Coupling type multicore optical fiber

Abstract

A coupling-type multicore optical fiber (10) comprises a cladding (11) and a plurality of step-index-type cores (12) provided in the cladding (11). The core radius of each core (12) and the relative refractive index difference between each core (12) and the cladding (11) are set to values such that the bending loss under bending conditions for which the recommendation of ITU-T G.652 is applied is less than or equal to a bending loss stipulated by the recommendation.

Description

Coupled multi-core optical fiber

[0001] The present disclosure relates to coupled multi-core optical fibers.

[0002] Space division multiplexing (SDM) technology using multicore optical fibers is being investigated as one of the transmission technologies for optical transmission systems that will support next-generation high-capacity communications. Coupled multicore fibers (C-MCFs) are a type of multicore optical fiber that allows mode coupling between cores. Since the spacing between adjacent cores can be shortened in coupled multicore fibers, multiple cores can be densely packed without increasing the outer diameter of the cladding. Furthermore, mode-coupled optical signals can be compensated for using MIMO (Multiple-Input Multiple-Output) signal processing technology. This reduces the differential mode group delay (i.e., spatial mode dispersion) and reduces the load of MIMO signal processing.

[0003] R. Imada, T. Sakamoto, T. Mori, Y. Yamada, and K. Nakajima, “Unique Bending Loss Properties and Design Consideration for Coupled Multi-core Fiber,” in Optical Fiber Communication Conference (OFC), 2023, p. M3B.1.B. Huang et al., “Minimizing the Modal Delay Spread in Coupled-Core Two-Core Fiber,” in Conference on Lasers and Electro-Optics (CLEO), 2016, p. STu1F.3.

[0004] According to Non-Patent Document 1, assuming the same core radius and relative refractive index difference, the bending loss of a coupled multi-core optical fiber is worse than that of a single-mode optical fiber at any bending radius. In this case, during wiring and installation work, the fiber needs to be handled differently from a single-mode optical fiber, for example, to prevent unnecessary excessive bending, which makes the work more complicated.

[0005] The present disclosure has been made in view of the above circumstances, and aims to provide a multi-core optical fiber that can be handled in the same manner as a single-mode optical fiber during wiring, installation, and other work.

[0006] A coupled multi-core optical fiber according to one aspect of the present disclosure includes a cladding and a plurality of step-index cores provided in the cladding, wherein the core radius of each of the cores and the relative refractive index difference between each of the cores and the cladding are set to values ​​such that the bending loss under bending conditions, to which the bending loss specified in the ITU-T G.652 Recommendation is applied mutatis mutandis, is equal to or less than the bending loss (macrobending loss) specified in the Recommendation.

[0007] According to the present disclosure, it is possible to provide a multi-core optical fiber that can be handled in the same manner as a single-mode optical fiber during wiring, installation, and other work.

[0008] FIG. 1A is a diagram showing an example of a cross section of a C-MCF 10 according to an embodiment of the present disclosure. FIG. 1B is a diagram showing an example of a cross section of a C-MCF 10 according to the present embodiment. FIG. 1C is a diagram showing an example of a cross section of a C-MCF 10 according to the present embodiment. FIG. 1D is a diagram showing an example of a cross section of a C-MCF 10 according to the present embodiment. FIG. 2 is a graph for explaining the set value of the core spacing Λ. FIG. 3A is a diagram showing an example of a first curve in a-Δ space. FIG. 3B is a diagram showing an example of a second curve in a-Δ space. FIG. 3C is a diagram showing an example of a third curve in a-Δ space. FIG. 3D is a diagram showing a region surrounded by the first curve, the second curve, and the third curve. FIG. 4 is a diagram showing the first and second curves when the core spacing Λ is set to 14 μm, 20 μm, and 25 μm under the condition that the number of cores n is 2 and the cutoff wavelength is 1.53 μm. FIG. 5 is a graph showing the first and second curves when the cutoff wavelength is 1.53 μm, the core spacing Λ is set to a lower limit Λmin, and the number of cores n is set to 2, 4, 8, and 12. FIG. 6 is a table showing coefficients A, B, and C of a quadratic function approximating the first curve and coefficients D and E of a power function approximating the second curve when the cutoff wavelength is 1.53 μm. FIG. 7A is a graph showing the dependency of coefficient A on the number of cores n. FIG. 7B is a graph showing the dependency of coefficient B on the number of cores n. FIG. 7C is a graph showing the dependency of coefficient C on the number of cores n. FIG. 7D is a graph showing the dependency of coefficient D on the number of cores n. FIG. 7E is a graph showing the dependency of coefficient E on the number of cores n. FIG. 8 is a graph showing the first and second curves when the cutoff wavelength is 1.26 μm, the core spacing Λ is set to a lower limit Λmin, and the number of cores n is set to 2, 4, 8, and 12. FIG. 9 is a table showing coefficients D and E of the power function that approximates the second curve when a cutoff wavelength of 1.26 μm is assumed.

