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Abstract
We propose a modified configuration of the nonlinear-optical loop mirror (NOLM) unit by introducing the polarization-effect optimization (PE) into a nonlinear Sagnac interferometer through a polarization-maintaining optical coupler, enabling significant extension of the regeneration region (RR) of the all-optical multi-level amplitude regenerator. We carry out the thoughtful investigations on this PE-NOLM subsystem, and reveal the collaboration mechanism between the Kerr nonlinearity and the PE effect in only one unit. Moreover, the proof-of-concept experiment and its theoretical discussion of multiple-level operation have been performed, observing the 188% enhancement on the RR extending and the consequent 4.5 dB signal-to-noise ratio (SNR) improvement for a 4-level pulse amplitude modulated (PAM4) signal compared to the conventional NOLM scheme.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the exponential growth of the Internet traffic coming from the wide utilization of the online videos, VR/AR games, big data or other cloud-based applications, the capacity of the current standard single-mode fiber (SSMF)-based optical communication systems has approached the Shannon limit. To deal with this issue, all-optical signal regeneration as a promising technology provides a pure all-optical method to break through the system capacity by directly suppressing the signal’s distortion in the optical domain [1]. Nonlinear-optical loop mirror (NOLM) as an all-optical nonlinear interferometer possesses the oscillatory power-mapping nature, perfectly matching with the regeneration requirement of the multiple-level operation for the advanced modulation format. As a promising structure for the amplitude regenerator, the NOLM unit has been intensively investigated in recent years, especially for the multi-level amplitude-modulated signals [2–7]. However, the existing regeneration structures are facing with a variety of inherent problems. The major issue of the current NOLM regenerators is the limited noise tolerance, especially for the higher-order levels [8–10], which leads to the worse performance happened when dealing with the advanced modulation format in the high-capacity optical systems.
In order to solve this problem, several schemes have been proposed to improve the regeneration performance of the NOLM subsystem to support the advanced modulation format. The modified NOLM with an extra optical attenuator performed the phase-preserving operation on the amplitude regeneration [3]. A regenerative Fourier transformation was proposed through a combination structure of NOLM and Mach–Zehnder interferometer (MZI) to support rectangular quadrature amplitude modulated (QAM) signals [11]. We have demonstrated the cascaded structure achieved through connecting several NOLMs with an optical amplifier [7] or an optical phase conjugation (OPC) unit [12] to increase the regenerative level. The novel structure of the polarization-orthogonal continuous-wave-light-assisted NOLM (PC-NOLM) [13] have also been proposed to perform the uniform regeneration on multiple levels. These modifications have indeed improved the regenerative performance, but the defects are also obvious, e.g., the complexity of the regenerator subsystem requiring the extra NOLM or other optical processing units in these schemes, which prevents the real applications in the long-haul transmission systems.
The polarization effect (PE) has been considered in a nonlinear Sagnac configuration to perform the polarization sensitive optical switching [14,15] or the polarization attractor [16]. The PE impact could also be used as an effective tool to adjust the NOLM status [17,18] or even in the amplitude regularization [19,20]. Based on our previous work, the regenerative performance could be improved by considering the PE in the NOLM [21]. In this paper, we significantly extend the concept of the proposed PE optimized NOLM (PE-NOLM) [21], introducing the collaboration mechanism between the Kerr nonlinear phase shift and the PE optimization. The detail investigations are carried out in both simulation and experiment on the regeneration region (RR) extending and the working principle, as well as the transmission improvement due to the inserting the PE-NOLM inside the links. The rest of the paper is organized as follows: in Section 2 we carry out the experimental test of the PTF responses from the PE-NOLM regenerator and the noise suppression performance on the signal’s amplitude; in Section 3, we introduce the principle of the proposed PE-NOLM and investigate the influence of the polarization state on the power transferring function (PTF); moreover, we thoughtfully investigate the multi-level operation for the 4-level pulse amplitude modulated (PAM4) signal and its implementation in the transmission link; finally, we draw the conclusion of our study in Section 4.
