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Wave-based analog computing in the forms of inverse-designed metastructures and the meshes of Mach-Zehnder interferometers (MZI) have recently received considerable attention due to their capability in emulating linear operators, performing vector-matrix multiplication, inverting matrices, and solving integral and differential equations, via electromagnetic wave interaction and manipulation in such structures. Here, we combine these two platforms to propose a wave-based metadevice that can compute scattered fields in electromagnetic forward scattering problems. The proposed device consists of two sub-systems: a set of reconfigurable couplers with a proper feedback system and an inverse-designed inhomogeneous material block. The first sub-system computes the magnitude and phase of the dipole polarization induced in the scatterers when illuminated with a given incident wave (matrix inversion). The second sub-system computes the magnitude and phase of the scattered fields at given detection points (vector-matrix multiplication). We discuss the functionality of this metadevice, and through several examples, we theoretically evaluate its performance by comparing the simulation results of this device with full-wave numerical simulations and numerically evaluated matrix inversion. We also highlight that since the first section is reconfigurable, the proposed device can be used for different permittivity distributions of the scatterer and different incident excitations without changing the inverse-designed section. Our proposed device may provide a versatile platform for rapid computation in various scattering scenarios., Authors with equal contribution: Vahid Nikkhah and Dimitrios C. Tzarouchis

In this work we report the design process of tunable RF modules and their implementation towards specialized network architectures that are able to perform mathematical operations such as matrix inversion.

The problem of finding the optimal current distribution supported by small radiators yielding the minimum quality (Q) factor is a fundamental problem in electromagnetism. Q factor bounds constrain the maximum operational bandwidth of devices including antennas, metamaterials, and nanoresonators, and have been featured in seminal papers in the past decades. Here, we determine the lower bounds of Q factors of small-size plasmonic and high-permittivity dielectric resonators, which are characterized by quasi-electrostatic and quasi-magnetostatic natural modes, respectively. We expand the induced current density field in the resonator in terms of these modes, leading to closed-form analytical expressions for the electric and magnetic polarizability tensors, whose largest eigenvalue is directly linked to the minimum Q factor. Our results allow also to determine in closed form the corresponding optimal current density field. In particular, when the resonator exhibits two orthogonal reflection symmetries the minimum Q factor can be simply obtained from the Q factors of the single current modes with non-vanishing dipole moments aligned along the major axis of the resonator. Overall, our results open exciting opportunities in the context of nano-optics and metamaterials, facilitating the analysis and design of optimally shaped resonators for enhanced and tailored light-matter interactions.

In this work we present and discuss the case of a reconfigurable, Mach–Zehnder interferometer-based photonic network, specially designed for implementing any arbitrary matrix operator. After a brief discussion on the available architectures we describe the main elements of the proposed architecture. Finally, using simulations we demonstrate a practical example where an $11 \times11$ MZI network is implement for the solution of differential equation.

Metasurfaces, the ultrathin, 2D version of metamaterials, have recently attracted a surge of attention for their capability to manipulate electromagnetic waves. Recent advances in reconfigurable and programmable metasurfaces have greatly extended their scope and reach into practical applications. Such functional sheet materials can have enormous impact on imaging, communication, and sensing applications, serving as artificial skins that shape electromagnetic fields. Motivated by these opportunities, this progress report provides a review of the recent advances in tunable and reconfigurable metasurfaces, highlighting the current challenges and outlining directions for future research. To better trace the historical evolution of tunable metasurfaces, a classification into globally and locally tunable metasurfaces is first provided along with the different physical addressing mechanisms utilized. Subsequently, coding metasurfaces, a particular class of locally tunable metasurfaces in which each unit cell can acquire discrete response states, is surveyed, since it is naturally suited to programmatic control. Finally, a new research direction of software-defined metasurfaces is described, which attempts to push metasurfaces toward unprecedented levels of functionality by harnessing the opportunities offered by their software interface as well as their inter- and intranetwork connectivity and establish them in real-world applications. This work was supported by the European Union’s Horizon 2020 research and innovation programme-Future Emerging Topics (FETOPEN) under grant agreement No 736876 (VISORSURF). Financial support by the National Priorities Research Program grant No. NPRP9-383-1-083 from the Qatar National Research Fund is also acknowledged. O.T. acknowledges the financial support of the Stavros Niarchos Foundation within the framework of the project ARCHERS (“Advancing Young Researchers’ Human Capital in Cutting Edge Technologies in the Preservation of Cultural Heritage and the Tackling of Societal Challenges”).

