Mid-span optical phase conjugation (OPC) is a viable option for nonlinearity compensation in high-speed fiber-optic transmission systems. However, propagation symmetry is a key factor in the good performance of OPC. In other words, nonlinearity compensation is effective when the transmission link is symmetric with respect to OPC in terms of optical power and accumulated dispersion, which is the metric of OPC effectiveness, called the power versus accumulated dispersion diagram (PADD). Due to fiber loss, symmetric PADD cannot be obtained in common transmission systems based on the erbium-doped fiber amplifier (EDFA). Recently, a novel approach to satisfying the nonlinearity compensation criteria has been proposed, where symmetric PADD is obtained through optimized dispersion management with the inverse dispersion fiber (IDF). However, the approach relies on the availability of IDF which does exist, and IDF is not mass-produced. This paper numerically investigates the possibility of using the dispersion-compensating fiber (DCF) instead of IDF for link construction, which allows for a relatively simple modification and upgrades of installed fiber-optic links.

Numerical simulations are performed by the use of the split-step Fourier method, and pulse evolution in the fibers is described by the generalized nonlinear Schr?dinger equation, which includes intrachannel nonlinearities such as self-phase modulation (SPM), intrachannel cross-phase modulation (IXPM), and intrachannel four-wave mixing (IFWM). The performance of two links (for simplicity, called IDF-managed link and DCF-managed link, as shown in Fig. 1) is compared with respect to the IFWM-induced peak intensity fluctuation at the "1" bits and ghost pulse generation at the "0" bits. The links are made of three types of fibers with parameters near 1.55 μm, as listed in Table 1. In the IDF-managed link, the standard single-mode fiber (SSMF) and the IDF have the same length, same loss, and same nonlinearity except for the reversed group velocity dispersion (GVD). Whereas in the DCF-managed link, the loss and nonlinearity of the DCF are three times as large as those of the SSMF, and the GVD of the DCF is eight times as large as that of the SSMF. The span length (amplifier spacing) is fixed at 80 km for each link. Fiber loss is compensated by EDFA, and GVD is compensated by the IDF or DCF. The input is assumed to be 4 bit with a bit pattern of 1110. The "1" bits have the same initial width and initial amplitude. The "0" bit has much smaller amplitude than that of the "1" bits. All bits have the same initial width T_FWHM=3 ps, with a bit separation of 12.5 ps, representing a bit rate of 80 Gbit/s. The OPC is modeled by ideal conjugation of the complex envelope of the pulse as u(ξ,τ)→u^*(ξ,τ), without any penalties associated with the process.

Different transmission distances, i.e., two-span (N=1), six-span (N=3), and ten-span (N=5) are considered, and the compensation results of the two links are compared for each distance. In all cases, the same input is assumed. Figs. 2(a)-(c) compare the output pulse shapes, and Figs. 2(d)-(f) compare the spectra. It can be seen that in all cases, the IDF-managed link outperforms the DCF-managed link. As the transmission distance increases, the residual nonlinearity of the latter accumulates, and the nonlinear distortion is enlarged. For a quantitative comparison, two parameters of the output pulses are defined and calculated, i.e., the average peak intensity fluctuation (ΔP_aver) of the "1" bits and the relative peak intensity of the ghost pulse that is defined as the ratio of the peak intensity of the output ghost pulse to that of the input "0" bit. The results are compared in Fig. 3, where input energy is used, which is the total energy of the input 4 bit. In all cases, the input pulse width and bit slot are identical to those of the simulation in Fig. 2 except that the input energy varies with the amplitude of the input. For two-span transmission, there is little difference between the two links when the input energy is small. The difference is more and more significant as the input energy or the span number grows, and the performance of the DCF-managed link deteriorates rapidly relative to that of the IDF-managed link. The performance of the DCF-managed link could be improved by launching different energies into the spans before and after the OPC. The energy into the SSMF before OPC should be higher than that into the DCF after OPC because SSMF is less nonlinear than DCF. A variable gain amplifier (VGA) is inserted at the input end of the spans before OPC while a variable optical attenuator (VOA) is inserted at the input end of the spans after OPC, as shown in Fig. 4, where the magnification of the VGA equals the attenuation of the VOA. The energy into the spans before and after the OPC is denoted as E₁ and E₂, respectively, where E₁ or E₂ is calculated by the summation of the intensity values of the pulse shape. For a fixed value of E₁+E₂, the ratio E₁/E₂ is optimized to minimize the parameter ΔP_aver, which results in an optimum E₁/E₂ for optimum nonlinearity compensation. The results are shown in Fig. 5 for the three values of E₁+E₂, where all calculations are obtained through six-span transmission (N=3). It can be seen that when E₁/E₂ increases to a certain value, a minimum ΔP_aver is obtained for a given value of E₁+E₂, which indicates that an optimum counterbalance is achieved. Moreover, the optimum E₁/E₂ increases with E₁+E₂. Further simulations reveal that for a fixed value of E₁+E₂, the optimum E₁/E₂ is independent of the span number N. For example, Fig. 6 gives a comparison of the transmission results with and without nonlinearity counterbalance. The DCF-managed output is significantly improved by optimum nonlinearity counterbalance. Compared with the IDF-managed output, the DCF-managed output with optimum counterbalance is even closer to the input. This is reasonable since the pulse shapes depicted here are instantaneous power curves, and IFWM-induced pulse distortion occurs in the spans before the OPC while the bit-by-bit symmetry in the pulse shape about the OPC is not fulfilled. Thus, without a nonlinearity counterbalance, the OPC effectiveness would be decreased even with a perfect PADD as in the case of the IDF-managed link.

We have numerically investigated intrachannel nonlinearity compensation in dispersion-managed links with mid-span OPC. The compensation effectiveness of two different links is compared with respect to IFWM-induced intensity fluctuation of the "1" bits and the generation of the ghost pulse. Results show that by asymmetric energy transmission, the nonlinearity mismatch of the DCF-managed link can be counterbalanced, and the performance can be significantly improved. For a given input energy, there exists an optimum ratio of the energies into the spans before and after the OPC, at which the compensation effectiveness of the DCF-managed link is very close to that of the IDF-managed link. The optimum energy ratio increases with the input energy but is independent of the span number of the link.