Coupled multicore optical fiber

Abstract

This coupled type multicore optical fiber comprises: a first cladding; a second cladding formed in the first cladding and having a refractive index lower than that of the first cladding; and a plurality of cores formed in the second cladding, having a core radius (a1), and having a refractive index higher than that of the first cladding by a relative refractive index difference (∆1). The core radius (a1) and the relative refractive index difference (∆1) have values in a region (R6) surrounded by a first curve (G1L) indicating a prescribed bending loss under a condition that the lower limit value of the core interval changes according to the number of cores, a second curve (G2U) indicating a prescribed cutoff wavelength under the condition that the upper limit value of the core interval changes according to the number of cores, and a third curve (G3) indicating the mode field diameter at a prescribed wavelength, in a two-dimensional space represented by the core radius (a1) and the relative refractive index difference (∆1).

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 comprises a first cladding, a second cladding formed in the first cladding and having a refractive index lower than that of the first cladding, and a plurality of cores formed in the second cladding, having a core radius and a refractive index higher than that of the first cladding by a relative refractive index difference, wherein the core radius and the relative refractive index difference have values ​​within a region surrounded by a first curve showing a predetermined bending loss under conditions in which the lower limit of the core spacing changes depending on the number of cores, a second curve showing a predetermined cutoff wavelength under conditions in which the upper limit of the core spacing changes depending on the number of cores, and a third curve showing a mode field diameter at a predetermined wavelength, in a two-dimensional space represented by the core radius and the relative refractive index difference.

[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 according to an embodiment of the present disclosure. FIG. 1B is a diagram showing an example of a cross section of a C-MCF according to this embodiment. FIG. 1C is a diagram showing an example of a cross section of a C-MCF according to this embodiment. FIG. 1D is a diagram showing an example of a cross section of a C-MCF according to this embodiment. FIG. 2 is a graph for explaining the set value of the core spacing Λ. FIG. 3A is a diagram showing a １ -Δ １ FIG. 3B is a diagram illustrating an example of a first curve in space. １ -Δ １FIG. 3C is a diagram illustrating an example of a second curve in space. １ -Δ １ 3D is a diagram showing an example of the third curve in space. FIG. 3D is a diagram showing the area surrounded by the first curve, the second curve, and the third curve. FIG. 4 is a diagram showing the area surrounded by the first curve, the second curve, and the third curve. ａ is 3, ratio R Δ 5 is a diagram showing the first and second curves when the core spacing Λ is set to 14 μm, 16 μm, and 18 μm under the condition that λ is 0.71. FIG. 5 is a diagram showing the first and second curves when the cutoff wavelength is 1.53 μm and the number of cores n is 2, 4, 8, and 12. FIG. 6 is a diagram showing the coefficient A of the quadratic function approximating the first curve for each number of cores. １ , A ２ , A ３ , and the coefficient B of the quadratic function approximating the second curve for each number of cores n １ , B ２ , B ３ 7A is a diagram showing several second curves when different cutoff wavelengths are assumed under the condition that the number of cores is 12. FIG. 7B is a table showing the coefficients of Equation (1) when several cutoff wavelengths are assumed. FIG. 8 is a diagram showing the ratio R Δ 9A is a graph showing the changes in the first and second curves with respect to the coefficient A based on Equation (5). ３ 9B is a graph showing the change in coefficient B based on Equation (6). ３ 10 is a graph showing the change in the ratio R Δ 11 is a graph showing the relationship between the ratio R and the bending loss and the cutoff wavelength. ａ 10 is a diagram showing changes in the first and second curves with respect to

[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 13 among the plurality of cores 13.

[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 includes a first cladding 11, a second cladding 12 formed in the first cladding, and a plurality of cores 13 formed in the second cladding 12. The refractive index of the first cladding 11 has a relative refractive index difference Δ １ On the other hand, the refractive index of the second cladding 12 is lower than that of the core 13 by a value represented by the relative refractive index difference Δ ２ is lower than the refractive index of the core 13 and is also lower than the refractive index of the first cladding 11 by a value expressed as follows (see FIG. 1A). In other words, the C-MCF 10 according to this embodiment is a depressed type multi-core optical fiber. ２ relative refractive index difference Δ １ The ratio R Δ (=Δ １ / Δ ２ ) is defined.