[0009] Hereinafter, embodiments of the present disclosure will be described with reference to the drawings. In the description of the drawings, identical parts are designated by the same reference numerals, and description thereof will be omitted. The optical fiber according to this embodiment is a coupled multi-core optical fiber that allows mode coupling between cores. For convenience of explanation, the coupled multi-core optical fiber will be referred to as a C-MCF. Furthermore, a single-mode optical fiber in which a single core is provided in a single cladding will be referred to as an SMF. Furthermore, the X and Y directions, which are orthogonal to each other, will be defined. The X and Y directions are parallel to a cross section that is orthogonal to the extension direction of the C-MCF.

[0010] First, a description will be given of the setting of the core interval (pitch) Λ. The core interval Λ is the distance between the centers of the two most adjacent cores 12 among the plurality of cores 12.

[0011] 1A to 1D are diagrams showing an example of a cross section of a C-MCF 10 according to this embodiment. As shown in these figures, the C-MCF 10 has a refractive index n ２ (see FIG. 1A) and a cladding 11 having a refractive index n １ and a plurality of cores 12 provided within the cladding 11.

[0012] As shown in Figure 1A, the core 12 has a radius a. Hereinafter, for convenience of explanation, the radius of the core 12 will be referred to as the core radius. The C-MCF 10 according to this embodiment is a step-index multi-core optical fiber. Therefore, the refractive index n of the core 12 １ is uniformly distributed in the core. The cladding 11 does not have any structure with other refractive indexes, such as a trench. Therefore, the refractive index n ２ is uniformly distributed within the cladding.

[0013] The C-MCFs 10 shown in Figures 1A, 1B, 1C, and 1D each include two cores 12, four cores 12, eight cores 12, and twelve cores 12, respectively. As shown in these figures, the multiple cores 12 are arranged at periodic positions, such as in a line, a ring, a square lattice, or a triangular lattice, depending on the number of cores n. Note that the multiple cores 12 shown in each figure are distributed so as to have a predetermined rotational symmetry around the center of the C-MCF 10. The positions of the cores 12 are arbitrary as long as the core spacing Λ that allows mode coupling can be maintained.

[0014] The cladding 11 may have the same outer diameter (OD) as the SMF. For example, the outer diameter (OD) of the cladding 11 may be set to a value that conforms to the International Telecommunication Union Telecommunication Standardization Sector recommendation G.652 (ITU-T G.652). That is, the ITU-T G.652 recommendation specifies the outer diameter of SMF as 125 μm with a tolerance of ±1 μm. Therefore, the cladding 11 may have an outer diameter (OD) of 125±1 μm. The outer peripheral surface 11a of the cladding 11 may be covered with at least one layer of coating (not shown). The coating (not shown) may be formed of, for example, resin and have a predetermined thickness. The following description will be given using an example in which the outer diameter (OD) is 125 μm.

[0015] 2 is a graph illustrating the set value of the core spacing Λ. As described above, the outer diameter OD of the cladding 11 is 125 μm regardless of the number of cores 12. On the other hand, when a large number of cores 12 are arranged while maintaining the outer diameter of the cladding 11 constant, there is a limit to the set value of the core spacing Λ.

[0016] This limitation is due to an excessive increase in leakage loss. If the number of cores 12 is increased while maintaining the core spacing Λ, the outermost cores 12 inevitably move closer to the outer peripheral surface 11 a of the cladding 11. In other words, the distance from the outermost cores 12 to the outer peripheral surface 11 a of the cladding 11 becomes shorter. The shorter this distance becomes, the greater the leakage loss becomes. Therefore, depending on the number of cores 12, it may be necessary to lower the upper limit of the core spacing Λ in order to keep the leakage loss at or below a desired value.

[0017] The diamond-shaped markers in Figure 2 indicate the core spacing Λ at which the leakage loss reaches the allowable upper limit. The core spacing Λ can be calculated using numerical analysis using the finite element method for several core numbers n. The curves along the markers in Figure 2 are obtained by curve fitting a quadratic function to the calculated core spacing Λ.

