Nonlinear Birefringent Media Research Articles

Random motion theory of an optical vortex in nonlinear birefringent media.

A theoretical study is presented for the random aspect of an optical vortex inherent in the nonlinear birefringent Kerr effect, which is called the optical spin vortex. We start with the two-component nonlinear Schrödinger equation. The vortex is inherent in the spin texture caused by an anisotropy of the dielectric tensor, for which the role of spin is played by the Stokes vector (or pseudospin). The evolutional equation is derived for the vortex center coordinate using the effective Lagrangian of the pseudospin field. This is converted to the Langevin equation in the presence of the fluctuation together with the dissipation. The corresponding Fokker-Planck equation is derived and analytically solved for a particular form of the birefringence inspired from the Faraday effect. The main consequence is that the relaxation distance for the distribution function is expressed by the universal constant in the Faraday effect and the size of optical vortex. The result would provide a possible clue for future experimental study in polarization optics from a stochastic aspect.

Stochastic theory of polarized light in nonlinear birefringent media: An application to optical rotation

A stochastic theory is developed for the light transmitting the optical media exhibiting linear and nonlinear birefringence. The starting point is the two-component nonlinear Schrödinger equation (NLSE). On the basis of the ansatz of “soliton” solution for the NLSE, the evolution equation for the Stokes parameters is derived, which turns out to be the Langevin equation by taking account of randomness and dissipation inherent in the birefringent media. The Langevin equation is converted to the Fokker–Planck (FP) equation for the probability distribution by employing the technique of functional integral on the assumption of the Gaussian white noise for the random fluctuation. The specific application is considered for the optical rotation, which is described by the ellipticity (third component of the Stokes parameters) alone: (i) The asymptotic analysis is given for the functional integral, which leads to the transition rate on the Poincaré sphere. (ii) The FP equation is analyzed in the strong coupling approximation, by which the diffusive behavior is obtained for the linear and nonlinear birefringence. These would provide with a basis of statistical analysis for the polarization phenomena in nonlinear birefringent media.

Stochastic approach to polarized light in nonlinear birefringent media

Stochastic approach to polarized light in nonlinear birefringent media

Electromagnetic Gyration: -- Hamiltonian Dynamics of the Stokes Parameters --

Starting with a Schrodinger-type equation derived from the Maxwell theory of electro- magnetism, a general formalism is presented for the change of light polarization in nonlinear birefringent media, which we call gyration or more generally, electromagnetic gyration and applications are considered. The theory is formulated in terms of the Hamil- tonian dynamics of the Stokes parameters which turns out to be the equation for a classical spin. As applications, we consider two models: (a) As the first application, we analyze solvable models admitting analytic solutions, which exhibit the structure change in the be- havior of the Stokes parameter caused by the mutual interplay between linear and nonlinear birefringence. (b) The second application is the optical analogue of the so-called nuclear magnetic resonance (NMR) or Rabi resonance. This is investigated in the case of purely linear birefringence and coexisting of linear and nonlinear birefringence.

Nonlinear modulation of coupled waves in birefringent optical fibers

The propagation of polarized optical waves in a nonlinear birefringent medium is subject to polarization and modulational instabilities. We show here that stable and unstable manifolds of time periodic solutions of two coupled nonlinear Schrödinger equations for orthogonally polarized modes may be well described by phase-space portraits of a conservative one-degree-of-freedom nonlinear oscillator.

Quantum Dynamics of a Nonlinear Birefringent Model with Anticorrelated Field States

Abstract In this paper, anticorrelated field states with a binomial distribution over orthogonal polarizations, interacting with a nonlinear birefringent medium, are discussed. The field states are the SU(2) coherent states, where the angular momentum operators are realized as bilinear products of the boson operators associated with the two polarizations. The system discussed here provides an optical realization of a nonlinear rotator. We study the quantum dynamics of the statistical properties of the field and the evolution of the degree of polarization.

Squeezing in Nonlinear Birefringent Medium: An Exactly Soluble Model

Abstract Second- and fourth-order squeezing, produced by the propagation of a coherent light beam through a nonlinear birefringent medium, are investigated. The exact solutions for the presented model are obtained. A detailed numerical analysis of the results is performed and presented graphically.