Machine Learning Assisted Inverse Design for Ultrafine, Dynamic and Arbitrary Gain Spectrum Shaping of Raman Amplification
Machine Learning Assisted Inverse Design for Ultrafine, Dynamic and Arbitrary Gain Spectrum...
Huang, Yuting;Du, Jiangbing;Chen, Yufeng;Xu, Ke;He, Zuyuan
2021-07-06 00:00:00
hv photonics Article Machine Learning Assisted Inverse Design for Ultrafine, Dynamic and Arbitrary Gain Spectrum Shaping of Raman Amplification 1,† 1, 1,† 2 1 Yuting Huang , Jiangbing Du *, Yufeng Chen , Ke Xu and Zuyuan He State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai 200240, China; eu0828@alumni.sjtu.edu.cn (Y.H.); yufengchen@sjtu.edu.cn (Y.C.); zuyuanhe@sjtu.edu.cn (Z.H.) Department of Electronic and Information Engineering, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China; kxu@hit.edu.cn * Correspondence: dujiangbing@sjtu.edu.cn † These authors contributed equally to this work. Abstract: Distributed Raman amplifier (DRA) has been widely studied in recent decades because of its low noise figure and flexible gain. In this paper, we present a novel scheme of DRA with broadband amplified spontaneous emission(ASE) source as pump instead of discrete pump lasers. The broad- band pump is optimized by machine learning based inverse design and shaped by programmable waveshaper, so as to realize the ultrafine, dynamic and arbitrary gain spectrum shaping of Raman amplification. For the target of flat gain spectrum, the maximum gain flatness of 0.1086 dB is realized based on the simulation results. For the target of arbitrary gain spectrum, we demonstrate four gain profiles with maximum root mean square error (RMSE) of 0.074 dB. To further measure the perfor- mance of arbitrary gain spectrum optimization, the probability density functions (PDF) of RMSE and Error are presented. Meanwhile, the numeral relationship between the bands of broadband pump max and signal is also explored. Furthermore, this work has great application potential to compensate the gain distortion or dynamic change caused by other devices in communication systems. Citation: Huang, Y.; Du, J.; Chen, Y.; Xu, K.; He, Z. Machine Learning Keywords: optical fiber communication; Raman amplifier; machine learning; inverse design Assisted Inverse Design for Ultrafine, Dynamic and Arbitrary Gain Spectrum Shaping of Raman Amplification. Photonics 2021, 8, 260. https://doi.org/10.3390/ 1. Introduction photonics8070260 Distributed Raman amplifier (DRA) is an important amplification scheme for optical communication systems due to its low noise figure (NF) and wideband flexible gain [1,2]. Received: 15 June 2021 In order to enhance the performance of DRAs, many methods have been applied in DRAs Accepted: 2 July 2021 for achieving lower noise by improving Raman pumping scheme. The most common Published: 6 July 2021 used is backward pumping, which shows reduced penalty on relative intensity noise (RIN) compared to forward pumping [3]. High order pumping can also enhance RIN performance [4,5]. Publisher’s Note: MDPI stays neutral RIN is transferred from pump lasers to DRAs and for high order pumping scheme, RIN with regard to jurisdictional claims in can be effectively reduced because of multiple transfers from high order pump to sig- published maps and institutional affil- nals [6]. Another practical scheme is random fiber laser structure, which utilizes high order iations. pumps to generate first order random fiber laser with the fiber Rayleigh backscattering and fiber Bragg grating as reflectors [7,8]. However, random fiber laser structure is es- sentially bi-directional pumping, consequently offering relatively high RIN [9]. But the experiment demonstrated that this scheme can provide better balance between amplified Copyright: © 2021 by the authors. spontaneous emission (ASE) noise and nonlinear effects, which results in better transmis- Licensee MDPI, Basel, Switzerland. sion performance [10–12]. In addition to them, it is shown in recent studies that DRAs This article is an open access article using broadband optical pump exhibit superior RIN performance over conventional DRAs distributed under the terms and including backward pumping and random fiber laser [13]. The broadband optical pump conditions of the Creative Commons is generated by ASE of second order pump in the fiber with high Raman gain coefficient, Attribution (CC BY) license (https:// and then the broadband optical pump is launched into transmission fiber to amplify the creativecommons.org/licenses/by/ signal. It is demonstrated that although the broadband pump has the similar RIN to 4.0/). Photonics 2021, 8, 260. https://doi.org/10.3390/photonics8070260 https://www.mdpi.com/journal/photonics Photonics 2021, 8, 260 2 of 10 the semiconductor laser, the RIN of amplified signal with broadband pump is mitigated compared to low RIN laser pumping and pumping schemes mentioned above [14]. On the other hand, flat gain of amplifiers is usually demanded to achieve great transmission performance. For broader applications, arbitrary gain spectrum would be of great significance since different transmission spectrum will be needed varied with different systems and different circumstances. For example, Erbium-doped fiber amplifiers (EDFAs) are always utilized together with other amplifiers to build up a hybrid amplifier with large gain and low noise [15,16]. Then, the gain spectrum of that amplifier needs to be shaped to compensate the gain fluctuation of EDFA so as to achieve flat gain for the hybrid amplifier [17]. Arbitrary gain spectrum shaping with high precision and even dynamic operation is thus highly desired. Stimulated Raman scattering is only related to the power and frequency difference between two lights, so DRAs are able to realize flexible gain spectrum including bandwidth and profile by combining multiple pump lasers working in different wavelengths and powers [18]. Previous studies have focused on flat gain and tilted gain with 2 to 8 pumps or more [19]. Only 4 or more pumps can provide acceptable results which well fit the target of design, and the precision is highly limited by the number of pumps. Moreover, many specially customized pump lasers will also make it difficult in experiments and transmission systems. With the broadband pump arbitrarily shaped by waveshaper