[0018] In this embodiment, the range of the core spacing Λ for each number of cores n is determined as follows: Lower limit Λmin = 14 μm Upper limit Λmax = 25 μm (n≦6) or (0.3046n ２ -7.163n+57.97) μm (n≧7) In FIG. 2, dashed line 21 indicates the above-mentioned lower limit Λmin for the number of cores n, and solid line 22 indicates the above-mentioned upper limit Λmax for the number of cores n.

[0019] According to Non-Patent Document 2, when the core spacing Λ is reduced to 12 μm, mode mixing is suppressed due to the increase in the difference in effective refractive index between each mode, resulting in insufficient coupling of optical signals between cores. Therefore, in this embodiment, the lower limit Λmin of the core spacing Λ is set to 14 μm, at which desired mode coupling is obtained. On the other hand, the upper limit of the core spacing Λ is set to 25 μm, which is considered to be the upper limit at which random mode coupling between cores is obtained.

[0020] The core spacing Λ according to this embodiment is set to a value within a region Ra below the solid line 22 and above the dashed line 21 in the graph shown in Fig. 2. By setting the core spacing Λ to a value within the region Ra, sufficient coupling efficiency between cores can be obtained, and the multi-core optical fiber functions as a coupled-type optical fiber.

[0021] Next, the setting of the core radius a and the relative refractive index difference Δ between the core 12 and the cladding 11 will be described. The core radius a and the relative refractive index difference Δ according to this embodiment are set to satisfy the bending characteristics in accordance with the ITU-T G.652 recommendation. That is, the core radius a and the relative refractive index difference Δ are set to values ​​such that the bending loss under the bending conditions in accordance with the ITU-T G.652 recommendation is equal to or less than the bending loss specified in the recommendation. The bending conditions refer to a state in which the C-MCF 10 is wound 100 times around a cylindrical member (mandrel) with a bending radius of 30 mm. The bending loss is the so-called macrobending loss, and is a value in which the loss (insertion loss) when light with a wavelength of 1625 nm is passed through is 0.1 dB or less. Hereinafter, for convenience of explanation, the above-described bending conditions specified in the ITU-T G.652 recommendation may be referred to as the "specified bending conditions."

[0022] As described in Non-Patent Document 1, the bending loss of a C-MCF may be higher than that of an SMF. In consideration of this tendency, the C-MCF 10 according to this embodiment has a core radius a and a relative refractive index difference Δ such that the bending loss under specified bending conditions is 0.1 dB or less. Furthermore, the cladding 11 according to this embodiment has the same outer diameter as the cladding of an SMF. Therefore, the C-MCF 10 has similar characteristics to conventional SMF in terms of bending loss and mechanical properties. Therefore, the C-MCF can be handled in the same way as conventional SMF during wiring and installation work, thereby improving work efficiency. In other words, it is possible to provide a C-MCF that can be handled in the same way as a single-mode optical fiber during wiring and installation work.

[0023] The core radius a and the relative refractive index difference Δ can be set, for example, based on the following guidelines. Conventional SMFs can be designed based on three characteristics: (1) bending loss as defined by the ITU-T G.652 recommendation, (2) cutoff wavelength, and (3) mode field diameter (hereinafter referred to as MFD). Therefore, these guidelines are also applied to the design of the C-MCF according to this embodiment. In other words, the C-MCF is defined by the above three characteristics, taking into account the bending loss and cutoff wavelength changes caused by the multiple cores.

[0024] Guideline (1) is as described above. Guideline (2) cutoff wavelength is set depending on the application of the C-MCF. For example, the cutoff wavelength may be 1.53 μm. In this case, the C-MCF of this embodiment can be applied to undersea cables where optical signals of about 1.55 μm are frequently used. Alternatively, the cutoff wavelength may be 1.26 μm. In this case, the C-MCF of this embodiment can be applied to land cables where optical signals of 1.26 μm are frequently used. Furthermore, guideline (3) mode field diameter is, for example, 9.7 μm or more at 1550 nm. This value is equal to the geometric characteristic value defined in the ITU-T G.652 recommendation.

[0025] For convenience of explanation, the two-dimensional space represented by the core radius a and the relative refractive index difference Δ is referred to as the a-Δ space. Fig. 3A is a diagram showing an example of a first curve G1 in the a-Δ space, Fig. 3B is a diagram showing an example of a second curve G2 in the a-Δ space, and Fig. 3C is a diagram showing an example of a third curve G3 in the a-Δ space. Note that each of the curves shown in Figs. 3A to 3C assumes that the number of cores n is 2 and the core spacing Λ is 20 μm.