2. Experiment
2.1. Experimental setup
The PE-NOLM experiment consists of two parts: the test of the proposed regenerator's PTF and its all-optical amplitude regeneration performance. The system of the PE-NOLM regenerator is depicted in Fig. 1. In the process of the test, a continuous wave (CW) laser with the wavelength of 1550 nm was used as the light source, and connected to a phase modulator (PM) driven by the pseudorandom binary sequence (PRBS) with the length of 231-1 electrical signal generated from a pulse pattern generator 1 (PPG1), enabling increasing the threshold of the stimulated Brillouin scattering (SBS) effect of HNLF in the NOLM [22,23], The optical power input into the regenerator was adjusted by an Erbium-doped fiber amplifier (EDFA) with the maximum output power up to 37dBm. An optical circulator placed at the input of the regenerator was used to prevent the unwanted reflected light back into the optical transmitter, and an optical power meter (OPM) connected to the port 3 of the optical circulator was to monitor the reflected power from the NOLM.
The proposed PE-NOLM regenerator consisted of a polarization-maintaining optical coupler (labeled PM-OC1 in Fig. 1), a highly nonlinear fiber (HNLF) and a polarization controller (PC). The PM-OC1 with the coupling ratio of 75:25 is the main element of the proposed NOLM structure, which has two functions in the regenerative process. One is to split the input light into the two components and then propagating through the PE-NOLM structure with the opposite directions, i.e., the clockwise- and counter-clockwise paths as a normal OC. The other is to introduce the extra power loss into the OC when the state of polarization (SOP) of the input light misalignment with the principal axis of the PM-OC1, performing the fast-axis blocked or the slow-axis blocked functions. The second function is crucial to perform the PE optimization in the proposed NOLM configuration due to the effective power launched into the HNLF highly depending on it. We also placed the second OC into the NOLM, which split a small part of the light inside the NOLM to monitor the real optical power in the ring. The splitting ratio of the OC2 was 99:1. The nonlinear coefficient of HNLF used in the experiment was 11/W/km, the fiber length was 1 km, and the loss coefficient was 0.7 dB/km as our previous experiment [13]. A multichannel optical power meter (OPM) was used to monitor the optical powers from the whole system, including the launched optical power tested at the output-port of OC3, the reflected optical power from the PE-NOLM at the port 3 of the optical circulator, the power information inside the NOLM from the output-port of OC2 and the transmission power at the output-port of OC1. The power testing is important to the operation of the all-optical regenerator, which could monitor the regeneration state to locate the optimized operation. The power dependent testing was performed through adjusting the output power of the EDFA2, which controlled the total power that launched into the PE-NOLM.
2.2. Regenerative results
For the PTF test, the phase-modulated CW light was injected into the PE-NOLM, and sweeping the input power to collect one by one the transmission results at the output of the all-fiber interferometer, the curve depicted in Fig. 2(a). The clear power plateau has been achieved in the experimental measurement. The super-flat plateau suggests the remarkable distortion-suppression could be achieved by the proposed PE-NOLM. The much wider region obtained in the plateau is the benefit of the PE optimization in the NOLM, which could lead to the wide RR comparing to the conventional NOLM [5]. To give a clear result on the potential regenerative capability, we calculated the slope value of the PTF curve to define the RR, where the absolute value of the slope was less than 1. The slope results are depicted in Fig. 2(b), see the blue curve. And the RR obtained by the proposed PE-NOLM configuration is between the two blue-lines. Due to the flat response in the plateau region, the slope value was close to zero in a large area, which could effectively suppress the amplitude distortion when the level falling into the RR. More the number of the RR could be achieved if the launched input power is further increased, see the decreasing trend already obtained for the higher power in the experiment.
Fig. 2. (a) Comparison of the experimental and simulated PTF curves; (b) comparison of the experimental and simulated PTF slope curves.
