Exact linear stability analysis of the plane-wave Maxwell-Bloch equations for a ring laser

Lugiato, L. A.; Narducci, L. M.; Squicciarini, M.

doi:10.1103/physreva.34.3101

Cited by 37 publications

(32 citation statements)

References 13 publications

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“…The LSA is obtained by constructing the linearized evolution operator for which we can evaluate the Floquet multipliers and trace back the eigenvalues governing the stability. Our approach is quite general and could also be applied to other dynamical systems described by partial differential equations (PDE)s, and our results extend and generalize the previous studies performed for unidirectional ring lasers [7,[18][19][20][21]. We find that multistability is more easily reached in rings as compared to FP cavities, because of the different amounts of Spatial-Hole Burning in each configuration.…”

supporting

confidence: 81%

“…Within the Uniform Field Limit (UFL) approximation [7], this can be accomplished via a modal decomposition for either ring [16] or FP lasers [17]. Beyond the UFL, analytical results are available for unidirectional rings if one neglects internal losses [18] and/or invokes singular perturbation techniques [19]. When bidirectional emission, cavity losses or spatially dependent parameters come into play, no general method for the LSA is known, which hinders the study of many devices as bidirectional SRL, FP lasers, or devices for which the UFL or singular perturbations methods are inadequate.…”

mentioning

confidence: 99%

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Longitudinal mode multistability in Ring and Fabry-Pérot lasers: the effect of spatial hole burning

Pérez-Serrano¹,

Javaloyes²,

Balle³

2011

Opt. Express

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Abstract:We theoretically discuss the impact of the cavity configuration on the possible longitudinal mode multistability in homogeneously broadened lasers. Our analysis is based on the most general form of a Travelling-Wave Model for which we present a method that allows us to evaluate the monochromatic solutions as well as their eigenvalue spectrum. We find, in agreement with recent experimental reports, that multistability is more easily reached in Ring than in Fabry-Pérot cavities which we attribute to the different amount of Spatial-Hole Burning in each configuration.

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supporting

confidence: 81%

mentioning

confidence: 99%

Longitudinal mode multistability in Ring and Fabry-Pérot lasers: the effect of spatial hole burning

Pérez-Serrano¹,

Javaloyes²,

Balle³

2011

Opt. Express

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“…To convey an understanding of how a lasing system with degenerate modes can be described in the SALT framework, let us first consider the well-known example of a rotationally symmetric ring laser whose solution can become unstable in certain parameter regimes [32,33,[40][41][42][43][44][45][46][47][48]. We model the system as a one-dimensional, homogeneous medium with periodic boundary conditions (see Fig.…”

Section: Example 1: Symmetric 1d Ring Lasermentioning

confidence: 99%

“…This leaves only two possible steady-state lasing solutions of the ringlaser at¯, corresponding to the well known clockwise and counterclockwise traveling wave states. However, from the literature it is known that ring lasers show complex behavior, including the fact that these traveling wave solutions are not always stable [32,33,[40][41][42][43][44][45][46][47][48].…”

Section: Example 1: Symmetric 1d Ring Lasermentioning

confidence: 99%

Steady-stateab initiolaser theory for fully or nearly degenerate cavity modes

et al. 2015

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We investigate the range of validity of the recently developed steady-state ab-initio laser theory (SALT). While very efficient in describing various microlasers, SALT is conventionally believed not to be applicable to lasers featuring fully or nearly degenerate pairs of resonator modes above the lasing threshold. Here we demonstrate how SALT can indeed be extended to describe such cases as well, with the effect that we significantly broaden the theory's scope. In particular, we show how to use SALT in conjunction with a linear stability analysis to obtain stable single-mode lasing solutions that involve a degenerate mode pair. Our flexible and efficient approach is tested on one-dimensional ring lasers as well as on two-dimensional microdisk lasers with broken symmetry.

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“…The literature on degenerate lasing modes has almost invariably dealt with whispering-gallery modes in microdisks and ring resonators [1][2][3][4]. Many of these earlier works discussed the stability of traveling-wave modes in ring resonators under perturbations that break the symmetry [15][16][17][18][19]. A very limited number of other works on degenerate lasing modes in other geometries exist [27], which were mostly experimental and focused on the linear cavity rather than the nonlinear lasing regime.…”

Section: B Effects Of Exact Degeneraciesmentioning

confidence: 99%

Symmetry, stability, and computation of degenerate lasing modes

Liu

Zhen

et al. 2017

Phys. Rev. A

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We present a general method to obtain the stable lasing solutions for the steady-state ab initio lasing theory (SALT) for the case of a degenerate symmetric laser in two dimensions (2D). We find that under most regimes (with one pathological exception), the stable solutions are clockwise and counterclockwise circulating modes, generalizing previously known results of ring lasers to all 2D rotational symmetry groups. Our method uses a combination of semianalytical solutions close to lasing threshold and numerical solvers to track the lasing modes far above threshold. Near threshold, we find closed-form expressions for both circulating modes and other types of lasing solutions as well as for their linearized Maxwell-Bloch eigenvalues, providing a simple way to determine their stability without having to do a full nonlinear numerical calculation. Above threshold, we show that a key feature of the circulating mode is its "chiral" intensity pattern, which arises from spontaneous symmetry breaking of mirror symmetry, and whose symmetry group requires that the degeneracy persists even when nonlinear effects become important. Finally, we introduce a numerical technique to solve the degenerate SALT equations far above threshold even when spatial discretization artificially breaks the degeneracy.

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Exact linear stability analysis of the plane-wave Maxwell-Bloch equations for a ring laser

Cited by 37 publications

References 13 publications

Longitudinal mode multistability in Ring and Fabry-Pérot lasers: the effect of spatial hole burning

Longitudinal mode multistability in Ring and Fabry-Pérot lasers: the effect of spatial hole burning

Steady-stateab initiolaser theory for fully or nearly degenerate cavity modes

Symmetry, stability, and computation of degenerate lasing modes

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