Multi-core optical fiber and its design method

Abstract

The purpose of this invention is to provide a multi-core optical fiber and its design method, which can extend the transmission wavelength range and reduce crosstalk to prolong the transmission distance. The multi-core optical fiber of this invention has four cores arranged in a square lattice along its length. Its key feature is that the outer periphery of each core has a cladding region with an absolute value Δ of the relative refractive index difference with respect to the cores and a refractive index lower than that of the cores; the diameter of the cladding region is 125±1μm; the cutoff wavelength is 1.45μm or less; the mode field diameter (MFD) at wavelength 1.55μm is 9.5~10.0μm; the bending loss at wavelength 1.625μm and a bending radius of 30mm is 0.1dB / 100turn or less; and the inter-core crosstalk at wavelength 1.625μm is -47dB / km or less.

Description

Technical Field

[0001] This disclosure relates to multi-core optical fibers and their design methods. Background Technology

[0002] Multi-core fiber (MCF) with multiple core regions is actively being explored for its potential to significantly increase transmission capacity based on spatial division multiplexing (SDM) technology. In particular, MCFs with standard cladding diameters that utilize fiber manufacturability and high interchangeability with existing standard technologies have attracted considerable attention in recent years. Non-Patent Document 2 demonstrates the use of a trench-type refractive index distribution with strong optical closure to configure four identical cores. Furthermore, Patent Document 2 and Non-Patent Document 1 propose standard cladding diameter MCFs with a step-index (SI) type refractive index distribution suitable for mass production. While these MCFs, like conventional SMFs, guarantee single-mode operation across all communication bands, Patent Document 1 also discloses an MCF that reduces crosstalk and enables long-distance transmission by limiting the single-mode operating region of each core to 1.530–1.625 μm.

[0003] On the other hand, with the aim of increasing the capacity of transmission systems, the expansion of the single-mode operating frequency band is being discussed. In international standardization discussions, in addition to considering wavelengths below 1.53 μm as transmission bands, the utilization of the S-band (1460–1530 nm) is also receiving considerable attention for further increasing capacity. Furthermore, although distributed Raman amplifiers are used in long-distance transmission, to obtain stable amplification characteristics, single-mode operation at a wavelength other than the signal wavelength, including the Raman pump light wavelength, is preferred.

[0004] Existing technical documents

[0005] Patent documents

[0006] Patent Document 1: Japanese Invention Patent No. 6560806

[0007] Non-patent literature

[0008] Non-patent literature 1: T. Matsui, et al., “Applicability of Step-Index Type StandardCling Multi-core Fiber to Full-Band Transmission” in Proc. ECOC, Dublin, Ireland, Sep, 2019, M.1.D.3.

[0009] Non-patent literature 2: T. Matsui, et al., “Design of multi-core fiber in 125μm cladding diameter with full compliance to conventional SMF,” in Proc. ECOC, Valencia, Spain, Sep. 2015, We. 4.3. Summary of the Invention

[0010] The problem the invention aims to solve

[0011] However, among the standard cladding diameter MCFs discussed so far, those types that can achieve single-mode operation in all communication bands suffer from limitations due to crosstalk, making it difficult to extend the transmission distance. Furthermore, in the MCF of Patent Document 1, the single-mode operating region is limited, making it impossible to guarantee single-mode operation below 1.53 μm wavelength, thus hindering the expansion of the aforementioned transmission bands (towards the S-band).

[0012] Therefore, in order to solve the above problems, the purpose of this invention is to provide a multi-core optical fiber and its design method, which can expand the transmission band and reduce crosstalk to extend the transmission distance.

[0013] The means used to solve the problem

[0014] To achieve the above objectives, the multi-core optical fiber of the present invention has a structure that satisfies the following conditions.

[0015] Specifically, the first multi-core optical fiber of the present invention is a multi-core optical fiber having four cores arranged in a square lattice along its length, characterized in that...

[0016] The outer periphery of the fiber core has a cladding region with an absolute value of Δ for the relative refractive index difference with respect to the fiber core and a refractive index lower than that of the fiber core.

[0017] The diameter of the cladding region is 125±1μm;

[0018] The cutoff wavelength is below 1.45 μm;

[0019] The mode field diameter (MFD) at a wavelength of 1.55 μm is 9.5–10.0 μm.

[0020] The bending loss at a wavelength of 1.625μm and a bending radius of 30mm is less than 0.1dB / 100turns;

[0021] The crosstalk between fiber cores at a wavelength of 1.625 μm is below -47 dB / km.

[0022] The first multi-core optical fiber is characterized in that the shortest distance from the center of the fiber core to the outer periphery of the cladding region is more than 33 μm, and the radius a of the fiber core and the relative refractive index difference Δ between the fiber core and the cladding region are within the range of mathematical formula C1.

[0023] [Mathematical expression C1]

[0024]

[0025] Furthermore, the second multi-core optical fiber of the present invention is a multi-core optical fiber having four cores arranged in a square lattice along its length, characterized in that...

[0026] It has a first cladding region and a second cladding region. The first cladding regions respectively surround each of the fiber cores, and the second cladding regions surround all four first cladding regions. The refractive index increases in the order of the fiber core, the second cladding region, and the first cladding region. The relative refractive index difference between the fiber core and the first cladding region is less than 0.8%, and the ratio of the diameter of the fiber core to the diameter of the first cladding region is in the range of 2.0 to 3.0.

[0027] The diameter of the cladding region, including the first cladding region and the second cladding region, is 125±1μm;

[0028] The cutoff wavelength is below 1.45 μm;

[0029] The mode field diameter (MFD) at a wavelength of 1.55 μm is 9.5–11.4 μm.

[0030] The bending loss at a wavelength of 1.625μm and a bending radius of 30mm is less than 0.1dB / 100turns;

[0031] The crosstalk between fiber cores at a wavelength of 1.625 μm is below -54 dB / km.

