Ray Optical Scattering from Uniform Reflective Cylindrical Metasurfaces using Surface Susceptibility Tensors

A ray optical methodology based on the uniform theory of diffraction is proposed to model electromagnetic field scattering from curved metasurfaces. The problem addressed is the illumination of a purely reflective uniform cylindrical metasurface by a line source, models the surface with susceptibilities and employs a methodology previously used for cylinders coated in thin dielectric layers [1]. The approach is fundamentally based on a representation of the metasurface using the General Sheet Transition Conditions (GSTCs) which characterizes the surface in terms of susceptibility dyadics. An eigenfunction description of the metasurface problem is derived considering both tangential and normal surface susceptibilities, and used to develop a ray optics (RO) description of the scattered fields; including the specular geometrical optical field, surface diffraction described by creeping waves and a transition region over the shadow boundary. The specification of the fields in the transition region is dependent on the evaluation of the Pekeris caret function integral and the method follows [1]. The proposed RO-GSTC model is then successfully demonstrated for a variety of cases and is independently verified using a rigorous eigenfunction solution (EF-GSTC) and full-wave Integral Equation method (IE-GSTC), over the entire domain from the deep lit to deep shadow.

Ray Optical Scattering from Uniform Reflective Cylindrical Metasurfaces using Surface Susceptibility Tensors

A ray optical methodology based on the uniform theory of diffraction is proposed to model electromagnetic field scattering from curved metasurfaces. The problem addressed is the illumination of a purely reflective uniform cylindrical metasurface by a line source, models the surface with susceptibilities and employs a methodology previously used for cylinders coated in thin dielectric layers [1]. The approach is fundamentally based on a representation of the metasurface using the General Sheet Transition Conditions (GSTCs) which characterizes the surface in terms of susceptibility dyadics. An eigenfunction description of the metasurface problem is derived considering both tangential and normal surface susceptibilities, and used to develop a ray optics (RO) description of the scattered fields; including the specular geometrical optical field, surface diffraction described by creeping waves and a transition region over the shadow boundary. The specification of the fields in the transition region is dependent on the evaluation of the Pekeris caret function integral and the method follows [1]. The proposed RO-GSTC model is then successfully demonstrated for a variety of cases and is independently verified using a rigorous eigenfunction solution (EF-GSTC) and full-wave Integral Equation method (IE-GSTC), over the entire domain from the deep lit to deep shadow.

Resolution of Born Scattering in Curve Geometries: Aspect-Limited Observations and Excitations

In inverse scattering problems, the most accurate possible imaging results require plane waves impinging from all directions and scattered fields observed in all observation directions around the object. Since this full information is infrequently available in actual applications, this paper is concerned with the mathematical analysis and numerical simulations to estimate the achievable resolution in object reconstruction from the knowledge of the scattered far-field when limited data are available at a single frequency. The investigation focuses on evaluating the Number of Degrees of Freedom (NDF) and the Point Spread Function (PSF), which accounts for reconstructing a point-like unknown and depends on the NDF. The discussion concerns objects belonging to curve geometries, in this case, circumference and square scatterers. In addition, since the exact evaluation of the PSF can only be accomplished numerically, an approximated closed-form evaluation is introduced and compared with the exact one. The approximation accuracy of the PSF is verified by numerical results, at least within its main lobe region, which is the most critical as far as the resolution discussion is concerned. The main result of the analysis is the space variance of the PSF for the considered geometries, showing that the resolution is different over the investigation domain. Finally, two numerical applications of the PSF concept are shown, and their relevance in the presence of noisy data is outlined.

Electrostatic images and T-matrices for simple geometries

<p>This thesis is concerned with electrostatic boundary problems and how their solutions behave depending on the chosen basis of harmonic functions and the location of the fundamental singularities of the potential. The first part deals with the method of images for simple geometries where the exact nature of the image/fundamental singularity is unknown; essentially a study of analytic continuation for Laplace's equation in 3 dimensions. For the sphere, spheroid and cylinder, new deductions are made on the location of the images of point charges and their linear or surface charge densities, by using different harmonic series solutions that reveal the image. The second part looks for analytic expressions for the T-matrix for electromagnetic scattering of simple objects in the low frequency limit. In this formalism the incident and scattered fields are expanded on an orthogonal basis such as spherical harmonics, and the T-matrix is the transformation between the coefficients of these series, providing the general solution of any electromagnetic scattering problem by a given particle at a given wavelength. For the spheroid, bispherical system and torus, the natural basis of harmonic functions for the geometry of the scatterer are used to determine T-matrix expressed in that basis, which is then transformed onto a basis of canonical spherical harmonics via the linear relationships between different bases of harmonic functions.</p>

Electrostatic images and T-matrices for simple geometries

<p>This thesis is concerned with electrostatic boundary problems and how their solutions behave depending on the chosen basis of harmonic functions and the location of the fundamental singularities of the potential. The first part deals with the method of images for simple geometries where the exact nature of the image/fundamental singularity is unknown; essentially a study of analytic continuation for Laplace's equation in 3 dimensions. For the sphere, spheroid and cylinder, new deductions are made on the location of the images of point charges and their linear or surface charge densities, by using different harmonic series solutions that reveal the image. The second part looks for analytic expressions for the T-matrix for electromagnetic scattering of simple objects in the low frequency limit. In this formalism the incident and scattered fields are expanded on an orthogonal basis such as spherical harmonics, and the T-matrix is the transformation between the coefficients of these series, providing the general solution of any electromagnetic scattering problem by a given particle at a given wavelength. For the spheroid, bispherical system and torus, the natural basis of harmonic functions for the geometry of the scatterer are used to determine T-matrix expressed in that basis, which is then transformed onto a basis of canonical spherical harmonics via the linear relationships between different bases of harmonic functions.</p>

