Open Access
Add to BibSonomy
Abstract
Extensive investigations are undertaken on the feasibility of utilizing phase sensitive amplification (PSA) in highly nonlinear fiber (HNLF) to achieve a reconfigurable 16QAM/8QAM all-optical format conversion for optical data center networks. A comprehensive theoretical model is developed and subsequently verified, based on numerical simulations undertaken to explore the effectiveness of the nonlinear effects of phase insensitive amplification, PSA, and self phase modulation for the proposed all-optical format conversion scheme. It is demonstrated that the proposed scheme can achieve a reconfigurable all-optical format conversion from a 16QAM signal to two quadrature phase shift keying (QPSK) signals or from an 8QAM signal to one QPSK signal and one binary phase shift keying signal with data rates of 92Gbps and 69Gbps for 16QAM and 8QAM signals, respectively.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Recently, optical Data Center (DC) networks have gained increasing attention due to their high throughput, low latency, and reduced energy consumption [1–3]. Generally, there is a large amount of traffic with frequent transmission inside short-reach optical intra-DC, where higher modulation formats (such as 16QAM/8QAM) can be utilized for larger throughput and faster processing speed. While for long-haul optical inter-DC interconnection, lower modulation formats (such as QPSK/BPSK) can be used for better bit error rate performance [4]. Therefore, format conversion is required in the gateway node when optical signals are transmitted in optical DC networks [5,6]. The traditional format conversion is completed in the electrical domain by using photo-electric-photo conversion. However, as the fixed network enters the 5th Generation Fixed network era [7–9], all-optical networks without optical-electrical-optical conversion have attracted extensive attention from academia and industry, which inevitably requires full-fiber-connected optical DC networks are equipped with the basic capability of all-optical format conversion.
Currently, researchers have proposed various all-optical modulation format conversion schemes, most of which employ signal and pump to stimulate the nonlinear effects (e.g., Four-Wave Mixing (FWM), Cross-Polarization Modulation (XPolM)) of the nonlinear medium including Semiconductor Optical Amplifier (SOA) and Highly Nonlinear Fiber (HNLF), thus the all-optical modulation format conversion is realized by changing the relationship between the phase and amplitude of the signal via the abovementioned nonlinear effects. The authors in [10] proposed an all-optical modulation format conversion method for Octal Phase Shift Keying (8PSK) to Fourth-level Pulse Amplitude Modulation (PAM4) conversion, in which the FWM of HNLF was utilized to generate conjugate waves and signal waves, then the Phase Sensitive Amplification (PSA) [11–13] was realized through coupler-based interference. However, a complex feedback circuit is required before entering the coupler for phase locking between the pump and the signal carrier. The authors in [14] and [15] achieved the all-optical modulation format conversion from 16-ary Quadrature Amplitude Modulation (16QAM) to Quadrature PSK (QPSK) by using HNLF’s FWM and SOA’s Self Phase Modulation (SPM) [16] in orthogonal polarization states. Note that the FWM efficiency is low in the orthogonal polarization state, and the conversion result is sensitive to the signal polarization angle, causing format conversion errors. Furthermore, the use of SOA as the nonlinear medium will result in a limited format conversion rate due to the long carrier recovery time of SOA. In addition, most of the existing solutions [17–19] only considered the format conversion for a single modulation format, which could not realize that different modulation formats share one format conversion system.
To address the abovementioned technical challenges, in this paper, we propose a reconfigurable all-optical format conversion from 16QAM/8QAM to QPSK/BPSK by employing PSA in HNLF. Firstly, a comprehensive theoretical derivation of 16QAM/8QAM format conversion is developed describing the physical mechanism from a 16QAM signal to two QPSK signals or an 8QAM signal to one QPSK signal and one BPSK signal. To verify the effectiveness and feasibility of the developed theoretical model, numerical simulations are undertaken, which show that the proposed scheme can achieve all-optical modulation format conversion at rates up to 92Gbps and 69Gbps for 16QAM and 8QAM signals, respectively. Furthermore, the system does not depend on the input format and can be extended to any signals owning rectangular constellation, which supports a reconfigurable all-optical modulation format conversion.
