Електродинамічне моделювання лазера на основі решітки зі скінченної кількості срібних нанониток з активними оболонками
| Jazyk: | angličtina |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Electromagnetic field
Physics Field (physics) lcsh:T58.5-58.64 lcsh:Information technology Mathematical analysis Plane wave Characteristic equation Physics::Optics 02 engineering and technology 01 natural sciences 010309 optics Lattice (module) symbols.namesake 020210 optoelectronics & photonics Maxwell's equations 0103 physical sciences 0202 electrical engineering electronic engineering information engineering symbols Lasing threshold Eigenvalues and eigenvectors нанонитка срібло решітка власна мода ґраткова мода поріг лазерна генерація |
| Zdroj: | Системи обробки інформації, Iss 1(160), Pp 73-79 (2020) |
| ISSN: | 2518-1696 1681-7710 |
| Popis: | We solve a source-free problem of the electromagnetic field in the presence of a grating from finite number of silver nanowires coated with active shells. For the electrodynamic modeling we use the mathematically grounded Lasing Eigenvalue Problem (LEP) approach. The LEP is a specific electromagnetic-field eigenvalue problem, which is tailored to extract the wavelengths of the modes together with the associated threshold material gain values from linear Maxwell equations. In our problem statement we look for the frequency of the lasing mode, which has real values in the LEP statement, and for the correspondent value of material gain threshold in the active shell. We find such two-component eigenvalues from characteristic equation, built using the each wire field expansions in local coordinates and addition theorems for cylindrical functions. This is a homogeneous Fredholm second-kind block-type matrix equation. This means that its determinant exists as a function of the parameters of LEP. The Fredholm nature of the matrix operator guarantees that the zeros of the truncated determinant converge to the exact ones if the truncation order gets larger. The roots of such equation we find using the secant method. We find them numerically with controlled accuracy. We look for a lattice lasing modes and study dependences of their threshold values and wavelengths on the variant parameters: silver core radii, number of wires in a grating, shell thickness. We take the initial-guess values of mode’s wavelength as the wavelengths of the resonance peaks of the total scattering cross-section spectra in the corresponding scattering problem with the plane wave normal incidence. We demonstrate that the lattice lasing modes have many times lower self-excitation thresholds (about 10–2–10–3) than other types of modes. We also demonstrate that in large gratings, besides the principle lattice mode, there are also other secondary lattice modes. With an increase of the number of nanowires in the grating, the self-excitation threshold of the lattice modes decreases, because of its periodically-caused nature. |
| Databáze: | OpenAIRE |
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