All-Optical Nonlinear Pre-Compensation of Long-Reach Unrepeatered Systems

We numerically demonstrate an all-optical nonlinearity pre-compensation module for state-ofthe-art long-reach Raman-amplified unrepeatered links. The compensator design is optimized in terms of propagation symmetry to maximize the performance gains under WDM transmission, achieving 4.0dB and 2.6dB of SNR improvement for 250-km and 350-km links. Introduction Optical technologies are currently being pushed to their limits due to the ever-increasing traffic demands[1]. In particular, the inherent nonlinearity of silica glass is causing difficult-to-compensate signal degradations in fiber-optic systems. These Kerr-related impairments currently set the upperbound on achievable information rates and transmission distances[1]. Consequently, there has been significant effort to compensate nonlinear degradations, and it is generally possible in both digital and optical domains. Digital methods often require substantial processing time, and are unsuitable for multichannel applications due to limited receiver bandwidth[1]-[3]. On the other hand, optical techniques are not only instantaneous, but also capable of simultaneous processing of all frequency channels in wavelength-divisionmultiplexed (WDM) systems. Among them, optical-phase conjugation (OPC) has been shown to successfully address nonlinear distortions, but it heavily relies on specific link design to achieve a relevant performance improvement[4],[5]. In particular, symmetric pulse propagation is required on each side of the OPC device, which is challenging to achieve in most practical applications. Moreover, the standard OPC approach is unsuitable for unrepeatered transmission, where it is not feasible to perform optical conjugation along the link. For such systems, lumped compensation modules based on OPC have been previously considered at both the transmitter[6] and receiver[7],[8]. However, they were limited to standard links using erbiumdoped fiber amplifiers (EDFA), and achieved only partial propagation symmetry due to the power profile mismatch between the compensator and the link. A numerical analysis from[9] was able to show strong system symmetry, but relied on unrealistic fiber types for compensation, and thus it remains unattainable in practice. In this work, we revisit the OPC requirements, and numerically demonstrate how the technique can be applied to a state-of-the-art Ramanamplified unrepeatered link by using an OPCbased pre-compensation module at the transmitter side. We only consider commercially available equipment and optimize the symmetry of propagation through the design of the optical pre-compensation unit by means of: (1) scaled down compensation medium, (2) novel dispersion mapping, and (3) Raman amplification for fine power profile tuning. Ultimately, we establish a high degree of propagation symmetry, and achieve net signal-to-noise ratio (SNR) improvements ranging from 2.6 dB up to 4.0 dB, depending on the link configuration. The standard split-step Fourier method (SSFM) is employed for the propagation, and the particle swarm optimization (PSO) algorithm is used for finding the optimum system parameters. Symmetry Requirements The fundamental principle of OPC is based on reversing the sign of distortions by phaseconjugation of the optical field, and reapplying them throughout the transmission system. Perfect cancellation requires identical accumulated nonlinear phase-shifts to be induced on both sides of the OPC device, for the signal and its conjugated copy, respectively. As the phase-shift is both power and pulse shape dependent, it is necessary to continuously restore the nominal power at the correct pulse shapes over the entire propagation distance. Pulse shape is predominantly determined by the accumulated dispersion, and so it is common to express the degree of nonlinearity matching through power versus accumulated dispersion diagrams (PADD), where perfect compensation is attained for identical powers at the opposite values of accumulated dispersion[10],[11]. The diagrams accurately predict the symmetry for homogenous links, but they ignore a possible mismatch of other fiber parameters. Instead of focusing on power alone, in this work we express the nonlinear phase-shift as = ∫ by using = ∗ , and employ the integral to completely describe the symmetry through more general nonlinearity versus accumulated dispersion diagrams (NADD). The advantage of this scheme over PADD is illustrated in Fig. 1. In this example (Fig. 1a), the length of the second span is only half of the length of the first span, while the power and dispersion in the second span are doubled to induce the same pulse evolution over a smaller distance. As the powers of the signal (blue) and the conjugate (red) are not strictly matched, the PADD of this link is highly asymmetric (Fig. 1b). However, the corresponding NADD (Fig. 1c) accurately depicts the matching of nonlinearities because it also incorporates the other propagation parameters. Fig. 1: a) Symmetric system with unequal powers and lengths, with the corresponding PADD (b) and NADD (c). Propagation of signal (blue) and conjugate (red). It is also noted that we employ a nonstandard power/dispersion symmetry from[12],[13], where each span accumulates dispersion with opposite sign, both starting from zero. This simplifies the design, but requires a lumped dispersion compensating module in between the spans to compensate the dispersion of the first part.