We theoretically explore a reconfigurable, Mach—Zehnder interferometer-based photonic network capable of solving linear equations by implementing arbitrary matrix operators. The solutions of various differential equations are numerically demonstrated and discussed.

A novel surface integral equation (SIE)-based theory of characteristic modes (TCM) formulation is proposed for homogeneous penetrable bodies. Analytical expressions for the characteristic eigenvalues are presented and good agreement between the numerical and analytical results is observed for both lossless and lossy, as well as for dielectric and magnetodielectric objects. The new formulations, without any postprocessing methods, avoid spurious modes and resonances appearing in existing SIE-based TCM formulations. For lossy objects, the obtained eigenvalues are complex. The real part of an eigenvalue is related to the ratio of the reactive and radiated power, as in the original TCM formulation for perfect electric conductor structures, and the imaginary part gives the ratio between the dissipated and radiated power.

In this study we discuss the plasmonic subwavelength scattering resonances of five regular polyhedra, i.e., the Platonic solids tetrahedron, hexahedron, octahedron, dodecahedron, and icosahedron. A brief discussion regarding their geometrical characteristics and the numerical method used in the study is given. All results are compared with the benchmark case of a sphere, in order to observe how the geometry of the solid affects the spectral characteristics. The principal finding is that the shift of the main dipole resonance exhibits a solid-vertex hierarchical order, in other words, the position of the resonance correlates with the solid angle of the vertex of the given solid. This is in contrast with the blackhedra-hierarchical order found for the electrostatic dielectric response of these solids. These results can create new avenues for applications and devices that require plasmonic particles with on-demand functionalities.

Resonances, i.e., extrema of the eigenvalues of characteristic modes for closed perfectly conducting objects are investigated. The characteristic modal solutions based on the electric, magnetic, and combined field integral operators (EFIO, MFIO, and CFIO) are studied and compared with analytical solutions for a sphere. All these formulations are found to capture both external (radiating) and internal (cavity) resonances predicted by the analytical expressions. At the internal resonances, the eigenvalues obtained with the EFIO- and MFIO-based approaches are not correct, and the corresponding modes are nonunique. These solutions also exhibit a strong duality between the electric (TM) and magnetic (TE) type modes. A connection is found between the external and internal resonances and the condition numbers of the matrices. The modal expansion of the CFIO-based solution is correct, even though it also experiences the nonuniqueness of the EFIO- and MFIO-based solutions.

In the present article the classical problem of electromagnetic scattering by a single homogeneous sphere is revisited. Main focus is the study of the scattering behavior as a function of the material contrast and the size parameters for all electric and magnetic resonances of a dielectric sphere. Specifically, the Pad\'e approximants are introduced and utilized as an alternative system expansion of the Mie coefficients. Low order Pad\'e approximants can give compact and physically insightful expressions for the scattering system and the enabled dynamic mechanisms. Higher order approximants are used for predicting accurately the resonant pole spectrum. These results are summarized into general pole formulae, covering up to fifth order magnetic and forth order electric resonances of a small dielectric sphere. Additionally, the connection between the radiative damping process and the resonant linewidth is investigated. The results obtained reveal the fundamental connection of the radiative damping mechanism with the maximum width occurring for each resonance. Finally, the suggested system ansatz is used for studying the resonant absorption maximum through a circuit-inspired perspective., Comment: 8 pages, 4 figures

The theory of characteristic modes (TCMs) based on the surface integral equation (SIE) formalism is presented for the analysis of plasmonic nanostructures. With TCM, excitation-independent characteristic solutions of the underlying electromagnetic field problem are obtained. Both single and multiple particle nanostructures are analyzed using the conventional SIE approach and the TCM formalism. By comparing these results, the modes that are responsible of the observed scattering and absorption characteristics can be identified. These solutions can be further utilized in the design and tuning nanoantenna configurations for specific application purposes.

We theoretically investigate whether a dielectric sphere can mimic the behavior of an equivalent surface impedance sphere and we discuss some of the of emergent properties, such as cloaking (minimum scattering) and maximum absorption conditions.

