Volodymyr O. Byelobrov

Periodicity-induced effects in the scattering and absorption of light by infinite and finite gratings of circular silver nanowires

We study numerically the effect of periodicity on the plasmon-assisted scattering and absorption of visible light by infinite and finite gratings of circular silver nanowires. The infinite grating is a convenient object of analysis because of the possibility to reduce the scattering problem to one period. We use the well-established method of partial separation of variables however make an important improvement by casting the resulting matrix equation to the Fredholm second-kind type, which guarantees convergence. If the silver wires have sub-wavelength radii, then two types of resonances co-exist and may lead to enhanced reflection and absorption: the plasmon-type and the grating-type. Each type is caused by different complex poles of the field function. The low-Q plasmon poles cluster near the wavelength where dielectric function equals -1. The grating-type poles make multiplets located in close proximity of Rayleigh wavelengths, tending to them if the wires get thinner. They have high Q-factors and, if excited, display intensive near-field patterns. A similar interplay between the two types of resonances takes place for finite gratings of silver wires, the sharpness of the grating-type peak getting greater for longer gratings. By tuning carefully the grating period, one can bring together two resonances and enhance the resonant scattering of light per wire by several times.

Optical Theorem Helps Understand Thresholds of Lasing in Microcavities With Active Regions

Within the framework of the recently proposed approach to view the lasing in open microcavities as a linear eigenproblem for the Maxwell equations with exact boundary and radiation conditions, we study the correspondence between the modal thresholds and field overlap coefficients. Macroscopic gain is introduced into the cavity material within the active region via the “active” imaginary part of the refractive index. Each eigenvalue is constituted of two positive numbers, namely, the lasing wavenumber and the threshold value of material gain. This approach yields clear insight into the lasing thresholds of individual modes. The Optical Theorem, if applied to the lasing-mode field, puts the familiar “” condition on firm footing. It rigorously quantifies the role of the spatial overlap of the mode E-field with the active region, whose shape and location are efficient tools of the threshold manipulation. Here, the effective mode volume in open resonator is introduced from first principles. Examples are given for the 1-D cavities equipped with active layers and distributed Bragg reflectors and 2-D cavities with active disks and annular Bragg reflectors.

Binary Grating of Subwavelength Silver and Quantum Wires as a Photonic-Plasmonic Lasing Platform With Nanoscale Elements

This paper considers the scattering of an H-polarized plane wave by a freestanding periodic grating that contains two circular cylinders on each period, one made of silver and the other of dielectric. If such a grating is made of deeply subwavelength wires, the reflection and transmission coefficients demonstrate both plasmon and grating resonances. To clarify them, we also discuss the scattering by similar gratings made of either silver or dielectric wires only. However, the main attention is paid to the associated lasing eigenvalue problem for the dielectric cylinders pumped to become quantum wires, i.e., to obtain a “negative-absorption” complex refractive index. The analysis is done using a meshless analytical-numerical method with guaranteed convergence. The computations show that, in this composite periodic cavity, material thresholds of lasing for the grating modes can be much lower than for the plasmon modes.

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

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 noble-metal 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.

Reflection properties and lasing modes in the H-polarization case for an infinite chain of dielectric and silver nanowires

We study the scattering of the H-polarized plane wave by a freestanding periodic grating that contains two circular cylinders on a single period, one made of silver and another dielectric. The reflection and transmission coefficients for such a grating demonstrate several types of resonances including plasmons and grating resonances. Besides, we analyze the associated eigenvalue problem where the dielectric cylinders are so-called quantum wires, i.e. have “negative-absorption” or “active” refractive index. The comparison of eigensolutions for the grating modes of two active chains, one with and another without silver elements shows that the thresholds of lasing are higher in the former case, apparently because of the losses in silver.

Comparison of resonance optical scattering of plane waves by infinite gratings of silver cylinders and strips

Periodic structures possess a specific feature, there is a set of high quality resonances near to the wavelength equal to the grating period and their Q-factors rise higher if the grating becomes sparser. Making a grating from silver elements brings other resonances - surface-plasmon ones appearing in the visible-light band. We investigate interaction between the grating and the plasmon resonances in the scattering and absorption by infinite gratings of silver circular cylinders and silver thin strips, for the E and H-polarization cases.

Plasmon and structure resonances in the scattering of light by a periodic chain of silver nanocylinders

In this paper, we study the scattering of the H-polarized plane wave by an infinite periodic chain of silver circular cylinders standing in free space. The scattering problem is reduced to a matrix equation with favourable features using the method of partial separation of variables. In the visible-light band, we demonstrate an interesting interaction of two types of resonances: the localized surface plasmons of the nanosize cylinders and a specific grating-type resonance near the wavelength equal to the chain period.

Lasing modes of infinite periodic chain of quantum wires

In this paper, we study the scattering and eigenvalue problems for a periodic open optical resonator that is an infinite chain of active circular cylindrical quantum wires standing in free space. The scattering problem is solved by the method of partial separation of variables. The eigenvalue problem differs from the first one by the absence of the incident field and presence of “active properties” of cylinders and yields the frequencies and thresholds of lasing.

Basic ideas and advantages of the method of analytical regularization in wave optics: Overview

By the method of analytical regularization (MAR) we understand a family of techniques casting the electromagnetic boundary-value problems to the Fredholm second-kind infinite- matrix equations, with or without intermediate stage of the Fredholm second kind integral equation (IE). This approach possesses many merits however is rarely used in computational optics and photonics. In the optical, infrared and THz ranges, perfect electrical conductor (PEC) condition cannot be used to approximate even noble-metal scatterers. Therefore for thick material bodies the most universal and reliable computational instrument of MAR is Muller boundary IE. Still thinner-than- wavelength material screens can be characterized with effective (i.e. resistive, dielectric, and impedance) boundary conditions, which allow adapting the MAR solutions previously developed in the scattering by PEC zero-thickness screens. In any case MAR enables numerically exact analysis of both the scattering and the absorption of optical, infrared and THz waves by various scatterers made of graphene, dielectrics and metals.

Essentials and merits of the method of analytical regularization in computational optics and photonics

Although still underestimated in computational optics and photonics, the conversion of electromagnetic field problems to the Fredholm second kind integral equations (IEs), also called analytical regularization, and finally Fredholm second-kind infinite-matrix equations has many remarkable merits. We discuss them at the background of specific features of material properties of metals and dielectrics in the optical range.