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

2022 ◽  
Author(s):  
Shulabh Gupta ◽  
Tom J. Smy ◽  
Scott Stewart
Keyword(s):  
Transition Region ◽  
Integral Equation Method ◽  
Optical Scattering ◽  
Normal Surface ◽  
Shadow Boundary ◽  
Uniform Theory Of Diffraction ◽  
Full Wave ◽  
Source Models ◽  
Scattered Fields ◽  
Surface Diffraction

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.

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

2022 ◽  
Author(s):  
Shulabh Gupta ◽  
Tom J. Smy ◽  
Scott Stewart
Keyword(s):  
Transition Region ◽  
Integral Equation Method ◽  
Optical Scattering ◽  
Normal Surface ◽  
Shadow Boundary ◽  
Uniform Theory Of Diffraction ◽  
Full Wave ◽  
Source Models ◽  
Scattered Fields ◽  
Surface Diffraction

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.

scholarly journals Computing the T-matrix of a scattering object with multiple plane wave illuminations

2017 ◽  
Vol 8 ◽  
pp. 614-626 ◽  
Author(s):  
Martin Fruhnert ◽  
Ivan Fernandez-Corbaton ◽  
Vassilios Yannopapas ◽  
Carsten Rockstuhl
Keyword(s):  
Plane Waves ◽  
The Finite Element Method ◽  
Full Wave ◽  
Electric Dipoles ◽  
Complicated Object ◽  
T Matrix ◽  
Multiple Plane ◽  
Optical Nanostructures ◽  
Scattered Fields ◽  
Matrix Calculation

Given an arbitrarily complicated object, it is often difficult to say immediately how it interacts with a specific illumination. Optically small objects, e.g., spheres, can often be modeled as electric dipoles, but which multipole moments are excited for larger particles possessing a much more complicated shape? The T-matrix answers this question, as it contains the entire information about how an object interacts with any electromagnetic illumination. Moreover, a multitude of interesting properties can be derived from the T-matrix such as the scattering cross section for a specific illumination and information about symmetries of the object. Here, we present a method to calculate the T-matrix of an arbitrary object numerically, solely by illuminating it with multiple plane waves and analyzing the scattered fields. Calculating these fields is readily done by widely available tools. The finite element method is particularly advantageous, because it is fast and efficient. We demonstrate the T-matrix calculation at four examples of relevant optical nanostructures currently at the focus of research interest. We show the advantages of the method to obtain useful information, which is hard to access when relying solely on full wave solvers.

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

2021 ◽  
Author(s):  
Ville Tiukuvaara ◽  
Tom J. Smy ◽  
Karim Achouri ◽  
Shulabh Gupta
Keyword(s):  
Computational Cost ◽  
Simulation Models ◽  
Arbitrary Field ◽  
Simulation Techniques ◽  
Full Wave ◽  
Unit Cells ◽  
Scattered Fields ◽  
Two Sides ◽  
Model Structures ◽  
High Computational Cost

<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>

scholarly journals Part 2: Spatially Dispersive Metasurfaces - IE-GSTC-SD Field Solver with Extended GSTCs

2021 ◽  
Author(s):  
Tom J. Smy ◽  
Joao Guilherme Nizer Rahmeier Rahmeier ◽  
jordan dugan ◽  
Shulabh Gupta
Keyword(s):  
Simulation Framework ◽  
Fourier Decomposition ◽  
Full Wave ◽  
Unit Cells ◽  
Conducting Wire ◽  
Spatial Derivatives ◽  
The Difference ◽  
Scattered Fields ◽  
Spatially Dispersive ◽  
Derivatives Of