The structure of this paper is organized as follows. In Section 2, the detailed theoretical analysis based on the nonlinear effects of Phase Insensitive Amplification (PIA), PSA and SPM for the proposed format conversion is presented. Numerical simulations are then undertaken in Section 3 to verify the feasibility of the proposed scheme by sending fixed and random sequences of 16QAM and 8QAM signals, respectively. Finally, this paper is concluded in Section 4.
2. Theoretical analysis
Figure 1 shows the schematic diagram of the proposed reconfigurable all-optical format conversion for the 16QAM/8QAM signal. It mainly contains three consecutive parts, PIA-based phase-locked pump generation, PSA-based extraction of In-phase (I) and Quadrature (Q) components, and SPM-based phase rotation.
Fig. 1. The schematic diagram of the proposed reconfigurable all-optical format conversion for 16QAM/8QAM signal.
Before conducting the specific theoretical analysis, we first introduce the generation of the pump and optical carrier involved in the format conversion process. As shown in Fig. 1, the optical signal $A_1$ generated by Continuous-Wave Laser (CW1) is divided into two branches through an Optical Coupler (OC1). One is amplified by an Erbium-Doped Fiber Amplifier (EDFA1) and then participates in the following PIA as a pump, and the other is used as an optical carrier for generating 16QAM/8QAM optical signal. The optical signal $A_2$ generated by CW2 is divided into three channels through OC2. One is considered as the signal and coupled into HNLF1 to participate in PIA, together with pump $A_1$. Another is amplified by EDFA2 and then participates in PSA1 as a pump. The other is amplified by EDFA3 after a $180^{\circ }$ phase shift and then participates in PSA2 as a pump. In the following part, a detailed theoretical analysis will be carried out concerning Fig. 1.
2.1 PIA-based phase-locked pump generation
Supposing that the slow-varying envelope of the pump generated by the amplification of optical signal $A_1$ is represented as ${A_1}(z)$, the propagation constant is ${\beta _1}$, the center frequency is ${f_0}$, and the initial phase is ${\theta _1}$. The slow-varying envelope of the optical signal ${A_2}$ is denoted as ${A_2}\left ( z \right )$, the propagation constant is ${\beta _2}$, the center frequency is ${f_0} + \Delta f$, and the initial phase is ${\theta _2}$. In addition, the pump and the signal are both quasi-continuous and have the same polarization state. Since the power of the pump $A_1$ is large enough (${\left | {{A_1}} \right |^2} \gg {\left | {{A_2}} \right |^2}$), the influence of the FWM effect on the power of the pump can be ignored. Therefore, the pump ${A_1}$ and the signal ${A_2}$ are injected into HNLF1 through the coupling of OC3, and the PIA process is stimulated generating the idler ${A_3}$ at the frequency of ${f_0} - \Delta f$. The above process is depicted in Fig. 2(a) and satisfies the Coupling Amplitude Equation (CAE) given by
After the above-mentioned PIA, the output signal of HNLF1 passes through the Optical Filter (OF1) to filter out the idler ${A_3}$ which is then amplified by EDFA4 and divided into two channels by the OC5 to participate in PSA1 and PSA2 extracting the I and Q components, respectively.