[0032] The second multi-core optical fiber is characterized in that the radius a of the fiber core, the relative refractive index difference Δ between the fiber core and the first cladding region, and the relative refractive index difference Δ2 between the fiber core and the second cladding region satisfy the conditions of mathematical formulas C2 to C4.

[0033] [Mathematical expression C2]

[0034] 0.0003a 2 -0.0024a+0.0079≤Δ≤0.0005a 2 -0.0032a+0.0094 (C2)

[0035] [Mathematical expression C3]

[0036] (0.0013MFD 2 -0.0296MFD+0.1735)(a2 / a) 2 +(-0.0129MFD 2 +0.2885MFD-1.6141)(a2 / a)+(0.0419MFD 2 -0.9096MFD+4.9388)≤Δ≤-0.0015MFD+0.0223 (C3)

[0037] [Mathematical expression C4]

[0038] (0.0026MFD 2 -0.0573MFD+0.31)(a2 / a) 2 +(-0.0124MFD 2 +0.2683MFD-1.4515)(a2 / a)+(0.0141MFD 2 -0.3045MFD+1.6488)≤Δ2≤(0.002MFD 2 -0.0422MFD+0.2215)(a2 / a) 2 +(-0.0098MFD 2 +0.205MFD-1.0734)(a2 / a)+(0.012MFD 2 -0.2533MFD+1.3312) (C4)

[0039] Where a2 is the radius of the first cladding layer (μm), and MFD is the desired mode field diameter (μm).

[0040] Furthermore, the third multi-core optical fiber of the present invention is characterized in that, within the first cladding region, it further comprises: a third cladding region having a refractive index approximately the same as that of the second cladding region and surrounding the fiber core.

[0041] The first to third multi-core optical fibers of the present invention are characterized in that they further have a coating layer surrounding the cladding region, and the diameter including the coating layer is 200±20μm.

[0042] The design method for this multi-core optical fiber is characterized by having four cores arranged in a square lattice along its length.

[0043] In the optical property analysis of optical fiber using the finite element method, the mode field diameter MFD, cutoff wavelength λc, and bending loss αb are calculated while changing the radius a of the fiber core and the absolute value Δ of the relative refractive index difference between the fiber core and the cladding region.

[0044] In the graph of the radius a of the fiber core and the absolute value Δ of the relative refractive index difference, the curves of the desired mode field diameter MFD, the desired cutoff wavelength λc, and the desired bending loss αb are recorded; and,

[0045] The absolute value Δ of the radius a of the fiber core within the region enclosed by the curve and the relative refractive index difference is taken as the design value of the multi-core optical fiber.

[0046] Furthermore, the above inventions can be combined as much as possible.

[0047] Invention Effects

[0048] This invention provides a multi-core optical fiber and its design method, which can expand the transmission band and reduce crosstalk to extend the transmission distance. Attached Figure Description

[0049] Figure 1 This is a diagram illustrating the structure of the multi-core optical fiber of the present invention.

[0050] Figure 2 This is a diagram illustrating the relationship between the structural parameters and optical properties of the multi-core optical fiber of the present invention.

[0051] Figure 3 This is a graph illustrating the relationship between mode field diameter (MFD), required cladding thickness (minimum OCT), and crosstalk (XT) in the multi-core optical fiber of the present invention.

[0052] Figure 4 This is a diagram illustrating the structure of the multi-core optical fiber of the present invention.

[0053] Figure 5 This is a diagram illustrating the structural conditions of the multi-core optical fiber of the present invention.

[0054] Figure 6 This is a diagram illustrating the structural conditions of the multi-core optical fiber of the present invention.

[0055] Figure 7 This is a diagram illustrating the structural conditions of the multi-core optical fiber of the present invention.

[0056] Figure 8 This is a diagram illustrating the structural conditions of the multi-core optical fiber of the present invention.

[0057] Figure 9 This is a diagram illustrating the structural conditions of the multi-core optical fiber of the present invention.

[0058] Figure 10 This is a diagram illustrating the structural conditions of the multi-core optical fiber of the present invention.

[0059] Figure 11 This is a diagram illustrating the structural conditions of the multi-core optical fiber of the present invention.

[0060] Figure 12 This is a diagram illustrating the structural conditions of the multi-core optical fiber of the present invention.

[0061] Figure 13 This is a diagram illustrating the structural conditions of the multi-core optical fiber of the present invention.

[0062] Figure 14 This is a diagram illustrating the structure of the multi-core optical fiber of the present invention.

[0063] Figure 15 This is a diagram illustrating the structure of the multi-core optical fiber of the present invention.

[0064] Figure 16 This is a flowchart illustrating the design method of the present invention.

[0065] Figure 17 This is a flowchart illustrating the design method of the present invention. Detailed Implementation

[0066] Embodiments of the present invention will be described with reference to the accompanying drawings. The embodiments described below are examples of the present invention, and the present invention is not limited to the embodiments described below. Furthermore, in this specification and the accompanying drawings, the same structural elements are designated by the same reference numerals to indicate the same structural elements.

[0067] (Implementation Method 1)

[0068] Figure 1 This is a diagram illustrating the structure of the multi-core optical fiber 301 in this embodiment. Figure 1 (a) is a cross-sectional view of the multi-core optical fiber 301. Figure 1 (b) is a diagram illustrating the refractive index distribution near the core of the multi-core optical fiber 301. The multi-core optical fiber 301 is an MCF with a cladding 11 having a diameter of 125 ± 1 μm and four cores 12. The four cores 12 have approximately the same refractive index distribution, which is set to a step-index (SI) type or equivalent. Here, a is the core radius, and Δ is the relative refractive index difference between the core 12 and the cladding 11. By making all cores 12 of type SI or equivalent refractive index distribution, the mass production and yield of the multi-core optical fiber 301 can be significantly improved.

[0069] Figure 2 This is a characteristic graph showing the relationship between the structural parameters and optical properties of MCF. In this characteristic graph, the horizontal axis represents the core radius *a*, and the vertical axis represents the relative refractive index difference *Δ*.

