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Abstract
We report the design of an elliptical-core five-mode group selective photonic lantern (EC-F-MGS-PL) supporting ten spatial modes over the C-band, whose output fiber is an elliptical-core few mode fiber (EC-FMF). Initially, we fix the cladding diameters of all input fibers to form an elliptical structure. With the help of beam propagation methods (BPM), we carry out comprehensive geometrical optimization of various input fiber bundle, and identify the optimal setting of input fiber bundle in order to achieve the maximum mode selectivity, low insertion loss (IL), and high mode conversion efficiency (MCE) for all five mode groups. Next, we optimize each fiber core diameter and propose a two-step tapering process, for the ease of performance enhancement for the EC-F-MGS-PL. Finally, the mode field evolution and the wavelength dependent operation of the proposed EC-F-MGS-PL is numerically investigated. A mode selectivity of 9∼17 dB and IL of 0.1∼0.38 dB for all five mode groups can be achieved over the C-band, while MCE keeps between 83.3%–95.8%. By taking into account of the fabrication process, we believe that both the design strategy and optimization procedure of the EC-F-MGS-PL are helpful for the implementation of multi-input-multi-output (MIMO)-less mode division multiplexing (MDM) transmission.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Due to the rapid development of the information society, the standard single-mode fiber (SSMF) based optical communication system is approaching its capacity limits. By utilizing spatial modes as the transmission channel, mode division multiplexing (MDM) based on few-mode fiber (FMF) is regarded as one of the most promising technique to further increase the transmission capacity [1–3]. In particular, how to realize multiple and efficient mode division multiplexing and de-multiplexing (MUX/De-MUX) has been attracted worldwide research interests. All-fiber photonic lantern (PL), providing a low insertion loss (IL), low mode dependent loss (MDL), and wide operation wavelength, is believed as the ideal MUX/De-MUX [4]. Generally, PL is fabricated by placing a series of fibers into a capillary tube and then tapered adiabatically, in case the refractive index (RI) of the capillary tube is lower than that of input fiber cladding. When the input fiber cores nearly vanish, the fused fiber cladding becomes the new FMF core and the low RI capillary becomes the new FMF cladding [4–5]. The adiabatic conditions during the PL fabrication can be satisfied by increasing the propagation constant difference between neighboring modes [6]. Consequently, the difference of either the core diameters or the RI of fiber core among input fibers must be enlarged. Alternatively, the mode evolution must be slow during the PL tapering, leading to the extension of device size. Generally, PL can be divided into three categories according to its mode selectivity. The first type is mode selective photonic lantern (MS-PL) [7–9], where each input fiber excites exactly one spatial mode. The second one is mode-group selective photonic lantern (MGS-PL) [10–14], each input fiber selectively excites a superposition of degenerate modes having the approximate propagation constants within a mode group. The last type is mode none-selective photonic lantern (MNS-PL) [15–17], and each input fiber excites a superposition of all guided modes. Due to the fiber bending and twisting, spatial modes within the same mode group will be strongly coupled during the MDM transmission. Therefore, MGS-PL without de-multiplexing the degenerate modes among single specific mode group is sufficient for practical applications, and research on MGS-PL is attracting more interests nowadays.