[0012] As shown in FIG. 1A, the core 13 has a radius a １ The boundary 14 of the second cladding 12 with the first cladding 11 is located at a distance a from the outermost core of the plurality of cores 13. ２ For convenience of explanation, the radius of the core 13 will be referred to as the core radius. １ Distance a to ２ The ratio R ａ (= a ２ / a １ ) is defined.

[0013] The C-MCFs 10 shown in Figures 1A, 1B, 1C, and 1D each include two cores 13, four cores 13, eight cores 13, and twelve cores 13, respectively. As shown in these figures, the multiple cores 13 are arranged in 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 13 shown in each figure are distributed so as to have a predetermined rotational symmetry around the center of the C-MCF 10. The core spacing Λ has a value that allows mode coupling. As long as this condition is satisfied, the arrangement of the cores 13 is arbitrary.

[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 ITU-T G.652 (International Telecommunication Union Telecommunication Standardization Sector recommendation G.652). 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 has 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) is formed, for example, of resin and has 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 13. On the other hand, when a large number of cores 13 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 13 is increased while maintaining the core spacing Λ, the outermost cores 13 will inevitably move closer to the outer peripheral surface 11 a of the cladding 11. In other words, the distance from the outermost cores 13 to the outer peripheral surface 11 a of the cladding 11 will become shorter. The shorter this distance becomes, the greater the leakage loss will be. Therefore, depending on the number of cores 13, 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 quadratic function curves obtained by curve fitting 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 (0.34n ２ -8.0n+65) 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 R 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 region R, sufficient coupling efficiency between cores can be obtained, and the multi-core optical fiber according to this embodiment functions as a coupled-type multi-core optical fiber.

[0021] Next, the core radius a １ and the relative refractive index difference Δ １ The setting value of the core radius a １ and the relative refractive index difference Δ １ is set to satisfy the bending characteristics in accordance with the ITU-T G. 652 recommendation. １ and the relative refractive index difference Δ １is set to a value that ensures that the bending loss under bending conditions that comply 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 that ensures that the loss (insertion loss) when light with a wavelength of 1625 nm is passed through is 0.1 dB or less. For ease of explanation, the above-mentioned 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 where the bending loss under the specified bending conditions is 0.1 dB or less. １ and the relative refractive index difference Δ １ Furthermore, the first cladding 11 according to this embodiment has the same outer diameter as the cladding of an SMF. Therefore, the C-MCF 10 has similar bending loss and mechanical properties to conventional SMF. This allows the C-MCF to be handled in the same manner as conventional SMF in wiring, installation, and other work, thereby improving work efficiency. In other words, it is possible to provide a C-MCF that can be handled in the same manner as a single-mode optical fiber in wiring, installation, and other work.

[0023] Core radius a １ and the relative refractive index difference Δ １ can be set, for example, based on the following guidelines. Conventional SMF can be designed based on three characteristics: (1) bending loss as defined in the ITU-T G.652 recommendation, (2) cutoff wavelength, and (3) mode field diameter (hereinafter referred to as MFD). Therefore, this guideline is 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 multi-core.

[0024] Guideline (1) is as described above. Guideline (2) - the cutoff wavelength - is set according to 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) - the mode field diameter - is, for example, 9.5 μm or more at 1550 nm. This value is equal to the geometric characteristic value defined in the ITU-T G.654 recommendation.

[0025] Here, the core radius a １ and the relative refractive index difference Δ １ The two-dimensional space represented by a １ -Δ １ The space is called a １ -Δ １ FIG. 3B is a diagram showing an example of a first curve G1 in space. １ -Δ １ FIG. 3C is a diagram showing an example of a second curve G2 in space. １ -Δ １ 3A to 3D are diagrams illustrating an example of a third curve G3 in space. Each curve shown in FIGS. 3A to 3D is for a case where the number of cores n is 12, the core spacing Λ is 14 μm, and R ａ = 3, R Δ = 0.71.

[0026] The first curve G1 is a １ -Δ １ This is a curve showing the bending loss in space as defined in the ITU-T G.652 and G.654 recommendations. 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 given core spacing Λ is 0.1 dB.

[0027] a １ -Δ １ The region R1 above the first curve G1 in space satisfies the requirements of the ITU-T G.652 and G.654 recommendations regarding bending loss. That is, the core radius a １ and the relative refractive index difference Δ １When this is set, the bending loss is 0.1 dB / 100 turns or less under the specified bending conditions.

[0028] The second curve G2 shown in FIG. １ -Δ １ The second curve G2 is a curve that indicates a predetermined cutoff wavelength in 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 is 19.3 dB for a predetermined core spacing Λ. The predetermined wavelength (predetermined cutoff wavelength) under this condition is, for example, 1.53 μm.