[0070] Solid lines represent the core structures used to obtain the specified mode field diameter (MFD). In this figure, structures with MFDs of 9.5 μm, 10.0 μm, and 11.4 μm at a wavelength of 1.55 μm are shown.

[0071] The dashed lines represent the fiber core structures used to obtain the specified cutoff wavelength λc. In this figure, structures with cutoff wavelengths λc of 1.45 μm, 1.48 μm, 1.51 μm, and 1.53 μm are shown.

[0072] The dotted lines represent the fiber core structure used to obtain the specified bending loss (αb). In this figure, a structure with a bending loss λc of 0.1 dB / 100 turns at a wavelength of 1.625 μm and a bending radius of 30 mm is shown.

[0073] in addition, Figure 2 This is a characteristic diagram obtained through numerical calculation (optical characteristic analysis of optical fiber using the finite element method). Specifically, this diagram is created by numerically calculating the MFD, cutoff wavelength λc, and bending loss αb while changing the core radius a and relative refractive index difference Δ of the MCF, and plotting the structure with the same values ​​(e.g., MFD = 9.5 μm) in the diagram.

[0074] In the SI type, the optical properties can be uniquely determined once the core structure is determined; for example, to obtain an MCF with the same MFD (=9.5μm [wavelength 1.55μm]) and bending loss αb (=0.1dB / 100turn) as the SMF, and a cutoff wavelength λc below 1.45μm, let's say... Figure 2 The core structure can be determined by the area enclosed by the solid, dashed, and dotted lines of each value, including the core radius a and the relative refractive index difference Δ.

[0075] Specifically, in order to obtain an MFD of 9.5 μm or more at a wavelength of 1.55 μm, the following solid line is defined as [Mathematical Formula 1].

[0076] [Mathematical Expression 1]

[0077] Δ≤0.0005a 2 -0.0032a+0.0094 (1)

[0078] Furthermore, in order to make the cutoff wavelength λc below 1.45 μm, it is set as the dashed line in the following [Mathematical Equation 2].

[0079] [Mathematical Expression 2]

[0080] Δ≤0.0874a -2 (2)

[0081] Furthermore, in order to set the bending loss at a wavelength of 1.625μm and a bending radius of 30mm to be below 0.1dB / 100turn, the following [Mathematical Equation 3] is used as the dotted line.

[0082] [Mathematical Expression 3]

[0083] Δ≥0.0101a -758 (3)

[0084] Next, the method for detecting the upper limit of MFD and the necessary cladding thickness (minimum OCT) is explained. Minimum OCT refers to the shortest distance between the center of the outermost core and the outer periphery of the cladding at an additional loss of less than 0.01 dB / km at a wavelength of 1.625 μm. Figure 3 This is a graph illustrating the relationship between the cutoff wavelength λc, MFD, minimum OCT, and crosstalk XT in multi-core fiber 301. Here, crosstalk XT is the value at wavelength 1.625 μm, and MFD is the value at wavelength 1.55 μm. Figure 3 This is a characteristic diagram obtained through numerical calculation (optical characteristic analysis of optical fiber using the finite element method). Specifically, this diagram is created by numerically calculating the crosstalk XT, minimum OCT, and cutoff wavelength λc while changing the MCF, and plotting the structure with the same cutoff wavelength λc value (e.g., λc = 1.45 μm).

[0085] according to Figure 3 The solid line represents the maximum MFD, which in turn increases the minimum OCT. According to... Figure 3 As shown by the dashed line, the larger the FD, the larger the XT. On the other hand, it can be seen that when the cutoff wavelength λc is shortened, the minimum OCT increases (solid line), but XT remains approximately constant (dashed line). Here, assuming a QPSK signal is used for transmission over 1000km, the required XT is -47dB / km. Figure 3 As shown by the dashed line, in order to achieve a cutoff wavelength λc below 1.45 μm at XT = -47 dB / km, the MFD needs to be below 10 μm (upper limit MFD = 10 μm). Furthermore, according to... Figure 3 The solid line indicates that in order to set the MFD to 10 μm and the cutoff wavelength λc to below 1.45 μm, the minimum OCT needs to be set to above 33 μm (the thickness of the cladding 11 from the center of the core 12 to the outer periphery of the MCF is above 33 μm).

[0086] Figure 2 The middle also drew according to Figure 3 The curve with an upper limit MFD of 10 μm is obtained (Mathematical Formula 4).

[0087] [Mathematical Expression 4]

[0088] Δ≥0.0004α 2 -0.003a+0.0091 (4)

[0089] Figure 2In the region enclosed by the curves with MFD = 9.5 μm, MFD = 10 μm, cutoff wavelength λc = 1.45 μm, and bending loss αb = 0.1 dB / 100 turns, the core radius a and relative refractive index difference Δ are contained within this region, and according to... Figure 3 The calculated minimum OCT of 33μm is used as the design value for multi-core optical fiber 301.

[0090] That is, the multi-core optical fiber 301 is characterized by including:

[0091] The cladding 11 in the cross-section has a diameter of 125±1μm; and,

[0092] Four fiber cores 12 are arranged in a square lattice pattern in the cladding in the cross section;

[0093] In the cross-section, the shortest distance (minimum OCT) from the center of the core 12 to the outer periphery of the cladding 11 is 33 μm or more; and,

[0094] The relationship between the radius a of the core 12 and the absolute value Δ of the relative refractive index difference between the core 12 and the cladding 11 satisfies mathematical equations 1 to 4.

[0095] Furthermore, the design method of multi-core optical fiber 301 is as follows: Figure 16 As shown. That is, this design method performs the following steps:

[0096] The cutoff wavelength, crosstalk upper limit, mode field diameter, and bending loss of the multi-core optical fiber are determined as specification values ​​(step S11).