The surface integral equation (SIE) method, discretized with the method of moments, is a well-established methodology for the scattering analysis of subwavelength plasmonic nanoparticles. SIEs are usually discretized with low-order basis functions that preserve the normal continuity of the surface currents across the edges arising in the meshed boundary, such as Rao-Wilton-Glisson (RWG) functions. However, the plasmonic enhancement modeling on sharp-edged particles is an extremely challenging task, especially due to the singular fields exerted at sharp corners, exposing a slow (or no) convergence in the computation of the scattering and absorption spectra. In this paper, we propose an alternative discretization strategy based on a discontinuous basis function set in conjunction with a volumetric-tetrahedral testing scheme. We demonstrate the potential of the proposed discretization scheme by studying scattering and absorption spectra of three canonical plasmonic polyhedra, i.e., a hexahedral, an octahedral, and a tetrahedral silver inclusion. The results expose an improved accuracy and faster convergence in both far-field and near-field regions when compared to the standard RWG implementation. The proposed discretization scheme can offer faster and more accurate routes towards the exploration and design of the plasmonic resonant spectrum of sharp-edged nanoparticles and nanoantennas.

The absorption characteristics of a dielectric, isotropic sphere in the plasmonic regime are analyzed. Relations are derived for the position of the maximum absorption efficiency for the first electric dipole resonance mode. The dissipation results are connected with the natural frequencies of the sphere as well as to the circuit-inspired matching analogy for optimum absorption.

With analytical (generalized Mie scattering) and numerical (integral-equation-based) considerations we show the existence of strong resonances in the scattering response of small spheres with a lossless impedance boundary. With increasing size, these multipolar resonances are damped and shifted with respect to the magnitude of the surface impedance. The electric-type resonances are inductive and the magnetic ones capacitive. Interestingly, these subwavelength resonances resemble plasmonic resonances in small negative-permittivity scatterers but occur in two families unlike the only-electric multipoles in the plasmonic case. The fundamental dipolar mode is also analyzed from the point of view of surface currents and the effect of the change of the shape into a nonspherical geometry. For dissipative impedance scatterers, maximum absorption is shown to result in the matched-impedance case.

In this work the polarizability of a subwavelength core-shell sphere is considered, where the shell exhibits a radially inhomogeneous permittivity profile. A mathematical treatment of the elec- trostatic polarizability is formulated in terms of the scattering potentials and the corresponding scattering amplitudes. As a result, a generalized expression of the polarizability is presented as a function of the radial inhomogeneity function. The extracted general model is applied for two particular cases, i.e., the well-known power-law profile and a new class of permittivity profiles that exhibit exponential radial dependence. The proposed analysis quantifies in a simple manner the inhomogeneity effects, allowing the direct implementation of naturally or artificially occurring permittivity inhomogeneities for a wide range of applications within and beyond the metamaterial paradigm. Furthermore, the described analysis open avenues towards the phenomenological and first-principles modeling of the electrodynamic scattering effects for graded-index plasmonic par- ticles at the nanoscale. Finally, such description can be readily used either for the benchmarking of novel computational methods incorporating inhomogeneous materials or for inverse scattering purposes., 21 pages, 4 figures

IB054. The general mathematical treatment for the electrostatic polarizability will be presented in terms of scattering potentials. The case of a power-law profile and a new class of permittivity profiles that exhibit an exponential-radial dependence are considered. The presented theoretical results can open multiple avenues towards the exploration/implementation of scatterers with more exotic permittivity profiles for RF/optics and remote sensing applications.

Using Mie scattering, we derive the characteristic modes of both conducting and dielectric spheres. The results also provide a physically clear interpretation of the imaginary part of the characteristic eigenvalues for lossy objects in general.

The use of the theory of characteristic modes for the study of plasmonic eigenstates of rounded hexahedral and octahedral nanoscatterers is proposed and presented. After a brief study of electrostatic modes in an hexahedral structure follows the corresponding characteristic mode analysis. The analysis reveals the existence, for the first time, of highly symmetric dark modes on the surface of a rounded cube, enhancing our views on the triggered scattering mechanisms for single nanoparticles.

A new surface integral equation based formulation for computing characteristic modes of lossless and lossy dielectric and magneto-dielectric bodies is presented. For lossy objects, the imaginary part of an eigenvalue gives the ratio of the dissipated and radiated power, while the real part is connected to the ratio of the reactive and radiated power.

TPID5200891TCMSIE. These solutions can provide important insights into the fundamental scattering and radiation properties of arbitrary structures that can be difficult and time consuming to achieve with conventional scattering analysis techniques. TCM has been found to be a particularly powerful tool in antenna design. It can enable systematic and intuitive antenna analysis with increased physical understanding and lead to antenna configurations with enhanced properties.