[0026] The first curve G1 is a curve that indicates the bending loss in the a-Δ space as defined in the ITU-T G. 652 recommendation. The first curve G1 can be calculated by numerical analysis using the finite element analysis method, under the condition that the average bending loss of the guided modes at a predetermined core spacing Λ is 0.1 dB.

[0027] In the a-Δ space, the region R1 above the first curve G1 satisfies the bending loss requirements of the ITU-T G.652 recommendation. That is, when the core radius a and relative refractive index difference Δ in region R1 are set, the bending loss is 0.1 dB or less under the specified bending conditions.

[0028] The second curve G2 shown in Figure 3B is a curve that indicates a predetermined cutoff wavelength in the a-Δ space. The second curve G2 can be calculated by numerical analysis using finite element analysis under the condition that the predetermined wavelength is the wavelength at which the average loss of the leaky modes at a predetermined core spacing Λ is 19.3 dB. The predetermined wavelength (predetermined cutoff wavelength) under this condition is, for example, 1.53 µm.

[0029] In the a-Δ space, the region R2 below the second curve G2 satisfies the condition that the cutoff wavelength is equal to or shorter than a predetermined wavelength (i.e., 1.53 μm in this example). That is, when the core radius a and the relative refractive index difference Δ in the region R2 are set, the cutoff wavelength is equal to or shorter than the predetermined wavelength (i.e., 1.53 μm).

[0030] The third curve G3 shown in FIG. 3C is a curve showing the MFD at a predetermined wavelength in the a-Δ space. The third curve G3 can be calculated using the following well-known approximation formula: W = (0.65 + 1.619v －１．５ +2.879v －６ )×a where W is the mode field diameter, a is the core radius, and v is the V parameter (normalized frequency).

[0031] In the a-Δ space, a region R3 to the right of the third curve G3 satisfies the condition that the MFD at a predetermined wavelength is equal to or greater than a predetermined value. That is, when the core radius a and the relative refractive index difference Δ in region R3 are set, the MFD at the predetermined wavelength is equal to or greater than a predetermined value. The predetermined wavelength is, for example, 1.55 μm, and the predetermined value is, for example, 9.7 μm.

[0032] As shown in Fig. 3D , the core radius a and the relative refractive index difference Δ according to this embodiment are set to values ​​within a region R4 surrounded by the first curve G1, the second curve G2, and the third curve G3 described above. Region R4 is a region where region R1 shown in Fig. 3A , region R2 shown in Fig. 3B , and region R3 shown in Fig. 3C overlap. Furthermore, as described above, the core spacing Λ is set within the range from the lower limit value Λmin to the upper limit value Λmax according to the number of cores n.

[0033] 3D represents a group of combinations of core radius a and relative refractive index difference Δ such that, when the number of cores n is 2 and the core spacing Λ is 20 μm, the bending loss is 0.1 dB or less under the specified bending conditions, the cutoff wavelength is 1.53 μm or less, and the MFD is 9.7 μm at a wavelength of 1.55 μm. In this way, by selecting the core radius a and the relative refractive index difference Δ using the above-mentioned three curves, it is possible to easily design a coupled multicore fiber having characteristics equivalent to those of a conventional SMF.

[0034] The first curve G1 and the second curve G2 shown in Fig. 3D are curves when the core spacing Λ is assumed to be 20 µm. However, as shown in Fig. 2, the core spacing Λ at which mode coupling is obtained can be set within a range that depends on the number of cores n. Therefore, the first curve G1 and the second curve G2 vary within the range of the allowable core spacing Λ (see Fig. 4). In other words, the core spacing Λ may be set within a predetermined range within which mode coupling between the two cores 12 is obtained.

[0035] 4 shows a first curve G1 and a second curve G2 when the core spacing Λ is set to 14 μm, 20 μm, and 25 μm under the condition that the number of cores n is 2 and the cutoff wavelength is 1.53 μm. Note that a third curve G3 is shown by a single curve, independent of changes in the core spacing Λ.

[0036] 4 , when the core radius a is constant, the relative refractive index difference Δ indicated by the first curve G1 increases as the core spacing Λ decreases. The same is true for the relative refractive index difference Δ indicated by the second curve G2. In view of this tendency, region R4 may be region R5 surrounded by the first curve G1L when the core spacing Λ's lower limit value Λmin is assumed, and the second curve G2U when the core spacing Λ's upper limit value Λmax is assumed, and the third curve G3.