[0097] The relationship between the mode field diameter and crosstalk at the cutoff wavelength of the specified value is shown in the diagram. Figure 3 (the second vertical axis), detect the corresponding mode field diameter corresponding to the upper limit value of the crosstalk of the specification value (step S12);

[0098] A graph showing the relationship between the mode field diameter at the cutoff wavelength of the specified value and the shortest distance (minimum OTC) from the center of the core to the outer periphery of the cladding in the cross-section of the multi-core optical fiber. Figure 3 (the first vertical axis), detect the minimum OTC corresponding to the corresponding mold field diameter (step S13);

[0099] Optical property diagram of the radius a of the fiber core and the absolute value Δ of the relative refractive index difference between the fiber core and the cladding. Figure 2 In the diagram, a first curve for the mode field diameter that satisfies the specified value, a second curve for the cutoff wavelength that satisfies the specified value, a third curve for the bending loss that satisfies the specified value, and a fourth curve for the corresponding mode field diameter are plotted (S14).

[0100] Detect the radius a of the fiber core and the absolute value Δ of the relative refractive index difference contained in the region enclosed by the first curve, the second curve, the third curve and the fourth curve in the optical characteristic diagram (step S15).

[0101] The detected minimum OTC, the core radius a, and the absolute value Δ of the relative refractive index difference are used as the design values ​​for the multi-core optical fiber (step S16).

[0102] (Implementation Method Two)

[0103] Figure 4 This is a diagram illustrating the structure of the multi-core optical fiber 302 in this embodiment. Figure 4 (a) is a cross-sectional view of the multi-core optical fiber 302. Figure 4 (b) is a diagram illustrating the refractive index distribution near the core of the multi-core optical fiber 302. The cladding diameter and the number of cores of the multi-core optical fiber 302 are related to... Figure 1 The multi-core fiber 301 is also 125±1μm long and has 4 cores, with each core having approximately the same refractive index distribution.

[0104] The multi-core optical fiber 302 has a first cladding region 11-1 and a second cladding region 11-2. The first cladding region 11-1 surrounds the fiber core 12 and the second cladding region 11-2 surrounds the first cladding region 11-1. The refractive index decreases in the order of the fiber core 12, the second cladding region 11-2, and the first cladding region 11-1. This structure improves the control characteristics of optical confinement and enhances... Figure 3 The range and transmission distance of the MFD are shown.

[0105] Figure 5 This is an example of a structural condition used to obtain specified MFD, cutoff wavelength, and XT in multi-core optical fiber 302. Figure 5 This is a characteristic diagram obtained through numerical calculation (optical characteristic analysis of optical fiber using the finite element method). Specifically, this diagram is created for each MFD by changing the relative refractive index difference Δ of the MCF, while numerically calculating the relative refractive index difference Δ2, crosstalk XT, and cutoff wavelength λc. The diagram is then drawn with the same cutoff wavelength (λc = 1.45 μm) and the same crosstalk (XT = -54 dB / km). Figure 5 (a)~(c) respectively set the MFD at wavelength 1.55μm to 10.1μm, 10.7μm and 11.3μm, and a2 / a to 3.0 for each calculation.

[0106] exist Figure 5In the region on the origin side of the dashed line, the cutoff wavelength λc can be made below 1.45 μm. Furthermore, the core position (the radial position from the center of the MCF) is set such that the additional loss at wavelength 1.625 μm is below 0.01 dB / km. Figure 5 In the region opposite to the origin of the solid line, the XT at a wavelength of 1.625 μm is below -54 dB / km. Under this crosstalk XT condition, in addition to being able to extend the signal format to 16QAM over a transmission distance of 1000 km, the transmission distance can also be extended to approximately 5000 km using QPSK signals.

[0107] according to Figure 5 (a) to Figure 5 (c) It can be seen that the structural condition for obtaining a cutoff wavelength below 1.45 μm is: for each MFD, there is an upper limit value Δmax of the relative refractive index difference Δ (the maximum value relative to the dashed horizontal axis), and the upper limit value Δmax decreases as the MFD increases.

[0108] Furthermore, the lower limit Δmin of the relative refractive index difference Δ that enables crosstalk XT to be below -54dB / km, and the range of the relative refractive index difference Δ2 (Δ2max-Δ2min) are determined based on the intersection of the solid and dashed lines.

[0109] In other words, Figure 5 This can be described as a diagram illustrating the range of relative refractive index differences Δ and Δ2 that can be achieved for each MFD with a cutoff wavelength λc below 1.45 μm and a crosstalk XT below -54 dB / km.

[0110] Figure 6 This also illustrates an example of the structural conditions used to obtain the specified MFD, cutoff wavelength, and XT in multi-core optical fiber 302. Figure 6 The characteristic diagram was also obtained through numerical calculation (optical characteristic analysis of optical fiber using the finite element method). Specifically, this diagram was created for each MFD by changing the relative refractive index difference Δ of the MCF, while numerically calculating the relative refractive index difference Δ2, crosstalk XT, and cutoff wavelength λc, and plotting structures with the same cutoff wavelength (λc = 1.45 μm) and the same crosstalk (XT = -54 dB / km). Figure 6 In (a) to (c), a² / a is set to 3.0, 2.5, and 2.0 respectively, and the MFD at a wavelength of 1.55 μm is set to 10.1 μm for all calculations. Furthermore, Figure 6 (a) is related to Figure 5 (a) Same content.

[0111] The maximum value of the relative refractive index difference Δ along the horizontal axis is 0.8%. This is because, when the core is made of pure quartz glass, it is generally difficult to reduce the refractive index of the cladding by more than 0.8% relative to the refractive index of the core. Although... Figure 6 (b) and Figure 6 (c) When a2 / a is 2 or 2.5, Δmax becomes 0.8% or higher. However, for the reasons mentioned above, pursuing Δmax above 0.8% is meaningless, so it is omitted in this figure.

[0112] like Figure 6 (a) to Figure 6 As shown in (c), if a2 / a decreases, Δmin increases. On the other hand, it can be seen that the range of the relative refractive index difference Δ2 (Δ2max-Δ2min) decreases.