Furthermore, we discuss the impact of the linear polarization rotation (PR) on the RR results in the proposed PE-NOLM. The linear PR is introduced by the PC placed at the inside of the NOLM. By tuning the PC, we located the widest RR where the state of the PC was labelled at the optimized polarization at “0”, see the peak in Fig. 3. Therefore, the normalized regeneration width was obtained from the measured data divided by the maximum RR value from simulation, and the normalized polarization deviation was equal to the polarization rotation minus the optimized polarization value. Further drifting from the optimized polarization, the RR value was narrowed down accordingly, the experimental data labelled marks depicted in Fig. 3. The dependency of the obtained RR on the PC-induced linear PR is due to the extra power loss caused by the misalignment between the principal axis of the PM-OC1 and the SOP of input signal, which reduces the effective power for the input signal. Therefore, the “stressing behavior” only happened at the x-axis of the PTF curve affects the RR value as the experimental testing.
Moreover, the signal test is carried out to evaluate the regeneration performance of the proposed PE-NOLM. In this scenario, we launched into On-Off Keying (OOK) signal with the data rate of 10Gb/s. The phase modulation was also applied as the pre-processing, to increase the threshold of the SBS effect in HNLF. The SOP information was the same as the previous discussion to guarantee the good performance achieved by the regenerator. The input signal was distorted by the amplifier spontaneous emission (ASE) noise from EDFA1 and EDFA2, and the misalignment between two modulators, see the amplitude distortion observed in the input signal from Fig. 4(a). Adjusting the output power of EDFA2 makes sure the signal’s amplitude falling into the power plateau region, where the noise suppression happened. The optical non-return-to-zero (NRZ) signal was detected by a photodetector and monitored by a sampling oscilloscope.
Fig. 4. (a) Experimental and (b) simulated signals before regeneration; (c) experimental and (d) simulated signals after regeneration.
Passing through the PE-NOLM, the amplitude regeneration was performed, see the regenerated output in Fig. 4(c). The clear amplitude with large eye opening was obtained after the noise suppression thanks to the flat response from the proposed regenerator. The signal quality was increased by 1.2 dB for the input SNR of 10 dB, confirming the amplitude noise suppression happened in the PE-NOLM. Compared to the noise reduction ratio (NRR) improvement of only 0.8 dB around [24], the proposed PE-NOLM could perform the excellent amplitude-distortion suppression thanks to the extremely wide RR. Therefore, the much better regeneration performance was naturally expected when the PE-NOLM implemented into the transmission link.
In order to further analyze the influence of the regenerator on the signal quality in the experiment, we tested the relationship between the input signal-to-noise ratio (SNR) and the output signal quality-Q factor. By increasing the distortion strength of the input NRZ, we measured the output Q-factor at the transmission port of the PE-NOLM, results depicted in Fig. 5. The Q-factor was calculated directly from the eye diagram in the sampled oscilloscope. According to the experimental data, the maximum Q-factor improvement of 3.5 dB was achieved at the input SNR of 22 dB. Over 10 dB operational input-SNR region was also observed due to the extremely wide RR from the PE-NOLM regenerator, confirming the importance of the polarization optimization in the all-fiber nonlinear interferometer configuration. We also see the output variation of 1 dB detected around the input SNR = 21 dB, which might be caused by the instability of the test process from oscilloscope. But it doesn’t lead to serious impact on the trend of this quality-mapping curve.
