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Abstract
We present a rapid and precise method to design the multiple step-index bridge fiber for ultra-low insertion loss few-mode multi-core fiber Fan-in/Fan-out device. The genetic algorithm is applied to optimize the structural parameters to support multi-mode operation. Based on the proposed intelligent iteration platform, core-based multiplex/demultiplex optimization can be achieved with less than 1.0 dB insertion loss for the first 6 LP modes in space division multiplexing system consisting of few-mode multi-core fibers. Besides, we have successfully drew the designed bridge fiber and fabricated the corresponding Fan-in/Fan-out device. When connecting it with the single-core 6-mode fiber and 7-core 6-mode fiber, the average insertion losses of mode LP01, LP11a, LP11b, LP21a, LP21b, and LP02 are 0.88 dB, 1.11 dB, 1.07 dB, 1.42 dB, 1.33 dB, and 1.04 dB, respectively.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the rapid development of the network traffic, optical fiber communication system mainly based on the existing single-mode fibers (SMFs) is reaching its critical capacity because of the nonlinear Shannon limit [1]. Space division multiplexing (SDM) is regarded as one of the most promising candidates to further increase the transmission capacity by exploiting the multiplicity of spatial channels as an additional degree of freedom. Recently, multifarious specialty optical fiber based on SDM technology, like multi-core fibers (MCFs), few-mode fibers (FMFs), couple-mode fibers, have been demonstrated and investigated in many applications [2,3]. Particularly, few-mode multicore fibers (FM-MCFs), combining both SDM approaches, have the enormous potential to achieve the higher spatial density and energy efficiency in optical communication networks [4].
For SDM systems consisting of MCF or FM-MCF, the Fan-in/Fan-out (Fi/Fo) device is nevertheless indispensable to realize optical interconnection between SMF/FMF and MCF/FM-MCF. Different kinds of Fi/Fo devices have been claimed, including free space coupling type [5], fiber bundle type [6] based on chemical etching, planar or 3D waveguide type [7] and fused taper type [8–10]. Among them, fused taper type Fi/Fo device has emerged as an interesting solution to access all independent channels formed by core in MCF/FM-MCF and can be utilized for core-multiplexing/de-multiplexing with ultra-low insertion loss (IL). A fused taper type Fi/Fo device comprises a set of individual peculiarly designed fiber named “bridge fibers” (BF) inserted into a glass tube and tapered adiabatically to form a bunch of fiber bundle, then splices with the MCF/FM-MCF. Obviously, as a key component to link SMF/FMF and MCF/FM-MCF, the BF structure has closely correlation with optical properties of fabricated Fi/Fo devices. In order to reduce the IL of all operating modes in Fi/Fo device as low as possible, the BF needs to be optimized thoroughly.
To date, most of optimization in structure of optical fiber generally adopts conventional forward procedure on the basics of parameter-sweeping method, which has been pointed out the defects of sluggish running speed and complicated researching process [11,12]. In terms of BF design, simple high-Δ single-core fiber (HSF) structure gradually turns into the main means for avoiding mode field mismatching between BF and SMF/MCF due to its minor parameter space need to be optimized. With this approach, fused tapered type MCF Fi/Fo devices have been reported with the maximum IL in fundamental mode LP01 of 4.7 dB for 12-core MCF [13], and 1.27 dB for 7-core MCF [8]. Nonetheless, Fi/Fo devices constituted by HSF are insufficient to balance coupling loss of different guided modes and cannot to be tailored compatible with existing FM-MCF so as to accomplish ultra-large capacity optical transmission system. Besides, the high refractive index profile always leads to the increment in fabrication cost and complexity. On the contrary, for the BF with multiple step-index structure (MSI-BF), the inner core can be utilized to realize low splicing loss with SMF/FMF, and the new core consisting of outer cladding after elongation can be also used to achieve mode field match with MCF/FM-MCF. Therefore, it has a more remarkable performance in reducing the IL in Fi/Fo device. In recent experimental demonstrations, the maximum IL in fundamental mode LP01 of Fi/Fo device formed by MSI-BF has significantly dropped and can be neglected in some application scenarios, with a reported 0.4 dB for 7-core MCF [6]. However, the majority