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Abstract
We propose a novel scheme of high doped core and stairway-index trench structure to design a manufacturable graded-index 13-core 5-LP mode fiber with low inter-core crosstalk (ICXT) and large mode differential group delay (MDGD). By using the couple power theory and the finite element method (FEM), the change ICXT of with fiber parameters are investigated. The design of core graded profile and trench structure are optimized to achieve better performance and to meet the fabrication conditions. The numerical result demonstrate that this fiber achieves a low ICXT of lower than −30dB/km (Rb≤500 mm). The bending loss values satisfy the ITU-T recommendation G.655 in 195 µm cladding diameter. Furthermore, the dispersion and the MDGD dependences on wavelength are calculated. The relative core multiplicity factor (RCMF) is obtained as 75.17, which realizes the high density multiplexing. The fabrication methods of this fiber are briefly introduced. The designed fiber may be used for Space-division multiplexing (SDM) system to solve the problem of fiber capacity limitation.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As a new multiplexing technology, SDM is expected to play a very important role in the next stage of optical fiber transmission technology [1,2]. By making full use of the spatial dimension of the fiber, SDM will greatly improve the transmission capacity of a single fiber and effectively overcome the limited capacity problem of single-mode fiber. Nowadays, SDM attracted more and more researchers’ attention. SDM has emerged as a strong candidate to solve the transmission capacity crisis in the future [3–5].
SDM includes multi-core multiplexing and few-mode multiplexing, corresponding to multi-core fiber and few-mode fiber, respectively. The multi-core few-mode fiber (MC-FMF) overcomes the transmission capacity limitations of traditional single-mode fiber (SMF) while crosstalk becomes an issue that must be solve [6–8]. It is well known that there is a trade-off between increasing spatial density and reducing ICXT [5,7]. As the number of cores increase in same cladding region, ICXT generated by the narrowing of core pitch. The existence of crosstalk will shorten the signal transmission distance and lead to signal distortion. Therefore, controlling ICXT at a low level and maintaining the number of cores and modes has become the key to use SDM [8]. In order to achieve larger capacity for SDM, many types of structures have been proposed to suppress the ICXT, including trench assisted structure [1,5,7,8], heterogeneous core structure [9] and air-hole assisted structure [2,10]. These three structures have the advantage of limit the signal in the core, which reduce the coupling between cores. In recent years, due to the applicability and design flexibility of the trench structure, some special trench assisted structures have been proposed [11–16]. An optimized design scheme of heterogeneous trench assisted structure has been reported [12,13]. A novel scheme of dense hole-assisted structure in homogeneous 4-mode 7-core fibers is proposed, the dense hole-assisted structure can be equivalent to a trench structure, enabling significantly suppress the ICXT and bending loss, which reached ICXT of lower than −32dB/100km [14]. At the same time, the author also designed a heterogeneous graded-index profile 4-mode 12-core fiber with the novel air-trench (AT) assisted structure. This AT structure has higher core density and lower ICXT [14]. A design scheme of multi-core fiber combining rod-assisted and trench assisted is proposed [16,17]. Literature [17] first introduced a heterogeneous rod-assisted and trench-assisted multi-core fiber with 32 cores arranged in square-lattice structure, this fiber achieves low ICXT of about −31dB/100km and RCMF of 8.74. Although the above designs have many advantages, they all have one disadvantage in common: these fibers cannot be actually manufactured or can only be fabricated over short distances.
In this paper, we present a novel stairway-index trench structure and high doped graded-index core in homogeneous 13-core 5-LP mode fiber, the design scheme satisfies the actual preparation standard while maintaining low-crosstalk characteristic and large MDGD. we use COMSOL Multiphysics software to simulate the model and analyze the data. Firstly, the design idea of core and assisted structure is introduced, and we investigate the preparation standard of fiber in the section 2. Then the section 3 analyzes the ICXT dependence on fiber parameters, the results of crosstalk analysis demonstrate that the designed fiber is able to satisfy the requirement of long-distance transmission. Further, sections 4 and 5 discuss the bending loss, optimize the fiber parameters and introduce the preparation method of 13-core 5-LP mode fiber. Finally, we calculate the dispersion, MDGD and RCMF of the fiber. The performance of the fiber designed conforms to the communication standards and it is expected to be applied to large-capacity communication networks in the future.