[0113] according to Figure 5 as well as Figure 6 Therefore, we can conclude that:

[0114] (1) Δmax is determined by the structural condition a2 / a = 3.0 (a2 / a = 2.5 or 2.0 is meaningless since it exceeds 0.8%).

[0115] (2) The ranges of Δmin and Δ2 can be defined as functions of a2 / a and MFD.

[0116] Figure 7 This is a diagram illustrating the relationship between the range of MFD and Δ in multi-core optical fiber 302. Considering the above (1), let a2 / a = 3.0. Figure 5 The upper limit (Δmax) and lower limit (Δmin) of Δ shown are expressed as functions of the MFD with a wavelength of 1.55 μm. According to... Figure 7 Δmax decreases linearly with respect to MFD as shown in the following equation.

[0117] [Mathematical Expression 5]

[0118] Δ≤-0.0015MFD+0.0223 (5)

[0119] In addition, it satisfies that λc is below 1.45 μm and XT is below -54 dB / km. Figure 5 The maximum MFD (as described in the text) is the intersection of Δmax and Δmin, i.e., MFD = 11.4 μm. Figure 2 The curve of the maximum MFD is also recorded (Mathematical Formula 6).

[0120] [Mathematical Expression 6]

[0121] Δ≥0.0003a 2 -0.0024a+0.0079 (6)

[0122] exist Figure 4 In the MCF structure, the shape of the electric field distribution (MDF) is dominated by the radius 'a' of the core 12 and the relative refractive index difference 'Δ' between the core 12 and the first cladding 11-1. Therefore, using Figure 2 The conditions for finding the radius a and the relative refractive index difference Δ of the fiber core 12 can be determined.

[0123] In other words, when a² / a = 3.0, in Figure 2 In the MDF curve, the core radius *a* and relative refractive index difference *Δ* within the region enclosed by the curves with MFD = 9.5 μm and MFD = 11.4 μm become the design values ​​for the multi-core fiber 302 calculated from the MDF. Furthermore, in... Figure 4 In the MCF structure, since the cutoff wavelength λc and bending loss αb vary depending on the relative refractive index difference Δ2, they are not considered. Figure 2 The dashed and dotted lines.

[0124] Therefore, according to Figure 2 The ranges of the calculated core radius a and relative refractive index difference Δ are limited as follows.

[0125] (a) The upper limit of the relative refractive index difference Δmax

[0126] Equation 5 represents the change of Δmax relative to MFD when a² / a = 3.0. For different values ​​of a² / a, different mathematical expressions apply. However, according to... Figure 5 and Figure 6 It can be determined that if a² / a is less than 3.0, then Δmax will increase, exceeding 0.8%. As mentioned above, a structure with Δ exceeding 0.8% is unrealistic. Therefore, if we define mathematical formula 5 when a² / a = 3.0... Figure 7 If the straight line in the equation is taken as the upper limit of Δ, then even if a2 / a is other values, the result of mathematical formula 5 can still be applied.

[0127] (b) Regarding the lower limit Δmin of the relative refractive index difference Δ

[0128] like Figure 6 As shown, if a² / a is less than 3.0, then Δmin increases. That is, for Δmin, since if a² / a is less than 3.0, then... Figure 7 The curve shown rises, therefore, the result of Equation 5 cannot be applied to a2 / a relative to other values ​​(the curve of Δmin varies with each a2 / a).

[0129] Figure 8 This illustrates the curve for Δmin calculated according to each a2 / a( Figure 7 The graph shows the changes in the curve. In detail, Figure 8This is a graph showing the variation of Δmin relative to a² / a of multi-core fiber 302, expressed for each MFD at a wavelength of 1.55 μm. (See figure.) Figure 5 as well as Figure 6 As shown, Δmin varies according to a2 / a and MFD. Wherein, according to Figure 8 Consider using a² / a and MFD to represent the variation of Δmin.

[0130] Figure 9 To be Figure 8 The relationship between a2 / a and Δmin shown in the figure is represented by a quadratic function (k1x). 2 A graph showing the coefficients (k1, k2, k3) expressed as a function of MFD when x is approximated by a2 / a). Based on these results, the lower limit Δmin is given by the following equation.

[0131] [Mathematical Expression 7]

[0132]

[0133] In other words, Figure 7 The curve for Δmin varies with a2 / a. Furthermore, the maximum value of MFD (11.4 when a2 / a = 3.0) also varies with a2 / a.

[0134] Furthermore, the multi-core fiber 302 also has a parameter of Δ2.

[0135] (b) Regarding the upper limit of the relative refractive index difference Δ2, Δ2max

[0136] Figure 10 It is used to illustrate that Δ2max varies with each a2 / a (in Figure 6 The graph shows the changes in Δ2max in (a) to (c). In detail, Figure 10 This is a graph showing the variation of Δ2max relative to a2 / a of multi-core fiber 302, expressed for each MFD at a wavelength of 1.55 μm. (See figure.) Figure 5 as well as Figure 6 As shown, Δ2_max varies according to a2 / a and MFD. Wherein, according to Figure 10 Consider using a2 / a and MFD to represent the variation of Δ2max.

[0137] Figure 11 To be Figure 10 The graph shown illustrates the relationship between a² / a and Δ²max when approximated by a quadratic function (k₁x² + k₂x + k₃; x is a² / a), and represents the coefficients (k₁, k₂, k₃) as functions of MFD. Based on these results, the upper limit Δ²max is given by the following equation.

[0138] [Mathematical Expression 8]

[0139]

[0140] (d) Regarding the lower limit Δ2min of the relative refractive index difference Δ2

[0141] Figure 12 It is used to illustrate that Δ2min varies with each a2 / a (in Figure 6 The graph shows the changes in Δ2min in (a) to (c). In detail, Figure 12 This is a graph showing the variation of Δ2min relative to a2 / a of multi-core fiber 302, expressed for each MFD at a wavelength of 1.55 μm. (See figure.) Figure 5 as well as Figure 6 As shown, Δ2min varies according to a2 / a and MFD. Wherein, according to Figure 12 Consider using a2 / a and MFD to represent the variation of Δ2min.