2.2 PSA-based extraction of I and Q components
As illustrated in Fig. 1, the 16QAM/8QAM optical signal is denoted as S whose slow-varying envelope is $S\left ( z \right )$. By passing through the OC4, $S$ is then divided into two branches to participate in PSA1 and PSA2 for the extraction of I and Q components, respectively. For PSA1, supposing that the power satisfies ${\left | {{A_2}} \right |^2},\;{\left | {{A_3}} \right |^2} \gg {\left | S \right |^2}$. Then signal $S$, pump $A_2$ and $A_3$ are coupled into HNLF2 through OC6 to stimulate PSA1, generating a conjugate signal $\overline S$ at the frequency of ${f_0}$. The above process is depicted in Fig. 2(b) and satisfies the CAE given by
Let the initial phase of the 16QAM/8QAM signal $S$ be ${\theta _{01}} = {\theta _{01c}} + {\theta _{01sig}}$, ${\theta _{01c}}$ and ${\theta _{01sig}}$ are the initial phase of the optical carrier and the phase information of the 16QAM/8QAM electrical signal, respectively. By mathematically solving Eq. (3), the signal $S_D^I$ generated by the interference of $S$ and $\overline S$ at the frequency of ${f_0}$ is obtained and expressed as
Since ${e^{{g_2}z}} \gg {e^{ - {g_2}z}}$, thus ${e^{ - {g_2}z}}$ can be ignored, then Eq. (5) can be further expressed as
It is seen from Eq. (6) that $\left | {S\left ( 0 \right )} \right | \left [ e^{g_2 z}\left ({e^{j{\theta _{01sig}}}} + {e^{ - j{\theta _{01sig}}}}\right )/2 \right ]$ is equivalent to the coherent superposition of the original and the conjugate 16QAM/8QAM electrical signal at each point of the constellation diagram. Therefore, the I (cos) component is acquired according to Eq. (6). For 16QAM/8QAM signal with a conventional square constellation diagram, a PAM4 signal with four discrete levels representing the I component can be obtained by Eq. (6). The PAM4 signal is not ideal but has a certain degree of phase shift due to the interference of other components. If the above phase offset is ignored, Figs. 3(a) and 3(c) describe the coherent superposition of 16QAM and 8QAM signals, respectively.
Similarly, signal $S$, pump ${A_2}$ and ${A_3}$ with a phase shift of $180^{\circ }$ are coupled into the HNLF3 through OC7 to excite PSA2, generating a conjugate signal $\overline S$ at the frequency of ${f_0}$, which satisfies the CAE similar to Eq. (3). By mathematically solving the equation, the resulting optical signal $S_D^Q$ is given by
It can be seen from Eq. (7) that $\left | {S\left ( 0 \right )} \right | \left [ e^{g_2 z}\left ( {e^{j{\theta _{01sig}}}} - {e^{ - j{\theta _{01sig}}}} \right )/2 \right ]$ is equivalent to the coherent subtraction of the original and the conjugate 16QAM/8QAM electrical signal at each point of the constellation diagram. Therefore, the Q (sin) component is acquired according to Eq. (7). That is, a PAM4 signal with four discrete levels and a BPSK signal representing the Q component can be obtained for the 16QAM and 8QAM signals, respectively. The PAM4 and BPSK signals also have a certain degree of phase shift due to the interference of other components. Figures 3(b) and 3(d) describe the coherent subtraction of 16QAM and 8QAM signals, respectively.
After the abovementioned PSA, the output signals of HNLF2 and HNLF3, i.e., $S_D^I\left ( z \right )$ and $S_D^Q\left ( z \right )$, pass through OF2 and OF3, respectively, obtaining the final I component ${S_I}\left ( z \right ) = S_D^I\left ( z \right )$ and Q component ${S_Q}\left ( z \right ) = S_D^Q\left ( z \right )$. ${S_I}\left ( z \right )$ and ${S_Q}\left ( z \right )$ are then amplified by EDFA5 and EDFA6 before coupling to HNLF to stimulate SPM.
2.3 SPM-based phase rotation
This subsection will discuss how to perform phase rotation for getting the target modulation format. It should be noted that the principle of phase rotation is the same for the I and Q components. Firstly, the I component ${S_I}$ is injected into HNLF4 to excite SPM, which satisfies the CAE given by
${S_I}\left ( {z'} \right )$ denote the solution of Eq. (8), i.e., the slow-varying envelope of the optical signal representing the I component after SPM. Let ${S_I}\left ( {z'} \right ) = V\left ( {z'} \right ){e^{j{\varphi _{NL}}\left ( {z'} \right )}}$, where $V\left ( z' \right )$ is the amplitude and ${\varphi _{NL}}\left ( {z'} \right )$ is the phase shift of the signal after passing through the HNLF. By solving Eq. (8) [20], ${S_I}\left ( {z'} \right )$ is expressed as
According to Eq. (6), Eq. (9) can be further rewritten as
Similarly, the Q component ${S_Q}$ is injected into the HNLF5 to excite the SPM, which also satisfies the CAE given by Eq. (8). By mathematically solving the equation, the slow-varying envelope of the optical signal representing the Q component after SPM is governed by Eq. (11).