2. Design of homogeneous graded-index core and a stairway-index trench structure
2.1 Core design
In this paper, we employ the high index doped core to limit the mode coupling. This type of core endows the fiber low-crosstalk characteristics, but the high doped core will rise the difficulty of manufacturing. The graded-index core can overcome this difficulty effectively. Therefore, we adopted scheme of the graded-index high doped core, while it also reduces the polarization mode dispersion between the modes [4,15]. Graded cores are also used in fiber communication systems. Different graded-index profile represented by α will make the core obtain different transmission characteristics, we firstly calculate different α and summarize the change rule. The transmission performance of the core is studied as α changes from 1 to 4. Each few-mode graded-core can transmit 5 LP modes (including 8 spatial modes, LP01, LP11x, LP11y, LP21x, LP21y, LP02, LP31x, LP31y). Figure 1(a) and (b) shows graded-index curves (α=1–4) and the effective mode refractive index (neff) distribution for 5-LP mode and LP01 effective mode area (Aeff), respectively. The dash line represents the neff curve of 5-LP mode, while the solid orange line represents Aeff curve of LP01. As can be seen from Fig. 1(b), when the doped concentration in the core center stay the same, neff of 5-LP mode increases with the increase of α. Large effective refractive index differences between modes enable LP modes to keep independent and it is helpful to suppress inter-mode crosstalk. The effective refractive index difference of LP21-LP02 modes has the largest difference when α is equal to 1 and 4. The Aeff of LP01 is approximately proportional to α, and LP modes should keep a larger Aeff to suppress the nonlinear effect. Therefore, we choose α=4 to design the graded-index core.
Fig. 1. (a) The graded-index curves and (b) the neff of 5-LP mode and the Aeff of LP01 mode when α ranges from 1 to 4
2.2 Design of a stairway-index trench structure
It is worth noting that the trench-assisted structure must match with the refractive index of the highly doped core, otherwise the refractive index of sudden change will crack the fiber during the drawing process. Therefore, we optimize the traditional trench assisted structure and propose a novel trench assisted structure with stairway-index distribution, as shown in Fig. 2. The meaning of the symbols in Fig. 2 is shown in Table 1. The stairway-index trench structure consists of three doped regions (the first trench, the second trench and the third trench) with progressively diminishing refractive index and flexibly adjusted. This trench structure can be matched with the high-index graded-core, make MC-FMF obtain strong crosstalk suppression ability while meeting the preparation conditions. This structure still maintains the characteristics of the traditional trench. The function of the first trench and the second trench ensure smooth transition between the highly doped core and the third trench. The function of the third trench and the high doped core is to suppress the crosstalk between the cores. By adjusting the index distribution of the stairway-index trench structure, the match of trench index and high-index cores achieve the manufactural standard. At the same time, the stairway-index distribution of the trench structure is able to adjust flexibly to match the index of the core, thus reduce the manufacturing difficulty and raise yield. The stairway-index trench can effectively solve the problem that the high doped MC-FMF cannot be prepared. However, the prefabrication process of the stairway trench structure is complicated, which requires deposition of the SiO2 tube in different index regions for several times.