[0142] Figure 13 To be Figure 12 The relationship between a2 / a and Δ2min shown in the figure is represented by a quadratic function (k1x). 2 A graph showing the coefficients (k1, k2, k3) expressed as a function of MFD when x is approximated by a2 / a). Based on these results, the lower limit Δ2min is given by the following equation.

[0143] [Mathematical Expression 9]

[0144]

[0145] As described above, in the structure of the multi-core optical fiber 302, although in Figure 2 The cutoff wavelength λc (dashed line) and bending loss αb (dotted line) are not considered. However, according to mathematical formulas 8 and 9, the range of the relative refractive index difference Δ2 is limited, and the cutoff wavelength λc is below 1.45 μm.

[0146] That is, the multi-core optical fiber 302 is characterized by including:

[0147] Cladding 11 with a diameter of 125±1μm in the cross section; and,

[0148] In the cross section, four fiber cores 12 are configured in a square lattice pattern in the cladding 11;

[0149] The cladding 11 is composed of a first cladding 11-1 surrounding each fiber core 12 and a second cladding 11-2 surrounding all the first cladding 11-1;

[0150] The refractive index is highest in the core (12) and lowest in the first cladding (11-1).

[0151] The relationship between the radius a (μm) of the core 12 and the absolute value Δ of the relative refractive index difference between the core 12 and the first cladding 11-1 satisfies the mathematical formula C2;

[0152] The absolute value Δ of the relative refractive index difference satisfies the mathematical formula C3;

[0153] Furthermore, the absolute value Δ2 of the relative refractive index difference between the second cladding 11-2 and the fiber core 12 satisfies the mathematical formula C4;

[0154] [Mathematical expression C2]

[0155] 0.0003a 2 -0.0024a+0.0079≤Δ≤0.0005a 2 -0.0032a+0.0094 (C2)

[0156] [Mathematical expression C3]

[0157] (0.0013MFD 2 -0.0296MFD+0.1735)(a2 / a) 2 +(-0.0129MFD 2 +0.2885MFD-1.6141)(a2 / a)+(0.0419MFD 2 -0.9096MFD+4.9388)≤Δ≤-0.0015MFD+0.0223 (C3)

[0158] [Mathematical expression C4]

[0159] (0.0026MFD 2 -0.0573MFD+0.31)(a2 / a) 2 +(-0.0124MFD 2 +0.2683MFD-1.4515)(a2 / a)+(0.0141MFD 2 -0.3045MFD+1.6488)≤Δ2≤(0.002MFD 2 -0.0422MFD+0.2215)(a2 / a) 2 +(-0.0098MFD 2 +0.205MFD-1.0734)(a2 / a)+(0.012MFD ２ -0.2533MFD+1.3312) (C4)

[0160] Where a2 is the radius (μm) of the first cladding 11-1, and MFD is the desired mode field diameter (μm).

[0161] In addition, the design method of multi-core optical fiber 302 is as follows: Figure 17 As shown. That is, this design method performs the following steps:

[0162] The cutoff wavelength λc, the upper limit of crosstalk XT, the mode field diameter MFD, and the bending loss αb of the multi-core optical fiber 302 are determined as the specified values ​​(step S21).

[0163] A graph showing the relationship between the absolute value of the relative refractive index difference Δ between the fiber core and the first cladding, the absolute value of the relative refractive index difference Δ2 between the fiber core and the second cladding, the mode field diameter MFD, and the ratio (a2 / a) of the radius a of the fiber core to the radius a2 of the first cladding. Figure 5 as well as Figure 6 In the diagram, a region with a wavelength shorter than the cutoff wavelength of the specified value and below the upper limit of the crosstalk of the specified value is drawn (step S22).

[0164] The maximum and minimum values ​​of the absolute values ​​of the relative refractive index difference between the fiber core and the first cladding are detected in the region containing the ratio (a2 / a) of any temporarily determined arbitrary ratio of the radius of the fiber core to the radius of the first cladding (steps S23, S24; for Δmin, the relationship between MFD and a2 / a can be expressed by mathematical formula 7).

[0165] The graph of MFD and Δ shows the variation curves of Δmax and Δmin relative to the change of MFD, and the corresponding MFD when the variation curves intersect is detected (step S25).

[0166] In the optical characteristic diagram of the radius a of the fiber core and the absolute value Δ of the relative refractive index difference between the fiber core and the cladding, a first curve satisfying the specified value of the mode field diameter and a second curve satisfying the corresponding mode field diameter are plotted (step S26).

[0167] Detect the absolute value Δ of the difference between the radius a of the fiber core and the relative refractive index in the region enclosed by the first curve and the second curve in the optical characteristic diagram (step S27);

[0168] Calculate the range of absolute values ​​Δ of the relative refractive index difference that satisfy mathematical formula C3 within the region enclosed by the first curve and the second curve (step S28).

[0169] Substitute the absolute value Δ of the relative refractive index difference contained in the region enclosed by the first curve and the second curve and the arbitrary ratio (a2 / a) into mathematical formula C4 to calculate the range of the absolute value Δ2 of the relative refractive index difference between the second cladding and the fiber core (step S29).

[0170] Furthermore, the detected radius a of the fiber core, the ratio (a2 / a), the range of the absolute value Δ of the relative refractive index difference, and the range of the absolute value Δ2 of the relative refractive index difference between the second cladding and the fiber core are used as the design values ​​for the multi-core optical fiber (step S30).

[0171] Alternatively, if the design value is not obtained in step S30, change a2 / a and repeat the operation starting from step S23.

[0172] (Implementation Method 3)

[0173] Figure 14 This is a diagram illustrating the structure of the multi-core optical fiber 303 in this embodiment. Figure 14 (a) is a cross-sectional view of multi-core optical fiber 303. Figure 14 (b) is a diagram illustrating the refractive index distribution near the core of the multi-core optical fiber 303. The cladding diameter and the number of cores of the multi-core optical fiber 303 are related to... Figure 1 The multi-core fiber 301 is also 125±1μm long and has 4 cores, with each core having approximately the same refractive index distribution.

