Zinenko Tatiana L, Ctyroky Jiri, Nosych Oleksandr I
O Ya Usikov Institute for Radiophysics and Electronics National Academy of Sciences of Ukraine, Kharkiv, Ukraine.
Institute of Photonics and Electronics Czech Academy of Sciences, Prague, Czech Republic.
Philos Trans A Math Phys Eng Sci. 2025 Aug 14;383(2303):20240350. doi: 10.1098/rsta.2024.0350.
We study the threshold conditions for the natural modes of the microsize plasmonic laser shaped as an infinite flat graphene strip grating symmetrically embedded into the gain-material layer, in the H-polarization case. For this purpose, we solve the lasing eigenvalue problem (LEP), which is a classical source-free electromagnetic field boundary-value problem, adapted to the presence of the active region by the corresponding sign of the imaginary part of the refractive index. In such a way we look for the eigenpairs, i.e. the stimulated emission real-valued frequency and the threshold gain index, specific to each mode. We transform LEP to a hypersingular integral equation for the on-strip current density and discretize it by the regularizing Galerkin technique. This procedure leads to a determinantal equation with guaranteed convergence to the exact LEP eigenpairs and controlled accuracy of their computation. The numerical analysis allows us to study the threshold conditions for various lasing modes of the microsize laser, identify them and trace their change when varying the parameters of the lasing structure.This article is part of the theme issue 'Analytically grounded full-wave methods for advances in computational electromagnetics'.
我们研究了在H偏振情况下，形状为对称嵌入增益材料层的无限扁平石墨烯带光栅的微尺寸等离子体激光器自然模式的阈值条件。为此，我们求解激光本征值问题（LEP），这是一个经典的无源电磁场边值问题，通过折射率虚部的相应符号来适应有源区的存在。通过这种方式，我们寻找特定于每种模式的本征对，即受激发射实值频率和阈值增益指数。我们将LEP转换为带状电流密度的超奇异积分方程，并通过正则化伽辽金技术对其进行离散化。这一过程导致一个行列式方程，保证收敛到精确的LEP本征对，并控制其计算精度。数值分析使我们能够研究微尺寸激光器各种激光模式的阈值条件，识别它们并跟踪在改变激光结构参数时它们的变化。本文是主题为“计算电磁学进展的解析基础全波方法”的一部分。
