Homogeneous Dielectric Cylinder Research Articles

Evaluation of the Resolution in Inverse Scattering of Dielectric Cylinders for Medical Applications.

The inverse scattering problem has numerous significant applications, including in geophysical explorations, medical imaging, and radar imaging. To achieve better performance of the imaging system, theoretical knowledge of the resolution of the algorithm is required for most of these applications. However, analytical investigations about the resolution presently feel inadequate. In order to estimate the achievable resolution, we address the point spread function (PSF) evaluation of the scattered field for a single frequency and the multi-view case both for the near and the far fields and the scalar case when the angular domain of the incident field and observation ranges is a round angle. Instead of the common free space condition, an inhomogeneous background medium, consisting of a homogeneous dielectric cylinder with a circular cross-section in free space, is assumed. In addition, since the exact evaluation of the PSF can only be accomplished numerically, an analytical approximation of the resolution is also considered. For the sake of its comparison, the truncated singular value decomposition (TSVD) algorithm can be used to implement the exact PSF. We show how the behavior of the singular values and the resolution change by varying the permittivity of the background medium. The usefulness of the theoretical discussion is demonstrated in localizing point-like scatterers within a dielectric cylinder, so mimicking a scenario that may occur in breast cancer imaging. Numerical results are provided to validate the analytical investigations.

Bound states in the continuum in strong-coupling and weak-coupling regimes under the cylinder – ring transition

Abstract Bound states in the continuum (BIC) have been at the forefront of research in optics and photonics over the past decade. It is of great interest to study the effects associated with quasi-BICs in the simplest structures, where quasi-BICs are very pronounced. An example is a dielectric cylinder, and in a number of works, quasi-BICs have been studied both in single cylinders and in structures composed of cylinders. In this work, we studied the properties of quasi-BICs during the transition from a homogeneous dielectric cylinder in an air environment to a ring with narrow walls while increasing the diameter of the inner air cylinder gradually. The results demonstrate the quasi-BIC crossover from the strong-coupling to the weak-coupling regime, which manifests itself in the transition from the avoided crossing of branches to their intersection with the quasi-BIC being preserved on only one straight branch. In the regime of strong-coupling and quasi-BIC, three waves interfere in the far-field zone: two waves corresponding to the resonant modes of the structure and the wave scattered by the structure as a whole. The validity of the Fano resonance concept is discussed since it describes the interference of only two waves under weak coupling conditions.

Resonance Scattering by a Circular Dielectric Cylinder

AbstractA unified approach is developed for the analysis of singularities of the scattered field and vanishing of scattering harmonics. Rigorous proofs are presented of the existence of complex resonance singularities of the solution to the problem of the plane wave scattering by a circular homogeneous dielectric cylinder. The method employs a mathematically correct approach of the spectral theory of open structures involving generalized conditions at infinity when complex resonance frequencies may be considered. The result is obtained by verifying the existence of complex singularities of the series solution coefficients considered as functions of the problem parameters. The recently developed theory of generalized cylindrical polynomials (GCPs) is used that enables one to reduce determination of singularities (resonances) to finding zeros (real or complex) of a particular subfamily of GCPs.

Transition between a Photonic Crystal and a Metamaterial with Electric Response in Dielectric Structures

The feasibility of dielectric structures possessing metamaterial properties owing to electric Mie resonances is theoretically demonstrated. The structures are formed by homogeneous dielectric cylinders occupying the sites of a simple hexagonal or square lattice. The (normalized cylinder radius, dielectric constant) phase diagram is constructed and demonstrates a region where the effective dielectric constant eeff of the metamaterial is close to zero. The simulation of the propagation of a Gaussian beam through a prism made of this metamaterial shows that the vanishingly small value of eeff is insensitive to the orientation of the crystal axes.

Analysis of dielectric circular cylinder light spot narrowing by whispering gallery modes and influence of material absorption

We present results of numerical analysis of the diffraction of a plane monochromatic TE-wave on an ideal homogeneous dielectric cylinder with several resonant wavelength scale radii. Two subsequent near-surface maxima of intensity (two focuses) generated at the cylinder output were found on the optical axis. The first subwavelength focus is formed by one of the whispering gallery mode lobes. Its intensity is 50 times the incident light intensity and its full width at the half maximum of the intensity is equal to 0.155 of the incident wavelength. The second focus is two times less in intensity. Its focal spot known as a photonic nanojet is stretched toward the optical axis. The second focus is formed at a distance about the wavelength from the cylinder surface. Its width is equal to 0.44 of the wavelength and its length is two wavelengths. The influence of material absorption on the light focusing is also examined by numerical simulation.