[0174] The multi-core optical fiber 303 has a third cladding region 11-3, a first cladding region 11-1, and a second cladding region 11-2. The third cladding region 11-3 surrounds the fiber core 12, the first cladding region 11-1 surrounds the third cladding region 11-3, and the second cladding region 11-2 surrounds the first cladding region 11-1. The refractive index decreases in the order of the fiber core 12, the second cladding region 11-2, and the first cladding region 11-1. The refractive index of the third cladding region 11-3 is the same as that of the second cladding region 11-2.

[0175] The cladding refractive index of multi-core fiber 303 is higher than that of multi-core fiber 302, resulting in increased parameters. Therefore, compared to multi-core fiber 302, multi-core fiber 303 can expand the MFD and reduce XT. In this case, if it is designed within the range of a, a2, Δ, Δ2 described in Embodiment 2, equivalent optical properties can be obtained, which is preferred.

[0176] (Implementation Method 4)

[0177] Figure 15 This is a diagram comparing the cross-sectional structures of multi-core optical fibers. Generally, from the point of view of ensuring mechanical reliability, optical fibers have a coating layer formed of resin or the like around the glass (cladding). Figure 15 (a) is a diagram illustrating a standard multi-core optical fiber with a diameter of 250±15μm containing the coating. Figure 15(b) is a diagram illustrating a multi-core optical fiber with a diameter of 200±20μm including the coating layer. It can be seen that even with a diameter of 200±20μm including the coating layer, mechanical reliability and loss characteristics can be maintained. Among the aforementioned multi-core optical fibers (301-303), by setting the diameter of the coating layer to 200±20μm, finer-diameter multi-core optical fibers can be installed in optical cables, enabling high-density, multi-core optical cables, and is therefore preferred.

[0178] [Postscript]

[0179] The key point of this invention is that, in a standard cladding diameter MCF, by setting the refractive index distribution and core position to predetermined conditions, it is possible to simultaneously achieve single-mode bandwidth expansion and crosstalk (XT) reduction. The specific multi-core fiber of this invention is shown below.

[0180] The first multi-core optical fiber is Figure 1 The structure includes:

[0181] A cladding layer with a diameter of 125±1μm in the cross-section; and,

[0182] Four fiber cores are configured in a square lattice pattern within the cladding in the cross section;

[0183] In the cross-section, the shortest distance from the center of the fiber core to the outer periphery of the cladding is 33 μm or more; and,

[0184] The relationship between the radius a (μm) of the fiber core and the absolute value Δ of the relative refractive index difference between the fiber core and the cladding satisfies the mathematical formula C1.

[0185] [Mathematical expression C1]

[0186]

[0187] Furthermore, the design method for the first multi-core optical fiber involves the following steps:

[0188] The cutoff wavelength, upper limit of crosstalk, mode field diameter, and bending loss of the multi-core optical fiber are determined as specification values.

[0189] The relationship between the mode field diameter and crosstalk at the cutoff wavelength of the specified value is shown in the diagram. Figure 3 The second vertical axis), detects the corresponding mode field diameter corresponding to the upper limit value of crosstalk with the specification value;

[0190] A graph showing the relationship between the mode field diameter at the cutoff wavelength of the specified value and the shortest distance (minimum OTC) from the center of the core to the outer periphery of the cladding in the cross-section of the multi-core optical fiber. Figure 3 (the first vertical axis), detect the minimum OTC corresponding to the corresponding mold field diameter;

[0191] Optical property diagram of the radius a of the fiber core and the absolute value Δ of the relative refractive index difference between the fiber core and the cladding. Figure 2 In the curve graph, a first curve for the mode field diameter that meets the specified value, a second curve for the cutoff wavelength that meets the specified value, a third curve for the bending loss that meets the specified value, and a fourth curve for the corresponding mode field diameter are plotted.

[0192] The radius a of the fiber core and the absolute value Δ of the relative refractive index difference are detected in the region enclosed by the first curve, the second curve, the third curve, and the fourth curve in the optical characteristic diagram.

[0193] The detected minimum OTC, the core radius a, and the absolute value Δ of the relative refractive index difference are used as the design values ​​for the multi-core optical fiber.

[0194] In addition, the second multi-core optical fiber is Figure 4 The structure is characterized by comprising:

[0195] A cladding layer with a diameter of 125±1 μm in the cross-section; and,

[0196] The cross-section contains four fiber cores arranged in a square lattice pattern within the cladding.

[0197] The cladding consists of a first cladding surrounding each of the fiber cores and a second cladding surrounding all of the first cladding;

[0198] The refractive index is highest in the fiber core and lowest in the first cladding.

[0199] The relationship between the radius a (μm) of the fiber core and the absolute value Δ of the relative refractive index difference between the fiber core and the first cladding satisfies the mathematical formula C2;

[0200] The absolute value Δ of the relative refractive index difference satisfies mathematical formula C3; and,

[0201] The absolute value Δ2 of the relative refractive index difference between the second cladding and the fiber core satisfies the mathematical formula C4.

[0202] [Mathematical expression C2]

[0203] 0.0003a 2 -0.0024a+0.0079≤Δ≤0.0005a 2 -0.0032a+0.0094 (C2)

[0204] [Mathematical expression C3]

[0205] (0.0013MFD 2-0.0296MFD+0.1735)(a2 / a) 2 +(-0.0129MFD 2 +0.2885MFD-1.6141)(a2 / a)+(0.0419MFD 2 -0.9096MFD+4.9388)≤Δ≤-0.0015MFD+0.0223 (C3)

[0206] [Mathematical expression C4]

[0207] (0.0026MFD 2 -0.0573MFD+0.31)(a2 / a) 2 +(-0.0124MFD 2 +0.2683MFD-1.4515)(α2 / a)+(0.0141MFD 2 -0.3045MFD+1.6488)≤Δ2≤(0.002MFD 2 -0.0422MFD+0.2215)(a2 / a) 2 +(-0.0098MFD 2 +0.205MFD-1.0734)(a2 / a)+(0.012MFD 2 -0.2533MFD+1.3312) (C4)

[0208] Where a2 is the radius of the first cladding layer (μm), and MFD is the desired mode field diameter (μm).

