基于双偏振调制的可变对称三角波形的生成

王创业; 宁提纲; 李晶; 裴丽; 郑晶晶; 李雨键; 艾渤

doi:10.7498/aps.70.20210751

摘要

提出并验证了一种基于双偏振调制生成可变对称三角波形的方法. 通过设置合适的调制器的调制指数和移相器的相移, 使得调制器生成信号光的强度近似等于理想三角波形傅里叶级数展开式的前三项, 从而生成不同对称因子的三角波形(三阶近似波形). 之前的三角波形生成方案大多生成对称三角波形或锯齿波形(锯齿波形可认为是非对称三角波形), 且对称因子不可调谐, 而本方案生成的三角波形的对称因子可调谐范围可达0%—100%, 这极大地拓展了三角波形的应用范围. 引入均方根误差(root-mean-square error, RMSE)来衡量生成波形与理论波形的相似度, 计算可发现, 理论上本方案生成的对称因子范围在14%—86%的三角波形与理想波形有良好的相似度(RMSE < 0.044), 仿真中生成波形的RMSE也非常接近理论误差. 在实验中, 通过使用频率为4GHz的射频信号生成了对称因子范围在20%—80%的三角波形.

关键词:

Abstract

Photonic generation of triangular-shaped waveform with variable symmetry based on dual-polarization modulation is proposed and demonstrated. Based on the external modulation method, a dual-polarization modulator is used to modulate the radio frequency signal to generate the needed optical signal. By setting the modulation index of the modulator and phase shift of phase shifters appropriately, the optical intensity of generated signal can equal approximately the first three terms of the Fourier series expansion of the ideal triangular-shaped waveform, so triangular-shaped waveforms with different symmetry factors can be generated. Most of previous triangular waveform generation schemes generate symmetrical triangular waveform or sawtooth waveform (sawtooth waveform can be regarded as an asymmetrical triangular waveform), and the symmetry factor is not tunable. The tunable range of symmetry factor of triangular-shaped waveform generated by this scheme can reach 0%–100%, which will greatly expand the application range of triangular-shaped waveforms. The root-mean-square error (RMSE) is introduced to measure the similarity between the generated waveform and the theoretical waveform. It can be found that theoretically the triangular-shaped waveform with a symmetry factor in a range from 14% to 86% has a good similarity to the ideal waveform (RMSE < 0.044), and the RMSE of the generated waveform in the simulation is also very close to the theoretical RMSE. Experimentally, the 4GHz triangular-shaped waveforms with different values of symmetry factor (20%–80%) are obtained by using 4GHz radio frequency signal.

Keywords:

作者及机构信息

1.
北京交通大学光波所，全光网络与现代通信网教育部重点实验室，北京　100044

2.
北京交通大学，轨道交通控制与安全国家重点实验室，北京　100044

通信作者: 李晶, lijing@bjtu.edu.cn

基金项目: 国家自然科学基金(批准号: 61827817, 62005012)和北京市自然科学基金(批准号: 4192022)资助的课题

Authors and contacts

1.
Key Laboratory of All Optical Network and Advanced Telecommunication Network of EMC, Institute of Lightwave Technology, Beijing Jiaotong University, Beijing 100044, China

2.
State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China

Corresponding author: Li Jing, lijing@bjtu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61827817, 62005012) and the Natural Science foundation of Beijing, China (Grant No. 4192022).