of MSI-BF design become rather intricate due to the fact that optical properties do not vary in a simple way with the shift of single optical parameter. For this reason, most of reported Fi/Fo devices based on MSI-BF only optimize the IL on the fundamental mode. To manipulate the IL of guided modes besides the fundamental mode mentioned above, it is quite necessary to control multiple structural parameters simultaneously in MSI-BF, which is tough to meet by means of manual regulation. Recently, researchers have exploited neural network (NN) assisted inverse methods in designs of optical fibers [14–17]. This way cannot guarantee the computed results with the high accuracy because NN merely fits the relationship between optical structure and electromagnetic response nonlinearly within tolerable error. Furthermore, for some design works without carrying on repeatedly, the NN model seems a little redundant. Compared to NN, Genetic algorithm (GA) is a more suitable approach for the optimization of MSI-BF [18,19]. It can seek out the fiber parameters matching the optimized goals rapidly from high-dimensional data space with the aid of stochastic global search. In addition, it also can converge to more precise design results by a series of iterations imitating biological evolution.
In this paper, we propose a stochastic global search design method based on GA to optimize the structural parameters of MSI-BF, so that it is possible to control the IL of first 6 LP modes to be less than 1.0 dB in SDM system consisting of 7-core 6-mode fibers. And the Fi/Fo device has been fabricated with ultra-low IL by the designed MSI-BF, which can be compatible with existing 7-core 6-mode fibers and single-core 6-mode fibers, to provide 42 channels for transmission. Moreover, this method provides a path of high-accuracy, high-robustness and low-complexity for multi-parameter design of optical fiber, which has enormous potential in accomplishing customized schemes relating to optical fibers.
2. Process of GA design of MSI-BF
2.1 Fabrication process and design principles
Here, we fabricate the MCF Fi/Fo device by using fused taper equipment and special technique. Figure 1 shows the schematic diagram for fabricating Fi/Fo device. Several BFs are stacked into the glass tube simultaneously and tapered adiabatically in a certain proportion via a high-accuracy taper platform (Vytran GPX3400). Then the tapered BF bundles and the pigtail MCF/FM-MCF are spliced by a specialty fiber fusion splicer (FSM-100P+), and the other end without elongation is linked with SMF/FMF as input port. The IL of fabricated Fi/Fo device is highly dependent on the mode field mismatch of all splicing points, which can be analyzed by using the coupled mode theory. We use subscript i to represent the light coupled into input fiber (SMF/FMF) mapping to LP mode i. And the ${{\textbf E}_{\mu i}}$ and ${{\textbf E}_{\nu i}}$ are the electric field distribution of transmitting fiber and receiving fiber respectively. then the normalized power coupling efficiency of LP mode i between two different fibers during splicing can be calculated by the overlap integration method [20], as shown in Eq. (1),
According to recent reports on the MSI-BF structural arrangements for Fi/Fo device [23], we design the MSI-BF with ring-core structure, and the cross-section profile is shown as Fig. 2. The background material of cladding in this design is silica glass, with the refractive index of 1.4442 at 1550 nm. In order to reduce the searching time via GA process, the number of ring-core layers is set to 3. Besides, considering suppressing the macro-bend loss and maintaining the high-order mode matching with FMF/FM-MCF before and after elongation simultaneously, a depressed cladding is designed between inner cladding and outer cladding. Notably, the cladding of designed MSI-BF is adjusted to 80 µm, as a result of lowering the taper radio moderately for restraining the perturbation of mode field during the process of tapering.
In a practical GA procedure, the retrieval of multi-parameters ought to be limited in a confined high-dimension space, which needs to establish the reasonable value ranges for optimized structural parameters. For the design of MSI-BF, the initial range of fiber parameters should take account of the following conditions: 1) the value of refractive index and radius in predicted MSI-BF can be achieved at actual fiber fabrication process. 2) the structural parameters of MSI-BF in range can support all guided modes corresponding to target Fi/Fo device. The initial ranges are shown in Table 1.