Table 1. Fiber initial parameters
2.3 Fiber parameters
The design parameter must be based on the number of mode transmission. According to the current germanium doped technology, the maximum relative refractive index difference of core and cladding is 2% by doping different concentration of GeO2. Setting the concentration of germanium, 5-LP mode can be stably transmitted in the high doped core. Limited of fluorine-doped technology, the relative refractive index difference of trench and cladding is as low as −0.7%. In order to achieve the best suppressed effect, the relative refractive index difference of trench-cladding is set to −0.7%. In reality, the doping concentration gradient of the preform should not exceed 1%. The relative refractive index difference between the core and the first trench should not be greater than 1%, and that between the first trench and the third trench must be less than 1%. At present, Japan has applied for multi-core fiber standard core pitch of 42 µm. Large core pitch has a variety of core arrangement [18]. Employing hexagonal core arrangement to achieve greater transmission capacity and low ICXT. In order to ensure that design parameter meets the actual preparation requirements, we investigated fiber preparation standard and consulted the fiber manufacturer. The initial design value of fiber manufacturing as shown in Table 1. Figure 3 shows the cross-sectional view of a hexagonally arranged high-doped 13-core 5-LP mode fiber with stairway-index trench structure, the meaning of the symbols is shown in Table 1. The initial cladding diameter set as 240 µm for preventing the bending loss of the outer core from exceeding the standard value [14]. Adopting the width and index of the first and second trench as the transition layer ensure that the fiber can be actually manufactured condition. The main function of the third trench is to suppress ICXT and bending loss.
Fig. 3. The cross-section view of a hexagonally arranged high-doped 13-core 5-LP mode fiber with stairway-index trench structure
3. Inter-core crosstalk analysis
ICXT is a crucial factor for weakly coupled multi-core few-mode fiber. ICXT caused by coupling between each core will lead to the reduction of the signal-to-noise ratio of transmitted signals [18,19]. The coupled mode theory (CMT) [20] and the coupled power theory [21] are widely applied to calculate the average crosstalk of multi-core and low-mode fiber [6,7]. Here, the coupled power theory is used to calculate the average crosstalk of 13-core 5-LP mode fiber. For homogeneous multi-core few-mode fiber, the average power coupling coefficient can be written as [14]:
where κmn is the mode coupling coefficient in electromagnetic form, Rb is the bending radius and βm is the propagation constant of core m.ICXT between two cores with length L in the dB form can be written as [15]:
Considering that the important influence of fiber bending on ICXT, we introduced the equivalent index model to the theoretical calculation. A bending fiber can be represented as a corresponding straight fiber, which has an equivalent refractive-index profile [12,19,22]:
Figure 4 shows the influence of fiber bending on the refractive index of the core unit at 1.55 µm and Rb=140 mm. It can be observed in Fig. 4 that fiber bend resulted in refractive index difference in the three adjacent cores unit. For homogeneous cores, bend will lead to slight index differences in the performance of each core.
The high-doped core and the stairway-index trench structure are used for obtaining low crosstalk characteristics, it is necessary to analyze the influence of optical fiber parameters on ICXT. Both the high refractive index core and the stairway-index trench can effectively suppress the mode field overlap between adjacent cores. Because of the large pitch between the secondary adjacent cores, their ICXT is small enough to be ignored [19]. Therefore, we take the ICXT between the center core and the adjacent core as the standard. Figure 5(a) and (b) show the relationship between Δco, W3 and ICXT at 1.55 µm Rb=140 mm. As shown in Fig. 5, ICXT of 5-LP mode is inversely proportional to Δco and W3. The ICXT decreases linearly with the Δco and W3, increasing the Δco and W3 enables the fiber to diminish ICXT. It can be observed that the ICXT of LP31 mode is less than −30 dB/100km when Δco of larger than 1.2% and W3 of larger than 4.5 µm, respectively. In the words, the larger Δco and W3, the less power will be coupled. In order to study the effects of trenches W1 and W2 on crosstalk, a comparison of crosstalk with and without trenches W1 and W2 is given in Fig. 5(b). The solid line represents the refractive index of the first and second trenches of the values in Table 1, and the dotted line represents that the refractive index of these two trenches is changed to silica. The comparison results show that the trenches W1 and W2 slightly increase ICXT, but the added value is less than 5 dB. Although the first and second trenches have some adverse effects on ICXT, it can greatly reduce the difficulty of optical fiber fabrication. The function of the high-doped core and the third trench is to suppress the ICXT and maintain the low-crosstalk characteristics.