文章全文 : translate this paragraph

参考文献

[1]	Bhamber R S, Latkin A I, Boscolo S, Turitsyn S K 2008 34th European Conference on Optical Communication, September 21–25, 2008 p1
[2]	Cho S W, Rassau A, Gornisiewicz W 2007 6th International Conference on Polymers and Adhesives in Microelectronics and Photonics, January 16–18, 2007 p217
[3]	Xu S Z, Wang P, Dong Y G 2016 Sensors 16 576 Google Scholar
[4]	Won Y S, Kim C H, Lee S G 2015 IEEE Sens. J. 15 7142 Google Scholar
[5]	Verscheure N, Finot C 2011 Electron. Lett. 47 1194 Google Scholar
[6]	Ye J, Yan L S, Pan W, Luo B, Zou X H, Yi A L, Yao S 2011 Opt. Lett. 36 1458 Google Scholar
[7]	Jiang H Y, Yan L S, Sun Y F, Ye J, Pan W, Luo B, Zou X H 2013 Opt. Express 21 6488 Google Scholar
[8]	Li W, Wang W Y, Sun W H, Wang W T, Liu J G, Zhu N H 2014 Opt. Lett. 39 4758 Google Scholar
[9]	Dai B, Gao Z S, Wang X, Chen H W, Kataoka N, Wada N 2013 J. LightwaveTechnol. 31 145 Google Scholar
[10]	Li J, Ning T G, Pei L, Zheng J J, Li Y Q, Yuan J, Wang Y Q, Zhang C, Chen H Y 2014 Chin. Opt. Lett. 12 120602 Google Scholar
[11]	Gao Y S, Wen A J, Liu W Y, Zhang H X, Xiang S Y 2016 IEEE Photonics J. 8 7801609 Google Scholar
[12]	Li W, Wang W T, Zhu N H 2014 IEEE Photonics J. 6 5500608 Google Scholar
[13]	Liu X K, Pan W, Zou X H, Zheng D, Yan L S, Luo B, Lu B 2014 J. Lightwave Technol. 32 3797 Google Scholar
[14]	Huang L, Chen D L, Wang P, Zhang T T, Xiang P, Zhang Y Y, Pu T, Chen X F 2015 IEEE Photonics Technol. Lett. 27 2500 Google Scholar
[15]	Wang W Y, Li W, Sun W H, Wang W T, Liu J G, Zhu N H 2015 IEEE Photonics Technol. Lett. 27 522 Google Scholar
[16]	Li Y Y, Wen A J, Zhang W, Wang Q, Li X R 2019 Opt. Commun. 445 231 Google Scholar
[17]	He Y T, Jiang Y, Zi Y J, Bai G F, Tian J, Xia Y, Zhang X Y, Dong R Y, Luo H 2018 Opt. Express 26 7829 Google Scholar
[18]	Wei C, Jiang Y, Luo H, Dong R Y, Tian J, Zi Y J, Liu H F, Wang R 2020 Opt. Express 28 8098 Google Scholar
[19]	Xia Y, Jiang Y, Zi Y J, He Y T, Tian J, Zhang X Y, Luo H, Dong R Y 2018 Opt. Commun. 414 177 Google Scholar
[20]	Bai G F, Hu L, Jiang Y, Tian J, Zi Y J, Wu T W, Huang F Q 2017 Opt. Commun. 396 134 Google Scholar
[21]	Li J, Ning T G, Pei L, Zheng J J 2019 J. Mod. Opt. 66 1457 Google Scholar

施引文献

图 1 不同对称因子对应的b₁, b₂, b₃值

Fig. 1. Magnitude of b₁, b₂ and b₃ versus symmetry factor δ.

下载: 全尺寸图片幻灯片

图 2 可变对称三角波形生成方案的原理示意图. CW laser, 连续波激光器; PC, 偏振控制器; RF source, 射频源; EPS, 电功分器; EA, 电放大器; PS, 电移相器; OPS, 光功分器; MZM, 单驱动马赫曾德尔调制器; PBC, 偏振合束器; 90°PR, 90°偏振旋转器; PD, 光电探测器

Fig. 2. Schematic diagram of the proposed scheme. CW laser, continuous wave laser; PC, polarization controller; RF source, radio frequency source; EPS, electrical power splitter; EA, electrical amplifier; PS, phase shifter; OPS, optical power splitter; MZM, single-drive Mach-Zehnder Modulator; PBC, polarization beam combiner; 90° PR, 90° polarization rotator; PD, photodiode.

下载: 全尺寸图片幻灯片

图 3 仿真生成的对称因子为0%—100%的时域波形

Fig. 3. Simulated generated temporal triangular-shaped waveforms with δ = 0%−100%.

下载: 全尺寸图片幻灯片

图 4 仿真生成的对称因子为20%的三角波形　(a) 时域波形; (b) 对应的电谱

Fig. 4. Simulated generated triangular-shaped waveform with δ = 20%: (a) Temporal waveform; (b) corresponding electrical spectrum.

下载: 全尺寸图片幻灯片

图 5 对称因子为20%的三角波形的合成示意图

Fig. 5. Synthesis schematic diagram of triangular-shaped waveform with δ = 20%.

下载: 全尺寸图片幻灯片

图 6 (a) 三阶近似波形、五阶近似波形和十阶近似波形的理论RMSE; (b) 仿真生成波形的RMSE

Fig. 6. (a) Theoretical RMSE for third-order approximate waveform, fifth-order approximate waveform and tenth-order approximate waveform; (b) the RMSE of simulated generated waveforms.

下载: 全尺寸图片幻灯片

图 7 可变对称三角波形生成方案的实验平台. Dual-wavelength laser, 双波长激光器; Polarization controller, 偏振控制器; Signal generator, 信号发生器; Power splitter, 电功分器; Electrical delay line, 电延迟线; Electrical amplifier, 电放大器; 180° hybrid coupler, 180°电桥; DP-BPSK modulator, 双偏振BPSK调制器; Photodiode, 光电探测器; Oscilloscope, 示波器

Fig. 7. Experimental platform for triangular-shaped waveform with variable symmetry generation scheme.