[0037] By setting the core radius a and the relative refractive index difference Δ to values ​​within region R5, it is possible to fabricate a coupled two-core multi-core optical fiber that has a cutoff wavelength of 1.53 μm or less, bending loss characteristics equivalent to those of an SMF, and an MFD equivalent to those of an SMF, with a core spacing Λ of any desired value in the range from 14 μm to 25 μm.

[0038] The core radius a and relative refractive index difference Δ of a C-MCF 10 whose number of cores n is 3 or more can also be set based on the above-mentioned principles. Fig. 5 is a diagram showing the first curve G1L and the second curve G2U when the cutoff wavelength is assumed to be 1.53 µm, the core spacing Λ has a lower limit value Λmin, and the number of cores n is assumed to be 2, 4, 8, or 12 (see Figs. 1A to 1D).

[0039] The core radius a and the relative refractive index difference Δ for each number of cores n are set to values ​​within the region surrounded by the first curve G1L, the second curve G2U, and the third curve G3. Note that, taking into consideration the results shown in Figure 2, the upper limit value Λmax was set to 25 μm, 25 μm, 18 μm, and 16 μm when the number of cores n was 2, 4, 8, and 12, respectively. On the other hand, the lower limit value Λmin was set to 14 μm for all numbers of cores n.

[0040] 6 is a table showing coefficients A, B, and C of a quadratic function that approximates the first curve G1L, and coefficients D and E of a power function that approximates the second curve G2U. The cutoff wavelength is assumed to be 1.53 μm.

[0041] The quadratic function of the relative refractive index difference Δ [%] that approximates the first curve G1L is expressed by the following formula (1) using the coefficients A, B, and C in the table, with the core radius a [μm] as a variable. On the other hand, the power function of the relative refractive index difference Δ [%] that approximates the second curve G2U is expressed by the following formula (2) using the coefficients D and E in the table, with the core radius a [μm] as a variable. Note that all of the coefficients are calculated using the least squares method. However, the approximation method is not limited to the least squares method. Δ=Aa ２ +Ba+C...(1) Δ=(a / E) （１／Ｄ） ...(2) Incidentally, the formula (2) can be transformed as follows: a = EΔ Ｄ ...(3)

[0042] That is, the core radius a and the relative refractive index difference Δ in the region above the first curve G1L shown in FIG. 4 satisfy the following inequality (4): Δ≧Aa ２ +Ba+C (4) Furthermore, the core radius a and the relative refractive index difference Δ in the region below the second curve G2U shown in FIG. 4 satisfy the following inequality (5): a≦EΔ Ｄ ...(5)

[0043] By using equations (4) and (5) and the coefficients shown in FIG. 6, the setting range of the core radius a and the relative refractive index difference Δ for the number of cores n can be easily calculated. In other words, without performing complex analyses such as finite element analysis on the C-MCF, the core and cladding of a C-MCF with optical characteristics equivalent to those of a standard SMF (cutoff wavelength of 1.53 μm and bending loss of 0.1 dB or less) can be efficiently calculated. Furthermore, the core according to this embodiment is assumed to be a step-index core, which is structurally simple. Therefore, a complex core structure (such as a trench type) is not adopted. This also contributes to the efficient calculation described above.

[0044] 7A to 7E are graphs showing the dependence of the coefficients A to E on the number of cores n. From these graphs, using an approximation method such as the least squares method, it is possible to derive calculation formulas for the coefficients A to E with the number of cores n as a variable. Specific calculation formulas for the coefficients A to E at a cutoff wavelength of 1.53 μm are as follows: A=0.0003n+0.0142 (6) B=-0.197 (7) C=-0.0034n+0.9314 (8) D=-0.0127n-0.5524 (9) E=-0.00008n ２ +0.0154n+3.0422 (10) By using formulas (6) to (10), the setting ranges of the core radius a and the relative refractive index difference Δ of a C-MCF having optical characteristics of a cutoff wavelength of 1.53 μm and a bending loss of 0.1 dB or less can be easily derived for any number of cores n.

[0045] 8 is a diagram showing the first curve G1L and the second curve G2U when the cutoff wavelength is assumed to be 1.26 μm, the core spacing Λ is assumed to be the lower limit value Λmin, and the number of cores n is assumed to be 2, 4, 8, or 12 (see FIGS. 1A to 1D). The first curve G1 and the third curve G3 do not change depending on the cutoff wavelength. On the other hand, the second curve G2 changes depending on the assumed cutoff wavelength.