Table 1. The initial parameter ranges of designed bridge fiber
2.2 GA process
In the light of the discussion about structure design in MSI-BF shown above, we seek to use a global, random, parallel procedure to achieve the multi-parameter optimization of MSI-BF. The entire design process is shown in Fig. 3, which can be divided into two parts: data group initialization, iteration and data upgrade. In the process of data group initialization, a “population” that involves numbers of random “individuals” is created, where each “individual” corresponds to all parameters need to be adjusted. In this work, each “individual” should be comprised of all structural parameters group [r1, r2, ……Δn1, Δn2, ……] in predicted MSI-BF, where ri is the core radius of each layer, Δni is the refractive index difference between the ith layer and background material of cladding, i = 1∼6. Then, in order to convert each “individual” into “genotype” appropriate for subsequent GA operation, each “individual” needs to be represented as a string of binary digits bm……b2b1b0. While adopting the binary encoding format, the mapping relation between “individual” and “genotype” can be expressed as:
Next, we need to calculate the “fitness” of each coded “individual”. In a GA process, the “fitness” acts as a criterion of how to distinguish the quality of each “individual” in “population” and its value should be related to the optical performance of designed MSI-BF structure. For selecting proper “fitness” function to describe the superior or interior of this design, we are obliged to consider comprehensively the IL of all modes in Fi/Fo devices, so the “fitness function” is finally defined as:
where ILi is the total coupling loss at splicing points between predicted MSI-BF and FMF/FM-MCF in the ith LP mode. After evaluating the “figure of merit” of each “individual” with the aid of “fitness function”, we will commence the following inverse iteration process.In the inverse iteration process, we will first remove a small number of “individuals” with inferior quality from “population” and rebuild the new “population” without losing critical genetic information via a series of crossover operations. The crossover function can be expressed as [18]:
where $P_{new}^{({\ast} )}$ are generated parameter sets, $P_{old}^{({\ast} )}$ are old coded parameter sets, which is chosen randomly based on the fitness values of “individuals”, and α is a stochastic sequence consisting of 0 or 1 with the same length as $P_{new}^{({\ast} )}$ or $P_{new}^{({\ast} )}$ . The crossover operator in this work adopts one-point crossover, where α is a stochastic sequence with zeros in front and ones in rear. To improve the robustness and randomness of algorithm and avoid the slow convergence and premature convergence while using GA, the mutation process has to be implemented at each new generated “population”, and modifies randomly the parameter sets from a new “population”. The mutation rate is set to 5%. And the algorithm will be stopped when the following two conditions are satisfied at the same time: (1) the maximum fitness value of “population” does not upgrade for a long time (in this work, we set it as 30 loops), and (2) the IL has reached the target value (less than 1.0 dB for the first 6 LP modes) in this task.3. Iteration results via GA
As discussed in Section 2, we have realized the design of MSI-BF for fused tapered type Fi/Fo linking 6-mode fiber and 7-core 6-mode fiber. The fabricated 7-core 6-mode fiber in this work is shown in Fig. 4, based on the refractive index profile of the ultra-high-mode-isolation and ultra-low-loss 6-mode fiber. And the values of refractive profile are shown in Table 2. Moreover, its core-pitch is found to be 42.5 µm with hexagonally-arranged silica cores for the inhibition of inter-core crosstalk.
Fig. 4. 7-core 6-mode fiber used in this work: (a) cross-section, and (b) refractive index profile on a radial line on a core center.