下载: 全尺寸图片幻灯片

图 8 实验生成的对称因子为20%, 30%, 40%, 50%, 60%, 70%和80%的三角波形

Fig. 8. Generated triangular-shaped waveforms with δ = 20%, 30%, 40%, 50%, 60%, 70% and 80% in the experiment.

下载: 全尺寸图片幻灯片

图 9 实验生成的对称因子为20%的三角波形　(a) 时域波形; (b) 对应的电谱

Fig. 9. Generated triangular-shaped waveform with δ = 20%: (a) Temporal waveform; (b) corresponding electrical spectrum.

下载: 全尺寸图片幻灯片

表 1 不同对称因子三角波形的生成条件

Table 1. Generated conditions for triangular-shaped waveforms with different symmetry factor.

对称因子	相移1	相移2	相移3	调制系数1	调制系数2
δ	θ₁	θ₂	θ₃	m₁	m₂
0%	0	π/4	0	1.15	0.83
10%	0	π/4	0	1.1	0.81
20%	0	π/4	0	0.92	0.76
30%	0	π/4	0	0.49	0.53
40%	π/2	π/2	3π/2	0.61	0.41
50%	π/2	0	3π/2	0.76	0
60%	π/2	0	3π/2	0.61	0.41
70%	0	3π/4	0	0.49	0.53
80%	0	3π/4	0	0.92	0.76
90%	0	3π/4	0	1.1	0.81
100%	0	3π/4	0	1.15	0.83

下载: 导出CSV

[1]	Bhamber R S, Latkin A I, Boscolo S, Turitsyn S K 2008 34th European Conference on Optical Communication, September 21–25, 2008 p1
[2]	Cho S W, Rassau A, Gornisiewicz W 2007 6th International Conference on Polymers and Adhesives in Microelectronics and Photonics, January 16–18, 2007 p217
[3]	Xu S Z, Wang P, Dong Y G 2016 Sensors 16 576 Google Scholar
[4]	Won Y S, Kim C H, Lee S G 2015 IEEE Sens. J. 15 7142 Google Scholar
[5]	Verscheure N, Finot C 2011 Electron. Lett. 47 1194 Google Scholar
[6]	Ye J, Yan L S, Pan W, Luo B, Zou X H, Yi A L, Yao S 2011 Opt. Lett. 36 1458 Google Scholar
[7]	Jiang H Y, Yan L S, Sun Y F, Ye J, Pan W, Luo B, Zou X H 2013 Opt. Express 21 6488 Google Scholar
[8]	Li W, Wang W Y, Sun W H, Wang W T, Liu J G, Zhu N H 2014 Opt. Lett. 39 4758 Google Scholar
[9]	Dai B, Gao Z S, Wang X, Chen H W, Kataoka N, Wada N 2013 J. LightwaveTechnol. 31 145 Google Scholar
[10]	Li J, Ning T G, Pei L, Zheng J J, Li Y Q, Yuan J, Wang Y Q, Zhang C, Chen H Y 2014 Chin. Opt. Lett. 12 120602 Google Scholar
[11]	Gao Y S, Wen A J, Liu W Y, Zhang H X, Xiang S Y 2016 IEEE Photonics J. 8 7801609 Google Scholar
[12]	Li W, Wang W T, Zhu N H 2014 IEEE Photonics J. 6 5500608 Google Scholar
[13]	Liu X K, Pan W, Zou X H, Zheng D, Yan L S, Luo B, Lu B 2014 J. Lightwave Technol. 32 3797 Google Scholar
[14]	Huang L, Chen D L, Wang P, Zhang T T, Xiang P, Zhang Y Y, Pu T, Chen X F 2015 IEEE Photonics Technol. Lett. 27 2500 Google Scholar
[15]	Wang W Y, Li W, Sun W H, Wang W T, Liu J G, Zhu N H 2015 IEEE Photonics Technol. Lett. 27 522 Google Scholar
[16]	Li Y Y, Wen A J, Zhang W, Wang Q, Li X R 2019 Opt. Commun. 445 231 Google Scholar
[17]	He Y T, Jiang Y, Zi Y J, Bai G F, Tian J, Xia Y, Zhang X Y, Dong R Y, Luo H 2018 Opt. Express 26 7829 Google Scholar
[18]	Wei C, Jiang Y, Luo H, Dong R Y, Tian J, Zi Y J, Liu H F, Wang R 2020 Opt. Express 28 8098 Google Scholar
[19]	Xia Y, Jiang Y, Zi Y J, He Y T, Tian J, Zhang X Y, Luo H, Dong R Y 2018 Opt. Commun. 414 177 Google Scholar
[20]	Bai G F, Hu L, Jiang Y, Tian J, Zi Y J, Wu T W, Huang F Q 2017 Opt. Commun. 396 134 Google Scholar
[21]	Li J, Ning T G, Pei L, Zheng J J 2019 J. Mod. Opt. 66 1457 Google Scholar

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