[0029] a １ -Δ １ The region R2 below the second curve G2 in space satisfies the condition that the cutoff wavelength is equal to or less than a predetermined wavelength (i.e., 1.53 μm in this example). １ and the relative refractive index difference Δ １ When the above formula is set, the cutoff wavelength is equal to or less than a predetermined wavelength (i.e., 1.53 μm).

[0030] The third curve G3 shown in FIG. １ -Δ １ The third curve G3 is a curve that shows the MFD at a predetermined wavelength in space. １ and Δ １ It can be calculated from the combination of W = 2 × (0.65 + 1.619v －１．５ +2.879v －６ ) v = 2πa １ × 1.44 × (2Δ １ ) ０．５ / λ where W is the mode field diameter, v is the V parameter (normalized frequency), a １ is the core radius, Δ １ is the relative refractive index difference between the core and the first cladding, and λ is the cutoff wavelength.

[0031] a １ -Δ １ The region R3 on the right side of the third curve G3 in space satisfies the condition that the MFD at a predetermined wavelength is equal to or greater than a predetermined value. １ and the relative refractive index difference Δ １When the above formula is set, the MFD at a predetermined wavelength is equal to or greater than a predetermined value. The predetermined wavelength is, for example, 1.53 μm, and the predetermined value is, for example, 9.5 μm.

[0032] 3D shows a region R4 in which the region R1 shown in FIG. 3A, the region R2 shown in FIG. 3B, and the region R3 shown in FIG. 3C are superimposed. That is, the core radius a １ and the relative refractive index difference Δ １ is set to a value within a region R4 surrounded by the first curve G1, the second curve G2, and the third curve G3 described above. 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] For example, in region R4 shown in FIG. 3D, when the number of cores n is 12 and the core spacing Λ is 14 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 9.5 μm or more. １ and the relative refractive index difference Δ １ In this way, the core radius a １ and the relative refractive index difference Δ １ By selecting the above, it is possible to easily design a coupled multi-core fiber having the same characteristics as 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 14 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 13 is obtained.

[0035] FIG. 4 shows the case where the number of cores n is 12, the cutoff wavelength is 1.53 μm, and the ratio R ａ (= a ２ / a １ ) is 3, the ratio R Δ (=Δ １ / Δ ２4 shows the first curve G1 and the second curve G2 when the core spacing Λ is set to 14 μm, 16 μm, and 18 μm under the condition that ρ (ρ ) is 0.71. Note that in FIG. 4, the third curve G3 does not depend on the change in the core spacing Λ.

[0036] As shown in Figure 4, the first curve G1 indicating the bending loss and the second curve G2 indicating the cutoff wavelength shift upward as the core spacing Λ decreases. This is because, with the same structure, as the core spacing decreases, the bending loss increases and the cutoff wavelength becomes shorter. Therefore, for any core spacing Λ within the design range, the core radius a that satisfies the desired bending loss, cutoff wavelength characteristics, and MFD can be calculated. １ and the relative refractive index difference Δ １ takes a value within a region R5 surrounded by a first curve G1L when the lower limit value Λmin of the core spacing Λ is assumed, a second curve G2U when the upper limit value Λmax of the core spacing Λ is assumed, and a third curve G3.

[0037] Core radius a １ and the relative refractive index difference Δ １ to a value within region R5, a coupled 12-core multi-core optical fiber that satisfies bending loss characteristics equivalent to those of an SMF (i.e., 0.1 dB / 100 turns or less), a cutoff wavelength of 1.53 μm or less, and an MFD equivalent to those of an SMF can be obtained with any core spacing Λ in the range from 14 μm to 28 μm.

[0038] Core radius a of C-MCF10 with core number n of 3 or more １ and the relative refractive index difference Δ １ 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 and the number of cores n is assumed to be 2, 4, 8, and 12.

[0039] Core radius a for each number of cores n １ and the relative refractive index difference Δ １ are set to values ​​within a region R6 surrounded by the first curve G1L, the second curve G2U, and the third curve G3. The region R6 is a region where the core radius a １ and the relative refractive index difference Δ １In other words, region R6 is a region surrounded by a first curve G1L showing a predetermined bending loss (e.g., 0.1 dB / 100 turns) under the condition that the lower limit value Λmin of the core spacing Λ changes according to the number of cores n, a second curve G2U showing a predetermined cutoff wavelength (e.g., 1530 nm) under the condition that the upper limit value Λmax of the core spacing Λ changes according to the number of cores n, and a third curve G3 showing the mode field diameter at a predetermined wavelength. １ and the relative refractive index difference Δ １ has a value within this region R6.