[0046] Assuming a cutoff wavelength of 1.26 μm, the core radius a and the relative refractive index difference Δ for each number of cores n are set to values ​​within the area surrounded by the first curve G1L, the second curve G2U, and the third curve G3 showing the MFD shown in Figure 8.

[0047] 9 is a table showing coefficients D and E of a power function approximating the second curve G2U when the core spacing Λ is at the upper limit value Λmax. The cutoff wavelength is assumed to be 1.26 μm.

[0048] As described above, the first curve G1 does not change depending on the cutoff wavelength. Therefore, when the cutoff wavelength is 1.26 μm, the coefficients A to C in formula (1) and the coefficients D and E in formula (2) are expressed as follows: A = 0.0003n + 0.0142 (11) B = -0.197 (12) C = -0.0034n + 0.9314 (13) D = -0.004n - 0.5966 (14) E = -0.0001n ２ +0.0004n+2.3822 (15) By using formulas (11) to (15), the setting ranges of the core radius a and the relative refractive index difference Δ of a C-MCF having optical characteristics of a cutoff wavelength of 1.26 μm and a bending loss of 0.1 dB or less can be easily derived for any number of cores n.

[0049] 10 Multi-core optical fiber (C-MCF) 11 Cladding 11a Outer circumferential surface 12 Core Ra, R1 to R5 Regions G1, G1L First curve G2, G2U Second curve G3 Third curve

Claims

1. A coupled multi-core optical fiber comprising: a cladding; and a plurality of step-index cores provided in said cladding, wherein the core radius of each of said cores and the relative refractive index difference between each of said cores and said cladding are set to values ​​such that the bending loss under bending conditions, applying mutatis mutandis the bending loss specified in ITU-T G.652 Recommendation, is equal to or less than the bending loss specified in said Recommendation.

2. The coupled multi-core optical fiber according to claim 1, wherein the core radius and the relative refractive index difference are set to values ​​within a region surrounded by a first curve indicating the bending loss specified in the Recommendation, a second curve indicating a predetermined cutoff wavelength, and a third curve indicating a predetermined mode field diameter at a predetermined wavelength, in a two-dimensional space represented by the core radius and the relative refractive index difference.

3. A coupled multi-core optical fiber according to claim 2, wherein the core spacing between two adjacent cores among the plurality of cores is set within a predetermined range in which mode coupling between the two cores is obtained, the first curve is a curve obtained when a lower limit value of the core spacing within the predetermined range is assumed, and the second curve is a curve obtained when an upper limit value of the core spacing within the predetermined range is assumed.

4. The coupled multi-core optical fiber according to claim 3, wherein the cladding has an outer diameter of 125±1 μm, the predetermined cutoff wavelength is 1.53 μm, the first curve is approximated by the following formula 1, and the second curve is approximated by the following formula 2. Δ=Aa ２ +Ba+C...(1) a=EΔ Ｄ ...(2) a: the core radius [μm] Δ: the relative refractive index difference [%] A = 0.0003n + 0.0142 B = -0.197 C = -0.0034n + 0.9314 D = -0.0127n - 0.5524 E = -0.00008n ２ +0.0154n+3.0422, n: the number of cores 5. The coupled multi-core optical fiber according to claim 3, wherein the cladding has an outer diameter of 125±1 μm, the predetermined cutoff wavelength is 1.26 μm, the first curve is approximated by the following formula 1, and the second curve is approximated by the following formula 2. Δ=Aa ２ +Ba+C...(1) a=EΔ Ｄ ...(2) a: the core radius [μm] Δ: the relative refractive index difference [%] A=0.0003n+0.0142 B=−0.197 C=−0.0034n+0.9314 D=−0.004n−0.5966 E=−0.0001n ２ +0.0004n+2.3822, n: the number of cores 6. The lower limit of the core spacing in the plurality of cores is set to 14 μm, and the upper limit of the core spacing is set to 25 μm when n≦6, and 0.3046n when n≧7, where n is the number of cores. ２ The coupled multi-core optical fiber according to any one of claims 1 to 5, wherein the wavelength of the optical fiber is set to (-7.163n+57.97) μm.

7. The coupled multi-core optical fiber according to claim 2, wherein the predetermined wavelength is 1550 nm and the predetermined mode field diameter is 9.7 μm or more.

8. The coupled multi-core optical fiber according to any one of claims 2 to 5, wherein the predetermined cutoff wavelength is 1.53 μm or 1.26 μm.

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