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Journal of Lightwave Technology

Fundamental and Random Birefringence Limitations to Delay in Slow Light Fiber Parametric Amplification

Luca Schenato, Marco Santagiustina, Carlo Giacomo Someda

Published Dec 1, 2008• 12 citations
Publisher

Abstract

Narrowband fiber parametric amplification is known to provide slow and fast light capabilities. Here, an analytical expression of the maximum slow light time delay achievable in ideal, isotropic fibers is derived. Then, the effects of random birefringence on the slow and fast light ability are numerically investigated by integrating the governing equations over a large number of statistical realizations of the fiber. The different polarization rotation along the fiber for the signal, the idler, and the pump reduces the amplifier mean gain and the mean time delay. For small random birefringence, the decrease of the mean delay can be directly imputed to the reduction of the mean gain. For large random birefringence, severe pulse distortion occurs, the mean delay is further reduced and the delay uncertainty highly enhanced. The influence of the stimulated Raman scattering is finally addressed.

DOI
10.1109/jlt.2008.2004970

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Narrowband fiber parametric amplification is known to provide slow and fast light capabilities. Here, an analytical expression of the maximum slow light time delay achievable in ideal, isotropic fibers is derived. Then, the effects of random birefringence on the slow and fast light ability are numerically investigated by integrating the governing equations over a large number of statistical realizations of the fiber. The different polarization rotation along the fiber for the signal, the idler, and the pump reduces the amplifier mean gain and the mean time delay. For small random birefringence, the decrease of the mean delay can be directly imputed to the reduction of the mean gain. For large random birefringence, severe pulse distortion occurs, the mean delay is further reduced and the delay uncertainty highly enhanced. The influence of the stimulated Raman scattering is finally addressed.
We theoretically study parametric amplification in highly birefringent optical fibers and show that large tunable optical delay or advancement can be achieved via slow and fast light propagation. We provide a clear derivation of the formula for the optical delay that originates from the imaginary part of the parametric gain. We also perform numerical simulations in both normal and anomalous dispersion regimes. In the latter case, results show that large nanosecond optical delay could, in principle, be obtained at 1550 nm in a 1-km-long polarization-maintaining fiber. We further demonstrate that the optical delay and advancement rely on a group-velocity locking between the two cross-polarized signal and idler pulses.
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 propose and demonstrate the use of narrow band optical parametric amplification for tunable slow and fast light propagation in optical fibers. The parametric gain is coupled to the Raman process which changes the gain value moderately but modifies the gain spectral shape. Consequently, the delay is enhanced at short wavelengths while it is moderated at long wavelengths. The maximum delay and tuning range can be optimized with respect to each other considering saturation effects in long fibers. The proposed scheme offers tunable delay in the presence of gain and with a bandwidth which is sufficiently wide to process digital data streams at tens of Gbit/s rates as well as picoseconds pulses.