Table 2. Specific values of refractive distribution in 7-core 6-mode fiber
For validating this GA based multi-parameter optimization of MSI-BF, we have searched the “individual” (structural parameters of MSI-BF) corresponding to maximum “fitness” from “population” at each iteration, and calculated the maximum IL from all LP modes supported by Fi/Fo device. The specific optimization process of IL is displayed in Fig. 5. It can be seen that the ILmax drops dramatically and converges gradually to 0.85 dB or thereabouts as the iteration proceeds. After about 50 generations, the optimization of MSI-BF is basically completed. The entire iteration requires approximately 1500 data sets on the assumption that the number of “individuals” in each generation is fixed at 30, which are far from enough for training NN with high-accuracy. Compared with NN, GA is a more efficient approach for MSI-BF design because it need not to spend huge amounts of time and computing resources obtaining a large number of data sets. Most remarkably, the performance of predicted MSI-BF via GA has been far outstripped most of reports about BF for Fi/Fo device, although sometimes it may tend to fall into local optimum.
The refractive index profile of MSI-BF predicted by GA procedure is shown in Fig. 6(a) and the specific structural parameters are displayed in Table 3. Before tapering, the inner core n1 is regarded as the fiber core guiding input light, and other layers are together formed the cladding. During the process of tapering, the inner core n1 slowly but surely vanish, and, as a result, cannot support mode field to propagate steadily. Then, the tapered ring-core structure (n1, n2, n3) constitute the new core together for constraining the light field, while other cladding structure (n4, n5, n6) turn into the new cladding. It is assumed that only the size of radius of each layer will decrease after tapering, while the change of refractive index will be neglected. We have calculated the mode field of predicted MSI-BF before and after tapering by using finite element method, as shown in Fig. 6(c) and (d) respectively. And the mode field of single core in 7-core 6-mode fiber (presented in Fig. 4) is displayed in Fig. 6(b). Apparently, the mode field in both ends of predicted MSI-BF have a marvelous mode matching with 7-core 6-mode fiber. The total IL of each mode for fabricated Fi/Fo device via designed MSI-BF can be computed by the above overlap integration method, as shown in Table 4. The minimum and maximum IL of all modes are 0.849 dB in LP02 and 0.401 dB in LP11b, respectively. And the predicted MSI-BF has outstanding IL property in linking 6 mode fiber and 7-core 6-mode fiber.
Fig. 6. (a) Predicted structural profile of MSI-BF. Mode field intensity distribution of (b)7-core 6-mode fiber, (c) predicted MSI-BF, (d) MSI-BF after tapering.
Table 3. the specific structural parameters of designed MSI-BF
Table 4. Theoretical IL of Fi/Fo device fabricated by predicted BF
In the process of actual fiber drawing, the dopant concentrations in different layers of heated glass preform will change due to dopant diffusion and convective transport induced by the flow [24]. As a result, the refractive index difference Δn and the radius r of each layer in fabricated MSI-BF have slight deviations compared with the theoretical prediction. Considering this effect, we calculated the impact while tiny fluctuations occurred in structural parameters of MSI-BF on ILmax of Fi/Fo device, as shown in Fig. 7. In contrast with other parameters, Δn is a more critical factor for the variation of ILmax. Meanwhile, structural parameters of the first 2 layers play a dominant role in IL, which need to be controlled in actual manufacture. Nevertheless, the slight changes of structural parameters hardly have any effect on ILmax. Moreover, we also calculated the excess loss induced by misalignment between predicted MSI-BF and FMF/FM-MCF, as shown in Fig. 8. We found that the transmission performance of mode LP02 is relatively sensitive to the misalignment in splicing, and The IL of LP02 mode in fabricated Fi/Fo device will be added approximately 0.25 dB if the designed MSI-BF has a radial deviation with 2 µm at these two splicing points simultaneously.
Fig. 7. Distribution of ILmax while different deviations occurred in single parameter of designed MSI-BF.
Fig. 8. Excess loss while misalignment occurred in different splicing points: (a) FMF and MSI-BF, (b) tapered MSI-BF and FM-MCF.