Let the length of HNLF used in SPM be $L$ and $z' = L$. It is seen from Eq. (10) and (11) that the phase of the input signal has been changed after SPM, and the phase change is jointly determined by the power of input signal, the nonlinear parameter $\gamma$ and the length of HNLF $L$.
Specifically, for the 16QAM signal, the four discrete levels of PAM4 signals representing I and Q components are transformed into four discrete phases through the abovementioned phase changes, that is, the QPSK signal can be obtained, as illustrated in Figs 4(a) and 4(b). Similarly, for the 8QAM signal, the four discrete levels in the I component representing a PAM4 signal and the two discrete levels in the Q component representing a BPSK signal are transformed into a QPSK signal and a BPSK signal after phase rotation. Therefore, a 16QAM signal is converted into two QPSK signals and an 8QAM signal is converted into one QPSK and one BPSK signal through the all-optical modulation format.
3. Simulation setup and results analysis
Having theoretically demonstrated the physical mechanisms of the all-optical format conversion based on the nonlinear effects of HNLF in Section 2, the next major objective is to verify the validity and reliability of the above theoretical analysis. Simulation setup based on VPI TransmissionMaker for the reconfigurable all-optical format conversion of 16QAM/8QAM signal is presented according to Fig. 1. Before analyzing the results, the parameter settings of the system are given first. The symbol rate of 16QAM/8QAM signal is set to 23GBaud, thus the data rates of 16QAM and 8QAM signals are 92Gb/s and 69Gb/s, respectively, the power of CW lasers is 10dBm. The nonlinear coefficient of HNLF is 10 $\text {W}^{-1}/\text {km}$, the length of HNLF1, HNLF2 and HNLF3 is 200m, the length of HNLF4 and HNLF5 is 1km, the power of EDFA1, EDFA2 and EDFA3 is set to 23dBm, the power of EDFA4, EDFA5 and EDFA6 is set to 20dBm, the noise figure of EDFAs is 4 dB, the frequency ${f_0}$ of CW1 is 193.414THz, the frequency ${f_0} + \Delta f$ of CW2 is 193.782THz, where $\Delta f$ represents the frequency difference between CW1 and CW2. A summary of these parameters is listed in Table 1. In addition, the Costas ring [21] (Costas) is used for the coherent receiver as shown in Fig. 1 to process the received signal.
Table 1. Parameter settings for 16QAM/8QAM all-optical modulation format conversion
Next, a fixed sequence and a random sequence of sending 16QAM/8QAM signal are simulated and verified, respectively. The constellation mapping correspondence of the signal before and after format conversion is obtained through a fixed sequence test, and the accuracy and reliability of the system are verified through random sequence analysis.
3.1 Results analysis for 16QAM all-optical format conversion
Firstly, we send a sequence of sixteen fixed 16QAM symbols covering all constellation points and analyze the constellations and waveform diagrams of the I and Q components in the all-optical modulation format conversion process. Figure 6 presents the constellation and waveform diagrams of the I and Q components after PSA. Specifically, Fig. 5(a) depicts the constellation diagram of the PAM4 signal representing the I component. The constellation diagram is compressed to the horizontal axis and owns only four discrete levels. Due to other interferences, there is a slight phase deviation compared to the ideal PAM4 constellation, which is consistent with the theoretical analysis of Eq. (6). Figure 5(b) displays the waveform diagram of the PAM4 signal representing the Q component, in which the I branch and Q branch waveforms diagram are denoted by dashed and solid lines, respectively. Compared with the I branch, the waveform of the Q branch is compressed to zero, which can be ignored. Therefore, the PAM4 signal of the I component can be obtained through the PSA process. Figure 6(a) demonstrates the PAM4 signal constellation diagram of the Q component obtained after PSA. The constellation diagram is compressed to the vertical axis and only owns four discrete levels. Similarly, due to other interferences, there is also a slight phase deviation compared to the ideal PAM4 signal constellation, which is consistent with the theoretical analysis of Eq. (7). Figure 6(b) illustrates the waveform diagram of I and Q branches represented by dashed and solid lines, respectively. Compared with the Q branch, the waveform of the I branch is compressed to an amplitude close to zero, which can also be ignored. Therefore, the PAM4 signals representing I and Q components can be obtained by employing PSA.
