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Abstract
Trapped in the stringent adiabatic transmission condition of high-order modes, low-loss fused biconical taper mode selective coupler (FBT-MSC) has long been challenging to achieve. We identify the adiabatic predicament of high-order modes to stem from the rapid variation of the eigenmode field diameter, which is caused by the large core-cladding diameter difference of few-mode fiber (FMF). We demonstrate that introducing a positive-index inner cladding in FMF is an effective approach to address this predicament. The optimized FMF can be used as dedicated fiber for FBT-MSC fabrication, and exhibits good compatibility with the original fibers, which is critical for the wide adoption of MSC. As an example, we add inner cladding in a step-index FMF to achieve excellent adiabatic high-order mode characteristics. The optimized fiber is used to manufacture ultra-low-loss 5-LP MSC. The insertion losses of the fabricated LP01, LP11, LP21, LP02 and LP12 MSCs are 0.13 dB at 1541 nm, 0.02 dB at 1553 nm, 0.08 dB at 1538 nm, 0.20 dB at 1523 nm, and 0.15 dB at 1539 nm, respectively, with smoothly varying insertion loss across the wavelength domain. Additional loss is less than 0.20 dB from 1465.00 nm to 1639.31 nm, and the 90% conversion bandwidth exceeds 68.03 nm, 166.68 nm, 174.31 nm, 132.83 nm, and 84.17 nm, respectively. MSCs are manufactured using commercial equipment and a standardized process that takes just 15 minutes, making them a potential candidate for low-cost batch manufacturing in a space division multiplexing system.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Space-division multiplexing (SDM) has been proposed as a solution to address the potential capacity crisis in future communications [1–5]. In SDM, the primary medium for data transmission is the few-mode fiber (FMF) that can support multiple higher-order modes [6–12]. However, a fundamental challenge in SDM is the controlled excitation of these high-order fiber modes.
Several mode converters have been proposed and demonstrated to address the challenge of controlled excitation of high-order fiber modes in the SDM technique. Mode converters can be generally classified into two categories: free-space optical devices and all-optical fiber devices. Free space devices were widely used in early SDM research, allowing easy phase and amplitude modulation in laboratory environments using optical components, making mode conversion simple and convenient [13–16]. However, the high cost and bulkiness of the components limit system integration, and high insertion loss (IL) has become a critical issue. In recent years, compact all-fiber mode extraction methods have attracted more interest due to their good compatibility and low intrinsic loss. Mature fiber processing technologies such as cutting, fusion, melting, carving, and others make the cost even lower. Based on the number of ports, all-fiber mode converters are categorized as photon lanterns (PLs) [17–19], mode selective couplers (MSCs) [20–28], and long period fiber gratings (LPFGs) [29–35]. A PL that has a loss of less than 2 dB, a mode extinction ratio of 9.80 dB, and a mode number of 9 is demonstrated [18]. However, the fusion loss between the PL and FMF is 5 dB and the manufacturing of high-quality PL is extremely challenging. LPFG is proposed to generate up to $\textrm{L}{\textrm{P}_{41}}$ mode [34], but cannot be used for multiplexing due to port restrictions. MSCs provide a balance between structural complexity and potential functionality.
