Efficient method for lasing eigenvalue problems of periodic structures

Huang, Yuexia; Lu, Ya Yan

doi:10.1080/09500340.2014.887799

Cited by 11 publications

(4 citation statements)

References 24 publications

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“…Note that other LEP-like formulations exist [22][23][24][25][26]. They differ from what is presented by us in the way of introduction of the gain, for instance, as the imaginary part of not the refractive index but of the dielectric permittivity in active region, or a product of the imaginary part of the refractive index and the frequency.…”

Section: Introductionmentioning

confidence: 82%

Mathematical and Numerical Modeling of On-Threshold Modes of 2-D Microcavity Lasers with Piercing Holes

Spiridonov

Karchevskii

Nosich³

2019

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This study considers the mathematical analysis framework aimed at the adequate description of the modes of lasers on the threshold of non-attenuated in time light emission. The lasers are viewed as open dielectric resonators equipped with active regions, filled in with gain material. We introduce a generalized complex-frequency eigenvalue problem for such cavities and prove important properties of the spectrum of its eigensolutions. This involves reduction of the problem to the set of the Muller boundary integral equations and their discretization with the Nystrom technique. Embedded into this general framework is the application-oriented lasing eigenvalue problem, where the real emission frequencies and the threshold gain values together form two-component eigenvalues. As an example of on-threshold mode study, we present numerical results related to the two-dimensional laser shaped as an active equilateral triangle with a round piercing hole. It is demonstrated that the threshold of lasing and the directivity of light emission, for each mode, can be efficiently manipulated with the aid of the size and, especially, the placement of the piercing hole, while the frequency of emission remains largely intact.

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Section: Introductionmentioning

confidence: 82%

Mathematical and Numerical Modeling of On-Threshold Modes of 2-D Microcavity Lasers with Piercing Holes

Spiridonov

Karchevskii

Nosich³

2019

Axioms

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“…将折射率虚部引入增益项, 通过激光特征值公式可以得到激射波长和阈值的数值解 [110] , Vahala研究组 [22] 基于微球腔建立了拉曼激光阈值P th 与谐振腔Q 值、模式体积V之间的关系 [22] : : 力学; 与基于表面等离激元共振(Surface Plasmon Resonance, SPR)技术获得的灵敏度处于同一量级, 且具有更快的响应速度 [114] . 马仁敏研究组 [115] 提出一种激光增强型SPR传感器, 在金膜和氟化镁中间插入一层硒化镉作为增益层, 在光泵浦条件下与无源SPR器件相比其灵敏度提升约400倍, 将等离激元纳米激光器引入生化传感领域.…”

Section: 激光阈值变化unclassified

Micro- and nano-laser sensing: Principles and applications

Hu¹,

Wang²,

Jiang³

et al. 2023

Sci. Sin.-Phys. Mech. Astron.

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“…That is, we look for the frequencies and gain-index thresholds of laser modes as eigenvalue pairs. It is worth to note that the other LEP-like formulations exist, see [31][32][33][34][35], where the threshold gain is characterized with Im 0 e < instead of g or with the product, g k . g = In the dimer case, we introduce the global Cartesian and polar coordinates, with the origins at the midpoint between QW axes so that r x y r , , , ( ) (…”

Section: Lep Statementmentioning

confidence: 99%

Threshold conditions for transversal modes of tunable plasmonic nanolasers shaped as single and twin graphene-covered circular quantum wires

Herasymova¹,

Dukhopelnykov

Natarov³

et al. 2022

Nanotechnology

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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 10 μm, 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 suggests certain engineering rules for their design.

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Efficient method for lasing eigenvalue problems of periodic structures

Cited by 11 publications

References 24 publications

Mathematical and Numerical Modeling of On-Threshold Modes of 2-D Microcavity Lasers with Piercing Holes

Mathematical and Numerical Modeling of On-Threshold Modes of 2-D Microcavity Lasers with Piercing Holes

Micro- and nano-laser sensing: Principles and applications

Threshold conditions for transversal modes of tunable plasmonic nanolasers shaped as single and twin graphene-covered circular quantum wires

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