Modulational Instability in a Communication Link Exploiting a Negative Nonlinearity for Compensation of Self-phase Modulation

In optical communication systems, the technique of alternating dispersion is commonly used as a way to counteract the dispersive pulse broadening. The main limitations, in terms of bit-rate, then come from the fiber Kerr nonlinearity acting through self-phase modulation and four-wave mixing [1]. The recently introduced method of " dispersion management ", where the dispersion compensation is only partial, appears as a very promising approach for coping with this problem (for a recent review, see [2]). But it might still be worth exploring alternatives such as the one suggesting that besides the sign of the dispersion parameter one might also alternate the sign of the nonlinearity [3]. Similar, in some respect, to optical phase conjugation, this method would ensure the perfect restoration of a pulse after its passage through a medium of opposite dispersion and exhibiting a negative nonlinearity (n 2 < 0). A simplified and approximate version of this compensation scheme is illustrated in Fig.1. A material with a negative n 2 (e.g. a semiconductor or a χ (2) :χ (2) cascaded system) is inserted symmetrically between two gratings or two compensating fibers. Besides being more suitable to an experimental testing, this split compensator has been shown, through numerical simulations, to be effective in minimizing the impact of fiber nonlinearities on the quality of the transmitted signal in a long-haul communication system [4]. However, extensive numerical work also gives to think that, as with dispersion-managed systems [5,6], this compensation scheme might be subject to a modulation instability (MI). This paper presents a linear stability analysis which confirms this observation.