Manufacturing of MSCs is typically achieved through two methods: side-polishing (SP) [25–27] and fused biconical taper (FBT) [20–24,28] technique. In FBT-MSC, light spills out of the core of single-mode fiber (SMF) at the down-taper and enters the cladding of the FMF at the waist of the taper, before re-entering the core of the FMF at the up-taper. The FMF taper must be smoothly varying to minimize optical power loss, which is called the adiabatic transmission condition [36]. In 2014, FBT-MSCs for $\textrm{L}{\textrm{P}_{11}},\textrm{L}{\textrm{P}_{21}}$, and $\textrm{L}{\textrm{P}_{02}}$ modes have been demonstrated with coupling efficiencies exceeding 91%, 95%, and 92%, respectively [22]. However, the length of the fiber taper exceeds 75 mm to achieve adiabatic transmission of $\textrm{L}{\textrm{P}_{21}}$ mode. It is estimated that the taper length required for higher-order modes is even longer. The excessively long fiber taper is difficult to manufacture and package. In 2020, $\textrm{L}{\textrm{P}_{01}}$ and $\textrm{L}{\textrm{P}_{11}}$ FBT-MSCs with standard length have been demonstrated with losses of 0.1 dB and 0.3 dB, respectively [24]. By precisely controlling the phase-matching condition, a mode extinction ratio exceeding 28 dB is achieved, with a smoothly varying curve for the IL across the wavelength domain. The ultra-low loss, high purity, and smoothly varying IL curve demonstrate the ability of FBT technique to achieve high-quality mode conversion. However, the taper length required for adiabatic transmission of $\textrm{L}{\textrm{P}_{21}}$ mode exceeds the limits of the equipment, resulting in an additional loss (AL) of over 10 dB for FBT-MSCs fabricated by the same method. FBT-MSCs have been demonstrated to excite up to 7 modes, but a minimum high loss of 6.8 dB is still encountered due to non-adiabatic transmission of high-order modes [28].
SP-MSCs achieve resonant coupling by partially removing the cladding and bonding fibers. In SP-MSCs, the light waves always propagate in the fiber core, thus avoiding the problem of adiabatic transfer conditions, which makes it possible to manufacture low-loss high-order MSC. SP-MSCs for $\textrm{L}{\textrm{P}_{11}},\textrm{L}{\textrm{P}_{21}}$, and $\textrm{L}{\textrm{P}_{31}}$ modes with minimum losses of 2.5 dB, 1.9 dB, and 1.6 dB have been demonstrated [26]. By optimizing the polishing process and precise control of phase matching conditions, SP-MSCs with 6-mode groups exhibit losses below 1.8 dB and purity higher than 88.0% in the 1530-1600 nm wavelength range [27]. Three different types of SMF are used to fabricate different MSCs.
When fabricating MSCs for modes higher than $\textrm{L}{\textrm{P}_{21}}$, SP-MSCs appear to be a better option compared to FBT-MSCs due to their lower losses. However, mechanical processing introduces additional intrinsic losses. The use of multiple types of SMFs increases the compatibility cost between the MSC and the SDM system. In contrast, FBT-MSCs have been demonstrated to have lower intrinsic losses, simpler processing, and more time-efficient. However, it is urgent to solve the problem of adiabatic transmission in higher-order modes.
In this work, the adiabatic predicament of high-order mode conversion in FMFs is analyzed and resolved by modifying the fiber refractive index distribution, leading to the realization of ultra-low-loss 5-LP FBT-MSCs with ideal performance. We demonstrate that the difficulty of adiabatic transmission for higher-order modes arises from the rapid variation of the mode field diameter (MFD) of the eigenmodes in the FMF taper. A universal optimization method for FMF is proposed to achieve excellent adiabatic performance. The optimized fiber can be specifically used for FBT-MSC fabrication and has good compatibility with the original fiber, which is essential for the widespread use of MSCs. The optimized FMF is fabricated and used for the manufacture of high-performance FBT-MSCs. FBT-MSCs covering $\textrm{L}{\textrm{P}_{01}}$, $\textrm{L}{\textrm{P}_{11}}$, $\textrm{L}{\textrm{P}_{21}}$, $\textrm{L}{\textrm{P}_{02}}$ and $\textrm{L}{\textrm{P}_{12}}$ modes are then fabricated, exhibiting IL as low as 0.13 dB, 0.02 dB, 0.08 dB, 0.20 dB, and 0.15 dB, respectively. The MSCs feature an ideal structure, with IL smoothly varying across the wavelength domain, and AL lower than 0.20 dB. To the best of our knowledge, this is the 5-mode MSC with the lowest reported loss. The fabrication process employs commercial equipment and standard procedures, with smooth power curves and good repeatability suitable for mass production. This work demonstrates that FBT-MSCs can achieve ultra-low-loss high-order mode conversion and have commercial potential. The fabricated MSCs are promising to inspire further research on FMF-based FBT couplers.
