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

Coherent transients in non-linear birefringent resonance impurity doped fiber

S. O. Elyutin

Published Jun 15, 2007• 0 citations
Publisher

Abstract

The polarization and spatio-temporal dynamics of coherent pulses propagating in an active birefringent Kerr non-linear fiber are discussed basing on the numerical solutions of the fiber effects full set self-consistent system of equations for the circularly polarized components of a coherent optical pulse coupled to the ensemble of the doped resonance atoms.

DOI
10.1117/12.752117

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The polarization and spatio-temporal dynamics of coherent pulses propagating in an active birefringent Kerr non-linear fiber are discussed basing on the numerical solutions of the fiber effects full set self-consistent system of equations for the circularly polarized components of a coherent optical pulse coupled to the ensemble of the doped resonance atoms.
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.
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.
Optical fibers have proven to be one of the most important nonlinear media, even though in most cases the nonlinearity exploited is the notoriously weak Kerr effect of the silica-based fiber. By using doped fibers, new, stronger nonlinearities are possible. These stronger effects could allow for new phenomena and applications. Coherent effects, in particular, should be important when pulses shorter or comparable to the dephasing time of the impurity ions propagate in the fiber. Here we report, for the first time, the observation of accumulated photon-echo and free induction decay during the propagation of femtosecond pulses in Er doped fibers at 4.2°K.
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.