skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Theoretical and experimental study of stochastic effects on polarization rotation in a vectorial bistable laser

Abstract

We investigate the two-dimensional optical rotor of a weakly modulated vectorial bistable laser submitted to a single or multiple stochastic perturbations. In the Langevin-type equation of the rotor the role of an even or odd input forcing function on the system dynamics is isolated. Through these two inputs of optical and magnetic natures we verify that the stochastic resonance exists only when the periodic modulation acts on the even parity optical input. When two mutually correlated noises are simultaneously submitted to the input functions of opposite parities, we find a critical regime of the noise interplay whereby one stable state becomes noise-free. In this case, the residence time of the light vector in the noise-free state diverges which leads to a collapse of the output signal-to-noise ratio. But, in this critical regime also obtained when one noise drives both the even and odd functions, if the system symmetry is broken through an independent lever control, we can recover the switching cycle due to a new response mechanism, namely, the dual stochastic response, with a specific output signal-to-noise ratio expression. Both the theoretical analysis and the experiment show that the signal-to-noise ratio now displays a robust behavior for a large rangemore » of the input noise amplitude, and a plateau with respect to the input signal amplitude. Furthermore, we isolate an original signature of this synchronization mechanism in the residence-time distribution leading to a broadband forcing frequency range. These noise interplay effects in a double well potential are of generic nature and could be found in other nonlinear systems.« less

Authors:
; ; ;  [1]
  1. Laboratoire d'Electronique Quantique-Physique des Lasers, Unite Mixte de Recherche du Centre National de la Recherche Scientifique 6627, Universite de Rennes I, Campus de Beaulieu, F-35042 Rennes Cedex (France)
Publication Date:
OSTI Identifier:
20786987
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.73.033807; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; AMPLITUDES; CONTROL; DISTRIBUTION FUNCTIONS; DISTURBANCES; LANGEVIN EQUATION; MODULATION; NOISE; NONLINEAR OPTICS; NONLINEAR PROBLEMS; PARITY; PERIODICITY; POLARIZATION; POTENTIALS; RESIDENCE HALF-TIME; RESONANCE; ROTATION; ROTORS; SIGNAL-TO-NOISE RATIO; STOCHASTIC PROCESSES; SYMMETRY; SYNCHRONIZATION; TWO-DIMENSIONAL CALCULATIONS; VECTORS; VISIBLE RADIATION

Citation Formats

Singh, Kamal P., Ropars, Guy, Brunel, Marc, and Le Floch, Albert. Theoretical and experimental study of stochastic effects on polarization rotation in a vectorial bistable laser. United States: N. p., 2006. Web. doi:10.1103/PHYSREVA.73.0.
Singh, Kamal P., Ropars, Guy, Brunel, Marc, & Le Floch, Albert. Theoretical and experimental study of stochastic effects on polarization rotation in a vectorial bistable laser. United States. doi:10.1103/PHYSREVA.73.0.
Singh, Kamal P., Ropars, Guy, Brunel, Marc, and Le Floch, Albert. Wed . "Theoretical and experimental study of stochastic effects on polarization rotation in a vectorial bistable laser". United States. doi:10.1103/PHYSREVA.73.0.
@article{osti_20786987,
title = {Theoretical and experimental study of stochastic effects on polarization rotation in a vectorial bistable laser},
author = {Singh, Kamal P. and Ropars, Guy and Brunel, Marc and Le Floch, Albert},
abstractNote = {We investigate the two-dimensional optical rotor of a weakly modulated vectorial bistable laser submitted to a single or multiple stochastic perturbations. In the Langevin-type equation of the rotor the role of an even or odd input forcing function on the system dynamics is isolated. Through these two inputs of optical and magnetic natures we verify that the stochastic resonance exists only when the periodic modulation acts on the even parity optical input. When two mutually correlated noises are simultaneously submitted to the input functions of opposite parities, we find a critical regime of the noise interplay whereby one stable state becomes noise-free. In this case, the residence time of the light vector in the noise-free state diverges which leads to a collapse of the output signal-to-noise ratio. But, in this critical regime also obtained when one noise drives both the even and odd functions, if the system symmetry is broken through an independent lever control, we can recover the switching cycle due to a new response mechanism, namely, the dual stochastic response, with a specific output signal-to-noise ratio expression. Both the theoretical analysis and the experiment show that the signal-to-noise ratio now displays a robust behavior for a large range of the input noise amplitude, and a plateau with respect to the input signal amplitude. Furthermore, we isolate an original signature of this synchronization mechanism in the residence-time distribution leading to a broadband forcing frequency range. These noise interplay effects in a double well potential are of generic nature and could be found in other nonlinear systems.},
doi = {10.1103/PHYSREVA.73.0},
journal = {Physical Review. A},
number = 3,
volume = 73,
place = {United States},
year = {Wed Mar 15 00:00:00 EST 2006},
month = {Wed Mar 15 00:00:00 EST 2006}
}
  • We investigate theoretically the mode-locking properties of an erbium-doped birefringent fiber laser in a unidirectional cavity containing an optical isolator. The mode-locking is achieved through nonlinear polarization rotation. The approach is based on a master equation which takes explicitly into account the angles between the eigen axis of the fiber at each side of the polarizer. The stability conditions of both the stationary and localized solutions are determined. This allows to establish a stability diagram versus the angles which gives the domains where the laser operates in continuous, mode-locked or unstable regime. The model also allows to calculate the pulsemore » duration together with the pulse energy as a function of the orientation of the eigen axis of the fiber with respect to the polarizer.« less
  • Nonlinear radiation dynamics of a solid-state ring laser is studied in the region of laser parameters corresponding to the parametric resonance between the self-modulation and relaxation oscillations. Bistable regions are found in which, apart from the self-modulation regime of the first kind, a stable quasi-periodic self-modulation regime exists. Temporal and spectral emission parameters of counterpropagating waves are considered in the bistable self-modulation generation regimes. The effect of noise on the bistable self-modulation oscillations is studied. It is shown that during the interaction of noise, spectral peaks split at relaxation and self-modulation frequencies. (control of laser radiation parameters)
  • The dynamics of a fiber laser passively mode-locked through nonlinear polarization rotation is theoretically investigated. The model is based on an iterative equation for the nonlinear polarization rotation and the phase plates and on a scalar differential equation for the gain, the Kerr nonlinearity, and the dispersion. It is demonstrated that depending on the orientation of the phase plates, the laser can be continuous, mode-locked, or Q-switched. In the latter case, an additional equation for the gain dynamics must be taken into account. Hysteresis dependence of the operating regime versus the orientation angles of the phase plates is shown. Amore » large bistability domain between the Q-switch and the continuous regimes is demonstrated. This model allows us to obtain the main features observed in passively-mode-locked fiber lasers.« less
  • Stochastic resonance was recently observed in a bistable ring laser. It isa phenomenon in which the response of a bistable system to a periodicmodulation is enhanced by the injection of noise along with the modulation. Sofar, comparisons of the experimental observations with theory have been madeonly for models that are much simplified compared with the more realistictwo-mode equations that describe the ring laser. We report here the results of numerical simulations of the stochastic differential equations for the laser with periodic modulation of the asymmetry between the two modes and injected noise. The simulations reveal the phenomenon of stochastic resonancemore » in a manner closely resembling the experimental observations. The appearance of second-harmonic frequencies in the output power spectrum and the role of the colored nature of the pump laser noise are studied. Finally, we discuss the relation of the recent experimental measurements of hysteresis in a ring dye laser by Gage and Mandel (J. Opt. Soc. Am. B (to be published)) to the observation of stochastic resonance.« less