ICXT accumulates along with the transmission length of the fiber. To realize the long-distance transmission, it is necessary to strictly control the ICXT. Usually, ICXT lower than −30dB/100km is taken as the design standard for the long-distance transmission of weakly coupled multi-core fiber [14]. Figure 6 describes the relationship between ICXT and transmission distance at 1.55µm Rb=140 mm. The results show that ICXT of the 5-LP mode increases with the length of transmission distance, and ICXT of the high-order LP mode is higher than that of the low-order LP mode. After 100 km of fiber transmission, ICXT of LP01, LP11, LP21, LP02 and LP31 mode are all below −30 dB/100km.
Bending results in phase mismatch of adjacent cores, phase mismatch will help to suppress crosstalk in homogeneous multi-core fibers. The bending radius of 500 mm used in the calculation be approximately considered as the condition of straight optical fiber [4]. Figure 7 shows the relationship between ICXT and Rb at 1.55 µm. ICXT increases with the increase of Rb, but the ICXT of LP21, LP02 and LP31 mode appears a peak near 75 mm. This is due to the fact that the effective refractive index of the three higher-order modes is close to the first trench, and then the energy leaks into trench, which cause the crosstalk of the higher-order modes to fluctuate around 75 mm. For all this, ICXT of LP31 mode is less than −30 dB/100km (Rb≤500 mm). It is worth noting that ICXT is the maximum under the condition of straight fiber for homogeneous multi-core fiber. As Rb decreases, the difference of the propagation constant caused by bend becomes larger and larger. Thus, ICXT decreases with the decrease of Rb.
4. Bending loss
The trench assisted structure and the outer cladding thickness (OCT) have great influence on the bending loss, which needs further study. The outer core is closer to the edge of the fiber, this will result in stronger leakage of the outer core, we will focus on the bending loss of the outer core. Refer to ITU-T recommendation G.655 and IEC 60793-1-44 document, to ensure that each core transmits 5-LP mode stably at the C + L band, the bending loss should lower than 0.5 dB/100 turns (Rb=30 mm) for LP31 mode at 1.625 µm [14–16]. The bending loss be expressed as [14]:
where imag(neff) means the imaginary parts of the neff. The bending loss of outer core are simulated with different W3 and OCT in Fig. 8 and Fig. 9, respectively. In Fig. 8(a), the solid and dashed lines represent the bending loss of LP31 and unwanted LP12 mode (at 1.53 µm Rb=140 mm and 1.625 µm Rb=30 mm) in outer cores, respectively. From Fig. 8(a), the bending loss of LP12 and LP31 modes decrease with the increase of W3, but the reduction degree of LP12 mode is greater than that of LP31 mode. With the increase of W3, the bending loss between the two modes become closer. Unwanted LP12 mode should maintain a large loss difference from the LP31 mode in order that the LP12 mode can be lost during transmission. Since the width of the trench limits the ICXT, the width needs to be a trade-off between bending loss and ICXT. Figure 8(b) shows that the bending loss of the LP31 mode is much less than 0.5 dB/100turns, so the LP31 mode can be transmitted stably in the core. Figure 9 reveals the relationship between the bending loss and OCT of LP12 and LP31 at 1.53 µm (Rb=140mm) and LP31 after 100 turns at 1.625 µm (Rb=30 mm). When OCT is less than 30 µm, the bending loss of LP12 and LP31 mode have a significant difference, while the bending loss of LP31 mode is far less than 0.5 dB/100 turns. As a result, the trade-off relationship between W3 and OCT can be balanced, the W3=5 µm and OCT = 25 µm is acceptable.Fig. 8. The bending loss of outer cores (a) the bending loss of LP31 and LP12 at 1.53 µm Rb=140 mm (solid lines) and 1.625 µm Rb=30 mm (dashed lines); (b) the bending loss of LP31 after 100 turns at 1.625 µm Rb=30 mm
Fig. 9. The relationship between the bending loss and OCT of LP12 and LP31 at 1.53 µm (Rb=140 mm) and LP31 after 100 turns at 1.625 µm (Rb=30 mm)
5. Fiber parameters optimization and fabrication process
Considering the influence of fiber parameters on ICXT and bending loss, we optimized the design parameters, as shown in Table 2. We think that OCT of 25 µm can resist stress damage in practical applications. In our design, the diameter of the 13-core fiber has reached 195 µm. After adding two layers of coating, the outer diameter of the fiber can reach about 300 µm, and its mechanical strength and flexibility can fully meet the requirements of practical applications.