2. Working principle of FBT-MSC
The FBT-MSC is composed of two parallel fiber tapers touched with each other, as shown in Fig. 1. FBT-MSC realizes mode conversion through the resonance between the source mode and the target mode. Resonance occurs in the coupling region, where the source mode and the target mode have strong evanescent field. When entering and leaving the coupling region, the lightwave is compressed and expanded in the taper region to match the mode in the untapered fiber. The process of compression and expansion changes the propagation constant of the original mode to promote resonance in the coupling region. The evolution of the optical field and the change in the propagation constant β depicted in Fig. 1. elucidate this process.
Fig. 1. FBT-MSC schematic diagram. The bottom curve depicts the process of altering the optical wave propagation constant β by FBT-MSC.
Each component of the FBT-MSC must satisfy appropriate conditions to achieve its intended function. In the coupling region, the same propagation constant of the source and target modes is a necessary condition for resonance, also known as the phase-matching condition. However, the phase-matching condition alone is insufficient to ensure high conversion efficiency. The length of the resonant region must match the coupling length to ensure the end of coupling at maximum conversion efficiency. Moreover, the purity of the target mode is also affected by the degree of fusion (DoF). On the other hand, the taper region should be sufficiently adiabatic to avoid power loss, namely adiabatic condition. When the taper angle fails to satisfy the adiabatic condition, the light will be coupled to other modes during the expansion and compression processes. In this work, the adiabatic condition is achieved by optimizing the fiber refractive index profile, while the other conditions in the coupling region are realized through optimized FBT processing techniques.
3. Adiabatic dilemma and fiber design
The adiabatic taper angle of $\textrm{L}{\textrm{P}_{\textrm{mn}}}$ can be estimated by [37]
The difficulty with adiabatic high-order modes transmission is caused by the rapid variation of the MFD relative to the taper ratio of the eigenmode in the fiber taper. Figure 2 shows the variation of the MFD of the fundamental mode $\textrm{L}{\textrm{P}_{01}}$ and higher-order modes $\textrm{L}{\textrm{P}_{11}}$, $\textrm{L}{\textrm{P}_{21}}$, and $\textrm{L}{\textrm{P}_{02}}$ as a function of the taper ratio, along with the side view of the corresponding mode profiles. The results are obtained through finite element analysis of a step-index FMF, characterized by a core diameter of 19 µm and a refractive index difference of 0.0090 between the core and cladding. As the taper ratio decreases, the mode gradually transitions from core-guided to cladding-guided accompanied by an increase in MFD. The red dashed line indicates the rate of change of MFD when the mode spills over to the cladding. The discussion here is focused on the changes in the eigenmode fields rather than the propagation of the optical fields. In a slowly varying waveguide structure like a fiber taper, sudden beam diameter expansions are not expected to occur during field propagation due to the paraxial component of the wave vector. Thus, non-adiabatic coupling occurs when the transmitted optical field fails to match the eigenmode fields, resulting in the loss of optical power.
Fig. 2. Side view of the eigenmode field as the taper ratio variating and the corresponding MFD of $\textrm{L}{\textrm{P}_{01}},\textrm{L}{\textrm{P}_{11}},\textrm{L}{\textrm{P}_{21}},\textrm{L}{\textrm{P}_{02}}$ in FMF.
The MFD of $\textrm{L}{\textrm{P}_{21}}$ mode exhibits the fastest variation in all eigenmodes in Fig. 2, and the fast-varying region of the mode profile is shown in Fig. 3(a). The process of the eigenmode field overflowing the core and filling the cladding is visible. Meanwhile, the evolution of the transmitted field during propagation is obtained experimentally, as shown in Fig. 3(b). $\textrm{L}{\textrm{P}_{21}}$ mode is excited in the fiber taper and transmitted towards the narrow end, where it is cleaved at the corresponding location marked as A∼E in Fig. 3(a) to observe the optical field. The same experiment is repeated multiple times to observe all five positions. The optical fields at positions A and B are similar to the corresponding eigenmode fields, with four lobes radiating outward. However, the optical fields at positions C, D, and E are different from the corresponding eigenmode fields. The optical fields at positions C, D, and E are divided into two layers radially, indicating the presence of LP22 components in the field. The LP22 mode is not supported by the core of the untapered fiber. The energy of LP22 will not be able to return to the fiber core and will dissipate within the cladding. Therefore, the experimental results indicate that the non-adiabatic transmission of modes is caused by the rapid variation of the eigenmode field MFD.