On transmittance and localization of the electromagnetic wave in two-dimensional graphene-based photonic crystals

Two-dimensional graphene-based photonic crystal (GPC) formed by a periodic array of the homogeneous dielectric cylinders etched in the alternating graphene and dielectric layers and its inverse counterpart are considered. The transmittance of the photonic crystal is obtained. The waveguide due to the localization of the electromagnetic wave on the lattice defect that breaks the translational symmetry of the GPC of two different topologies is studied. The different topologies of GPC are characterized by different photonic band structures with different widths of photonic band gaps (PBG) and provide different frequencies for the localized electromagnetic wave due to the defect. The frequencies of the localized mode for both type of the GPC, located inside the lowest PBG, are in the range of THz or tens of THz depending on the topology of the GPC. It is shown that the photonic band gap always can be tuned by changing the chemical potential of graphene to provide formation of the localized photonic mode due to the defect. The technological advantages of the GPC, as well as the opportunity to tune the PBG and the frequency of the localized electromagnetic wave in the terahertz region of spectrum for the GPC are discussed.

A Simple Approach for Estimating the Effective Electric Parameters of 2-D Targets

In this paper, we introduce a simple, noniterative algorithm to estimate the effective dielectric properties of unknown targets from the measurements of their backscattered fields. The proposed approach relies on the virtual experiments concept, as it exploits a combination of the incident fields to be able to focus the exciting field on a certain region. Then, it associates the effective parameters to the permittivity and conductivity values that minimize the mean square error between the virtual scattered field (obtained by recombining the measured data) and the field scattered by a homogeneous dielectric cylinder centered on the target, having approximately the same area. The center of this effective scatterer and its radius can be estimated with a qualitative imaging algorithm or can be given as a priori information. Notably, by properly designing the virtual incident fields, the proposed method can easily handle the case of multiple targets. The effectiveness of the method is assessed by both numerical and experimental examples.

Influence of whispering gallery modes on light focusing by dielectric circular cylinder

In this paper diffraction of a plane monochromatic TE-wave on an ideal homogeneous dielectric cylinder with several resonant wavelength scale radii is analyzed. Two subsequent near-surface maxima of intensity (two focuses) generated at the cylinder output were found on the optical axis. The first subwavelength focus is formed by one of the whispering gallery mode lobes. Its intensity is 50 times the incident light intensity and its full width at the half maximum of the intensity is equal to 0.155 of the incident wavelength. The second focus is two times less in intensity. Its focal spot known as a photonic nanojet is stretched toward the optical axis. The second focus is formed at a distance about the wavelength from the cylinder surface. Its width is equal to 0.44 of the wavelength and its length is two wavelengths. The abilities of light focusing by a two-layered cylinder and influence of materials absorption on the light focusing are also examined by numerical simulation.

Light scattering by dielectric bodies in the Born approximation

Light scattering is one of the most important elementary processes in near-field optics. We build up the Born series for scattering by dielectric bodies with sharp boundaries. The Green's function for a two-dimensional homogeneous dielectric cylinder is obtained. As an example, the formulas are derived for a scattered field of two parallel cylinders. The polar diagram is shown to agree with the numerical calculation by the known methods of discrete dipoles and boundary elements.

Whispering gallery modes in a dielectric cylinder with circular cross-section

As a result of diffraction of a plane monochromatic TE-wave by an ideal homogeneous dielectric cylinder with a wavelength-scale resonant radius, two on-axis near-surface focal spots are generated at the cylinder output. The first subwavelength focal spot is formed by a whispering gallery mode. Its peak intensity is 50 times the intensity of the incident plane wave, and its full width at half maximum can reach 0.155 of the incident wavelength. The second focal spot intensity is half as much as that of the first one. This focal spot, which is also known as the photonic nanojet, is stretched towards the optical axis. Its width is 0.44 of the wavelength, while the length can reach two wavelengths. In this paper, we numerically analyze the focusing ability of a two-layered cylinder and effects of the material absorption on the results of focusing of the whispering gallery mode.