3. Theoretical discussion
3.1. Collaboration mechanism between Kerr nonlinearity and PE optimization
In the proposed PE-NOLM, the Kerr nonlinearity and its polarization impact play the important role in the all-optical regeneration process with the property of the wide operation. Figure 6 depicts the simulation setup of the PE-NOLM based multi-level amplitude regenerator. In the core subsystem-PE-NOLM, it was composed of a PM-OC, a HNLF and a PC, as the experimental configuration. The device of the PM-OC performs the combined function of the ordinary OC and the optical polarizer in one unit, depicted in Fig. 6(a). The input light was coupled into the PM-OC from the port of Input 1 or Input 2, and split into the two parts with a certain splitting ratio, e.g., 75:25 used in the experiment. Then the two beams were launched into the two linear polarizers (LPs), separately. At the output ports, Output 1 or Output 2, the two beams with the orthogonal SOP were obtained. Moreover, the LP could also block part of the light due to the polarization misalignment, leading to the extra power loss detected from the output of the PM-OC. Therefore, we used one ordinary OC and two LPs to simulate the PM-OC in the simulation, see PM-OC in Fig. 6(b). ρ is the splitting ratio of the ordinary OC, and α and β are the azimuth angles of the two LPs. The relation between the two azimuth angles, e.g., |α|+ |β| = π / 2 due to the orthogonal polarization nature of PM-OC is also given in the inset of Fig. 6(b). Moreover, the second polarization related device in PE-NOLM was the PC. In the simulation we considered the PC introduced a fixed rotation of θ as the investigation in [25], for the clockwise path with the extra polarization angle of -θ, and for the counter-clockwise path with +θ. Then, the split light with the proper SOP was launched into the HNLF from the two opposite directions. Besides the nonlinear power dependency obtained from the NOLM, the polarization related nature of the Kerr nonlinear effects [26] could give the second freedom to control the response of the PE-NOLM. The polarization impacted Kerr effects are well expressed as follows [27]:
Fig. 6. (a) Working principle of the PM-OC and (b) simulation structure for the PE-NOLM based multi-level amplitude regeneration system.
We used OptiSystem simulation platform to set up the PE-NOLM based amplitude regeneration system, as the structure depicted in Fig. 6(b). The device parameters used in the simulation were the same as the experiment. Other parameter, such as the different group delay (DGD) of HNLF was chosen as 0.2ps/km because of the standard HNLF used in the experiment. Through the simulation, we could investigate the detail dependences of the regeneration performance on the device parameters, to reveal the operational nature of the proposed PE-NOLM.
Based on the simulation model, we firstly carried out the detail comparison between experimental data and theoretical results. Sweeping from -180° to 180°, the polarization rotation θ=45° induced by PC is defined when the calculated PTF matching with the experimental curve. The calculated PTF and its slope were plotted at Fig. 2. The well-agreement between experiment and simulation confirmed the model we used could be used to investigate the PE-NOLM structure. Moreover, we changed the value of the polarization rotation θ, to simulate the tuning operation of PC in the experiment, and collected the RR results according to the corresponding PTF’s slope curve, depicted in the blue-line in Fig. 3. The decreasing trend was obtained when the state of PC away from the optimized case, just as the experimental results. It reminds the importance of the optimization of the polarization state for the proposed PE-NOLM. In the same figure, we also calculated the RR result from the conventional NOLM [5], in which the ordinary OC instead of PM-OC were used. Due to the lack of the optimization from the view of the polarization rotation, the less regenerative capability, e.g., the smaller RR was obtained in the conventional configuration compared to the proposed novel PE-NOLM. Additionally, we performed the all-optical amplitude regeneration for NRZ signals. The calculated eye diagram and Q-factor results, depicted in Fig. 4 and 5 respectively, were well-matched with the experimental results, which further proved the regenerative capability of the PE-NOLM.
Secondly, we discuss the nonlinear response obtained from the proposed PE-NOLM when changing the value of the device parameters. According to our previous study on the conventional NOLM [6], the PTF could be impacted by the coupling ratio of OC. We also swept the value of the coupling ratio in the PE-NOLM simulation system, and collected the nonlinear power responses around the plateau region, see the results in Fig. 7. When increasing the power asymmetry from 70:30 to 95:5, the PTF curve shifted towards to the lower power region, just like the behavior we have observed in the conventional NOLM [6]. But, no significant improvement on the plateau detail was obtained from changing the coupling ratio in the region we discussed. Therefore, we can expect that the similar amplitude-regeneration performance would be achieved when changing the coupling ratio of the PM-OC around 75:25, because of the amplitude-distortion suppression only happened in the plateau region.