Table 2. The optimal fiber parameters of 13-core 5-LP mode fiber with stairway-index trench structure
Here, based on the knowledge of producing optical fiber preform, we present a method to fabricate a preform of 13-core 5-LP modes fiber. The fiber preform will be divided into two parts. The doped core unit is prepared by Modified Chemical Vapor Deposition (MCVD) and in-tube method, and the silica cladding is prepared by Perforating method. The preparation process of the prefabricated doped core unit is complex and difficult, the doping layers must be deposited layer by layer by MCVD and in-tube method. Figure 10 describes the preparation process of the fiber preform. Different dopants are added into the silica-based tube and deposited layer by layer to get the core preform. The silica cladding with 13 holes is prepared by Perforating method. Inserting the core preform into the hole for further melting and drawing.
Melt-drawing process is very important, which determines the quality of 13-core fiber. The temperature distribution on the cross section of perform is gradient during melt-drawing process. It is necessary to strictly control the temperature of heating furnace to prevent the deformation of outer core and central core due to temperature difference. During the cooling process, the temperature from the fiber surface to the central core is gradient distribution. The Ge-doped region will be subjected to tensile stress, while the F-doped and cladding regions will be subjected to compressive stress. The existence of internal stress will cause the Si-O chain to break and lead to the degradation of fiber quality. The fiber can be annealed in holding furnace to eliminate the internal temperature difference, control the drawing speed and tension, relieve and release the internal stress. The preparation of 13-core fiber can be completed by improving the drawing process and drawing parameters.
There must be manufacturing error in the production of fiber. We analyzed the fabrication tolerance of 13-core fiber, as shown in Fig. 11. The ICXT of LP31 is calculated by introducing ± 2% preparation error for W1, W2, W3 and Λ, respectively. The influence of several key parameters on ICXT for LP31 mode has been shown in Fig. 11. The 13-core fiber can meet the requirement that the ICXT of LP31 is less than −30 dB/100 km within the fabrication error of 2%. Finally, we summarize the optimal fiber parameters with fabrication tolerance in Table 3.
Table 3. the optimal fiber parameters with fabrication tolerance
6. Other properties
The existence of dispersion makes the transmitted signal pulse distorted, which limits the transmission capacity, transmission bandwidth and transmission distance of optical fiber. The existence of dispersion phenomenon is very unfavorable for optical fiber communication. The dispersion is composed of two components: material dispersion Dm and waveguide dispersion Dw, the formula of dispersion is written [14]:
where c is the velocity of light in a vacuum, nm is dependent on wavelength (λ) in dispersive media, Re(neff) is the real part of the neff, respectively. Figure 12 describes the dispersion curves of the 5-LP mode. The dispersion slopes for the 5-LP modes are similar, and the dispersion gradually increases with the increase of wavelength. The dispersion of LP11 mode is the strongest and that of LP31 mode is the weakest.In order to study the effects of trenches W1 and W2 on the dispersion, the solid line represents the dispersion of presence trenches W1 and W2, and the dotted line represents the dispersion of absence trenches W1 and W2 in the Fig. 12. It is obtained from Fig. 12 that the introduction of W1 and W2 can effectively reduce the dispersion of the designed fiber, which is important for optical fiber communication system. The dispersion values of each mode are summarized in Table 4.
