The original Kerker effect was introduced for a hypothetical magnetic sphere, and initially it did not attract much attention due to a lack of magnetic materials required. Rejuvenated by the recent explosive development of the field of metamaterials and especially its core concept of optically-induced artificial magnetism, the Kerker effect has gained an unprecedented impetus and rapidly pervaded different branches of nanophotonics. At the same time, the concept behind the effect itself has also been significantly expanded and generalized. Here we review the physics and various manifestations of the generalized Kerker effects, including the progress in the emerging field of meta-optics that focuses on interferences of electromagnetic multipoles of different orders and origins. We discuss not only the scattering by individual particles and particle clusters, but also the manipulation of reflection, transmission, diffraction, and absorption for metalattices and metasurfaces, revealing how various optical phenomena observed recently are all ubiquitously related to the Kerker’s concept.

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Generalized Kerker effects in nanophotonics and meta-optics [Invited]

http://ieeexplore.ieee.org/iel5/5/31314/01456639.pdf

Electromagnetic theory of gratings

The original Kerker effect was introduced for a hypothetical magnetic sphere, and initially it did not attract much attention due to a lack of magnetic materials required. Rejuvenated by the recent explosive development of the field of metamaterials and especially its core concept of optically-induced artificial magnetism, the Kerker effect has gained an unprecedented impetus and rapidly pervaded different branches of nanophotonics. At the same time, the concept behind the effect itself has also been significantly expanded and generalized. Here we review the physics and various manifestations of the generalized Kerker effects, including the progress in the emerging field of meta-optics that focuses on interferences of electromagnetic multipoles of different orders and origins. We discuss not only the scattering by individual particles and particle clusters, but also the manipulation of reflection, transmission, diffraction, and absorption for metalattices and metasurfaces, revealing how various optical phenomena observed recently are all ubiquitously related to the Kerker's concept.

Generalized Kerker Effects in Nanophotonics and Meta-Optics

We discuss the foundations and state-of-the-art of the method of analytical regularization (MAR) (also called the semi-inversion method). This is a collective name for a family of methods based on conversion of a first-kind or strongly-singular second-kind integral equation to a second-kind integral equation with a smoother kernel, to ensure point-wise convergence of the usual discretization schemes. This is done using analytical inversion of a singular part of the original equation; discretization and semi-inversion can be combined in one operation. Numerous problems being solved today with this approach are reviewed, although in some of them, MAR comes in disguise.

The method of analytical regularization in wave-scattering and eigenvalue problems: foundations and review of solutions

To achieve efficient light control at subwavelength dimensions, plasmonic and all-dielectric nanoparticles have been utilized both as a single element as well as in the arrays Here we study 2D periodic nanoparticle arrays (metasurfaces) that support lattice resonances near the Rayleigh anomaly due to the electric dipole (ED) and magnetic dipole (MD) resonant coupling between the nanoparticles Silicon and core-shell particles are considered Our investigations are carried out using two independent numerical techniques, namely, the finite-element method and the method of coupled-dipole equations based on the Green function approach We numerically demonstrate that choosing of lattice periods independently in each mutual-perpendicular direction, it is possible to achieve a full overlap between the ED-lattice resonance and MD resonances of nanoparticles in certain spectral range and to realize the resonant lattice Kerker effect (resonant suppression of the backward scattering or reflection) At the effect conditions, the strong suppression of light reflectance in the structure is appeared due to destructive interference between electromagnetic waves scattered by ED and MD moments of every nanoparticle in the backward direction with respect to the incident light wave Influence of the array size on the revealed reflectance and transmittance behavior is discussed The resonant lattice Kerker effect based on the overlap of both ED and MD lattice resonances is also demonstrated

Resonant Lattice Kerker Effect in Metasurfaces With Electric and Magnetic Optical Responses

As a generalization of the Gamma function defined for a single complex variable, a new special function called a generalized Gamma function, defined for two complex variables and a positive integer, is introduced, and several important analytical properties are investigated in detail, which include regularity, asymptotic expansions and analytic continuations. Furthermore, as a function closely related to a generalized Gamma function, a generalized incomplete Gamma function, which is a generalization of the incomplete Gamma function, is also introduced, and some fundamental properties are investigated briefly.

