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Journal of the Optical Society of America B

Maxwell–Bloch dynamics and modulation instabilities in fiber lasers and amplifiers

Guido H. M. van Tartwijk, Govind Prasad Agrawal

Published Oct 1, 1997• 22 citations
Publisher

Abstract

We investigate analytically the occurrence of modulation instability in doped fiber lasers and amplifiers using a Maxwell–Bloch description for the dopants and without making the usual parabolic-gain approximation. We find a new modulation instability occurring near the Rabi frequency, which is not predicted by the conventional complex Ginzburg–Landau model. We discuss the implications of this new instability for fiber amplifiers and lasers and analyze the effects of the saturable host absorption on the laser instabilities. Atomic detuning is shown to significantly enhance the new modulation instability, in both the normal- and the anomalous-dispersion regimes.

DOI
10.1364/josab.14.002618

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Presents an analytical model which describes the dynamics of the modulation instability in a nonlinear, dispersive, homogeneously broadened and nonsaturable fiber amplifiers. The general case of arbitrary detuning between the laser frequency and the resonance frequency and arbitrary bandwidth of the amplifying transition is treated. The model accounts both for the gain dispersion and for the gain-induced, near resonant refractive index dispersion, Simple closed form expressions for the combined gain coefficients of the Stokes and anti-Stokes frequencies are obtained.
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.
We investigated the sideband instability by numerical integration of the Maxwell-Bloch equations for propagation of a nearly resonant pump laser and a weak probe laser in a system of two-level atoms. In an optically thick medium, the probe gain (absorption) spectrum becomes a function of propagation distance. We find that the well-known gain resonance at the generalized Rabi frequency Ω' is suppressed and a broad asymmetric gain region forms on each side of the laser frequency. For probe-pump detunings inside these gain regions, the field envelope breaks up into periodic traveling waves that are compared to the polycnoidal solutions of the sine-Gordon equation with periodic boundary conditions.