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Journal of Experimental and Theoretical Physics

Short optical pulse polarization dynamics in a nonlinear birefringent doped fiber

S. O. Elyutin, Andrei I. Maimistov

Published Oct 1, 2001• 3 citations
Publisher

Abstract

Numerical solutions are obtained of the full self-consistent system of equations for the counter, rotating polarization components of the field of a short optical pulse propagating in a nonlinear birefringent fiber and in the ensemble of the energy-level degenerate doped resonance atoms implanted in the fiber material. In every cross section of the fiber, the ellipticity of the polarized wave experiences a complex evolution in time accompanied by rapid changes of the azimuthal angle due to the interplay of the dispersion and the Kerr nonlinear self-and cross-phase modulation. The reciprocal effect of the impurities on the traveling pulse causes oscillations of the pulse envelope that can completely distort the shape of the input signal, while the resonance absorption can drive the birefringence process from the nonlinear regime back to the linear one.

DOI
10.1134/1.1420442

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Numerical solutions are obtained of the full self-consistent system of equations for the counter, rotating polarization components of the field of a short optical pulse propagating in a nonlinear birefringent fiber and in the ensemble of the energy-level degenerate doped resonance atoms implanted in the fiber material. In every cross section of the fiber, the ellipticity of the polarized wave experiences a complex evolution in time accompanied by rapid changes of the azimuthal angle due to the interplay of the dispersion and the Kerr nonlinear self-and cross-phase modulation. The reciprocal effect of the impurities on the traveling pulse causes oscillations of the pulse envelope that can completely distort the shape of the input signal, while the resonance absorption can drive the birefringence process from the nonlinear regime back to the linear one.
Numerical solutions are obtained of the full self-consistent system of equations for the counter rotating polarization components of the field of short optical pulse propagating in birefringent non-linear fiber and the ensemble of the energy level degenerated dopant resonance atoms implanted in fiber material. In every cross-section of fiber the ellipticity of the polarized wave experiences a complex evolution in time accompanied by rapid changes of the azimuth angle due to interplay of dispersion and Kerr non- linear self- and cross-modulation. The reciprocal effect of the impurities on the traveling pulse causes the oscillations of the pulse envelope able to distort completely the shape of the input signal, while the resonance absorption can drive the birefringence from the non-linear back to linear regime.
The polarization and spatiotemporal dynamics of coherent pulses propagating in a doped birefringent nonlinear fiber are modeled with the inclusion of the local Lorentz field. The numerical solutions describe the full set of equations for circularly polarized components of a coherent optical pulse coupled to the inhomogeneously ensemble of doped resonance atoms. The local field is shown to degrade the stability of the $4\ensuremath{\pi}$-decay process. The development of a steady-state signal from the series of multiple photon echoes generated in active fiber is observed in simulations.
Results of study of nonlinear processes occurring during the propagation of light pulses in optical fibers doped with atoms of rare-earth elements under conditions of atomic coherence and interference are presented. For a three-level Λ scheme of interaction, the linear (χ (1) ) and nonlinear (χ (3) ) susceptibilities of such a medium are calculated. It is shown that the coefficients of Kerr nonlinearity and nonlinear absorption can reach extremely large values and can be negative. The competition between linear and nonlinear processes in the Λ scheme allows one to obtain compensation regimes when the coefficients of dispersion or absorption of the optical fiber material vanish. The efficient control of the optical properties of such a system over wide limits proves to be possible owing to variations in the parameters of light pulses at the input of the medium. The necessary conditions for realizing regimes with “slow” light, as well as for self-compression of a probing pulse on ultimately small spatial scales in a doped optical fiber, were obtained.
The temporal envelope profile and the phase of a steady-state pulse propagating through a resonant medium in the presence of nonresonant nonlinearity are derived. The formation of solitonlike pulses takes place as a result of the balance of the self-phase modulation generated by nonresonant nonlinearity and the nonlinear resonant group-velocity dispersion induced by the self-induced-transparency effect in a resonant medium. Self-phase-modulation action leads to distortion of the pulse when its power and inverse duration exceed the critical values Pcr and τcr-1. We show the destructive role of self-phase modulation in the case of self-induced-transparency pulse generation in a laser with erbium-doped fiber as an intracavity coherent absorber.
We consider the propagation of few-cycle pulses (FCPs) beyond the slowly varying envelope approximation in media in which the dynamics of constituent atoms is described by a two-level Hamiltonian by taking into account the wave polarization. We consider the short-wave approximation, assuming that the resonance frequency of the two-level atoms is well below the inverse of the characteristic duration of the optical pulse. By using the reductive perturbation method (multiscale analysis), we derive from the Maxwell-Bloch-Heisenberg equations the governing evolution equations for the two polarization components of the electric field in the first order of the perturbation approach. We show that propagation of circularly polarized (CP) few-optical-cycle solitons is described by a system of coupled nonlinear equations, which reduces in the scalar case to the standard sine Gordon equation describing the dynamics of linearly polarized FCPs in the short-wave-approximation regime. By direct numerical simulations, we calculate the lifetime of CP FCPs, and we study the transition to two orthogonally polarized single-humped pulses as a generic route of their instability.