Symmetry accounting in the integral-equation analysis of lasing eigenvalue problems for two-dimensional optical microcavities

Spiridonov, Alexander O.; Karchevskii, Evgenii M.; Nosich, Alexander I.

doi:10.1364/josab.34.001435

Cited by 27 publications

(8 citation statements)

References 26 publications

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“…Besides of the frequency and threshold gain, another important characteristic of the mode emission is the far-field directivity, which is defined as (see [16,17]),…”

Section: Numerical Results For Lep For Pierced Equilateral Triangle Lmentioning

confidence: 99%

“…Now, following [41], p. 69, we present the Nyström method for numerical solution of nonlinear eigenvalue problem (14). Note that this method was applied, in the simplest form, in [16] and then sophisticated in [17], to take full account of possible symmetry lines of a 2-D cavity. Assume that each contour Γ j has a parameterization r j (t) = (r 1 j (t), r 2 j (t)), where r 1 j (t) = f j (t) cos t, r 2 j (t) = f j (t) sin t, and t ∈ [0, 2π].…”

Section: Nyström Methodsmentioning

confidence: 99%

“…Such observations lied in the core of the lasing eigenvalue problem (LEP) approach, suggested in [9][10][11] and applied to the on-threshold analysis of lasing modes of 2-D circular [10][11][12][13], and non-circular cavities: Limacon [14], ellipse [15], kite [16], square and other regular polygons [17]. As is easy to see, a presence of both active regions with gain material and lossy regions with absorptive material can be taken into account, in LEP, without any difficulty.…”

Section: Introductionmentioning

confidence: 99%

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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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“…Besides of the frequency and threshold gain, another important characteristic of the mode emission is the far-field directivity, which is defined as (see [16,17]),…”

Section: Numerical Results For Lep For Pierced Equilateral Triangle Lmentioning

confidence: 99%

Section: Nyström Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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 approach reduces computational time significantly and increases computational stability and accuracy, as shown in Spiridonov et al. [13], where a Nystrom discretisation was implemented.…”

Section: Galerkin Methods Based On the Symmetry Of The Problemmentioning

confidence: 99%

Trade‐off between threshold gain and directionality of emission for modes of two‐dimensional eccentric microring lasers analysed using lasing eigenvalue problem

Repina

Oktyabrskaya

Spiridonov

et al. 2021

IET Microwaves Antenna & Prop

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This article discusses how a trade-off between the high directionality of emissions and low threshold gain can be achieved in active eccentric microring cavities. Our findings are based on the lasing eigenvalue problem formalism, considered using the method of analytical regularisation, and an extremely fast and accurate dedicated Galerkin method, applied to a set of associated Muller boundary integral equations. This method allows us to investigate symmetric and antisymmetric modes separately, on the threshold of nonattenuation in time emission. Numerical results show that the directivities of emission of working modes in a given frequency range, together with their threshold values of gain, are controlled by the size and location of the air hole in the cavity. The high efficiency of the developed code allows us to make an elementary optimisation of the considered cavity; this code is a promising engineering tool in the design of microring lasers.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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“…To date, the LEP approach has been successfully applied to a variety of 2D microlasers, which appear as reasonable approximations of 3D configurations shaped as thin flat “disks” or “patches”: single fully active microcavities in the form of a circle [19], kite [20], and square [21], active cyclic photonic molecules [22–23], active circular disks with passive annular Bragg reflectors [24], and partially active circular and elliptic cavities [25–26]. More recently the LEP was applied to the modes of a single plasmonic nanowire [5] and a single plasmonic nanostrip [8] placed into an active circular shell.…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic analysis of the lasing thresholds of hybrid plasmon modes of a silver tube nanolaser with active core and active shell

Natarov¹,

Benson²,

Nosich³

2019

Beilstein J. Nanotechnol.

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Results from the electromagnetic modeling of the threshold conditions of hybrid plasmon modes of a laser based on a silver nanotube with an active core and covered with an active shell are presented. We study the modes of such a nanolaser that have their emission wavelengths in the visible-light range. Our analysis uses the mathematically grounded approach called the lasing eigenvalue problem (LEP) for the set of the Maxwell equations and the boundary and radiation conditions. As we study the modes exactly at the threshold, there is no need to invoke nonlinear and quantum models of lasing. Instead, we consider a laser as an open plasmonic resonator equipped with an active region. This allows us to assume that at threshold the natural-mode frequency is real-valued, according to the situation where the losses, in the metal and for the radiation, are exactly balanced with the gain in the active region. Then the emission wavelength and the associated threshold gain can be viewed as parts of two-component eigenvalues, each corresponding to a certain mode. In the configuration considered, potentially there are three types of modes that can lase: the hybrid localized surface plasmon (HLSP) modes of the metal tube, the core modes, and the shell modes. The latter two types can be kept off the visible range in thin enough configurations. Keeping this in mind, we focus on the HLSP modes and study how their threshold gain values change with variations in the geometrical parameters of the nanotube, the core, and the shell. It is found that essentially a single-mode laser can be designed on the difference-type HLSP mode of the azimuth order m = 1, shining in the orange or red spectral region. Furthermore, the threshold values of gain for similar HLSP modes of order m = 2 and 3 can be several times lower, with emission in the violet or blue parts of the spectrum.

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Symmetry accounting in the integral-equation analysis of lasing eigenvalue problems for two-dimensional optical microcavities

Cited by 27 publications

References 26 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

Trade‐off between threshold gain and directionality of emission for modes of two‐dimensional eccentric microring lasers analysed using lasing eigenvalue problem

Electromagnetic analysis of the lasing thresholds of hybrid plasmon modes of a silver tube nanolaser with active core and active shell

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