Light scattering by subwavelength spheres exhibiting a radially inhomogeneous permittivity are presented. The theoretical model for power-law, exponential, and Drude-like inhomogeneous profiles are discussed, generalizing the concept of polarizability for graded-index nanoparticles.

This presentation focuses on the electromagnetic scattering characteristics of spheres with surface defined by the impedance boundary condition. The results include resonances that are very strong and sharp for small subwavelength particles, and analogous to the localized surface plasmons.

Light scattering by a subwavelength sphere exhibiting a radially inhomogeneous permittivity profile is considered here. A generalization of the polarizability for radially inhomogeneous sphere is given in terms of a so-called inhomogeneity factor. The special case of an inhomogeneous Drude profile unveils a series of scattering peculiarities, motivating further discussion for the implementation of spheres with graded-index plasmonic profiles.

This article presents and discusses the general features and aspects regarding the electromagnetic scattering by a small core-shell plasmonic sphere. First, the thickness effects on the plasmonic resonances are presented in the electrostatic (Rayleigh) limit, utilizing the MacLaurin expansion of the Mie coefficients of hollow scatterers. Several aspects regarding the core effects are given, illustrating the enabling mechanisms and peculiarities of its resonant scattering response on it electrostatic limit. The electrodynamic aspects of the scattering process are revealed through the newly introduced Pad\'e expansion of the Mie coefficients. Additionally we expose how the core material affects the dynamic mechanisms, such as the dynamic depolarization and radiative damping. The described method can be expanded for other type of resonances and canonical shapes, while the general characteristics presented here are expected to stimulate further studies regarding the functionalities of the core-shell scatterers., Comment: 8 pages, 3 figures, under review to IEEE TAP

In this extended paper we discuss the directive scattering characteristics of small dielectric spheres. Particularly, a recently introduced heuristic method utilizing the Pade approximants of the Mie coefficients is presented. With this method the resonant conditions of the magnetic multipole resonances are extracted. We expand the described method for exploring the Kerker radiation conditions, i.e., maximum forward and backscattering, for the case of a dielectric, non-magnetic sphere. The presented and results enhance our physical intuition of the triggered mechanisms and can be readily used as guidelines for the design of Huygens sources and other all-dielectric composites.

A classical way for exploring the scattering behavior of a small sphere is to approximate Mie coefficients with a Taylor series expansion. This ansatz delivered a plethora of insightful results, mostly for small spheres supporting localized plasmonic resonances. However, many scattering aspects are still uncharted, especially with regards to magnetic resonances. Here, an alternative system ansatz is proposed based on the Pad\'e approximants for the Mie coefficients. The result reveal the existence of a self-regulating radiative damping mechanism for the first magnetic resonance and new general resonating aspects for the higher order multipoles. Hence, a systematic way of exploring the scattering behavior is introduced, sharpening our understanding about the sphere's scattering behavior and its emergent functionalities., Comment: 10 pages, 2 figures

In this paper, the resonant spectrum of plasmonic, Drude-like, silver nano-antennas is presented. The central focus is the study of the radiation pattern of shapes, such as rounded cornered hexahedra and octahedra, under a full electrodynamic surface integral equation numerical scheme. Several aspects regarding their dipole, quadrupole, and higher order far-field distribution are revealed, giving special emphasis in their qualitative characteristics. Aspects of their resonant behavior, such as quadrupole mode “Huygens” nano-antennas or peculiarities related with their far field planes are further discussed, expanding our understanding on single plasmonic nano-antennas and their emerging functionalities.

We describe a teaching experiment conducted in a hands-on antenna course in Aalto University. The course was specifically designed to fulfill the higher level (senior master's and post-graduate) educational objectives and it was implemented by applying the principles of the “progressive inquiry” model. The model was introduced and applied in two practical assignments, giving special emphasis on skills such as group cooperation and expertise development within realistic scenes, i.e., reverse engineering and collaboration with a company.

The theory of characteristic modes (TCM) is applied to analyze optical properties of plasmonic nanoparticles. TCM gives excitation independent characteristic solutions of the electromagnetic problem formulated with surface integral equations and can provide additional information of the plasmonic resonances that can be difficult to obtain with conventional electromagnetic field analysis methods.