Then, we analyze the final format conversion results, i.e., the constellation and waveform diagrams of the two resulting QPSK signals obtained by SPM-enabled phase rotation for the abovementioned PAM4 signals representing I and Q components. Figure 7(a) shows the constellation diagram of the QPSK1 signal obtained by the phase rotation of the I component. The constellation points are also changed from the original four discrete levels to four discrete QPSK phases. It is worth noting that the phase information of the QPSK1 signal is not the same as the ideal QPSK signal because the SPM will generate four phases which are related to the amplitude of the PAM4 signal according to Eq. (11) so that the constellation of the QPSK1 is different from the ideal one. Figure 7(b) shows the waveform diagram of the QPSK1 signal after format conversion, in which the I and Q waveform diagrams are represented by dashed and solid lines, respectively. The waveform is in line with the QPSK signal waveform and relatively smooth. Similarly, Fig. 8(a) illustrates the constellation diagram of the QPSK2 signal obtained by the phase rotation of the Q component. The constellation points are also changed from the original four discrete levels to four discrete QPSK phases. Figure 8(b) displays the waveform diagram of the QPSK2 signal, in which the I and Q waveforms are represented by dotted lines and solid lines, respectively. The waveform is also in line with the QPSK signal waveform and is relatively smooth.
Note that, when we demodulate QPSK1 and QPSK2 signals, it is observed that the final demodulation result does not correspond one-to-one with the fixed transmitted sequence, but has the mapping rule as shown in Table 2. Thus, the original bit sequence can be computed from $I1$, $Q1$ of QPSK1, and $I2$, $Q2$ of QPSK2 according to the mapping rule, which ensures the integrity of the information after format conversion.
Table 2. Mapping rule of 16QAM all-optical modulation format conversion
Next, we send ${{2^9}}$ random 16QAM symbols to verify the accuracy of the proposed scheme. Figure 9 shows the constellation diagrams and waveforms of the converted QPSK signals. It can be seen from Fig. 9(a) and Fig. 9(c) that the constellation obtained after format conversion owns four discrete phases, which corresponds to the QPSK constellation distribution. It is also seen from Fig. 9(b) and Fig. 9(d) that the waveform of the I and Q branches are relatively smooth and complete. Finally, after demodulating the two QPSK signals via the coherent receivers, the original bit sequence without information loss can be computed by using the mapping rule as shown in Table 2.
3.2 Results analysis for 8QAM all-optical format conversion
Similar to 16QAM, we first analyze the constellation and waveform of QPSK and BPSK signals obtained by the 8QAM all-optical modulation format conversion by sending a sequence of eight fixed 8QAM symbols covering all constellation points. Figure 10(a) shows the constellation diagram of the QPSK signal, and its constellation points have also changed from the original four discrete levels to four discrete phases, which is consistent with the constellation distribution of QPSK. The waveform is relatively smooth, and corresponds to the QPSK signal waveform, as depicted in Fig. 10(b). Figure 10(c) illustrates the constellation diagram of the BPSK signal. The constellation distribution is the same as the BPSK constellation, but the phase is slightly shifted. Figure 10(d) exhibits the BPSK signal waveform. Compared with I-branch, the waveform of the Q branch is compressed close to zero and can be ignored. Therefore, a BPSK signal can be successfully acquired.
After the abovementioned 8QAM all-optical format conversion, it is calculated that the final coherent demodulation results of QPSK and BPSK signals have a mapping relationship with the original transmitted sequence as shown in Table 3. Therefore, the original bit sequence can be completely computed from $I1$, $Q1$ of QPSK, and $I2$ of BPSK according to the mapping rule, which also ensures no information loss after format conversion.
