Taking account of the coupling differential equations under the effect of Stokes and anti-Stokes for the pump wave linearly polarized and aligned with the x-axis direction,the gain coefficient for the Stokes and anti-Stokes have been derived from simultaneously act of stimulated Raman scattering and parametric amplification in the same x polarization.The Lorenz model of parallel gain coefficient is introduced in this equation. The correlation between the gain spectrum and correlative parameter studied in dispersion-shifted fiber.The conclusion shows that gain spectrum is dissymmetrical with the Stokes and anti-Stokes wave and has no relation with third-order dispersion.At the same time,the ratio of Stokes and anti-Stokes |E_(ax)/E_(sx)| increases with frequency shift,then it rapidly reduced.
Taking account of the coupling differential equations under the effect of Stokes and anti-Stokes for the pump wave linearly polarized and aligned with the x-axis direction,the gain coefficient for the Stokes and anti-Stokes have been derived from simultaneously act of stimulated Raman scattering and parametric amplification in the same x polarization.The Lorenz model of parallel gain coefficient is introduced in this equation. The correlation between the gain spectrum and correlative parameter studied in dispersion-shifted fiber.The conclusion shows that gain spectrum is dissymmetrical with the Stokes and anti-Stokes wave and has no relation with third-order dispersion.At the same time,the ratio of Stokes and anti-Stokes |E_(ax)/E_(sx)| increases with frequency shift,then it rapidly reduced.
The polarization-related properties of stimulated Brillouin scattering (SBS) processes in long, randomly birefringent, standard optical fibers are examined. Evolution equations for the pump and signal waves, in the presence of both birefringence and SBS, are provided in Jones and Stokes spaces. It is shown that in the undepleted pump regime, the amplification of the SBS signal wave is equivalent to that of a linear medium with polarization-dependent gain. The process is associated with a pair of orthogonal states of polarizations (SOPs) of the signal wave, which undergo maximum and minimum amplification. In long, standard fibers, the Jones vector of the probe SOP which corresponds to maximum amplification is aligned with the complex conjugate of the pump wave Jones vector. The maximum and minimum SBS gain coefficients in such fibers equal two-thirds and one-third of the gain coefficient that is predicted by scalar theory, respectively. The large differential gain of the SBS process gives rise to an effective pulling of the amplified Stokes probe wave SOP, towards that of maximum amplification. Lastly, Stokes wave pulses that are aligned for maximum and minimum amplification experience different group delays, which manifest as polarization-related distortions in SBS slow light setups.
We study the interplay between parametric and Raman gain in photonic crystal fibers by taking into account the vector nature of the electric field, the fiber frequency dependent birefringence, the Kerr nonlinear coefficient, the Raman gain profile and chromatic dispersion. In particular, we show that an accurate representation of the frequency dependence of the nonlinear and dispersive properties of a photonic crystal fiber is essential for correctly describing the overall gain profile for a probe signal at large frequency detuning from a continuous wave or pulsed pump. For example, we found that fourth and higher order dispersion have a striking influence on the spectrum of modulation polarization instability gain in both the high and low birefringence regime, in that the vector parametric gain is suppressed above a critical level of linear birefringence. We validated the theory by experimental observations of vector parametric amplification in high birefringence holey fiber with triple defects.
We present a detailed derivation of a new, rotationally invariant formalism for the theory of stimulated Raman scattering. The formalism is applied to Raman transitions of well-defined rotational symmetry, e.g., rotational Raman (S) transitions, yielding the explicit dependence of gain on light polarization, phase mismatch, and frequency offset. For a linearly polarized laser, the Stokes fields parallel and perpendicular to the laser field are decoupled. Far from Stokes--anti-Stokes phase matching, their gain coefficients are in the ratio of 4:3; at phase matching, both are suppressed and have zero exponential gain. For a circularly polarized laser, the circularly polarized Stokes fields circulating in the same and opposite senses as the laser field are decoupled. The gain of the opposite-sense field, which is decoupled from the anti-Stokes field, is independent of phase mismatch. Far from phase matching, the gain of the same-sense Stokes field is (1/6 that of the opposite-sense field; at phase matching, the same-sense field has zero exponential gain. An unpolarized laser is shown to have the lowest Raman gain; far from phase matching, its Stokes fields decouple into two incoherent, oppositely circularly polarized fields, but at phase matching all Stokes polarizations have zero exponential gain. The gradual transition away from phase matching is also treated explicitly, and it is shown that when the gain is suppressed the maximum Stokes growth occurs when the Stokes-laser beat is a fraction of a Raman linewidth off resonance.
We theoretically and experimentally study changes with pump power in the polarization of an optical signal as it simultaneously experiences Kerr-effect-induced birefringence and four-wave-mixing-based parametric amplification from a copropagating pump in an optical fiber. It is shown that the changes caused by the two nonlinear optical effects are orthogonal to each other in the Stokes space. Results also show that the pump polarization state works as an attractor for signal polarization. The implications of this feature to fiber parametric amplifiers and entangled-photon sources are discussed, and a fiber polarization switch is demonstrated.
The development of the Stokes spectrum and the dependence of Raman gain upon pump laser bandwidth in a narrow linewidth Raman medium are analyzed in terms of a closed set of multimode equations. The analysis predicts that the Stokes gain coefficient takes on its maximum value, which is independent of bandwidth, when the Stokes spectrum replicates the pump spectrum. It is also shown that in the absence of dispersion the spectrum of a weak Stokes wave is driven to duplicate the pump spectrum, and that for noise input the average power generated in the Stokes wave is independent of the pump bandwidth.
The influence of the scattering matrix elements that are responsible for the amplification of the Stokes and anti-Stokes components on the process of stimulated Raman scattering in the essentially nonstationary regime is analyzed. It is demonstrated that the optimum proportion between the scattering matrix elements, which maximizes the anti-Stokes component, is determined by the ratio between the optical frequencies of the components and the initial proportion between the intensities of the pump and initiating pulses. In the case of the optimum proportion between the scattering matrix elements, the variation in the excitation of a medium compensates the self-induced modulation of gain, and the efficiency of converting the radiation energy into the Stokes and anti-Stokes components increases substantially.