Scattering From Inhomogeneous Dielectric Cylinders With Finite Length

The electromagnetic scattering by a dielectric cylinder of finite length is important in many applications, particularly for microwave remote sensing of vegetated terrain. Yet, not only a unified analytical solution is still elusive in providing the scattering cross sections but also other important aspects, such as the phase of the scattering amplitude function, energy conservation, and reciprocity relation, have been scantly touched in the literature. The treatment of a dielectric inhomogeneous cylinder of finite length brings forth new challenges. Taking on such challenges is the focus of this paper. The main plan of attack is to extend the virtual partition method, which is a T-matrix-based semi-analytical model, that we have previously proposed to treat scattering from a homogeneous dielectric cylinder of finite length, to the inhomogeneous cases. The effectiveness of the proposed method is validated numerically, including: 1) high-fidelity prediction of the copolarized and cross-polarized cross sections for arbitrary bistatic scattering configuration; 2) high-fidelity predictions of the phase of the scattering amplitude function; 3) verification of energy conservation; and 4) verification of the reciprocity theorem.

Sharp resonant focusing of light by a dielectric cylinder with square cross-section and cube

In this paper a research on conditions for resonance excitation in a homogeneous dielectric cylinder with square cross-section is conducted using a FDTD-method. It is shown that in a cylinder with square cross-section resonant modes similar to whispering gallery modes can be excited, which allows one to reduce the transverse dimensions of the focal spot. FDTD method demonstrates an acceptable accuracy of the resonant mode detection. A similar result is obtained for a cube on a dielectric substrate: it is possible to achieve the reduction of the transverse dimensions of the focal spot by changing the corresponding cube size.

Invisibility of a finite dielectric cylinder under Fano resonance conditions

The effect of invisibility of a finite homogeneous dielectric cylinder due to a substantial decrease in the scattering of electromagnetic waves in specific spectral ranges has been investigated theoretically. A regime of invisibility of the cylinder in an air space without additional cloaking devices has been considered. The effect is based on the resonance suppression of scattered waves, which makes the cylinder invisible to an observer located at any point of the space. The invisibility condition is determined by the Fano resonance between the re-emitted Mie modes and the nonresonant scattering by the cylinder. The dependence of the spectra of the total scattering cross section on the ratio between the length and radius of the cylinder has been analyzed in detail. It has been shown that the transition from the model infinite cylinder to the cylinder of finite length is accompanied by the appearance of new resonances and additional scattering, which, however, does not disturb the lowest frequency region of invisibility at specific length-to-radius ratios of the cylinder.

Analyzing the properties of acceptor mode in two-dimensional plasma photonic crystals based on a modified finite-difference frequency-domain method

In this paper, the properties of acceptor mode in two-dimensional plasma photonic crystals (2D PPCs) composed of the homogeneous and isotropic dielectric cylinders inserted into nonmagnetized plasma background with square lattices under transverse-magnetic wave are theoretically investigated by a modified finite-difference frequency-domain (FDFD) method with supercell technique, whose symmetry of every supercell is broken by removing a central rod. A new FDFD method is developed to calculate the band structures of such PPCs. The novel FDFD method adopts a general function to describe the distribution of dielectric in the present PPCs, which can easily transform the complicated nonlinear eigenvalue equation to the simple linear equation. The details of convergence and effectiveness of proposed FDFD method are analyzed using a numerical example. The simulated results demonstrate that the enough accuracy of the proposed FDFD method can be observed compared to the plane wave expansion method, and the good convergence can also be obtained if the number of meshed grids is large enough. As a comparison, two different configurations of photonic crystals (PCs) but with similar defect are theoretically investigated. Compared to the conventional dielectric-air PCs, not only the acceptor mode has a higher frequency but also an additional photonic bandgap (PBG) can be found in the low frequency region. The calculated results also show that PBGs of proposed PPCs can be enlarged as the point defect is introduced. The influences of the parameters for present PPCs on the properties of acceptor mode are also discussed in detail. Numerical simulations reveal that the acceptor mode in the present PPCs can be easily tuned by changing those parameters. Those results can hold promise for designing the tunable applications in the signal process or time delay devices based on the present PPCs.

Assessing the Capabilities of a New Linear Inversion Method for Quantitative Microwave Imaging

We investigate the imaging capabilities of a new linear microwave imaging approach, which allows to quantitative retrieve the complex permittivity distribution of unknown nonweak targets. To this end, we carry out a parametric numerical analysis for a canonical scatterer (a homogeneous dielectric cylinder with circular cross section) and derive a quantitative criterion to foresee the method’s applicability. The reliability of the criterion is then tested against noncanonical scatterers to show the effectiveness of the method in imaging nonweak targets and in outperforming the linearized inversion method based on the standard Born approximation.

