Mode-mode competition and unstable behavior in a homogeneously broadened ring laser

Narducci, L. M.; Tredicce, J. R.; Lugiato, L. A.; Abraham, N. B.; Bandy, D. K.

doi:10.1103/physreva.33.1842

Cited by 87 publications

(23 citation statements)

References 12 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%

“…In addition, wavelength multistability in SRLs can coexist with the directional bistability [5], hence it can be of interest for all-optical signal processing applications at a higher-logical level [6]. Although early studies of unidirectional ring lasers, where only one propagation direction was allowed, suggested possible multistability among longitudinal modes [7,8], this behavior has, to our knowledge, never before been explained or experimentally observed in other types of single-cavity free-running devices lasers.…”

mentioning

confidence: 93%

“…These two problems are known to be difficult if not impossible to implement analytically in the general case, and solutions are only available under strong approximations. 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].…”

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: 93%

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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“…It is worthwhile noting that the operating modes are usually not consecutive ones, such as multimode instabilities in laser theory [14,15]. A physical interpretation can be based on a typical multimode laser instability.…”

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confidence: 99%

Temporal Dynamics of Semiconductor Lasers with Optical Feedback

Giudici²,

et al. 1998

Self Cite

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We measure the temporal evolution of the intensity of an edge emitting semiconductor laser with delayed optical feedback for time spans ranging from 4.5 to 65 ns with a time resolution from 16 to 230 ps, respectively. Spectrally resolved streak camera measurements show that the fast pulsing of the total intensity is a consequence of the time delay and multimode operation of the laser. We experimentally observe that the instabilities at low frequency are generated by the interaction among different modes of the laser. [S0031-9007(98)08077-6] PACS numbers: 05.45. + b, 05.40. + j, 42.60.Mi Nonlinear systems with delayed feedback are of interest because they can be widely found in economy, biology, chemistry, and physics [1]. These systems are in principle infinite dimensional, and from this point of view, it is difficult to classify them a priori as deterministic dynami-cal systems because the existence and uniqueness of a solution have to be demonstrated for each particular model [2]. It is also difficult to separate the role of noise from de-terminism, because complex solutions display a Gaussian-Markovian behavior as if they were solutions of a Langevin equation [3,4], thus nonconventional measurement techniques are required [5]. During the past years, there has been particular interest in understanding the dynamical behavior of one such system: a semiconductor laser with optical feedback. It was experimentally shown that weak optical feedback may induce bistability [6], oscillations, and chaos [7]. At moderate feedback levels, a special dynamical regime occurs which is characterized by the appearance of aperiodic, fast reductions of the total intensity of the laser [8,9], followed by a slower recovery stage. The average time between such intensity drops is much longer than all characteristic times of the system itself, so they are called low-frequency fluctuations (LFF). From numerical simulations it was recently proposed that LFF originate from a deterministic chaotic attrac-tor which encompasses a large number of unstable fixed points, either saddle-node points or foci [9-11]. This chaotic attractor coexists with one or more stable fixed points. The trajectory, if in the chaotic attractor, wanders in phase space around the foci until it approaches a saddle. The collision with a saddle gives rise to a large, fast excursion in phase space until the evolution recovers towards the foci. Since this process lasts for several delay times, it generates a long-time scale dynamics which contributes to the lower part of the spectrum, and it was called "chaotic itinerancy with a drift" because it involves a drift in the laser frequency. Furthermore, the model-which assumes single-mode operation of the laser and very weak feedback-predicted that the temporal behavior of the laser intensity is characterized by pulses departing from zero intensity level and whose amplitude grows steadily until the collision with a saddle takes place leading to a sudden reduction of the intensity. However, recent measurements of the time-res...

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“…What we study and present below is essentially the generalization of the complete Maxwell-Bloch equations, usually employed in the single-photon laser theory, to the two-photon case. We have found it most convenient to use a formulation presented some time ago by Narducci in the semiclassical theory of the single-photon laser [14]. We present in this paper an nanlysis which has inspired by the comparison between the linear stability analysis technique and the so-called weak sideband approach, first introduced by Casperson [15] and further elaborated by Hendow and Sargent [16] and by Boyd, Hillman, and Stroud [17].…”

Section: Introductionmentioning

confidence: 99%

Semiclassical stability analysis of a two-photon laser including spatial variation of the cavity field

Abdel‐Aty

Obada

2001

The European Physical Journal D

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We investigate the dynamics of a two-photon laser under conditions where the spatial variation of the cavity field along the cavity axis is important.The model assumes pumping to the upper state of the two-photon transition.We consider the Maxwell-Bloch equations on the basis of which we study the stability analysis of the steady state of the system. The system is taken to be contained in a ring-laser cavity. Asymptotic expansion of the eigenvalue and analytic information are obtained in some realistic limits, such as very large reflectivity, very small cavity losses, or very small population relaxation rate.The results are illustrated with an application to a specific atomic system (Potassium) as an amplifying medium.

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Mode-mode competition and unstable behavior in a homogeneously broadened ring laser

Cited by 87 publications

References 12 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

Temporal Dynamics of Semiconductor Lasers with Optical Feedback

Semiclassical stability analysis of a two-photon laser including spatial variation of the cavity field

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