Fig. 3. (a) The variation of MFD of $\textrm{L}{\textrm{P}_{21}}$ with taper ratio and eigenmode profile of marked points. (b) The optical field of the marked taper ratio in Fig. 3(a) after $\textrm{L}{\textrm{P}_{21}}$ injection.
One method to improve the adiabatic performance of a fiber taper is to reduce the rate of change of MFD relative to the taper ratio where the eigenmodes spill over to the cladding. Therefore, increasing the length of the fiber taper is an effective method to achieve adiabaticity, at least theoretically. Another feasible approach is to optimize the adiabatic characteristics of the fiber by changing its structure. Figure 4 shows the change in the MFD-taper ratio curve before and after optimizing a step-index FMF. In the original fiber, when the taper ratio is reduced to a critical value, the core is not sufficient to confine the mode field, and the mode is quickly confined by the cladding. It is evident that the mode field confined by the core is comparable to the core size, while the mode field confined by the cladding is comparable to the cladding size. Therefore, near the critical taper ratio, the mode expands from the core size to the cladding size. The change of MFD for $\textrm{L}{\textrm{P}_{21}}$, $\textrm{L}{\textrm{P}_{02}}$, and $\textrm{L}{\textrm{P}_{12}}$ is sharp near the critical taper ratio, which is not unique since the core diameter of most FMFs is in the range of 10∼35 µm, while the cladding diameter is 125 µm. The cladding diameter is 90 µm larger than the core diameter, leading to a drastic change in MFD near the critical taper ratio. The proposed optimized fiber in Fig. 4(a) right adds an inner cladding with a refractive index difference of 0.0020 and a diameter of 45 µm as a buffer layer. The modes will be confined by the inner cladding after spilling from the core. When the taper ratio is further reduced, the modes will then overflow from the inner cladding and be confined by the outer cladding. The optimized inner cladding diameter and refractive index difference make the MFD-taper ratio curve very smooth, as shown in Fig. 4(b) right, and the cladding and inner cladding diameters are annotated with dashed lines to aid understanding. Figure 5 shows a side view of five modes before and after optimization to intuitively demonstrate the suppression effect of the buffer layer on the slope of the MFD-taper ratio curve. The optimized fiber has adiabatic performance comparable to that of SMF, which will allow high-order modes adiabatically transmit in a short taper in MSCs.
Fig. 4. (a) Index profile of original fiber and optimized fiber. (b) MFD as a function of the taper ratio of original fiber and optimized fiber.
Fig. 5. Side view of the eigenmode profile as the taper ratio varies in original FMF and optimized FMF.
