Spontaneous polarization induced by natural thermalization of incoherent light.
ABSTRACT We analyze theoretically the polarization properties of a partially coherent optical field that propagates in a nonlinear Kerr medium. We consider the standard model of two resonantly coupled nonlinear Schrödinger equations, which account for a wave-vector mismatch between the orthogonal polarization components. We show that such a phase-mismatch is responsible for the existence of a spontaneous repolarization process of the partially incoherent optical field during its nonlinear propagation. The repolarization process is characterized by an irreversible evolution of the unpolarized beam towards a highly polarized state, without any loss of energy. This unexpected result contrasts with the commonly accepted idea that an optical field undergoes a depolarization process under nonlinear evolution. The repolarization effect can be described in details by simple thermodynamic arguments based on the kinetic wave theory: It is shown to result from the natural tendency of the optical field to approach its thermal equilibrium state. The theory then reveals that it is thermodynamically advantageous for the optical field to evolve towards a highly polarized state, because this permits the optical field to reach the ???most disordered state???, i.e., the state of maximum (nonequilibrium) entropy. The theory is in quantitative agreement with the numerical simulations, without adjustable parameters. The physics underlying the reversible property of the repolarization process is briefly discussed in analogy with the celebrated Joule???s experiment of free expansion of a gas. Besides its fundamental interest, the repolarization effect may be exploited to achieve complete polarization of unpolarized incoherent light without loss of energy.
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ABSTRACT: Wherever the polarization properties of a light beam are of concern, polarizers and polarizing beamsplitters (PBS) are indispensable devices in linear-, nonlinear- and quantum-optical schemes. By the very nature of their operation principle, transformation of incoming unpolarized or partially polarized beams through these devices introduces large intensity variations in the fully polarized outcoming beam(s). Such intensity fluctuations are often detrimental, particularly when light is post-processed by nonlinear crystals or other polarization-sensitive optic elements. Here we demonstrate the unexpected capability of light to self-organize its own state-of-polarization, upon propagation in optical fibers, into universal and environmentally robust states, namely right and left circular polarizations. We experimentally validate a novel polarizing device - the Omnipolarizer, which is understood as a nonlinear dual-mode polarizing optical element capable of operating in two modes - as a digital PBS and as an ideal polarizer. Switching between the two modes of operation requires changing beam's intensity.Scientific Reports 01/2012; 2:938.
Article: Kinetic Description of Random Optical Waves and Anomalous Thermalization of a Nearly Integrable Wave System[show abstract] [hide abstract]
ABSTRACT: This article is composed of two parts. The first part is aimed at providing an overview on the kinetic description of random nonlinear waves considering the one-dimen-sional nonlinear Sch odinger (NLS) equation as a representative model of optical wave propagation. We expose, in particular, the key problem of achieving a closure of the infi-nite hierarchy of moment equations for the random field. The hierarchy is closed at the first order when the statistics of the random wave is non-stationary or when the response time of the nonlinearity is non-instantaneous, which, respectively, leads to the Vlasov kinetic equation and the weak-Langmuir turbulence equation. When the amount of non-stationary statistics is comparable to the amount of non-instantaneous nonlinearity, we derive a generalized Vlasov–Langmuir equation that provides a unified formulation of the Vlasov and Langmuir approaches. On the other hand, when the statistics of the random wave is stationary and the nonlinear response instantaneous, the closure of the hierarchy of moment equations requires a second-order perturbation expansion procedure, which leads to the Hasselmann (or wave turbulence) kinetic equation. Contrarily to the Vlasov and Langmuir equations, the Hasselmann equation is irreversible, a feature which is expressed by a H -theorem of entropy growth that describes wave thermalization toward the thermo-dynamic equilibrium distribution, i.e. the Rayleigh–Jeans (RJ) spectrum. In the second part of the paper, we discuss a process of anomalous thermalization by considering the exam-ple of the scalar NLS equation whose integrability is broken by the presence of third-order dispersion. The anomalous thermalization is characterized by an irreversible evolution of the wave toward an equilibrium state of a fundamental different nature than the conven-tional RJ equilibrium state. The wave turbulence kinetic equation reveals that the anom-alous thermalization is due to the existence of a local invariant in frequency space J ω , which originates in degenerate resonances of the system. In contrast to integral invariants that lead to a generalized RJ distribution, here, it is the local nature of the invariant J ω that makes the new equilibrium states fundamentally different than the usual RJ equilib-CLAIRE MICHEL ET AL. rium states. We study in detail the anomalous thermalization by means of numerical sim-ulations of the NLS equation and of the wave turbulence equation by using an improved criterion of applicability of the kinetic theory. The spectrum of the field is shown to exhibit an intriguing asymmetric deformation, which is characterized by the unexpected emergence of a constant spectral pedestal in the long-term evolution of the field. It turns out that the local invariant J ω explains all the essential properties of the anomalous thermalization of the wave. Mathematics Subject Classification (2000) 74A25, 76Fxx, 78A10.Letters in Mathematical Physics 04/2012; 96(1). · 1.82 Impact Factor
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ABSTRACT: The study of the polarization dynamics of two counterpropagating beams in optical fibers has recently been the subject of a growing renewed interest, from both the theoretical and experimental points of view. This system exhibits a phenomenon of polarization attraction, which can be used to achieve a complete polarization of an initially unpolarized signal beam, almost without any loss of energy. Along the same way, an arbitrary polarization state of the signal beam can be controlled and converted into any other desired state of polarization, by adjusting the polarization state of the counterpropagating pump beam. These properties have been demonstrated in various different types of optical fibers, i.e., isotropic fibers, spun fibers, and telecommunication optical fibers. This article is aimed at providing a rather complete understanding of this phenomenon of polarization attraction on the basis of new mathematical techniques recently developed for the study of Hamiltonian singularities. In particular, we show the essential role that play the peculiar topological properties of singular tori in the process of polariza-tion attraction. We provide here a pedagogical introduction to this geometric approach of Hamiltonian singula-rities and give a unified description of the polarization attraction phenomenon in various types of optical fiber systems.Journal of the Optical Society of America B 01/2012; 29(4):559. · 2.18 Impact Factor