**1. Introduction**

Optical phase conjugator (OPC) in a long-haul transmission system can effectively compensate for both linear (e.g., chromatic dispersion) and nonlinear (e.g., the fiber Kerr nonlinearity) impairments, and therefore can improve the data capacity or transmission distance [1–27]. The efficiency of how much the fiber nonlinearity can be compensated assisted by mid-link OPC was limited by several factors, such as the slope of the chromatic dispersion map of the transmission fiber and the signal power profile along the fiber [1–6]. The symmetry of chromatic dispersion slope can be tailored by optimizing the dispersion map using a combination of transmission fiber and dispersion compensating fiber [9]. This can be used together with erbium-doped fiber amplifiers (EDFA) which is the most widely used amplification technique; however, it requires special transmission fiber and dispersion compensating fiber to maintain the dispersion map symmetry. Another way to maximize fiber nonlinearity compensation efficiency with OPC is to use distributed Raman amplification to make the signal power profile symmetrical. Distributed Raman amplification generates optical gain using Raman pump lasers over the standard transmission fiber, providing distributed amplification along the whole fiber rather than a discrete or lumped amplification within a few meters of doped fiber as in EDFA. DRA can be highly flexible to specifically tailor the signal power profiles to be highly symmetrical before and after the OPC [3–6]. The pump wavelength can be adjusted with fiber Bragg gratings (FBG) with selected center wavelength [28–40]. The use of distributed Raman amplification can improve the maximum transmission distance or data capacity without the mid-link OPC (or the first half of the link before the OPC) and therefore if the symmetry of the link can be maintained at a very high level for all channels, the overall transmission performances or data capacity can be significantly improved using mid-link OPC due to the efficient compensation of fiber nonlinearity [4–6].

We show, for the first time, that the transmission bandwidth can be extended using FBGs at two different wavelengths for transmitted and conjugated channels in mid-link optical phase conjugation. The novel design approach allows for the highest OPC bandwidth using Raman amplification and gives the lowest asymmetry for a single channel up to date

**Citation:** Rosa, P.; Martella, G.R.; Tan, M. Bandwidth Extension in a Mid-Link Optical Phase Conjugation. *Sensors* **2022**, *22*, 6385. https:// doi.org/10.3390/s22176385

Academic Editors: Carlos Marques, Jiangbing Du, Yang Yue, Jian Zhao and Yan-ge Liu

Received: 29 June 2022 Accepted: 22 August 2022 Published: 24 August 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

for designs of distributed Raman amplification schemes which are aimed to improve the symmetry of the link for the transmission systems.

#### **2. Distributed Raman Amplification**

In telecommunication systems, there are several Raman configurations that can be used. In a single span unrepeatered submarine transmission, second order bi-directional pumping with two FBGs in the front and the end of the span provides grea<sup>t</sup> signal power distribution along the fiber compared to first order amplification, which ultimately increases transmission reach [37–40]. Depending on the application, the same approach might not work in long-haul transmission. Forward pumping can help with signal power distribution creating a quasi-lossless transmission medium [32]; however, the benefits of low noise and signal power variation become meaningless in coherent data transmission due to forward relative intensity noise (RIN) [32–36]. In [36] we compared six different Raman configurations, including first order, second order and dual order and have shown, experimentally, that bi-directionally distributed Raman amplification with a single FBG at the end of the transmission span, forming a half-open cavity with random distributed feedback (DFB) lasing [28], significantly decreases accumulation of amplified spontaneous emission (ASE) noise built up across the transmission span and keeps signal power variation low [28–40], extending data transmission by almost 900 km to a record distance of 7915 km. In this particular scheme the forward Raman laser pump at 1366 nm amplifies the backward propagating random DFB lasing at the frequency specified by the wavelength of the FBG. This approach allows for a RIN transfer reduction [32–36] from the noisy forward Raman pump to the Stokes-shifted light, becoming an efficient solution for a long-haul coherent data transmission format [33–36].

The schematic design of the random DFB Raman laser amplifier is shown in Figure 1. Two Raman fiber laser pumps downshifted in wavelength to 1366 nm (approximately two Stokes shifts from the signal) were located at each end of the standard single mode fiber (SMF). The span length was 60 km. A half-open cavity random DFB laser was formed at the wavelength of the FBG at the end of the fiber that amplifies original and conjugated WDM channels in the OPC system. We assume that fiber used for the FBGs is the same as transmission fiber, which is standard SMF fiber. By optimizing the wavelength of the FBG, rather than deploying a seed at different wavelength, the spectral gain profile of the amplified WDM signals can be modified and enhanced. This is visualized by an example shown in Figure 2 where we compare the Raman gain shift resulting from FBGs at different wavelength. To avoid polarization gain dependance in WDM transmission, Raman pump lasers at both ends and lasing at the wavelength of the FBG were fully depolarized.

**Figure 1.** Raman fiber laser-based amplifier with a half-open cavity random lasing.

**Figure 2.** The Raman gain shift using FBGs centered at 1448 nm (red) and 1458 nm (black). The right figure is zoomed on the 16 WDM signals wavelength range.