To realize MGS-PL, the degeneracy among the mode groups throughout the tapering region must be broken. Such motivation can be only fulfilled, when the guided modes arising in different input fibers have different propagation constants [6]. The most common practice for satisfying such condition is to make the initial input fiber cores dissimilar [4,5]. SMFs are used as input fibers for PLs in the early time, a PL made by SMFs supporting two mode groups (3 spatial modes) is demonstrated with a mode selectivity of about 5.5 dB and an IL of 2 dB at 1550nm [13]. However, under a fixed operation wavelength, the SMF has a limited range of core diameters. When the number of modes to be multiplexed is increased, the difference of propagation constant cannot be enough large, in order to achieve high mode selectivity. Consequently, such problem can be solved by using FMFs as the PL input fibers [14]. When the FMF is used as the input fiber bundle of the MGS-PL, the fundamental mode of individual input FMF transforms to the corresponding high-order mode gradually, while high-order modes couple to the new cladding modes of the PL. MGS-PL made by FMFs supporting three mode groups (6 spatial modes) is demonstrated with an IL of 0.6 dB [14]. However, the worst mode selectivity is only 6 dB, when the operation wavelength is 1550nm. Please note that the effective RI of the fundamental mode for each input FMF must be larger than that of arbitrary high-order mode arising in all input fibers [14]. Otherwise, the mode mixing occurs during the tapering process, and the corresponding mode selective conversion from input fibers to the FMF at the MGS-PL output cannot be realized, leading to the diameter range constraints of input FMF core. In other words, the propagation constant difference between different input fundamental modes is limited. Thus, it is challenging to obtain a high mode selectivity of PL involved more modes. To further increase the number of supported modes as well as mode selectivity for MGS-PL, both SMF and FMF can be used simultaneously. The recent report of the MGS-PL can support four mode groups [18], and it is made by 4 types of FMFs and 2 types of SMFs. However, due to the extreme difficulty of high mode selectivity for the involved modes, the worst mode selectivity is just about 2.5 dB at 1550nm, and the highest mode selectivity for all mode groups is less than 6 dB. Elliptical-core PL is an effective method for the scalable design of MGS-PL with high mode selectivity. Recently, an elliptical-core MS-PL supporting LP01, LP11a and LP11b modes is designed with the mode crosstalk of below −20 dB among 3 modes [19]. Meanwhile, elliptical-core MGS-PL is verified with a mode crosstalk of below −20 dB for three mode groups [20]. However, the scale design is annoyed under the condition of stable performance over a wide operation wavelength. Moreover, both the proposed elliptical-core PL [19–20] can only work under the fixed wavelength. In particular, since the ellipticity of FMF at the PL output is relatively large [19–20], it is challenging to realize the compatible operation with traditional circular-core FMF.
In this submission, we report the design of an EC-MGS-PL supporting five mode groups over the C-band, where ten input fibers are elliptically distributed within the capillary tube. After the adiabatic tapering, the cladding of input fibers forms an elliptical core at the EC-MGS-PL output and the capillary tube become the new FMF cladding. Since the elliptical distribution of input fiber bundle can suppress the mode crosstalk during the tapering process, the proposed EC-MGS-PL can achieve high mode selectivity and MCE together with low IL. Since the ellipticity of FMF core at the EC-MGS-PL output is only 0.87, we believe that the elliptical-core five-mode group selective photonic lantern (EC-F-MGS-PL) is convenient for splicing with both circular-core and elliptical-core FMF.
2. Design principles
Here, we use both FMFs and SMFs as input fiber bundle for the EC-F-MGS-PL to maximize the mode selectivity. We propose to design an EC-F-MGS-PL supporting ten spatial modes for five mode groups. The mode groups division and corresponding mode profiles are shown in Fig. 1. Each mode group contains individual spatial mode. Considering the practical application, our design objective is to realize a mode selectivity of more than 10 dB for all five mode groups, the IL of less than 0.4 dB, and MCE of more than 90% at 1550nm.