On Generalized Gamma Functions Occurring in Diffraction Theory

This article reviews the nature and history of the discovery of high-quality natural modes existing on periodic arrays of many subwavelength scatterers; such arrays can be viewed as specific periodically structured open resonators. These grating modes (GMs), like any other natural modes, give rise to the associated resonances in electromagnetic-wave scattering and absorption. Their complex wavelengths are always located very close to (but not exactly at) the well-known Rayleigh anomalies (RAs), determined only by the period and the angle of incidence. This circumstance has long been a reason for their misinterpretation as RAs, especially in the measurements and simulations using low-resolution methods. In the frequency scans of the reflectance or transmittance, GM resonances usually develop as asymmetric Fano-shape spikes. In the optical range, if a grating is made of subwavelength-size noblemetal elements, then GMs exist together with better-known localized surface-plasmon (LSP) modes. Thanks to high tunability and considerably higher Q-factors, the GM resonances can potentially replace the LSP-mode resonances in the design of nanosensors, nanoantennas, and solar-cell nanoabsorbers.

Periodicity Matters: Grating or lattice resonances in the scattering by sparse arrays of subwavelength strips and wires.

The diffraction of a plane electromagnetic wave by a thick strip grating is solved rigorously by the Wiener-Hopf technique. The solution contains an infinite number of unknowns, which are shown to satisfy a certain infinite set of equations. By applying the modified residue calculus technique, this set of equations is solved and the approximate solution is derived. Representative numerical examples are given and the transmission characteristics of the grating are discussed. >

Diffraction of a plane wave by a thick strip grating

High-frequency diffraction by a strip was previously analyzed approximately by the Geometrical Theory of Diffraction (GTD), but the GTD solution has an essential difficulty that it is valid only in the limited range of incidence and observation angles. To overcome this difficulty, in this paper, plane wave diffraction by a strip is reconsidered using the Wiener-Hopf technique and the complete high-frequency asymptotic solution is obtained, which is uniformly valid everywhere in space and has no restrictions on incidence and observation angles. Further asymptotic expansion is also carried out to derive the non-uniform asymptotic solution, which is compared with the previous GTD solution. As a result, some discrepancies are recognized.

Plane Wave Diffraction by a Strip:Exact and Asymptotic Solutions*

We investigate the emission of waves by a thin silver nanostrip placed into the center of a circular quantum wire (QWR), in the visible-light range. Our analysis uses the mathematically grounded approach called lasing eigenvalue problem (LEP). Keeping in mind that at the threshold the lasing-mode frequency is real valued (does not attenuate in time), the LEP is formulated as a boundary-value problem for the Maxwell equations with exact boundary conditions and the Sommerfeld radiation condition. The eigenvalues are pairs of real numbers, where the first is the emission wavelength and the second is the associated threshold value of material gain in the QWR. Due to the twofold symmetry of the cross-sectional geometry, we split the studied problem into four different independent classes of symmetry and derive four symmetry-adapted Green's functions of the QWR without strip. On imposing the generalized boundary conditions and taking into account these Green's functions, we obtain four independent integral equations (IEs) at strip's median line. We discretize these IEs with the Nystrom-type schemes and further look for the eigenvalues of each class separately with the aid of iterative search algorithm. Our analysis shows that such a plasmonic-strip-based nanolaser can emit visible light on the localized surface plasmon modes and also on the shell modes or QWR polariton modes perturbed by the strip. Single-mode operation is apparently possible provided that the QWR diameter is small, and hence, the first shell mode is blue-shifted.

Kazuya Kobayashi

Papers

On Generalized Gamma Functions Occurring in Diffraction Theory

Periodicity Matters: Grating or lattice resonances in the scattering by sparse arrays of subwavelength strips and wires.

Diffraction of a plane wave by a thick strip grating

Plane Wave Diffraction by a Strip:Exact and Asymptotic Solutions*

Electromagnetic Engineering of a Single-Mode Nanolaser on a Metal Plasmonic Strip Placed into a Circular Quantum Wire