The method of adding a buffering layer to improve the adiabatic performance can be applied to almost any circularly symmetric fiber. Certain fibers intended for SDM systems feature complex ring structures in the core area to achieve high transmission robustness [12,38]. The optimization process preserves the core structure to maintain the fiber's original performance. The added inner cladding may compromise the fiber's bending performance, making it unsuitable for long-distance transmission. Fortunately, the optimized fiber has the same eigenmode profile as the original fiber since the fiber's eigenmode profile is determined by the difference rather than the absolute value of the refractive index. Therefore, the optimized fiber can be used specifically for MSC manufacturing and fused with the original fiber when a long-distance transmission is required. Due to the small refractive index difference between the original and optimized fibers, the Fresnel reflection loss is inevitable at the fusion splice and it can be estimated as
where ${n_1}$, ${n_2}$ represent the refractive indices of the inner layer and the cladding, respectively. In this work, ${n_1} = 1.4460$ and ${n_2} = 1.4440$, so $Los{s_{fusion}} \approx 4.79 \times {10^{ - 6}}\; \textrm{dB}$.4. Fabrication of MSCs
The FBT technique produces fiber tapers using a high-speed flame brush and a slowly stretching fiber holder block (FHB) module. The taper ratio is determined by the scanning length of the flame brush and the pull length of the FHB module
By adjusting the scanning width and the pull length, fiber tapers with any diameter can be obtained.To satisfy the phase-matching condition in the coupling region, a pre-pull of SMF is necessary. The SMF utilized in this study is CS1550 produced by YOFC, which features a core diameter of 9 µm and a numerical aperture of 0.13. The original effective index (EI)-taper ratio curve of the SMF is shown as a black dashed line in Fig. 6. After pre-pull, the EI-Taper ratio curve of the SMF shifts to the right in the figure. The EI-Taper ratio curves of the pre-pulled SMF are plotted with a flame scan width of 4 mm and pull lengths of 1 mm, 2 mm, and 3 mm, respectively. The blue curve in Fig. 6 shows the EI-Taper ratio curve of $\textrm{L}{\textrm{P}_{11}}$ in the designed FMF. The $\textrm{L}{\textrm{P}_{11}}$ curve intersects with the pre-pulled SMF curve at a specific taper ratio, indicating that the pre-pulled SMF and the $\textrm{L}{\textrm{P}_{11}}$ mode in the FMF have the same EI at this taper ratio. These intersection points are the phase-matching points, marked as red dots in the figure. When the pull length of the SMF is changed, the SMF and $\textrm{L}{\textrm{P}_{11}}$ match at different coordinates. During the manufacturing process, the selection of phase-matching points is flexible. However, not all phase-matching points will result in efficient coupling, and appropriate DoF and coupling lengths are also necessary. The DoF of MSC is dependent on the heating time and flame temperature which require precise control during the processing. Some phase-matching points have extremely close EI with adjacent modes, which can result in the involvement of neighboring modes in coupling and cause a decrease in mode purity. Therefore, it is crucial to carefully manage the processing parameters to maintain optimal DoF and minimize the impact of EI proximity on mode coupling. To optimize the coupling efficiency, it is essential to carefully select the phase-matching points during the manufacturing process.
Fig. 6. EI-Taper Ratio curve of $\textrm{L}{\textrm{P}_{01}}$ in pre-pulled SMF and $\textrm{L}{\textrm{P}_{11}}$ in FMF. The flame scan width is set to 4 mm.
Figure 7 displays all the phase-matching points used for the manufacture of MSCs and the corresponding pre-pull parameters of SMF. These parameters are determined gradually through repeated experiments. It should be noted that the pull length of SMF to $\textrm{L}{\textrm{P}_{01}}$ is a negative value, indicating that the SMF needs to be axially compressed to enlarge its diameter to meet the phase-matching condition, which is difficult to achieve in the experiment. Considering that the SMF and FMF will scale synchronously during the manufacturing process, pulling FMF to make the initial diameter of SMF larger than the diameter of FMF will achieve the same effect.
Fig. 7. EI of pre-pulled SMF (black line) and FMF. The red dots in the figure show the phase-matching point of the MSC.
We use the commercial FBTC manufacturing equipment (XQ7112, OSCOM) to fabricate the MSC. The SMF or FMF is pre-pulled to the estimated diameter, and then the SMF and FMF come into contact in the heating region and stretch together. In order to monitor the working state of the MSC, online optical power monitoring is necessary. As shown at the top of Fig. 8(a), a laser with a wavelength of 1550 nm is injected into the input port, and the power of Port 1 and Port 2 is recorded during the fusion process. The power variation of Port 1 and Port 2 is referred to as the taper characteristic curve (TCC) in FBT technique. In the initial phase, Port 2 occupies 100% of the power. As the tapering goes on, power coupling occurs in the waist, with Port 2 power decreasing and Port 1 power increasing. When the power of Port 1 reaches the maximum value, the pulling is stopped. The MSC is then encapsulated in a standard 32 mm long U-shaped glass tube and a 54 mm long stainless steel pipe, as shown at the bottom of Fig. 8(a). The pre-pull length is repeatedly fine-tuned to maximize the power of Port 1 as close to 100% as possible. The optimized pre-pull parameters are listed in the table in Fig. 7.