A second degree Newton method for an inverse scattering problem for a dielectric cylinder

The inverse obstacle scattering problem we are interested is to reconstruct the image of an innitely long homogeneous dielectric cylinder from the far eld pattern for scattering of a time-harmonic E-polarized electromagnetic plane wave. We extend the approach suggested by Kress and Lee [18] that combines the ideas of Hettlich and Rundell [10] and Johansson and Sleeman [14] for the case of the inverse problem for a perfectly conducting scatterer to the case of penetrable scatterer. The inverse problem is depended on a system of non-linear boundary integral equations associated with a single layer approach to solve the direct scattering problem. We show the mathematical foundations of the method and illustrate its feasibility by numerical examples. Keywords: Helmholtz equation; Inverse scattering; Transmission boundary condition; Non-linear integral equations; Gauss-Newton iteration methods; Single-layer approach. DOI: 10.17350/HJSE19030000013 Full Text:

Photonic properties of two-dimensional high-contrast periodic structures: Numerical calculations

The photon properties of two-dimensional periodic structures formed by infinite homogeneous dielectric cylinders packed in a square lattice have been investigated theoretically. Depending on the dielectric contrast between the cylinders and the surrounding medium, the photonic band structure, transmission spectra of crystals with a finite number of layers, and spectra of Mie scattering by an isolated cylinder have been calculated. The calculations have been performed for the TE polarization. The transformation of photonic stop-bands corresponding to Bragg and Mie resonances has been analyzed using the obtained data. The main effect consists in “castling” energy positions of the Bragg stop-bands and Mie stop-bands. For low-contrast photonic crystals, the low-frequency region of the energy spectrum is determined by Bragg stop-bands, and Mie stop-bands are located higher in energy. With an increase in the dielectric contrast, the energy of Mie stop-bands decreases, and they intersect the region of Bragg stop-bands weakly varying in the TE polarization and form the low-energy region of the spectrum.

Cascades of Fano resonances in Mie scattering

The interference nature of resonant Mie scattering, which is described within the Fano model, has been demonstrated. The interference is caused by interaction of an incident electromagnetic wave with reemitted waves that correspond to eigenmodes of a scattering particle. Mie scattering due to the interference can be represented in the form of cascades of resonance lines of different shapes, each of which is described by the classical Fano formula. The effect is observed in resonant light scattering by an arbitrary body of revolution and discussed in detail using the example of scattering by an infinite homogeneous dielectric cylinder.

Resonant state expansion applied to two-dimensional open optical systems

The resonant state expansion (RSE), a rigorous perturbative method in electrodynamics, is applied to two-dimensional open optical systems. The analytically solvable homogeneous dielectric cylinder is used as unperturbed system, and its Green's function is shown to contain a cut in the complex frequency plane, which is included in the RSE basis. The complex eigenfrequencies of modes are calculated using the RSE for a selection of perturbations which mix unperturbed modes of different orbital momentum, such as half-cylinder, thin-film and thin-wire perturbation, demonstrating the accuracy and convergency of the method. The resonant states for the thin-wire perturbation are shown to reproduce an approximative analytical solution.

Time Domain Microwave Imaging of a Buried Homogeneous Dielectric Cylinder in a Slab Medium by Asynchronous Particle Swarm Optimization

Abstract A time-domain inverse scattering technique for estimating the location, shape, and permittivity of a dielectric cylinder in a slab medium is proposed. In this paper, the finite-difference time domain is employed for the analysis of the forward scattering part, and asynchronous particle swarm optimization (APSO) is applied for the reconstruction of the two-dimensional homogeneous dielectric cylinder. For the forward scattering, several electromagnetic pulses are launched to illuminate the unknown scatterers, and then the surrounding scattered electromagnetic fields are measured. In order to efficiently describe the details of the shape, a sub-gridding technique is implemented in the finite-difference time domain method. Then, the simulated electromagnetic fields are used for inverse scattering, in which APSO is employed to transform the inverse scattering problem into an optimization problem. APSO is a population-based optimization approach that aims to minimize a cost function between measurements and computer-simulated data. The numerical results presented for the two examples of scatterers under transverse-electric incidence demonstrate that the proposed method is capable of reconstructing a complicated shape with a rapid rate of convergence and robust immunity to noise.