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Journal of the Optical Society of America B

Influence of third-order dispersion on delay performance in broadband Brillouin slow light

Zhiyao Zhang, Xiaojun Zhou, Rui Liang, Shenghui Shi

Published Nov 2, 2009• 5 citations
Publisher

Abstract

We investigate theoretically the delay performance of Brillouin slow light employing a broadband pump with a rectangular spectrum. Analytical expression of delayed Gaussian pulse amplitude is deduced with the second-order gain nonuniformity and the stimulated-Brillouin scattering-induced third-order dispersion effects involved. Calculated results show that the Gaussian pulse with full-width at half maximum of 200 ps is delayed by 80 ps with little pulse broadening in a single-stage Brillouin slow-light medium, and the time delay is extended to multi-hundred ps with low distortion in a cascaded Brillouin slow-light system. Comparing the analytical results with the numerical ones, we confirm that the pulse distortion is mainly attributed to the large third-order dispersion introduced by stimulated-Brillouin scattering.

DOI
10.1364/josab.26.002211

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We investigate theoretically the delay performance of Brillouin slow light employing a broadband pump with a rectangular spectrum. Analytical expression of delayed Gaussian pulse amplitude is deduced with the second-order gain nonuniformity and the stimulated-Brillouin scattering-induced third-order dispersion effects involved. Calculated results show that the Gaussian pulse with full-width at half maximum of 200 ps is delayed by 80 ps with little pulse broadening in a single-stage Brillouin slow-light medium, and the time delay is extended to multi-hundred ps with low distortion in a cascaded Brillouin slow-light system. Comparing the analytical results with the numerical ones, we confirm that the pulse distortion is mainly attributed to the large third-order dispersion introduced by stimulated-Brillouin scattering.
Assuming a Gaussian-shaped input signal pulse, we deduced the analytical expression of the output-pulse amplitude envelope in the Brillouin slow light system utilizing broadband pump with a rectangular spectrum under small-signal gain approximation. The expression is applicable in case that the pump spectrum has a sharp rising or trailing edge and a flat top. The influence of the fiber dispersion, the stimulated Brilouin scattering (SBS) gain non-uniformity and the SBS-gain-induced dispersion on the pulse distortion has also been quantitatively analyzed. The calculated results show that the analytical solution agrees well with the numerical one if the spectrum of the signal pulse lies in the pump spectrum. SBS-gain-induced third-order dispersion is the main physical factor responsible for the pulse distortion, which also limits the retardation increase of the short pulse in the cascaded Brillouin slow light system.
A theoretical model for quantifying the pulse distortion introduced by the stimulated-Brillouin-scattering (SBS)-induced (equivalent) dispersion in a linear Brillouin slow-light system is presented. Based on this model, a linear Brillouin slow-light system employing fast-light propagation for dispersion compensation is analyzed. The results show that the elimination of gain-nonuniformity-induced equivalent group-velocity dispersion can be achieved with the sacrifice of introducing much larger high-order (equivalent) dispersion effects. It is also shown that the simultaneous cancellation of gain-nonuniformity-induced equivalent group-velocity dispersion and third-order dispersion as presented in a recent article is impossible.
We describe a methodology for designing the optimal gain profiles for gain-based, tunable, broadband, slow-light pulse delay devices based on stimulated Brillouin scattering. Optimal gain profiles are obtained under system constraints such as distortion, total pump power, and maximum gain. The delay performance of three candidate systems: Gaussian noise pump broadened (GNPB), optimal gain-only, and optimal gain+absorption are studied using Gaussian and super-Gaussian pulses. For the same pulse bandwidth, we find that the optimal gain+absorption medium improves the delay performance by 2.1 times the GNPB medium delay and 1.3 times the optimal gain-only medium delay for Gaussian pulses. For the super-Gaussian pulses the optimal gain-only medium provides a fractional pulse delay 1.8 times the GNPB medium delay.
We study numerically all-optical slow-light delays in room-temperature single-mode optical fibers induced by stimulated Brillouin scattering. We consider the propagation of a pulse through a cw-pumped Brillouin fiber amplifier, where the carrier frequency of the pulse is tuned near the Stokes resonance. Pulse delay and broadening of the Stokes pulse are studied in the small-signal and gain-saturation regimes. Pulse delay is shown to be limited by saturation of the Brillouin amplifier. In the small-signal regime, both time delay and pulse broadening increase with increasing gain. In the gain-saturation regime, both time delay and broadening decrease with increasing gain, and the pulse even achieves advancement. Time delay of more than one pulse-width is observed with modest pulse distortion, and over one pulse-width advancement can be obtained with larger pulse distortion in the gain-saturation regime.
In this paper, we investigate slow light via stimulated Brillouin scattering (SBS) in a room temperature optical fiber that is pumped by a spectrally broadened laser. Broadening the spectrum of the pump field increases the linewidth Deltaomegapof the Stokes amplifying resonance, thereby increasing the slow-light bandwidth. One physical bandwidth limitation occurs when the linewidth becomes several times larger than the Brillouin frequency shift OmegaBso that the anti-Stokes absorbing resonance substantially cancels out the Stokes amplifying resonance and, hence, the slow-light effect. We find that partial overlap of the Stokes and anti-Stokes resonances can actually lead to an enhancement of the slow-light delay-bandwidth product when Deltaomegapsime1.3OmegaB. Using this general approach, we increase the Brillouin slow-light bandwidth to over 12 GHz from its nominal linewidth of ~30 MHz obtained for monochromatic pumping. We controllably delay 75-ps-long pulses by up to 47 ps and study the data-pattern dependence of the broadband SBS slow-light system
We analyse the stimulated Brillouin scattering （SBS） slow light using double broadband pumps in a single mode fiber. A new SBS gain spectrum tailoring method is proposed using two Gaussian-shaped broadband pumps with different powers and spectral widths, and the central frequency interval of them is carefully set at two Brillouin frequency shifts to make sure that the gain of one pump has the same center with the loss of the other. The top of the gain spectrum of the strong pump beam can be counteracted by the loss spectrum of the weak pump beam to construct a flat top gain spectrum. We give the optimized conditions of the laser powers and spectral widths between two broadband pumps to obtain a flat gain. Distortions of signal pulse under this flat top gain are studied and compared with that obtained using a single broadband pump. We find that the flat top gain profile can effectively reduce the pulse distortions.