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Optical Fiber Technology

A numerical method for pulse propagation in nonlinear fiber Bragg grating with ternary stability nature

Elham Yousefi, Mohsen Hatami

Published Dec 23, 2019• 3 citations
Publisher
DOI
10.1016/j.yofte.2019.102075

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We consider the continuous-wave (cw) propagation through a fiber Bragg grating that is uniformly doped with two-level resonant atoms. Wave propagation is governed by a system of nonlinear coupled-mode Maxwell-Bloch (NLCM-MB) equations. We identify modulational instability (MI) conditions required for the generation of ultrashort pulses in both anomalous and normal dispersion regimes. From a detailed linear stability analysis, we find that the atomic detuning frequency has a strong influence on the MI. That is, the atomic detuning frequency induces nonconventional MI sidebands at the photonic band gap (PBG) edges and near the PBG edges. Especially in the normal dispersion regime, MI occurs without any threshold condition, which is in contrast with that of conventional fiber Bragg gratings. We also perform a numerical analysis to solve the NLCM-MB equations. The numerical results of the prediction of both the optimum modulation wave number and the optimum gain agree well with that of the linear stability analysis. Another main result of the present work is the prediction of the existence of both bright and dark self-induced transparency gap solitons at the PBG edges.
The fiber Bragg gratings (FBGs) with Kerr nonlinearity exhibit optical soliton like phenomena known as the Bragg solitons. Due to the high dispersion of FBGs near the band edge, optical solitons in the anomalous dispersion side is produced when the input pulse has suitable pulse-width and peak intensity. The Bragg solitons belong to the class of bi-directional pulse propagation problems. In this paper, general quantum theory for bi-directional pulse propagation problems is developed and applied to the Bragg solitons. The output Bragg soliton pulses are quantum-mechanically squeezed and their squeezing ratios calculated.
Optical pulse propagation in photonic grating structures can show anomalous (i.e., superluminal or negative) group velocities under certain circumstances owing to the anomalous dispersive properties induced by the periodic grating structure. Such phenomena can be observed for either linear pulse propagation in passive dielectric grating structures, such as in fiber Bragg gratings (FBGs), as well as in frequency-conversion processes exploiting second-order cascading effects in quasi-phase-matched (QPM) nonlinear crystals. Engineering of the grating structure can be exploited to observe a wide variety of anomalous pulse transmission and reflection behaviors. In this article, we review the main recent experimental and theoretical achievements obtained by our group in this field. In particular, we report on superluminal propagation of picosecond optical pulses at the 1.5-μm wavelength of optical communications in FBGs, both in transmission and reflection configurations, with the observation of group velocities as large as ∼5c/sub 0/. We also show that the phenomenon of transparent pulse propagation at a negative group velocity in a gain doublet atomic amplifier, recently observed in cesium vapor by Wang and co-workers (L. J. Wang, A. Kuzmich, and A. Dogariu, Nature vol.406, p.277-9, 2000), can be achieved as well in a photonic parametric amplifier by exploiting the anomalous dispersive properties of the amplifier induced by a suitably designed QPM grating profile.