeneous spherical inclusions

Scattering of matter waves, present at multiple quantum setups, is required to be maximized in several applications from sensing and imaging to quantum switching and memory. The simplest case of a homogeneous spherical scatterer is rigorously solved and optimized with respect to its size, texture, and background by considering the effective quantum properties from a long directory of materials. In this context, several alternative layouts with maximal scattering efficiency are proposed, offering additional degrees of freedom in design without requirements for careful engineering of quantum texture. Many of the reported inclusions exhibit substantial selectivity in their scattering response, admitting them to operate as sharp filters for particle energies or sensitive detectors of electron beams.

Frequency-difference beamforming in the presence of strong random scattering

Frequency-difference beamforming [Abadi, Song, and Dowling (2012). J. Acoust. Soc. Am. 132, 3018-3029] is a nonlinear, out-of-band signal processing technique used to beamform non-zero bandwidth signals at below-band frequencies. This is accomplished with the frequency-difference autoproduct AP(Δω)=P(ω2)P*(ω1), a quadratic product of complex field amplitudes that mimics a genuine field at the difference frequency, Δω=ω2-ω1. For frequency-difference beamforming, AP(Δω) replaces the in-band complex field in the conventional beamforming algorithm. Here, the near-field performance of frequency-difference beamforming is evaluated in the presence of 1 to 30 high-contrast spherical scatterers with radius a placed between, and in the plane defined by the source and a 12-element linear receiving array with element spacing d. Based on the center frequency wave number, k, of the 150-200 kHz frequency sweep source signal, the scatterers are large, ka ≈ 15; the array is sparse, kd = 37; and the average source-to-receiver distance is up to 4.3 mean-free-path lengths. Beamforming results from simulations and experiments show that in-band beamforming loses peak-to-sidelobe ratio and fails to reliably locate the source as the scatterer count increases. Using the same signals, frequency-difference beamforming with difference frequencies from 5 to 25 kHz localizes sources reliably with higher peak-to-side-lobe ratios, though with reduced resolution.

Extracting pure absorbance spectra in infrared microspectroscopy by modeling absorption bands as Fano resonances.

Midinfrared absorbance spectra obtained from spatially inhomogeneous and finite samples often contain scattering effects characterized by derivative-like bands with shifted peak positions. Such features may be interpreted and accurately modeled by Fano theory when the imaginary part of the complex dielectric function is small and Lorentzian in nature-as is the case for many biological media. Furthermore, by fitting Fano line shapes to isolated absorbance bands, recovery of the peak position and pure absorption strength can be obtained with high accuracy. Additionally, for small and optically soft spherical scatterers, recovery of one or the other of constant refractive index or radius (given approximate knowledge of the other) is possible.