with frequency resolution up to 1GHz, it can be regarded as multiple pumps (depending on bandwidth and resolution) to achieve an ultrafine and arbitrary gain spectrum. Optimizing shapes of pump spectrum that can realize desired gain spectrum is an- other challenging problem, which revolves multiple parameters. The most conventional optimization algorithm is genetic algorithm (GA). However, GA needs many iterations for complex crossover, mutation and selection to converge to the optimal solution in parameter space, and it consumes long time. If the target is changed, all optimization processes must be repeated from the beginning again. Moreover, with the number of parameters increasing, the complexity of GA increases rapidly and the optimal solution might be difficult to converge [20]. Recent research shows neural networks (NN) based inverse design is a considerable scheme for DRAs [21–23]. The NN can be trained as a regression of parameters K and results G, whose input is results G and parameters K. In another way, well-trained NN can be regarded as an inverse mapping y = f (G). The advantage of this inverse structure is that the parameters corresponding to target can be directly calculated by inputting target into trained NN. If data set used for training is collected properly and extensively, the trained NN can be universal, which means when the target changed, desired parameters can also be directly calculated without retraining. Compared to GA, another advantage of NN is the tolerance to the number of parameters. NN has the capacity of handling the optimization of more parameters and solving a mapping with more complexity by deepening networks. Recent publication proposed a scheme of inverse NN, in which they utilized regression NN to predict flat and titled gain profile of DRAs. However, the performance of this NN might not meet an acceptable expection, therefore a fine-tuning phase is applied to further optimization [23]. This fine-tuning phase requires a trained NN as the direct mapping G = f (K), and the output of the inverse NN will be further optimized with this direct NN by gradient-descent algorithm. The optimization results show promising improvement on backward pumping DRAs over C and C+L band, achieving maximum error below 0.5 dB for C band and 1 dB for C+L band. However, this scheme requires training for two NNs and iterations of gradient-descent algorithm, which would be quite time-consuming. In this paper, a new approach by machine learning for inverse design of DRA with broadband pump is proposed for achieving ultrafine, dynamic and arbitrary gain spec- trum. The ASE source can be considered as multiple discrete pumps with power levels dynamically tunable which is typically achieved by passing the ASE source through a waveshaper filter. We promote the performance of NN by employing classification NN in- stead of regression NN. Finally, we realize maximum gain flatness of 0.1086 dB for flat gain Photonics 2021, 8, 260 3 of 10 spectrum. The probability density functions (PDF) of root mean square error (RMSE) and Error are presented for arbitrary gain spectrum, realizing mean of 0.0910 dB, 0.1956 dB max and standard deviation of 0.0269 dB, 0.0817 dB for RMSE and Error , respectively. We max also find the best match between the bands of pump and signal. Owing to programmability of waveshaper, dynamic Raman gain spectrum can be realized and has the potential to compensate the gain distortion caused by other devices in real time. 2. Broadband Pump Based DRA and Inverse Design Figure 1 shows the procedure of inverse design for ultrafine and arbitrary waveshap- ing of gain spectrum. Data set is obtained by numerical simulation of the configuration, and then employed to train our inverse NN, whose input is gain spectrum G and output is pump spectrum P. Once the NN has been well trained, it can be recognized as the mapping between gain spectrum and pump spectrum. Different target profiles of gain spectra are input to the trained NN for attaining corresponding pump spectrum. Nevertheless, trained NN only guarantees the reliability within training set. In order to validate the universal reliability of this inverse design, the targets of gain spectra out of training set are input into NN and the attained pump spectra need go through the numerical simulation of configuration to calculate actual gain spectrum, which will be compared with target gain spectrum to measure the accuracy of NN. Figure 1. The procedure of inverse design. 2.1. Data Set Generation The configuration of DRA with broadband pump is presented in Figure 2. The ASE source generates the broadband pump, which can be realized by ASE of EDFAs, so the band is set to 1530–1580 nm. Considering the power of the ASE is generally not high enough and the waveshaper does not support very high power, the ASE is firstly input into waveshaper and then the shaped ASE is launched into EDFA to acquire sufficient power. The waveshaper supports C band and its frequency setting resolution is 1 GHz. We can write the files to control attenuation spectrum of waveshaper through software, realizing arbitrary shaped ASE. Moreover, considering EDFA does not flatly amplify the shaped ASE, the attenuation spectrum of waveshaper should be adjusted to compensate the error caused by EDFA. The pump obtained from inverse design corresponds to the pump fed into transmission fiber. In order to reduce the RIN of this DRA, the shaped broadband pump is utilized as backward pump. The band of signals is 1655–1685 nm according the band of pump. The selection of signals band will be illustrated in Part III. The transmission fiber is 70 km EX2000 single-mode fiber fabricated by Corning, whose loss of pump is 0.15 dB/km and loss of signal is 0.277 dB/km. The parameters used are shown in Table 1. Table 1. Parameters in transmission setup. Settings Loss (dB/km) Loss (dB/km) Length (km) pump signal Sizes 0.15 0.277 70 Photonics 2021, 8, 260 4 of 10 Figure 2. The configuration of DRA with broadband pump. For a backward pumping single-mode DRA with N signals and N pumps, signal s p power evolution is described by following non-linear ordinary differential equations [24]: dP m m,n = a P P (P + P ) m m å n n dz GA m>n e f f (1) m,n P (P + P ) m å n n m GA e f f m<n where “+” “