Fig. 8. (a) The schematic diagram and the photo of the fabricated MSC. (b)∼(f) Typical taper characteristic curve of $\textrm{L}{\textrm{P}_{01}}$, $\textrm{L}{\textrm{P}_{11}}$, $\textrm{L}{\textrm{P}_{21}}$, $\textrm{L}{\textrm{P}_{02}}$ and $\textrm{L}{\textrm{P}_{12}}$ MSC fabrication and output mode field at 1550 nm.
Manufacturing takes place in a thermostatic cleanroom because the fabrication parameters are sensitive to temperature. The optimized process includes the function of automatically stopping stretching. Therefore, the manufacturing process has good repeatability. The manufacturing process including initial packaging takes 15 minutes. Figure 8 (b)∼(f) show the typical TCC of the manufactured MSCs. The TCC is smooth, indicating that the manufactured MSCs have healthy structures. The power at the stop point Port 2 approaches 0, indicating that the phase matching condition is well satisfied. The power of Port 1 is close to 100%, indicating that the adiabatic conditions of the mode are well satisfied.
It is worth noting that Fig. 8 (b)∼(f) show typical TCC to illustrate various situations in manufacturing. Due to the repeatability limit of the mechanical structure of the equipment, not every fabrication process can stop the stretching at the best coupling point. Figure 8 (b) and (e) show almost perfect stops, causing the stretching process to stop precisely at the highest coupling efficiency. Figure 8 (c) and (d) show examples of not stopping stretching at the accurate time, thus retaining a portion of optical power in SMF (blue curve), while FMF (red curve) does not receive all output optical power. In Fig. 8 (f), there is a significant additional loss at the stop stretching point. Part of the additional loss comes from the intrinsic losses of the MSC, while the other part is related to the cutting flatness and cleanliness of the fiber end surface at the power detection port. Given the ultra-low loss of the manufactured MSC, TCC is not the final characterization of MSC loss performance in this work.
5. Performance of MSCs
The IL and AL of the MSC are measured by the Keysight 8164B insertion loss test system (Light source: 81600B, Power detector: N7744A) and plotted in Fig. 9, respectively. IL and AL are defined as
where ${P_{Port\; 1}}$, ${P_{Port\; 2}}$ and ${P_{Input}}$ indicate the power of Port 1, Port 2, and the input port, respectively. The test wavelength covers 1465.00 nm∼1639.31 nm, and the wavelength step is 0.01 nm. During the testing process, the fiber end face at the power detector is precisely cut and inspected for quality to ensure that no additional power loss is introduced.Fig. 9. (a) The IL of MSCs. (b) The AL of MSCs. The abnormal jump around 1635 nm originates from the instability of the light source. All measurement results are from the best-performing sample.