In this work the extraction and evaluation of student's aptitude of a master's level, electromagnetics class (Fall 2015) at Aalto University has been done using both pre- and post-course conceptual tests and homework assignments. Several qualitative results obtained, mostly revealing trends in certain areas of electricity and magnetism. An almost linear trend regarding the pre- and post-test results is extracted, while a correlation scheme between homework scores and student's learning gain is obtained. These results might be used for both educational and statistical purposes, asserting the overall educational process with tools and knowledge towards properly designed courses and student oriented electromagnetics pedagogy.

The resonant response of prolate nano-spheroids is numerically investigated via a surface integral equation method. Several results, such as the surface field distribution of dipole and higher order modes, the normalized extinction and the plasmonic albedo as a function of the axial ratio of the nano-scatterer, are obtained. These results verify a geometrically induced red-shift for the main dipole mode, while several novel insights are also presented and discussed related to higher order modes characteristics of spheroidal nano-antennas.

In this paper, a simulated and measured results of a broadband monopole antenna is presented. The proposed design will be used in the RF power scavenger application of the 2016 IEEE AP-S Student Design Contest. The antenna has a −6-dB impedance bandwidth from 930 MHz up to 2420 MHz and omnidirectional radiation pattern in the horizontal plane. The simulated and measured results indicate that the antenna is applicable to an RF scavenger.

The localized surface plasmon resonances of silver nanoparticles are explored by applying numerical full-wave electrodynamic simulations. In this work the plasmonic response of spherical, cubic and cylindrical rod-shaped silver nanoparticles, and shapes varying continuously between them are presented. The electrodynamic characterization is done by their extinction, albedo, and the corresponding resonant surface field distributions. Several shape effects on the plasmonic resonances are elucidated, enabling the proper adjustment of their response for application-oriented purposes.

This presentation focuses on the way how geometrical shape of nanoparticles affects the spectral properties of their surface plasmon resonances. Furthermore, intuitive understanding of the shifting of the plasmonic peaks can be gathered from quasistatic results. The domain of validity of the quasistatic analysis is charted for different types of nanoparticles.

Light scattering by a small spherical particle, a central topic for electromagnetic scattering theory, is here considered. In this short review, some of the basic features of its resonant scattering behavior are covered. First, a general physical picture is described by a full electrodynamic perspective, the Lorenz–Mie theory. The resonant spectrum of a dielectric sphere reveals the existence of two distinctive types of polarization enhancement: the plasmonic and the dielectric resonances. The corresponding electrostatic (Rayleigh) picture is analyzed and the polarizability of a homogeneous spherical inclusion is extracted. This description facilitates the identification of the first type of resonance, i.e., the localized surface plasmon (plasmonic) resonance, as a function of the permittivity. Moreover, the electrostatic picture is linked with the plasmon hybridization model through the case of a step-inhomogeneous structure, i.e., a core–shell sphere. The connections between the electrostatic and electrodynamic models are reviewed in the small size limit and details on size-induced aspects, such as the dynamic depolarization and the radiation reaction on a small sphere are exposed through the newly introduced Mie–Padé approximative perspective. The applicability of this approximation is further expanded including the second type of resonances, i.e., the dielectric resonances. For this type of resonances, the Mie–Padé approximation reveals the main character of the two different cases of resonances of either magnetic or electric origin. A unified picture is therefore described encompassing both plasmonic and dielectric resonances, and the resonant conditions of all three different types are extracted as functions of the permittivity and the size of the sphere. Lastly, the directional scattering behavior of the first two dielectric resonances is exposed in a simple manner, namely the Kerker conditions for maximum forward and backscattering between the first magnetic and electric dipole contributions of a dielectric sphere. The presented results address several prominent functional features, aiming at readers with either theoretical or applied interest for the scattering aspects of a resonant sphere.

The scattering properties of a lossless isotropic dielectric sphere as a function of its relative permittivity are studied and presented. The analytically calculated extinction efficiency spectrum reveal several regions of particular interest, such as plasmonic and dielectric resonances. Additional details about the resonant properties are illustrated from a Poynting streamline perspective. As a result, different aspects of resonant spheres from microwave to optical regime are given physical interpretation, revealing emerging functionalities for plasmonic-dielectric engineered applications.

The resonant plasmonic properties of small dual rounded nanoscatterers are numerically investigated. A set of silver (Drude-like) hexahedral and octahedral structures are studied and compared with a reference spherical particle through a numerical surface integral equation technique. Surface, near-field, Poynting field, and streamline distributions are presented illustrating novel plasmonic features arising from the complex shapes of the nanoparticles, while several designing rules are described. These qualitative observations can be used appropriately toward sensing, sorting, harvesting, and radiation control applications.