Herasymova Dariia O, Dukhopelnykov Sergii V, Natarov Denys M, Zinenko Tatiana L, Lucido Mario, Nosich Alexander I
Laboratory of Micro and Nano Optics, Institute of Radio-Physics and Electronics NASU, Kharkiv, Ukraine.
Department of Applied Mathematics, V. N. Karazin Kharkiv National University, Kharkiv, Ukraine.
Nanotechnology. 2022 Sep 21;33(49). doi: 10.1088/1361-6528/ac8e0c.
We implement the lasing eigenvalue problem (LEP) approach to study the electromagnetic field in the presence of a circular quantum wire (QW) made of a gain material and wrapped in graphene cover and a dimer of two identical graphene-covered QWs, at the threshold of stationary emission. LEP delivers the mode-specific eigenvalue pairs, namely the frequencies and the threshold values of the QW gain index for the plasmon and the wire modes of such nanolasers. In our analysis, we use quantum Kubo formalism for the graphene conductivity and classical Maxwell boundary-value problem for the field functions. The technique involves the resistive boundary conditions, the separation of variables in the local coordinates, and, for the dimer, the addition theorem for the cylindrical functions. For single-wire plasmonic laser, we derive approximate engineering expressions for the lasing frequencies and threshold values of the gain index that complement the full-wave computations. For the dimer, we derive separate determinantal equations for four different classes of symmetry of the lasing supermodes and solve them numerically. Our investigation of the mode frequencies and thresholds versus the graphene and QW parameters shows that plasmon modes or, for the dimer, plasmon supermodes have lower frequencies and thresholds than the wire modes provided that the QW radius is smaller than 10m, however in thicker wires they are comparable. Only the plasmon-mode characteristics are well-tunable using the graphene chemical potential. In the dimer, all lasing supermodes form closely located quartets, however, they quickly approach the single-wire case if the inter-wire separation becomes comparable to the radius. These results open a way for building essentially single-mode plasmonic nanolasers and their arrays and suggest certain engineering rules for their design.
我们采用激光本征值问题（LEP）方法来研究在稳态发射阈值下，由增益材料制成并包裹在石墨烯中的圆形量子线（QW）以及两个相同的石墨烯包覆量子线二聚体存在时的电磁场。LEP给出了特定模式的本征值对，即此类纳米激光器的等离子体激元模式和量子线模式的频率以及量子线增益指数的阈值。在我们的分析中，我们对石墨烯电导率使用量子久保形式，对场函数使用经典麦克斯韦边值问题。该技术涉及电阻边界条件、局部坐标中的变量分离，对于二聚体，还涉及圆柱函数的加法定理。对于单线等离子体激元激光器，我们推导了激光频率和增益指数阈值的近似工程表达式，以补充全波计算。对于二聚体，我们为激光超模的四种不同对称类推导了单独的行列式方程并进行数值求解。我们对模式频率和阈值与石墨烯和量子线参数的研究表明，只要量子线半径小于10m，等离子体激元模式或对于二聚体而言的等离子体激元超模具有比量子线模式更低的频率和阈值，然而在较粗的量子线中它们相当。只有等离子体激元模式的特性可以通过石墨烯化学势很好地调节。在二聚体中，所有激光超模形成紧密相邻的四重态，然而，如果线间间距变得与半径相当，它们会迅速接近单线情况。这些结果为构建基本单模的等离子体激元纳米激光器及其阵列开辟了道路，并为其设计提出了某些工程规则。