Generally, when the power transmitted by the SSMF fused with the input fiber of the PL is normalized, the definition of mode selectivity, IL and MCE are described as Eq. (1)–(3). We use subscript i to represent the light launched into the input fiber mapping to mode group i. The mode selectivity is defined as the power ratio between the desired mode group and power in all the other mode groups at the PL output [21], as shown in Eq. (1),
3. Geometry structure design
Initially, the geometric arrangement and the parameters of input fibers are investigated. Based on early research on the PL geometric requirements [22], we design the input fiber arrangement of EC-F-MGS-PL with ten input fibers arranged in two rings. The inner ring has three input fibers and the outer ring has seven input fibers. In order to obtain an elliptical core FMF at the EC-F-MGS-PL output after the adiabatic tapering, an elliptical shape must be formed with ten input fibers, because the cladding of fused input fibers will form the FMF core at the EC-F-MGS-PL output after the tapering, and the adiabatic tapering process only change geometric size. Therefore, the cladding diameter of input fibers and corresponding arrangement in the capillary tube must be carefully optimized. As for the EC-F-MGS-PL, when the RI of input fibers keeps the same, input fibers mapping to low-order mode have to be with a larger core diameters, while input fibers mapping to high-order mode have smaller core diameters [14]. Therefore, for the proposed EC-F-MGS-PL, core diameters of input fibers mapping to mode group one to five decrease progressively. Taking into account of the commercially available input fibers, we choose input fibers with five different cladding diameters (105/96/81/70/60 µm), and the core diameters for input fibers mapping to mode groups one to five are 14.5/12/10.5/9/7.5 um, respectively. The un-tapered end and the structure of the EC-F-MGS-PL are schematically shown in Fig. 2(a) and 2(e), ten input fibers are positioned in a capillary tube in order. The inner part of the capillary tube is elliptical with major axis radius of a = 160µm and minor axis radius of b = 139µm, respectively. The RI of core and cladding are 1.45 and 1.444 for all input fibers, respectively. Meanwhile, the capillary tube has a RI of 1.439. Since the EC-F-MGS-PL is expected to achieve an optimal performance at 1550nm, the initial operation wavelength for the optimization is set as 1550nm. Then, the wavelength dependent characteristic is further investigated.
Fig. 2. (a) Schematic structure of un-tapered end for EC-F-MGS-PL, (b)–(d) various distributions of ten input fibers, and (e) structure of EC-F-MGS-PL.
The next step is to determine the core diameter for each input fibers. By considering the spatial degeneration of LP11, LP21, LP31 and LP12 modes, the structure of EC-F-MGS-PL require two identical input fibers mapping to two spatially degenerate modes of LP11, LP21, LP31 and LP12 modes, respectively. Consequently, two identical fibers need to be symmetrically distributed across the y-axis, as shown in Fig. 2(a). Since the spatial degeneracy do not occur for LP01 and LP02 modes, fibers mapping to LP01 and LP02 modes can be placed at an asymmetrical position, and thus input fibers numbered 1 and 8 can map to LP01 and LP02 modes. Furthermore, those input fibers mapping to LP21 and LP02 modes has a triangle distribution, because they are within the same mode group. Consequently, when each fiber core in Fig. 2(a) corresponding to individual mode has different diameters, there exist 18 different distributions of input fiber bundle in order to satisfy the requirements mentioned above, as shown in Figs. 2(b)–2(d). In order to obtain the optimal geometric distribution, we first model the whole tapering region for various fiber distributions, and calculate the mode selectivity, IL and MCE of each structure. For all simulations here, light is introduced into the EC-F-MGS-PL through a SSMF with a core diameter of 9 µm. The results are summarized in Figs. 3(a)–3(c). When the light is launched into the individual input fiber, only first ten geometry structures can achieve mode group selective excitation, because the mode selectivity of other structures are smaller than zero, indicating that the fundamental modes of input fibers can’t convert to the desired mode groups.
Fig. 3. (a) Mode selectivity, 3(b) IL, and 3(c) MCE for different geometry structures before optimization. Figure 3(d) Mode selectivity, 3(e) IL, and 3(f) MCE for first ten geometry structures after optimization.
After the preliminary calculation, we further to optimize the core diameters of each input fiber to improve mode selectivity and MCE, as well as to reduce the IL among the first nine geometry structures, as shown in Figs. 3(d)–3(f). We choose the first two structures for further investigation, because both mode selectivity, IL and MCE are better for all involved mode groups. In particular, the performance of five mode groups is relatively uniform in comparison with other options. Both two EC-F-MGS-PLs with structure 1 and 2 are called as PL-1 and PL-2 in next discussion. The parameters of all input fibers and the corresponding mode groups for two EC-F-MGS-PLs are summarized in Table 1.
