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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Polarization dynamics in nonlinear birefringent active fibers

S. O. Elyutin, Andrei I. Maimistov

Published Mar 9, 2001• 0 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 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.

DOI
10.1117/12.418821

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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 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.
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.
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.
The propagation of the solitary waves in the resonant birefringent amplifier with linear losses is considered. The birefringent optical linear medium contains two-level atoms with the upper state degenerated over projection of angular moment. It is assumed that population of resonance levels of atoms is inverted. The steady state pulse of polarized radiation that is vectonal generalization of the known π-pulse was analytically found. Numerical simulations demonstrate the formation dynamics solitary waves originated in birefringent amplifier.
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 equations of propagation for the polarisation components of an electromagnetic wave in non-linear birefringent media are often termed “non-linear Schrödinger equations”. In this letter, we pursue the analogy between the quantum dynamics of a 2-states oscillator and the time evolution of the wave polarisation. More specifically, we define exactly the optical analogue of the conditions for nuclear magnetic resonance, leading in the optical medium to resonant oscillations of the polarisation state when birefringence is periodically modulated along the wave propagation direction in addition to a static longitudinal magnetic field. Circular polarisation then exhibits Rabi oscillations. The non-linear influence of light intensity on the shape of the resonant polarisation line is discussed precisely.