<div>An Integral Equation (IE) based field solver to compute the scattered fields from spatially dispersive metasurfaces is proposed and numerically confirmed using various examples involving physical unit cells. The work is a continuation of Part-</div><div>1 [1], which proposed the basic methodology of representing spatially dispersive metasurface structure in the spatial frequency domain, k. By representing the angular dependence of the surface susceptibilities in k as a ratio of two polynomials, the standard Generalized Sheet Transition Conditions (GSTCs) have been extended to include the spatial derivatives of both the difference and average fields around the metasurface. These extended boundary conditions are successfully integrated here into a standard IE-GSTC solver, which leads to the new IEGSTC-SD simulation framework presented here. The proposed IE-GSTC-SD platform is applied to various uniform metasurfaces, including a practical short conducting wire unit cell, as a representative practical example, for various cases of finite-sized flat and curvilinear surfaces. In all cases, computed field distributions are successfully validated, either against the semi-analytical Fourier decomposition method or the brute-force full-wave simulation of volumetric metasurfaces in the commercial Ansys FEM-HFSS simulator.</div>

scholarly journals Part 2: Spatially Dispersive Metasurfaces - IE-GSTC-SD Field Solver with Extended GSTCs

2021 ◽  
Author(s):  
Tom J. Smy ◽  
Joao Guilherme Nizer Rahmeier Rahmeier ◽  
jordan dugan ◽  
Shulabh Gupta
Keyword(s):  
Simulation Framework ◽  
Fourier Decomposition ◽  
Full Wave ◽  
Unit Cells ◽  
Conducting Wire ◽  
Spatial Derivatives ◽  
The Difference ◽  
Scattered Fields ◽  
Spatially Dispersive ◽  
Derivatives Of

<div>An Integral Equation (IE) based field solver to compute the scattered fields from spatially dispersive metasurfaces is proposed and numerically confirmed using various examples involving physical unit cells. The work is a continuation of Part-</div><div>1 [1], which proposed the basic methodology of representing spatially dispersive metasurface structure in the spatial frequency domain, k. By representing the angular dependence of the surface susceptibilities in k as a ratio of two polynomials, the standard Generalized Sheet Transition Conditions (GSTCs) have been extended to include the spatial derivatives of both the difference and average fields around the metasurface. These extended boundary conditions are successfully integrated here into a standard IE-GSTC solver, which leads to the new IEGSTC-SD simulation framework presented here. The proposed IE-GSTC-SD platform is applied to various uniform metasurfaces, including a practical short conducting wire unit cell, as a representative practical example, for various cases of finite-sized flat and curvilinear surfaces. In all cases, computed field distributions are successfully validated, either against the semi-analytical Fourier decomposition method or the brute-force full-wave simulation of volumetric metasurfaces in the commercial Ansys FEM-HFSS simulator.</div>

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

2021 ◽  
Author(s):  
Ville Tiukuvaara ◽  
Tom J. Smy ◽  
Karim Achouri ◽  
Shulabh Gupta
Keyword(s):  
Computational Cost ◽  
Simulation Models ◽  
Arbitrary Field ◽  
Simulation Techniques ◽  
Full Wave ◽  
Unit Cells ◽  
Scattered Fields ◽  
Two Sides ◽  
Model Structures ◽  
High Computational Cost

<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>

Scattering from a Particular Class of Conducting Corrugated Cylinders

1971 ◽  
Vol 49 (1) ◽  
pp. 66-75 ◽  
Author(s):  
Lotfollah Shafai ◽  
Stanley S. H. Tse
Keyword(s):  
Electromagnetic Waves ◽  
Numerical Solutions ◽  
Integral Equation Method ◽  
Surface Currents ◽  
Two Dimensional ◽  
Matrix Formulation ◽  
Cross Sectional ◽  
Equipotential Surfaces ◽  
Scattered Fields ◽  
Special Case

The electrostatic equipotential surfaces of n identical strips intersecting azimuthally along an axis constitute the surfaces of certain corrugated cylinders. The cross sectional geometry of the corrugations varies from the limiting form of the intersecting strips to a circular cylinder at large distances from the intersecting axis. The problem of two-dimensional scattering of electromagnetic waves by these geometries is considered and numerical solutions are found by using two separate methods—a matrix formulation and an integral equation method. The special case of four intersecting strips illuminated by plane electromagnetic waves polarized parallel to the intersecting axis is considered in detail and the numerical results for the surface currents and the scattered fields are evaluated.

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