Table 1. Parameters of input fibers
4. Tapering process design
Initially, we model the transition at discrete points along the tapering length. At each point, the 2D waveguide geometry is taken into account, in order to understand the mode evolution. The effective RIs of each mode are presented with respect to the tapering ratio along the transition, as shown in Fig. 4(a). The horizontal dashed line indicate the cladding index of the input fibers. After the theoretical calculations, the tapering ratio is chosen as 1/12 to satisfy the ten-mode operation. Figure 4(a) verifies that, the adiabatic tapering ensures fundamental mode of each input fiber successfully convert into the designated mode groups at the EC-F-MGS-PL output, because the mode effective RIs of different mode groups are uncrossed in the entire tapering region. Meanwhile, modes within the same mode group keep indistinguishable, indicating of the successful design of EC-F-MGS-PL. Furthermore, with the reduction of the tapering ratio, the effective RIs are reduced below the dashed line, where the cores are too small to confine the light. The conversion of input fundamental modes to the high-order modes starts at the tapering ratio of 0.4, because the effective RI of LP12 modes become smaller than 1.444 under the condition of 0.4 taping ratio, indicating that the input fiber core is too small to restrict the light and the light escape to the input fiber cladding. As a result, new FMF core at the EC-F-MGS-PL output is formed.
Fig. 4. (a) Evolution of modes throughout the tapered transition, and (b) 3D schematic of the EC-F-MGS-PL.
In order to realize small package of EC-F-MGS-PL under the adiabatic condition, the tapering process can divide into two steps. The taper ratio of the first step is 1/2.5, meanwhile that of the second step is 1/4.8. The first tapering step can be faster as the input fiber core has a strong confinement on the modes, while the second taping step must be gentle enough to realize the modes leakage into the input fiber cladding slowly, for the purpose of the adiabatic tapering. The entire tapering length is initially set to 9 cm. The whole structure of the device is schematically shown in Fig. 4(b), where L1, L2, and L = L1+L2 represent the length of the first tapering step, the second tapering step, and the entire EC-F-MGS-PL, respectively. In order to determine the two tapering length for optimal performance, we calculate the relationship between mode selectivity, IL, and MCE as the function of L1/L for PL-1 and PL-2, as shown in Fig. 5. In order to achieve the mode selectivity and MCE of all modes as high as possible while keep IL low enough, L1/L = 0.15 is the best choice for both PL-1 and PL-2. Consequently, L1=1.35cm and L2=7.65cm are chosen. We can clearly observe that, as for PL-1, the mode selectivity of all mode groups is significantly greater than 10 dB, and the MCE is more than 90%. However, as for PL-2, the mode selectivity of mode group four is less than 10 dB. Consequently, we choose PL-1 as the recommended EC-F-MGS-PL design.
Fig. 5. (a) Mode selectivity, 5(b) IL, and 5(c) MCE as a function of L1/L for PL-1. Figure 5(d) Mode selectivity, 5(e) IL, and 5(f) MCE as a function of L1/L for PL-2.
In order to verify the excellent performance of two-step tapering process and investigate the mode characteristics of the EC-F-MGS-PL in details, Fig. 6 shows the calculated mode crosstalk matrix of the optimal EC-F-MGS-PL under conditions of different tapering steps, when the other parameters are fixed. We can clearly observe that, when the light is introduced to a specific input port of the EC-F-MGS-PL, the power distribution of each mode group at the EC-F-MGS-PL output. Therefore, the mode selective excitation of the EC-F-MGS-PL can be intuitively extracted. The rows of the matrix represent the selectively excited mode groups, and the columns represent the output mode groups. The power percent is displayed with the unit of decibels [dB] given by 10log10Pij ∕ Pii, where Pii represents the powers of the selectively excited mode groups and Pij represents the powers of other mode groups. For five mode groups, the calculated mode crosstalk is below-6.1 dB for the single-step tapered EC-F-MGS-PL and −16.8 dB for the two-step tapered EC-F-MGS-PL, respectively. The diagonal matrix elements representing the IL of the two EC-F-MGS-PL, and ILs for all mode groups are below 0.33 dB and 0.37 dB, respectively. Therefore, the advantages of two-step tapering process is obvious.
Fig. 6. (a) Calculated mode crosstalk matrix of one-step tapered EC-F-MGS-PL, and 6(b) calculated mode crosstalk matrix of two-step tapered EC-F-MGS-PL.