[0209] Furthermore, the design method for the second multi-core optical fiber performs the following steps:

[0210] The cutoff wavelength, upper limit of crosstalk, mode field diameter, and bending loss of the multi-core optical fiber are determined as specification values.

[0211] A graph showing the relationship between the absolute value of the relative refractive index difference Δ between the fiber core and the first cladding, the absolute value of the relative refractive index difference Δ2 between the fiber core and the second cladding, the mode field diameter MFD, and the ratio (a2 / a) of the radius a of the fiber core to the radius a2 of the first cladding. Figure 5 as well as Figure 6 In the diagram, the region that is shorter than the cutoff wavelength of the specified value and is below the upper limit of the crosstalk of the specified value is drawn.

[0212] The maximum value Amax and minimum value Δmin of the absolute value of the relative refractive index difference between the core and the first cladding are determined by detecting the ratio (a2 / a) of the core radius to the first cladding radius of any temporarily determined arbitrary region (MFD). (For Δmin, the relationship between MFD and a2 / a can be expressed by mathematical formula 7.)

[0213] The graph of MFD and Δ records the variation curves of Δmax and Δmin relative to the change of MFD, and detects the corresponding MFD when the variation curves intersect.

[0214] In the optical characteristic diagram of the radius a of the fiber core and the absolute value Δ of the relative refractive index difference between the fiber core and the cladding, a first curve satisfying the specified value of the mode field diameter and a second curve satisfying the corresponding mode field diameter are plotted.

[0215] The absolute value Δ of the difference between the radius a of the fiber core and the relative refractive index is detected in the region enclosed by the first curve and the second curve in the optical characteristic diagram.

[0216] Calculate the range of absolute values ​​Δ of the relative refractive index difference that satisfy mathematical formula C3 within the region enclosed by the first curve and the second curve.

[0217] Substituting the absolute value Δ of the relative refractive index difference within the region enclosed by the first curve and the second curve, and the arbitrary ratio (a² / a), into Equation 9, the range of the absolute value Δ² of the relative refractive index difference between the second cladding and the fiber core is calculated; and,

[0218] The detected radius a of the fiber core, the ratio (a2 / a), the range of the absolute value Δ of the relative refractive index difference, and the range of the absolute value Δ2 of the relative refractive index difference between the second cladding and the fiber core are used as the design values ​​for the multi-core optical fiber.

[0219] [Mathematical expression C3]

[0220] (0.0013MFD 2 -0.0296MFD+0.1735)(a2 / a) 2 +(-0.0129MFD 2 +0.2885MFD-1.6141)(a2 / a)+(0.0419MFD 2 -0.9096MFD+4.9388)≤Δ≤-0.0015MFD+0.0223 (C3)

[0221] [Mathematical expression C4]

[0222] (0.0026MFD 2 -0.0573MFD+0.31)(a2 / a) 2 +(-0.0124MFD 2 +0.2683MFD-1.4515)(a2 / a)+(0.0141MFD 2 -0.3045MFD+1.6488)≤Δ2≤(0.002MFD 2 -0.0422MFD+0.2215)(a2 / a) 2 +(-0.0098MFD 2 +0.205MFD-1.0734)(a2 / a)+(0.012MFD 2 -0.2533MFD+1.3312) (C4)

[0223] Where a2 is the radius of the first cladding layer (μm), and MFD is the desired mode field diameter (μm).

[0224] (Effect)

[0225] This invention enables the extension of the single-mode wavelength band to the S-band with low XT for an MCF having a standard cladding diameter.

[0226] Explanation of reference numerals in the attached figures

[0227] 11: Cladding

[0228] 11-1: First cladding

[0229] 11-2: Second cladding

[0230] 11-3: Third cladding

[0231] 12: Fiber Core

[0232] 301~303: Multi-core optical fiber.

Claims

1. A multi-core optical fiber, characterized in that it has four cores arranged in a square lattice along its length, and is further characterized in that... It has a first cladding region and a second cladding region. The first cladding regions respectively surround each of the fiber cores, and the second cladding regions surround all four first cladding regions. The refractive index increases in the order of the fiber core, the second cladding region, and the first cladding region. The relative refractive index difference between the fiber core and the first cladding region is less than 0.8%, and the ratio of the diameter of the fiber core to the diameter of the first cladding region is in the range of 2.0 to 3.

0. The diameter of the cladding region, including the first cladding region and the second cladding region, is 125±1μm; The cutoff wavelength is below 1.45 μm; The mode field diameter (MFD) at a wavelength of 1.55 μm is 9.5~11.4 μm; The bending loss at a wavelength of 1.625μm and a bending radius of 30mm is less than 0.1dB / 100turns; The crosstalk between fiber cores at a wavelength of 1.625 μm is below -54 dB / km; The radius a of the fiber core, the relative refractive index difference Δ between the fiber core and the first cladding region, and the relative refractive index difference Δ2 between the fiber core and the second cladding region satisfy the conditions of mathematical formulas C2 to C4. [Mathematical expression C2] [Mathematical expression C3] [Mathematical expression C4] Where a is in μm; a2 is the radius of the first cladding layer in μm; and MFD is the desired mode field diameter in μm.

2. The multi-core optical fiber according to claim 1, characterized in that, Within the first cladding region, there is also a third cladding region with a refractive index approximately the same as that of the second cladding region, which surrounds the fiber core.

3. The multi-core optical fiber according to claim 1 or 2, characterized in that, It also has a coating layer surrounding the cladding region, the diameter of which, including the coating layer, is 200±20μm.

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