## 1 Introduction  
With the help of multiplexing technologies such as wavelength division multiplexing (WDM), polarization division multiplexing (PDM), space division multiplexing (SDM), orbital angular momentum multiplexing (OAMM), most Internet traffic is handled through an optical network [1]. In order to increase the multiplexing efficiency of high data rate optical channels in a long-haul optical network, a transmission medium that minimizes temporal broadening of optical signals during transmission must be used. Dispersion that affects the temporal broadening of optical pulses is largely divided into inter-modal dispersion and intra-modal dispersion. When there are several modes propagating in an optical fiber core, the spread of pulses caused by the time difference between each arriving at the receiving end is called inter-mode dispersion. Thus, in order to suppress this, a single-mode fiber (SMF) is mainly used as a transmission medium of long-haul optical networks. However, even an optical network comprising a transmission link using only SMF cannot avoid the temporal spread due to intra-mode dispersion, also called chromatic dispersion. Moreover, since different wavelengths are used for each channel in the WDM system, signal distortion due to chromatic dispersion inevitably increases as the number of transmission channels within the same SMF increases [2]. Therefore, in order to implement an SMF-based WDM transmission network, a technique for minimizing signal distortion due to chromatic dispersion must be applied. The application of an erbium-doped fiber amplifier (EDFA) in optical transmission links has also made a great contribution to the long distance of super-multiplexed optical signals. That is, the EDFA dramatically increased the transmission distance without requiring a repeater, and eventually made it possible to use the SMF-based WDM network more simply, compactly, and economically [2]. Unfortunately, the EDFAs in an optical link amplify the intensity of the transmitted optical signal, and consequently induce the intensity-dependent nonlinear impairment of optical signals [3]. In an optically amplified and SMF-based transmission system, optical signal distortion due to nonlinear effects and chromatic dispersion effects may increase as the transmission distance increases, since the accumulated impacts of nonlinear effect interplaying with chromatic dispersion of SMF are not reset at the repeaters [2]. Optical phase conjugation (OPC), proposed by [PERSON] et al., was initially widely known as a method for compensating for chromatic dispersion [4]. It uses the principle of compensating for the signal distortion by inverting the spectrum of the transmission signal in the middle of the transmission link. That is, the signal distortion experienced in the front part of the link before the optical phase conjugator (OPC) is offset with damage caused in the rear part after the OPC, so that the original signal can be closely restored. It has been experimentally shown that OPC can compensate not only chromatic dispersion but also distortions caused by self-phase modulation (SPM), intra-channel nonlinear effect and nonlinear phase noise [5; 6; 7; 8; 9]. Dispersion management (DM) is method of mitigating signal distortion due to chromatic dispersion using only optical fibers [10]. When SMF is adopted as an optical transmission medium, since its dispersion coefficient is positive (typically +17 ps/nm/km), the optical pulse width increases as the transmission distance increases, ultimately resulting in inter-symbol interference (ISI). In order to eliminate or reduce the ISI, dispersion compensation fibers (DCFs) having the negative dispersion coefficient must be added at regular intervals or concentrated at a specific location in the transmission link so that the total cumulative dispersion is close to 0 ps/nm. In the DM link, the cumulative dispersion profile according to the entire transmission distance can be designed considering the positions, dispersion coefficient, and length of the SMF and DCF.