Bidirectional ring laser: Stability analysis and time-dependent solutions

Zeghlache, Hassina; Mandel, P.; Abraham, N. B.; Hoffer, L. M.; Lippi, G. L.; Mello, T.

doi:10.1103/physreva.37.470

Cited by 91 publications

(70 citation statements)

References 56 publications

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“…An in-depth understanding of the mode-hopping in SRLs would shed light on the stochastic properties of the large class of Z 2 -symmetric systems. In spite of its importance, the problem of spontaneous directional switches in SRLs remains unaddressed, partly due to the high dimensionality of the models that have been proposed for SRLs [9,13].In this paper, we address the problem of such fluctuations both theoretically and experimentally. We experimentally investigate the properties of the residence time distribution (RTD) that quantifies the mode hopping.…”

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confidence: 99%

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Topological Insight into the Non-Arrhenius Mode Hopping of Semiconductor Ring Lasers

et al. 2008

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We investigate both theoretically and experimentally the stochastic switching between two counter-propagating lasing modes of a semiconductor ring laser. Experimentally, the residence time distribution cannot be described by a simple one parameter Arrhenius exponential law and reveals the presence of two different mode-hop scenarios with distinct time scales. In order to elucidate the origin of these two time scales, we propose a topological approach based on a two-dimensional dynamical system. 42.55.Px,42.60.Mi Fluctuations in active optical systems such as lasers is one of today's technological challenges as well as a fundamental problem of modern physics as they are the result of the quantum nature of the interaction between light and matter [1]. Fluctuations are e.g. responsible for longitudinal mode switching in semiconductor lasers [2], polarization mode-hopping in Vertical Cavity Surface Emitting Lasers (VCSELs) [3][4][5], and they play a fundamental role in stochastic and coherence resonances of optical systems [6][7][8].Semiconductor ring lasers (SRLs) are a particular class of lasers whose operation is strongly affected by stochastic fluctuations. The circular geometry of the active cavity allows a SRL to operate in two possible directions, namely clockwise mode (CW ) and counter-clockwise mode (CCW ). From the application point of view, SRLs are ideal candidates for all-optical information-storage. [9][10][11]. From a theoretical point of view, SRLs represent the optical prototype of nonlinear Z 2 -symmetric systems [12], which appear in many fields of physics.Fluctuations induce spontaneous abrupt changes in the SRL's directional operation from CW to CCW and vice versa, and therefore represent a major limitation to their successful applications for instance as optical memories. An in-depth understanding of the mode-hopping in SRLs would shed light on the stochastic properties of the large class of Z 2 -symmetric systems. In spite of its importance, the problem of spontaneous directional switches in SRLs remains unaddressed, partly due to the high dimensionality of the models that have been proposed for SRLs [9,13].In this paper, we address the problem of such fluctuations both theoretically and experimentally. We experimentally investigate the properties of the residence time distribution (RTD) that quantifies the mode hopping. Our theoretical analysis is based on an asymptotic reduction of a full rate-equation model to a Z 2 -symmetric planar system [14].We consider here an InP-based multiquantum-well SRL with a racetrack geometry and a free-spectralrange of 53.6 GHz. The device operates in a singletransverse, single-longitudinal mode regime at wavelength λ = 1.56µm. However, it will be clear from the rest of the discussion that our analysis is general and applies to any kind of ring geometry. A waveguide has been integrated on the same chip in order to couple power out from the ring. This bus waveguide can be independently biased in order to reduce absorption losses. The waveguide crosses the fa...

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confidence: 99%

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confidence: 99%

Topological Insight into the Non-Arrhenius Mode Hopping of Semiconductor Ring Lasers

et al. 2008

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“…(16), and which we have observed are always the only stable modes] turn out to have C n symmetry as opposed to C nv symmetry, leading to spontaneous breaking of mirror symmetry as soon as the mode starts lasing (the only exception to this rule is for a C ∞v system, in which the circulating lasing modes have an intensity pattern |E| 2 ∝ |e i φ | 2 = 1, and hence still have mirror symmetry). We have also observed that circulating lasing modes in lossy C nv -symmetric cavities (such as that in Fig.…”

Section: Effects Of Chiralitymentioning

confidence: 98%

“…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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“…spectral hole burning effects. Self-and cross-saturation effects are added phenomenologically and are modeled by s and c. Contrary to the case of solid-state lasers [10], in the devices under study, the standing-wave pattern has a spatial period much smaller than the carrier diffusion length. Therefore, longitudinal variations of the carrier density will be washed out by the diffusion.…”

Section: Modelmentioning

confidence: 99%