To verify the advantage of our proposed PL structure, we numerically carry out performance comparison between the circular-core five mode-group-selective photonic lantern (CC-F-MGS-PL) with our proposed EC-F-MGS-PL, under conditions of the same parameters. Table 2 summaries the mode selectivity, IL, and MCE of two-step-tapered EC-F-MGS-PL, one-step-tapered EC-F-MGS-PL, and two-step-tapered CC-F-MGS-PL. It is clearly indicated that both the elliptical shape and the two-step tapering process are helpful to improve the mode selectivity.
Table 2. Mode selectivity, IL and MCE of the EC-F-MGS-PL and the CC-F-MGS-PL
5. Performance analysis
After the design optimization, we start to evaluate the performance of the optimal EC-F-MGS-PL design. High mode selectivity of the designed EC-F-MGS-PL can be examined by selectively exciting mode groups at the input port and observing the mode evolution. The mode evolution along the tapering length is monitored, when different mode groups are selectively excited, as shown in Fig. 7. The input modes gradually transfer into the specific mode group in the EC-F-MGS-PL. Only modes within the same mode group couple strongly, while the modes at different mode groups can separate well. As shown in Fig. 8, we also monitor the power of five mode groups during the tapering process, when individual mode groups are selectively excited. At the beginning, all mode groups coupled to each other strongly and cannot be distinguished. When the tapering length exceeds 6 cm, the mode coupling between different mode groups becomes weak, and the energy of the designated mode groups are much larger than the others. Especially, during the second tapering process, energy of the desired mode groups gradually increases and eventually reach up to 90%, while the power of other modes is reduced substantially.
Fig. 8. Power evolution throughout the tapered transition of the EC-F-MGS-PL, when selectively exciting and measuring the mode groups of 8(a) 1, 8(b) 2, 8(c) 3, 8(d) 4, 8(e) 5.
As the ellipticity of output fiber for the proposed EC-F-MGS-PL is 0.87, it is convenient for the fiber splicing with conventional circular-core FMF. In case we connect the output of EC-F-MGS-PL with a ten-mode circular-core FMF having a core diameter of 24um and relative refractive index difference of 0.35%, the mode selectivity values of five mode groups, after the fiber splicing, are 16.0dB, 14.7dB, 16.6dB,12.6dB, and 13.7dB, respectively. In particular, the corresponding crosstalk matrix after the fiber splicing is shown in Fig. 9.
Fig. 9. Calculated mode crosstalk matrix after the fiber splicing with conventional circular-core FMF.
Finally, we investigate the operation wavelength dependent operation for the proposed EC-F-MGS-PL. Since all mode groups supported by this EC-F-MGS-PL are not cut off over the C + L band, the relationship between mode selectivity, IL, and MCE as a function of operation wavelength is shown in Fig. 10. We can observe that the low-order modes from mode groups 1, 2, and 3 is insensitive to the operation wavelength. The mode selectivity are closed to 15 dB and the MCE are closed to 90% over the C + L band. However, the high-order modes from mode groups 4 and 5 have a significant performance penalty at longer wavelengths, because the high-order modes at the EC-F-MGS-PL output partially leak to the FMF cladding at the longer wavelength. Overall, the designed EC-F-MGS-PL can achieve mode selectivity of more than 9 dB, IL lower than 0.4 dB, and MCE higher than 83.3% for all mode groups over the C band.
Fig. 10. (a) Mode selectivity, 10(b) IL and 10(c) MCE of the EC-F-MGS-PL as a function of wavelength.
6. Conclusions
We have designed and numerically characterized an elliptical-core five mode group selective photonic lantern supporting 10 spatial modes. We introduce the design strategy and corresponding optimization procedure in details, especially the optimal geometry structure and the tapering process. After the optimization, the EC-F-MGS-PL is proposed to fabricate with two tapering steps, in order to realize highly mode selectivity, low IL and high MCE for all five mode groups. Finally we characterize the mode evolution and wavelength dependent operation of the proposed EC-F-MGS-PL. The proposed EC-F-MGS-PL can be fabricated by the micro-structured preforms method [18].
Funding
National Basic Research Program of China (973 Program) (2018YFB1801002); National Natural Science Foundation of China (61875061); Fundamental Research Funds for the Central Universities (2019kfyRCPY006).
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