Then, we discuss the PE optimization in the proposed scheme. According to the Eq. (1) and (2), the nonlinear phase shift is not only dependent on the launched optical power, but also related to the SOP of the propagating light. Therefore, we selected the different value of the polarization angle and calculated the corresponding PTF curves, results depicted in Fig. 8(a). The value of α was chosen as 37° for the case of α, α/3 and 2α in Fig. 8(a). The normalization was carried out by the maximum value obtained. To maintain the orthogonal polarization nature of the PM-OC, the value of β was also changed accordingly, following the relation |α|+ |β| = π / 2. The oscillatory behavior, especially the strength of the variation is obviously enhanced with the increase of the α. This positive response from the polarization dependent PTF reveals the operational nature of the PE-NOLM. We also plotted the PTF results when α=0 for the conventional NOLM case. The similar weak-regenerative capability for the first level was observed in our previous work [5]. Comparing the results from the PE induced configuration and the conventional scheme, the wider RR could be indeed achieved by the proposed PE-NOLM. In Fig. 8(b), we calculate the slope results to locate the RR for the different α value. More clear results were collected in Fig. 8(c), where the relationship between the RR with polarization angle α was given. According to the numerical simulation, we defined the optimized angle α=37° where the wider RR and the smaller slope value obtained. The wide RR suggests the large noise-handling capability, and the small slope value means the high distortion-suppression efficiency.
Fig. 8. (a) The influence of the initial polarization state a on the PTFs; (b) influence of the initial polarization state a on the slope results of PTFs; influence of the α on the width of regeneration region; (c) influence of the α on the width of regeneration region.
In the proposed PE-NOLM, the secondary polarization effect comes from the PC placed inside the interferometer. The polarization rotation induced from the PC could affect the SOP of the propagating light, and consequently the polarization misalignment between the light and the principal axis of PM-OC. This misalignment would introduce the extra power loss in the PE-NOLM, which equivalently reduce the effective optical power for the input light. Moreover, the polarization misalignment could also happen at the input of the PE-NOLM. Therefore, another PC was placed at the input-port of the all-optical regenerator to adjust the SOP of the input light. Locating the optimized polarization is the first step to optimize the regeneration performance of PE-NOLM. In Fig. 9, we plot the relationship between the transmission power and the polarization rotations from the inside and outside PCs. The normalization was carried out by the maximum value obtained. The red-star marks response to the required SOP by the experiment, where the best performance of the PE-NOLM is achieved. The periodic power response reveals the nature of this nonlinear interferometer, but which is also hard to define the optimized polarization angle just from the transmission power. In the experiment, we firstly adjusted the external PC to find the minimum and maximum transmission power. Then finding the red-star point in the region of the optical power rising from the minimum value to the maximum value, just as the figure. The adjustment method of the internal PC was also the same, but the difference is that the red-star point was located at the power reduction area between the maximum and minimum values.
Fig. 9. Relationship between the required polarization rotation of PC placed at (a) inside and (b) outside the ring and the transmission power.
3.2. Multilevel operation for the proposed PE-NOLM
To perform the multilevel operation for the amplitude regenerator, the staircase-like PTF should be achieved in the proposed PE-NOLM. Based on the simulation setup proposed in the previous section, a PTF curve with four plateaus is plotted in Fig. 10 with the polarization information of α=37° and θ=45°. The power plateau region on the PTF curve is called as the RR where the amplitude noise suppression happened, and the midpoint of the interval is named as working point (WP). We have obtained total 4 WPs, labelled A, B, C and D in the calculated PTF.
The advantage of the PE-NOLM in the view of the PTF is discussed in Fig. 11, where the comparison of the response curves between the conventional NOLM and the proposed one are depicted. To give a fair comparison, the normalized operations for the PE-NOLM and conventional NOLM were carried out based on the same standard-the step power for the PTF measurement of the conventional NOLM. Much wider regeneration interval, see RR-B in the figure, was obtained from the PE-NOLM, and increased by 188% compared to the conventional scheme [5,7]. It suggests the higher noise-handling capability could be achieved in the novel NOLM. Moreover, the flat response obtained in the power plateau also indicates the well-suppression efficiency could be achieved in the process of the amplitude regeneration.