4. Fabrication results
Based on the results of GA iteration mentioned above, we have successfully fabricated the Fi/Fo device for 7-core 6-mode fiber by using the designed MSI-BF. The refractive index profile and cross-sectional image of fabricated MSI-BF are shown in Fig. 9(a) and Fig. 9(b), respectively, which are in good agreement with predicted structure shown in Fig. 6. Figure 9(c) shows the end view of tapered MSI-BF bundle. The arrangement of MSI-BF stacked into glass tube is identical to 7-core 6-mode fiber displayed in Fig. 4. And the average core pitch is 41.8 µm with standard position deviation of 0.8 µm. Then, the tapered MSI-BF bundle should be spliced with 7-core 6-mode fiber via FSM-100P+. In this work, we adopt end-view-based digital image splicing procedure reported in [25] to realize the high-precision alignment in relative position and angle of specialty optical fibers. The image of fusing point is shown in Fig. 9(d). Meanwhile, the MSI-BF without tapering should be spliced with 6-mode fiber by arc fusion splicing, and the image of splicing point is shown in Fig. 9(e). Figure 9(f) shows the photograph of the metal tube packaged Fi/Fo device. The left and right part are wire jumpers of 6-mode fiber and 7-core 6-mode fiber pigtail, respectively.
Fig. 9. (a) Refractive index profile and (b) cross-sectional image of fabricated MSI-BF. (c) Cross-sectional image of tapered MSI-BF bundle. (d) Splicing point between tapered MSI-BF bundle and FM-MCF. (e) Splicing point between FMF and BF without tapering. (f) Photograph of Fi/Fo device fabricated by designed MSI-BF.
The experimental setup shown in Fig. 10 is used to measure the IL of all channels for fabricated Fi/Fo device. The distributed feedback laser (DFB) is connected with a 6-mode Photonic Lantern (PL) through the SMF and polarization controller (PC), then selectively excite LP01, LP11a, b, LP21a, b and LP02 modes as the input of each core. The input mode field images measured are shown in Fig. 11(a). At the output port of fabricated Fi/Fo device, the 7-core 6-mode fiber pigtail is inserted into optical power meter with the assist of bare fiber adapter. We also record the output far field images of center core within 7-core 6-mode fiber by using a CCD camera, which is shown in Fig. 11(b).
Fig. 11. Mode field images recorded by CCD camera: (a) 6-mode PL excitation, (b) center core of 7-core 6-mode fiber.
Table 5 shows the measured IL of all guided modes for Fi/Fo device. The average IL across mode LP01, LP11a, LP11b, LP21a, LP21b, and LP02 are measured to be 0.88 dB, 1.07 dB, 1.11 dB, 1.42 dB, 1.33 dB, and 1.04 dB, respectively. In addition, The IL for the first 6 LP modes in center core is maintained at about 1.0 dB. Comparatively, the IL for the first 6 LP modes in outer cores are higher, which is mainly caused by the core misalignment loss at splicing point between tapered MSI-BF bundle and FM-MCF. We believe the non-uniformity of IL in different cores can be addressed by the optimization of arc fusion conditions and alignment techniques for splicing between tapered MSI-BF bundle and FM-MCF. Overall, the designed MSI-BF can achieve core-division multiplexing over FM-MCFs, with ultra-low IL for all guided modes.
Table 5. Total IL of all channels for fabricated Fi/Fo device measured at 1550nm
5. Conclusion
In summary, we proposed a GA based searching approach to realize the optimization of BF for ultra-low IL Fi/Fo of FM-MCF. In this way, we have successfully designed a BF with multiple step-index profile providing multiplex/demultiplex with average IL less than 1.0 dB in the first 6 LP modes per core on a multi-core geometry. Furthermore, we achieved fused taper type Fi/Fo device for 7-core 6-mode hexagonal fiber with the help of designed MSI-BF, with the measured average IL of all seven cores less than 1.5 dB in each guided mode. The deviations of IL between simulation and measurement are mainly caused by imperfect arc fusion and alignment techniques during the fabrication process. And we believe the GA based optimization platform is rather efficient and accurate for specialty optical fiber design when multiple performance targets are to be fulfilled.
Funding
Hubei Province Key Research and Development Program (2020BAA006, 2021BAA008); National Natural Science Foundation of China (61931010); National Key Research and Development Program of China (2018YFB1801002).
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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