Nanolasers with Feedback as Low-Coherence Illumination Sources for Speckle-Free Imaging: A Numerical Analysis of the Superthermal Emission Regime

Lasers distinguish themselves for the high coherence and high brightness of their radiation, features which have been exploited both in fundamental research and a broad range of technologies. However, emerging applications in the field of imaging, which can benefit from brightness, directionality and efficiency, are impaired by the speckle noise superimposed onto the picture by the interference of coherent scattered fields. We contribute a novel approach to the longstanding efforts in speckle noise reduction by exploiting a new emission regime typical of nanolasers, where low-coherence laser pulses are spontaneously emitted below the laser threshold. Exploring the dynamic properties of this kind of emission in the presence of optical reinjection we show, through the numerical analysis of a fully stochastic approach, that it is possible to tailor some of the properties of the emitted radiation, in addition to exploiting this naturally existing regime. This investigation, therefore, proposes semiconductor nanolasers as potential attractive, miniaturized and versatile future sources of low-coherence radiation for imaging.

Numerical Simulation of Acoustic Scattering by a Cylinder Based on the Enhanced Optimized Scheme

The enhanced optimized scheme we developed in the early work is employed to simulate the scattering of acoustic waves from a two-dimensional cylinder by solving the Euler equations. The numerical results of a benchmark problem are found to be in excellent agreement with the exact solution. Our numerical results show that when acoustic waves propagate through a cylinder, the acoustic scattering results in a spatial redistribution of the acoustic energy as well as an alteration of the phase of the waves. The directivities of the scattered fields change significantly for the different length ratios of acoustic wavelength to the radius of the cylinder.

Modified Theory of Physical Optics Approach to Diffraction by an Interface between PEMC and Absorbing Half-Planes

The scattering of electromagnetic plane waves by an interface, located between perfect electromagnetic conductor and absorbing half-planes is investigated. The perfect electromagnetic conductor half-plane is divided into perfect electric conductor and perfect magnetic conductor half-screens. The same decomposition is done for the absorbing surface. Then four separate geometries are defined according to this approach. The scattered fields by the four sub-problems are obtained with the aid of the modified theory of physical optics. The resultant scattering integrals are combined in a single expression by using key formulas, defined for the perfect electromagnetic conductor and absorbing surfaces. The scattering integral is asymptotically evaluated for large values of the wave-number and the diffracted and geometric optics fields are obtained. The behaviors of the derived field expressions are analyzed numerically.

OPERATOR METHOD IN THE PROBLEM OF THE H-POLARIZED WAVE DIFFRACTION BY TWO SEMI-INFINITE GRATINGS PLACED IN THE SAME PLANE

Purpose: Problem of the H-polarized plane wave diffraction by the structure, which consists of two semi-infinite strip gratings, is considered. The gratings are placed in the same plane. The gap between the gratings is arbitrary. The purpose of the paper is to develop the operator method to the structures, which scattered fields have both discrete and continuous spatial spectra. Design/methodology/approach: In the spectral domain, in the domain of the Fourier transform, the scattered field is expressed in terms of the unknown Fourier amplitude. The field reflected by the considered structure is represented as a sum of two fields of currents on the strips of semi-infinite gratings. The operator equations are obtained for the Fourier amplitudes. These equations use the operators of reflection of semi-infinite gratings, which are supposed to be known. The field scattered by a semi-infinite grating can be represented as a sum of plane and cylindrical waves. The reflection operator of a semi-infinite grating has singularities at the points, which correspond to the propagation constants of plane waves. Consequently, the unknown Fourier amplitudes of the fi eld scattered by the considered structure also have singularities. To eliminate these latter, the regularization procedure has been carried out. As a result of this procedure, the operator equations are reduced to the system of integral equations containing the integrals, which should be understood as the Cauchy principal value and Hadamar finite part integrals. The discretization has been carried out. As a result, the system of linear equations is obtained, which is solved with the use of the iterative procedure. Findings: The operator equations with respect to the Fourier amplitudes of the field scattered by the structure, which consists of two semi-infinite gratings, are obtained. The computational investigation of convergence has been made. The near and far scattered fields are investigated for different values of the grating parameters. Conclusions: The effective algorithm to study the fields scattered by the strip grating, which has both discrete and continuous spatial spectra, is proposed. The developed approach can be an effective instrument in solving a series of problems of antennas and microwave electronics. Key words: semi-infinite grating, operator method, singular integral, hypersingular integral, regularization procedure

Surface Susceptibilities as Compact Full-Wave Simulation Models of Fully-Reflective Volumetric Metasurfaces

<p>While metasurfaces (MSs) are constructed from deeply-subwavelength unit cells, they are generally electrically-large and full-wave simulations of the complete structure are computationally expensive. Thus, to reduce this high computational cost, non-uniform MSs can be modeled as zero-thickness boundaries, with sheets of electric and magnetic polarizations related to the fields by surface susceptibilities and the generalized sheet transition conditions (GSTCs). While these two-sided boundary conditions have been extensively studied for single sheets of resonant particles, it has not been shown if they can correctly model structures where the two sides are electrically isolated, such as a fully-reflective surface. In particular, we consider in this work whether the fields scattered from a fully reflective metasurface can be correctly predicted for arbitrary field illuminations, with the source placed on either side of the surface. In the process, we also show the mapping of a PEC sheet with a dielectric cover layer to bi-anisotropic susceptibilities. Finally, we demonstrate the use of the susceptibilities as compact models for use in various simulation techniques, with an illustrative example of a parabolic reflector, for which the scattered fields are correctly computed using a integral equation (IE) based solver.<br></p>