Table 4. The optimal fiber performance of 13-core 5-LP mode fiber with stairway-index trench structure.
DMGD is one of the important factors reflecting the characteristics of few-mode fiber [23,24]. Due to the different propagation speed of each mode in the few-mode core, the optical signals between each mode channel will appear time delay after propagation for a certain distance, that is, the mode group time delay. It can be expressed as [15]:
The core multiplicity factor (CMF) can measure the spatial multiplexing degree of MC-FMF. CMF can be expressed as [25]:
where N is number of cores, l is number of spatial modes per core (for 5-LP mode, as l=8), Aeff is effective area of a particular mode. Further, RCMF is defined as the ratio of CMF value for MC-FMF with respect to the CMF value of conventional single mode fiber (Dcl = 125 µm, Aeff = 80 µm2). The RCMF can be expressed as [25]:The value of CMF and RCMF for the proposed 13-core 5-LP mode fiber are nearly 0.49 and 75.17 respectively, which is more than that report in [7] (CMF=0.42 and RCMF=64.4 for 12-core 5-LP mode).
Finally, we summarize the performance of 13-core 5-LP mode fiber with stairway-index trench structure in Table 4.
Many years of experience in fiber preparation tells us that doping will reduce the softening temperature of glass. If the silica layer is used as the transition layer, the softening temperature difference between the high-doped core, the silica layer and the low-doped trench is larger, which will increase the difficulty of drawing multi-core fiber. The abrupt change of softening temperature near each core area is very unfavorable to the maintenance of structure during the preparation of multi-core fiber. Using transitional trench W1 and W2 instead of thin silica layer can make the softening temperature evenly distributed between the core and trench, which is conducive to multi-core fiber’s drawing. The use of 19-core structure design can indeed improve the RCMF of multi-core fiber [26,27], but the 13-core structure in our design has some advantages in the actual preparation process. Considering the practical application of multi-core fiber in the future, the corresponding multi-core erbium-doped fiber amplifier must be developed. The 13-core erbium-doped fiber with similar core distribution is easier to achieve balanced pumping among these multiple cores. The main reason is that the outer two-layer cores can be regarded as the outer cores in the 13-core fiber arrangement designed in this paper, which is conducive to achieve more balanced side pumping of the corresponding 13-core erbium-doped fiber. In the future, the 13-core fiber is convenient for docking with erbium-doped 13-core fiber amplifier.
7. Conclusion
We propose a manufacturable low-crosstalk 13-core 5-LP mode fiber with graded-index and stairway-index trench structure in this paper. In order to suppress crosstalk and meet the actual preparation conditions, we adopt the high doped graded-index core and design the stairway-index trench structure to obtain low-crosstalk characteristics and satisfy the long-distance transmission conditions. MDGD is kept at a large level to effectively suppress inter-mode crosstalk and maintain mode independence. By the using FEM, we find that the 13-core 5-LP mode fiber with stairway-index trench structure achieves a ICXT of lower than −30 dB/km (Rb≤500mm), the max MDGD over C + L band of 8.5 ps/m and RCMF of 75.17. Considering the cutoff wavelength (λcc) would degrade due to bending and environmental reasons in the actual laying of the optical fiber. Therefore, while ensuring the low loss of LP31 mode, we tried to increase the loss of LP12 mode to ensure that the unwanted LP12 mode could be lost in the transmission. The dispersion characteristic also has been analyzed with respect to wavelength, which shows that the dispersion value of each mode is maintained at the normal level. The perform of 13-core 5-LP mode fiber with stairway-index trench structure can be fabricated by MCVD, in-tube method and Perforating methods. The result show that our proposed fiber can satisfy the actual transmission conditions, and can effectively increase the transmission capacity of information.
Funding
National Key Research and Development Program of China (2019YFB2204001); National Natural Science Foundation of China (12074331); the Program of the Natural Science Foundation of Hebei Province (F2017203110, F2017203193, F2020203050); the Postdoctoral preferred funding research project of Hebei Province (B2018003008).
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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