Several MSCs for each target mode are fabricated and the best test results for all types of MSCs are presented. The IL values of all MSCs are below 3 dB, and the AL values of all MSCs are below 0.2 dB in the test wavelength range. The central wavelengths of the MSCs are around 1550 nm, and the IL curves increase smoothly from the central wavelength to both sides, indicating that the structure of the MSCs is very ideal. The AL curves are flat and below 0.1 dB over the test wavelength range for MSCs to $\textrm{L}{\textrm{P}_{01}}$, $\textrm{L}{\textrm{P}_{11}}$, and $\textrm{L}{\textrm{P}_{02}}$ mode. In contrast, the AL curves of MSCs to $\textrm{L}{\textrm{P}_{21}}$ and $\textrm{L}{\textrm{P}_{12}}$ show significant variation across wavelength domain. The reason can be traced to the proximity of the EI of $\textrm{L}{\textrm{P}_{21}}$ and $\textrm{L}{\textrm{P}_{12}}$ at the taper ratios corresponding to the phase-matching points, as shown in Fig. 7, which leads to crosstalk between LP21 and LP12 in MSC. The central wavelength, IL, average AL, and 90% working bandwidth of the MSCs are listed in Table 1. The IL values of the $\textrm{L}{\textrm{P}_{01}}$, $\textrm{L}{\textrm{P}_{11}}$, $\textrm{L}{\textrm{P}_{21}}$, $\textrm{L}{\textrm{P}_{02}}$ and MSCs at central wavelengths are 0.13 dB, 0.02 dB, 0.08 dB, 0.20 dB, and 0.15 dB, respectively. The average AL values across the test wavelength range are less than 0.16 dB for all MSCs. The 90% conversion bandwidths for $\textrm{L}{\textrm{P}_{11}}$, $\textrm{L}{\textrm{P}_{21}}$, and $\textrm{L}{\textrm{P}_{02}}$ MSCs are found to exceed the test wavelength range, with values greater than 166.68 nm, 174.31 nm, and 132.83 nm, respectively, while these of LP01 and LP12 MSCs are 68.03 nm and 84.17 nm, respectively.
Table 1. Central wavelength, IL, average AL, and 90% working bandwidth of the fabricated MSCs
The output mode field is detected by injecting the output beam of the coupler into the infrared camera, without adding any polarization control elements, as shown in Fig. 10. The output mode fields show good LP mode profiles, and the intensity split line formed by the zero points of the radial and angular direction is clear, indicating that it has a relatively high mode purity. The mode purity is estimated by detecting the mode fields at the fiber output and executing mode decomposition [39]. The characteristic parameters extracted from the output field are linked to the proportions of each fiber mode by an equation group. Then the mode purities are calculated by solving the equation group. The mode purities of $\textrm{L}{\textrm{P}_{01}},\textrm{L}{\textrm{P}_{11}},\textrm{L}{\textrm{P}_{21}},\textrm{L}{\textrm{P}_{02}},\textrm{L}{\textrm{P}_{12}}$ are 98.16%, 93.47%, 96.08%, 97.20%, 93.57% at 1550 nm, respectively.
6. Conclusion
In summary, we fabricate FBT-MSCs for 5 modes with ultra-low loss and large bandwidth. An optimization method for FMF with universality is proposed to address the adiabatic transmission challenge. An optimized FMF is used for MSC fabrication and its adiabaticity for high-order mode is comparable to that of SMF. The phase-matching points are precisely adjusted to achieve optimal performance. The AL values of all MSCs in the test band are less than 0.2 dB. The MSCs for $\textrm{L}{\textrm{P}_{01}}$, $\textrm{L}{\textrm{P}_{11}}$, $\textrm{L}{\textrm{P}_{21}}$, $\textrm{L}{\textrm{P}_{02}}$, and $\textrm{L}{\textrm{P}_{12}}$ exhibited smooth IL curves across the wavelength domain. The IL values at the central wavelengths are 0.13 dB, 0.02 dB, 0.20 dB, 0.08 dB, and 0.15 dB, respectively. To the best of our knowledge, this is the 5-LP MSC with the lowest reported loss. The 90% conversion bandwidths of the MSCs are 68.03 nm, > 166.68 nm, > 174.31 nm, > 132.83 nm, and 84.17 nm, respectively. The purities of all output mode fields are 98.16%, 93.47%, 96.08%, 97.20%, and 93.57% at 1550 nm, respectively. The MSCs are fabricated and packaged using standard equipment, and a single fabrication process could be completed within 15 minutes with good repeatability. These MSCs are highly competitive in terms of performance and processing cost, making them a promising basic component in SDM systems. The low-loss, large-bandwidth, and high-fabrication-repeatability of MSCs make them suitable for low-cost MIMO-free SDM transmission and fiber sensing applications.
Funding
National Natural Science Foundation of China (61835006); National Key Research and Development Program of China (2018YFB1801802).
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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