ar X iv : n lin / 0 11 10 56 v 1 [ nl in . P S ] 2 5 N ov 2 00 1 Nonlinearity Management in Dispersion Managed System ∗

We propose using a nonlinear phase shift interferometric converter (NPSIC) (a new device) for lumped compensation of the nonlinearity in optical fibers. The NPSIC is a nonlinear analog of the Mach-Zehnder interferometer and provides a way to control the sign of the nonlinear phase shift. We investigate a potential use of NPSIC for compensation of the nonlinearity to make a dispersion-managed system closer to an ideal linear system. More importantly NPSIC can be used to essentially improve single channel capacity in the nonlinear regime. OCIS codes: 060.2330, 060.5530, 060.4370, 190.5530, 260.2030. The recent invention and testing2–5 of the dispersion management technique demonstrated the effectiveness of this approach for high speed communications. Optical pulse dynamics in fiber links with dispersion management are governed by the nonlinear Schrödinger equation (NLS) with periodic coefficients: iuz + d(z)utt + σ(z)|u|u = 0, (1) where z is the propagation distance, u is an optical pulse amplitude, d(z) ≡ − 2 β2(z), β2(z) is a first order group-velocity dispersion, σ(z) = (2πn2)/(λ0Aeff (z)) is the nonlinear Accepted to Optics Letters (2001) 1 coefficient, n2 is the nonlinear refractive index, λ0 = 1.55μm is the carrier wavelength, Aeff is the effective fiber area that in general case depends on z. On short scales, the dispersion managed (DM) system is practically linear. Linear transmission in an optical fiber is limited by a nonlinear distance z < znl ≡ (σ|u0|), which is determined by the Kerr nonlinearity σ and the characteristic pulse power |u0|. The characteristic power cannot be choosen too small in order to maintain appropriate value of the signal-to-noise ratio. It is natural to attempt to extend the scale of the applicability of the linear regime. This can be achieved through use of a new optical fiber with lower Kerr nonlinearity. Another obvious approach is “nonlinearity management”, which was considered in. However, the semiconductor material waveguides with negative Kerr nonlinearity proposed as an element for compensation of nonlinear phase shift are currently not practical. In this letter we consider lumped compensation of the nonlinearity, the analog of lumped compensation of the chromatic dispersion by means of chirped fiber gratings. We suggest the use of a nonlinear phase shift interferometric converter (NPSIC) as presented in Fig.1. The NPSIC consists of a silica-based fiber 1, a highly nonlinear fiber 2 (which could be chalcogenide glass based, having a Kerr coefficient about 400 times or even much more than that for silica, see e.g. reference), a linear amplifier A with amplitude amplification coefficient G, and two directional couplers 1,2. It is assumed that an optical terminator is installed at the end of the fiber 2 after coupler 2 to prevent beam reflection from the end of fiber 2. The incident light with amplitude Gu0 is split by the directional coupler 1 into two beams with amplitudes a1Gu0 and a2Gu0e iπ/2 (a1 > 0, a2 > 0), corresponding to the fibers 1 and 2, respectively. We assume that total power is conserved: a1+a 2 2 = 1 but a subsequent consideration can be easily generalized to include the directional coupler’s and fiber’s losses. The extra phase π/2 in the second fiber is due to light spliting in the directional coupler (see e.g. reference). The optical lengths l1, l2 in fibers 1 and 2 between couplers 1 and 2 are chosen in such a way that they provide a zero phase difference at the input of coupler 2: neff,1l1 − neff,2l2 = 0, where neff,1, neff,2 are effective linear refraction indexes in fibers 1,2. We assume that l1, l2 are small enough so that we can neglect the influence of dispersion in 2 both fibers and the nonlinear phase shift in fiber 1. Thus the amplitudes of optical beams at the input of the coupler 2 are given by a1Gu0 and a2Gu0e iπ/2+iφnl , where the nonlinear phase shift φnl = σhnla 2 2G |u0|l2 and σhnl correspond to the value of σ in the highly nonlinear fiber 2. Assuming that the propagation constants are the same for symmetric and antisymmetric modes of the coupler, the coupled-wave equation describing mode evolution in directional couplers can be written as (u1)z = iκu2, (u2)z = iκu1, (2)