Table 3. Mapping rule of 8QAM all-optical modulation format conversion
Next, ${2^9}$ random 8QAM symbol sequences are transmitted to test the accuracy of the 8QAM format conversion. The constellation and waveform diagrams of QPSK and BPSK signals obtained after the all-optical format conversion of the 8QAM signal are depicted in Fig. 11. It is viewed from Fig. 11(a) that the constellation points obtained after format conversion are four discrete phases, which conform to the QPSK constellation distribution. As shown in Fig. 11(b), the waveform is consistent with QPSK signal. Figure 11(c) describes the constellation points of two discrete phases after format conversion, which conforms to the BPSK constellation distribution. The waveform exhibited in Fig. 11(d) is in line with the BPSK signal only considering the I part because the Q part can be ignored compared with its I counterpart. Finally, the coherent receivers are employed to demodulate the converted QPSK and BPSK signals. We can successfully calculate the transmitted sequence without information loss by using the mapping rule of Table 3.
4. Conclusion
The feasibility of utilizing the nonlinear effects of PIA, PSA, and SPM over HNLF to achieve the reconfigurable all-optical format conversion for 16QAM/8QAM signal has been theoretically and numerically investigated. A comprehensive theoretical model describing the physical mechanisms underpinning the all-optical format conversion based on the abovementioned nonlinear effects has been developed and subsequently verified by numerical simulations. It has been shown that the proposed scheme can realize all-optical format conversion for 16QAM and 8QAM signals at rates of 92Gbps and 69Gbps, respectively. Furthermore, the proposed scheme is suitable for all-optical conversion of both 16QAM and 8QAM signals, which avoids the use of different all-optical conversion systems for 16QAM and 8QAM, thus realizing a reconfigurable format conversion. In addition, the proposed scheme can also achieve higher baud rates under certain conditions since it depends on the transient response of nonlinear effect over HNLF, which can satisfy the phase matching conditions to realize PIA and PSA. In the future work, we will investigate the transmission performance after a certain fiber link in the destination node.
Funding
National Natural Science Foundation of China (62025105, 62075024, 62201105, 62205043, 62221005, 62222103); Natural Science Foundation of Chongqing (CSTB2022NSCQ-MSX1334, cstc2021jcyj-msxmX0404); Chongqing Municipal Education Commission (CXQT21019, KJQN202100643).
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.
References
1. X. Zhou, R. Urata, and H. Liu, “Beyond 1Tb/s Intra-Data Center Interconnect Technology: IM-DD OR Coherent?” J. Lightwave Technol. 38(2), 475–484 (2020). [CrossRef]
2. G. Khanna, S. Zhu, M. Filer, C. Gkantsidis, F. Parmigiani, and T. Karagiannis, “Towards All Optical DCI Networks,” in Optical Fiber Communications Conference and Exhibition (2020) pp. 1–3.
3. M. Xu, C. Liu, and S. Subramaniam, “PODCA: A Passive Optical Data Center Network Architecture,” J. Opt. Commun. Netw. 10(4), 409–420 (2018). [CrossRef]
4. T. Kupfer, A. Bisplinghof, T. Duthel, C. Fludger, and S. Langenbach, “Optimizing Power Consumption of A Coherent DSP for Metro and Data Center Interconnects,” in Optical Fiber Communications Conference and Exhibition (2017) pp. 1–3.
5. Q. Li, X. Yang, H. Wen, Q. Xu, J. Yang, and H. Yang, “All-Optical Format Conversion for Star-8QAM Signals Based on Nonlinear Effects in Elastic Optical Networks,” J. Lightwave Technol. 41(2), 440–450 (2023). [CrossRef]
6. A. Fallahpour, A. Mohajerin-Ariaei, A. Almaiman, Y. Cao, F. Alishahi, C. Bao, P. Liao, M. Ziyadi, B. Shamee, D. Starodubov, M. Tur, C. Langrock, M. M. Fejer, J. Touch, and A. E. Willner, “Demonstration of 30Gbit/s QPSK-to-PAM4 Data-Format and Wavelength Conversion to Enable All-Optical Gateway from Long-haul to Datacenter,” in Optical Fiber Communication Conference (Optica Publishing Group) paper W2A.22.