The regeneration was only investigated by an NRZ signal with one amplitude due to the limitation of the power level used in the experiment. We further discuss the multi-level operation by the proposed PE-NOLM with simulation, also based on the experimentally verified NOLM. We measured the noise-suppression capability to each plateau, the results depicted in Fig. 12. The input power was normalized by the step power of PE-NOLM regenerator. From the red-solid-line, we could locate four RR through the gain of the error vector magnitude (EVM). The EVM is defined here only by the amplitude level of NRZ signals. Therefore, it could be used to quantify the distortion evolution of signals when increasing launched optical powers into the NOLM regenerators. The EVM of input signal was 24 dB. The highest value of 7.8 dB was obtained at the second RR, labeled B in Fig. 10, because of the flat response in this region. But similar power range was achieved by each RR, suggesting the equal noise-handling capability for every regenerative level. We also calculated the EVM gain by using the conventional NOLM schemes with different splitting ratios. Although four local peaks were obtained confirming the multi-level operation, the worse EVM results indicated the bad regeneration performance for the convention scheme.
Moreover, we took a 4-level pulse amplitude modulated (PAM-4) signal as an example to evaluate the multi-level operation. Through increasing the optical power of the PAM-4 signals, four amplitude levels were fallen into their corresponding plateau to perform the noise suppression behavior. The eye diagrams from the PAM-4 signal before and after regeneration are depicted in Fig. 13(a) and (b). The noise suppression on the second and third amplitude levels is better than the other levels, confirming the different regeneration performance obtained at the different level, see the EVM-gain curves obtained at Fig. 12. For the PAM-4 signal, the signal quality was increased by 4.32 dB, proving the well operation on the multi-level amplitude regeneration.
Furthermore, we put the multi-level amplitude regenerator into the middle of the link, to evaluate its transmission performance. The ASE noise was added before and after the regenerator, just as the EDFA performed in the link. The same ASE level was considered between the two noise sources, and increased to measure the dependence of the bit-error-rate (BER) results of the output signal vs. the signal-to-noise ratio (SNR) from the input. The calculated data are depicted in Fig. 14. The same transmission link was also investigated for the case of the conventional NOLM, see the blue-square line in the Fig. 14. A 4.5 dB improvement on the input SNR was achieved for this regenerative transmission of PAM-4 signals, suggesting the more distortion handled by the proposed PE-NOLM. This improvement was much larger than that obtained by the conventional scheme, only around 1 dB in [5], where it was compared with the power-restored only case. Such big improvement comes from the much wider RR demonstrated by the PE-NOLM, also proving the importance of the PR effect in the optimization procedure of the NOLM regenerator.
In order to further test the reliability of the proposed regenerator in the long-haul transmission, we placed the PE-NOLM regenerator to each span and performed the loop transmission simulation. Only ASE noise was considered in the loop transmission. We collected the input SNR for the first loop corresponding to the resulted BER = 10−3, and plotted the relationship between the number of loop and the input SNR requirement in Fig. 15. It can be seen that there is a big gap, about 4 dB of required input SNR between the proposed PE-NOLM and the conventional NOLM. The less requirement comes from the wide RR operation from the novel scheme.
Fig. 15. Input SNR requirements in the loop transmission for PE-NOLM, conventional NOLM and without regenerator cases.
4. Conclusion
We introduced the PE into the NOLM configuration to significantly improve the regenerative performance of the multi-level amplitude regenerator. The multiple-parameter optimization was carried out through simulation, including the initial SOP of signal, the polarization rotations induced by the PCs placed at the outside and inside the interferometer. The simulation results show that the regeneration range of PE-NOLM is nearly doubled compared with the traditional NOLM scheme. When placing the PE-NOLM into the middle of the transmission link, the requirement of the input SNR for PAM-4 signals is reduced by 4.5 dB compared to the convention NOLM. In the loop transmission, the 4 dB lower requirement on the input SNR is also obtained by PE-NOLM.
Funding
National Natural Science Foundation of China (61975027, 62001086); Sichuan Science and Technology Program (2021YFG0143); National Key Research and Development Program of China (2019YFB2203103).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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