Formation and Annihilation of Laser Light Pulse Quanta in a Thermodynamic-like Pathway

Vodonos, Boris; Weill, Rafi; Gordon, Ariel; Bekker, Alexander; Smulakovsky, Vladimir; Gat, Omri; Fischer, Baruch

doi:10.1103/physrevlett.93.153901

Cited by 38 publications

(50 citation statements)

References 28 publications

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“…Complex processes in laser physics, including nonlinear optics, are well known and studied (see e.g. [30,31]), up to recent investigations in multi-mode systems [32,33,34] and successful reformulations of standard laser thermodynamics [35,36,37,38,39]. The extension of these approaches to RL immediately leads to the application of the statistical theory of disordered systems, of which spin glass theory is a paradigm [40], and which is the subject of the present manuscript.…”

Section: Introductionmentioning

confidence: 99%

“…random but slowly varying) variables, and the phases are to be taken as the relevant dynamical variables. The mode-locking process in standard lasers is now recognized as a thermodynamic phase transition [35,36,37,38,39]; it is expected, therefore, that the mode-locking transition for a RL takes the form of a phase transition in a disordered system. This manuscript follows a recent letter [43], and furnishes: extensive and new details on the derivation of the analytical results (including the stability analysis that was previously not reported); a discussion of the underlying working hypotheses; a discussion on the nature of the considered electromagnetic modes; the analysis of possible experimental frameworks where glassy behavior of light can be observed.…”

Section: Introductionmentioning

confidence: 99%

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Glassy behavior of light in random lasers

et al. 2006

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A theoretical analysis [Angelani et al., Phys. Rev. Lett. 96, 065702 (2006)] predicts glassy behavior of light in a nonlinear random medium. This implies slow dynamics related to the presence of many metastable states. We consider very general equations (that also apply to other systems, like Bose-Condensed gases) describing light in a disordered non-linear medium and through some approximations we relate them to a mean-field spin-glass-like model. The model is solved by the replica method, and replica-symmetry breaking phase transition is predicted. The transition describes a mode-locking process in which the phases of the modes are locked to random (history and sample-dependent) values. An extended discussion of possible experimental implications of our analysis is reported.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Glassy behavior of light in random lasers

et al. 2006

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“…Since the equations of motion are random, the result is a statistical steady state. In previous works [16,17], statistical light-mode dynamics (SLD) theory was used to study this problem, and applied to multipulse mode locking in [12,13]. The global mode locking analysis determines in particular the properties of the sidebands, and in this way allows us to reach our goal of describing the width and power of the sidebands as a function of the laser parameters.…”

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confidence: 99%

“…We will assume that the multipulse waveform is of the simplest kind [12] that is also the most commonly observed experimentally, consisting of k pulses of equal amplitude a. In the equation of motion for the pulse amplitude we may neglect the noise term in the mas- ter equation, and use the results of soliton perturbation theory [3,24] to write…”

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confidence: 99%

Spectral sidebands and multipulse formation in passively mode-locked lasers

et al. 2011

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Pulse formation in passively mode locked lasers is often accompanied with dispersive waves that form of spectral sidebands due to spatial inhomogoneities in the laser cavity. Here we present an explicit calculation of the amplitude, frequency, and precise shape of the sidebands accompanying a soliton-like pulse. We then extend the study to the global steady state of mode locked laser with a variable number of pulses, and present experimental results in a mode locked fiber laser that confirm the theory. The strong correlation between the temporal width of the sidebands and the measured spacing between the pulses in multipulse operation suggests that the sidebands have an important role in the inter-pulse interaction. [1][2][3][4] studied the formation and of dispersive waves by solitons and their propagation in optical fibers with periodically spaced amplifiers. The same mechanism leads to the formation of sidebands in mode locked lasers, where inhomogeneities in the cavity act periodically on the pulse.When the power of a single pulse saturates the absorber, the steady state of a passively mode locked laser tends to bifurcate into configurations where two or more pulses run in the laser cavity simultaneously. Since the early experiments that demonstrated multipulse mode locking [5][6][7] it has been observed that the pulses display a very rich dynamics, often forming bunches, as a consequence of complex inter-pulse interactions. The interest in the dispersive waves in mode locked lasers, beyond their prominent effect on the pulse shape, arises because they have often been suggested as a means of inter-pulse interaction in multipulse mode locked lasers [8][9][10][11]. Here we focus on the role of the sidebands in multipulse mode locking.The absorber saturation leading to multipulse steady states is often modeled by adding a quintic term to the equations of motion. In former papers [12,13] we applied the statistical light-mode dynamics (SLD) theory to this system, and showed that multipulse mode locking is in effect a series of first order phase transitions. SLD uses the methods of statistical physics to analyze the dynamics of the interacting many body light mode system at an effective finite temperature generated by cavity noise [14][15][16]. Here we apply the SLD gain balance method [17] to derive the multipulse steady states with dispersive waves of mode locked lasers with cavity inhomogeneities.Our theoretical analysis is based on the master equation of mode-locked soliton lasers [18,19], with an additive noise term [20], where the inhomogeneities in the cyclic light propagation in the cavity are modeled by a periodic modulation of the gain and the saturable absorption. We first study the sidebands in a single-pulse steady state and show that, unlike free fiber sidebands, the mode locked laser sidebands reach a steady state with a well-defined bandwidth and a Lorentzian shape; in real time the dispersive waves form a wide pedestal with exponentially decaying tails. In particular we demonstrate how the overal...

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“…In a different context, it is worth mentioning the theoretical and experimental study of Vodonos et al ͑2004͒. These authors proposed a thermodynamic interpretation of multiple pulse formation in passively mode-locked lasers, reporting ͑among other observations͒ the occurrence of a noise-induced phase transition in this system, with the noise coming from spontaneous-emission fluctuations that were injected from an external source.…”

Section: ͒mentioning

confidence: 99%

Spatiotemporal order out of noise

2007

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Natural systems are undeniably subject to random fluctuations, arising from either environmental variability or thermal effects. The consideration of those fluctuations supposes to deal with noisy quantities whose variance might at times be a sizable fraction of their mean levels. It is known that, under these conditions, noisy fluctuations can interact with the system's nonlinearities to render counterintuitive behavior, in which an increase in the noise level produces a more regular behavior. In systems with spatial degrees of freedom, this regularity takes the form of spatiotemporal order. An overview is presented of the mechanisms through which noise induces, enhances, and sustains ordered behavior in passive and active nonlinear media, and different spatiotemporal phenomena are described resulting from these effects. The general theoretical framework used in the analysis of these effects is reviewed, encompassing the theory of stochastic partial differential equations and coupled sets of ordinary stochastic differential equations. Experimental observations of self-organized behavior arising out of noise are also described, and details on the numerical algorithms needed in the computer simulation of these problems are given.

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Formation and Annihilation of Laser Light Pulse Quanta in a Thermodynamic-like Pathway

Cited by 38 publications

References 28 publications

Glassy behavior of light in random lasers

Glassy behavior of light in random lasers

Spectral sidebands and multipulse formation in passively mode-locked lasers

Spatiotemporal order out of noise

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