7. X. Li, Y. Liu, Y. Zhao, Z. Li, Y. Li, and J. Zhang, “All Optical Service Network for F5G,” in 21st International Conference on Communication Technology (IEEE, 2021) pp. 710–714.
8. X. Li, Y. Zhao, Z. Li, Y. Li, H. Li, G. Xie, Y. Lin, and J. Zhang, “Experiment of Extended Segment Routing Enabled Fast End-to-End Service Provisioning in Multi-Domain for the Fifth Generation Fixed Network (F5G),” in Asia Communications and Photonics Conference (2021) pp. 1–3.
9. X. Li, Y. Zhao, Z. Li, Y. Li, G. Xie, Y. Lin, and J. Zhang, “Experiment of Segment Routing based Service-Oriented Fast Path Construction for F5G,” in Opto-Electronics and Communications Conference (2021) pp. 1–3.
10. H. Wang, Q. Wang, and Y. Ji, “All Optical Format Conversion of 8-PSK to 4-PAM Signals Based on Phase Sensitive Amplification,” in Asia Communications and Photonics Conference (2017) pp. 1–3.
11. H. Liu, H. Wang, J. Cui, and Y. Ji, “Design of All-Optical Modulation Format Converter From One 8PSK to Two QPSK Signals Based on Phase Sensitive Amplification in Elastic Optical Network,” IEEE Access 7, 51379–51385 (2019). [CrossRef]
12. J. Cui, Y. Ji, G.-W. Lu, H. Wang, and M. Zhang, “2D-to-1D Constellation Reforming Using Phase-sensitive Amplifier-based Constellation Squeezing and Shifting,” Opt. Express 29(3), 3724–3737 (2021). [CrossRef]
13. Q. Li, X. Yang, and J. Yang, “All-Optical Aggregation and De-Aggregation Between 8QAM and BPSK Signal Based on Nonlinear Effects in HNLF,” J. Lightwave Technol. 39(17), 5432–5438 (2021). [CrossRef]
14. H. Kishikawa and N. Goto, “Wavelength Preserved Modulation Format Conversion from 16QAM to QPSK Using FWM and SPM,” in Conference on Lasers and Electro-Optics Pacific Rim (2017) pp. 1–2.
15. B. Sukh, H. Kishikawa, and N. Goto, “Performance Verification of Optical Modulation Format Conversion from 16QAM to Symbol Rate Doubled QPSK,” in Advanced Photonics (Optica Publishing Group, 2018), paper JTu5A.60.
16. Q. Li, H. Zhang, Z. Liu, and S. Fu, “SPM-based Data Format Conversion from one 2ASK/4PSK to two 4PSK Signals with Wavelength Preservation,” in Asia Communications and Photonics Conference (2021) pp. 1–3.
17. J. Cui, Y. Ji, G.-W. Lu, H. Wang, and M. Zhang, “Phase-sensitive Amplifier-based Optical Conversion for Direct Detection of Complex Modulation Format to Bridge Long-haul Transmissions and Short-reach Interconnects,” Opt. Express 28(2), 2349–2365 (2020). [CrossRef]
18. D. Wang, M. Zhang, J. Qin, H. Wang, and S. Huang, “Dual-Channel Format Conversion from DQPSK to DPSK Based on FWM in a Single SOA,” in Asia Communications and Photonics Conference (2014) pp. 1–3.
19. K. Iwama, N. Goto, H. Kishikawa, and J. Fujikata, “All-Optical Modulation Format Conversion From DQPSK to OOK Using Cross-Polarization Modulation,” in Photonics Conference (IEEE, 2021) pp. 1–2.
20. Govind Agrawal, Nonlinear Fiber Optics (Fifth Edition) (Academic Press, 2013).
21. X. Yao, “Design and Realization of the Costas Loop,” in Advances in Materials, Machinery, Electrical Engineering (AMMEE) (Atlantis Press, 2017), pp. 532–535.
