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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...
Presented are preliminary results related to two electromagnetic-wave problems: of the plane-wave scattering by a silver strip placed into a circular dielectric shell and of the wave emission by the same strip inserted into a quantum wire (QW), in the optical range. Auxiliary analysis is focused on the wavelength dependence of the total scattering cross-section of such resonant scatterer. Then we...
Considered is the two-dimensional (2-D) source-free problem of the H-polarized electromagnetic field in the presence of a silver circular nanotube coated with a concentric layer of active material and with a core of similar active material. We assume that the natural-mode frequency is real-valued and look for it together with the threshold value of material gain in the active regions. As a method,...
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...
We present the results of numerical simulation of the scattering of the H-polarized electromagnetic wave by a finite grating made of dielectric nanowires, in the visible range of light. Numerical solution uses the field expansions in local coordinates of each wire and addition theorems for cylindrical functions and has a guaranteed convergence. Numerical results are presented for the analysis of the...
Considered is the two-dimensional (2-D) source-free problem of the H-polarized electromagnetic field in the presence of a silver circular cylindrical nanowire coated with a concentric layer of active material. We assume that the natural-mode frequency is real-valued and find it together with the corresponding threshold value of material gain in the active coating. To this end, we use the separation...
We present the results of numerical simulation of the scattering and absorption of the H-polarized electromagnetic wave by several discrete scatterers made of silver nanowires in visible range. Using the Fourier expansions and addition theorems for cylindrical functions, we perform analytical regularization and obtain a block-type Fredholm second-kind matrix equation for the scattered-field expansion...
Plasmon-assisted nanolasers are actively considered today as miniature sources of light for advanced photonics applications. We study the lasing modes a circular cylindrical nanowire made of silver, coated with a concentric layer of active material. The electromagnetic problem is two-dimensional (2-D) and implies the H-polarization regime where localized surface-plasmon (LSP) modes exist on metal...
We consider the two-dimensional (2-D) problem of the H-polarized electromagnetic field that can exist in the presence of a circular cylindrical nanowire made of silver, coated with a concentric layer of active material. Assuming that the natural-mode frequency is real-valued, we look for it together with the associated threshold value of material gain in the coating. Using the separation of variables,...
We consider the two-dimensional (2-D) scattering of the H- and E-polarized plane waves by several discrete configurations made of M> > 1 periodically arranged circular cylindrical silver wires. To find the scattered field, we use the field Fourier expansions in local coordinates and addition theorems for cylindrical functions. Resulting M × M block-type matrix equation is cast to the Fredholm...
We consider the problem of the H-polarized plane wave scattering by a linear chain of silver nanowires in a cloud of similar arbitrarily located wires, in the visible range. Numerical solution uses the field expansions in local coordinates and addition theorems for cylindrical functions and has a guaranteed convergence. The total scattering cross-sections and near-zone and far-zone field patterns...
This paper reviews the history of discovery and the study of the nature of the high-quality natural modes existing on periodic arrays of sub-wavelength scatterers as specific periodically structured open resonators. Here, the arrays can be finite and infinite, and their elements can be dielectric and metallic. These grating modes (G-modes), like any other natural modes, are the “parents” of corresponding...
Focusing of waves using solid reflectors is widely used in optics and quasioptics, parabolic reflectors being the most popular and efficient ones. Periodically structured scatterers have been attracting attention of researchers for a long time because of the interesting effects of extraordinary large reflection, transmission and near-field enhancement [1–4]. For the finite periodic gratings...
We present a mini-review on the discovery, nature and characterization of the specific family of natural modes existing on periodic arrays of both dielectric and metallic sub-wavelength scatterers, and the corresponding to them resonances in the optical-range wave scattering and absorption. These grating modes (G-modes) have been studied analytically for the gratings of thin flat strips and those...
We study the scattering and absorption of an H-polarized plane electromagnetic wave by a silver nanowire, in the visible range of wavelengths. The wire is assumed to have circular cross-section and coated with a concentric circular dielectric layer. The analytical solution of the wave-scattering problem is obtained in classical manner, using the separation of variables and the transfer-matrix method...
We consider the two-dimensional (2-D) problem of the H-polarized plane wave scattering by discrete arrays made of finite number of periodically arranged circular cylindrical nanowires. Using the Fourier expansions of the field in local coordinates and addition theorems for cylindrical functions, we perform analytical regularization and obtain a block-type matrix equation. This equation is cast to...
Two fundamental effects are known to influence the scattering of light by periodically structured metal scatterers. From the one hand, surface-plasmon resonances are observed for subwavelength noble-metal particles and wires in the mid-infrared and optical bands [1, 2]. Nanosize objects can exhibit resonance behavior at certain frequencies for which the object permittivity is negative. This results...
The scattering of the H-polarized wave by single- and double-layer grids of circular silver nanowires is considered. The obtained results demonstrate the presence of plasmon and grid resonances in such grids. These resonances are found and computed for the grids of a large number of wires. Extraordinary resonance enhancement is discovered if both kinds of resonances are tuned together. Comparison...
Using the field expansions in local coordinates and addition theorems for cylindrical functions, we consider the problem of the H-polarized waves scattered by finite chains of circular wires. The scattering and absorption cross-sections are found numerically and localized-plasmon and periodicity-caused resonances are studied for the visible light scattering by the grids of closely spaced nanowires...
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