[0040] The relative refractive index difference Δ that approximates the first curve G1L １ The quadratic function of [%] is the core radius a １ [μm] is the variable, and the coefficient A in the table １ , A ２ , A ３ On the other hand, the relative refractive index difference Δ １ The quadratic function of [%] is the core radius a １ [μm] is the variable, and the coefficient B in the table １ , B ２ , B ３ It should be noted that all coefficients are calculated using the least squares method. However, the approximation method is not limited to the least squares method. Δ １ = A １ a １ ２ +A ２ a １ +A ３ ... (1) Δ １ =B １ a １ ２ +B ２ a １ +B ３ ...(2) The table in FIG. 6 shows the coefficient A of the quadratic function that approximates the first curve G1L for each number of cores n. １ , A ２ , A ３ , and the coefficient B of the quadratic function approximating the second curve G2U for each number of cores n １ , B ２ , B ３It is assumed that the bending loss is 0.1 dB under the specified bending conditions and the cutoff wavelength is 1.53 μm.

[0041] That is, in the region R6 above the first curve G1L shown in FIG. 5, the core radius a １ and the relative refractive index difference Δ １ satisfies the inequality shown in the following formula (3). Δ １ ≧A １ a １ ２ +A ２ a １ +A ３ ...(3) In addition, in the region R6 below the second curve G2U shown in FIG. 5, the core radius a １ and the relative refractive index difference Δ １ satisfies the inequality shown in the following formula (4). Δ １ ≦B １ a １ ２ +B ２ a １ +B ３ ...(4)

[0042] The second curve G2U of each core changes depending on the assumed cutoff wavelength, and the range of the region R6 also changes accordingly. As an example, Fig. 7A shows several second curves G2U when different cutoff wavelengths are assumed under the condition of 12 cores. Fig. 7B shows the coefficient A of Equation (1) when the cutoff wavelengths are assumed to be 1.53 μm, 1.46 μm, and 1.26 μm. １ , A ２ , A ３ , and the coefficient B in Equation (2) １ , B ２ , B ３ 7A, the shorter the cutoff wavelength, the lower the second curve G2U moves on the graph. In other words, the shorter the cutoff wavelength, the narrower the region R6 when the number of cores is 12.

[0043] FIG. 8 shows the ratio R Δ 8 shows the changes of the first curve G1L and the second curve G2U with respect to the ratio R Δ This analysis shows the change in the range of region R6 with respect to the number of cores.Δ As shown in FIG. 8, the first curve G1L indicating the bending loss and the second curve G2U indicating the cutoff wavelength are Δ As the ratio R decreases, the graph moves upward. Δ On the other hand, the ratio R Δ The dependence of the refractive index difference Δ １ Therefore, the coefficient A in Equation (1) can be approximated by a parallel translation of the region R6. ３ , and the coefficient B of (2) ３ can be expressed by the following equations (5) and (6), respectively. ３ = 4.08R Δ ２ -5.10R Δ +4.00...(5) B ３ = 7.5R Δ ２ -9.2R Δ +4.24 ... (6) Coefficient A based on formula (5) ３ The change in coefficient B based on Equation (6) is shown in FIG. ３ The change in R is shown in FIG. 9B. By appropriately selecting the function shown in this figure and the coefficients shown in FIG. 6, an arbitrary ratio R Δ That is, based on the table of FIG. １ =0.028125,A ２ =-0.32781,B １ =0.034766, B ２ = -0.54278, coefficient A ３ is expressed by the formula (5), and the coefficient B ３ is expressed by Equation (6). In this case, the core radius a １ and the relative refractive index difference Δ １ is applicable to all cases with 12 or fewer cores.

[0044] FIG. 10 shows the ratio R ΔThis graph shows the relationship between the MFD and the bending loss and the cutoff wavelength. In this analysis, the MFD is set to 11.5 μm. This value is the standard value in ITU-T G.654.E, a recommendation for long-distance optical fibers. As shown in this graph, in order to obtain a cutoff wavelength of 1.53 μm or more, the ratio R Δ is set to 0.77 or less. Similarly, to obtain a bending loss of 0.1 dB or less, the ratio R Δ is set to 0.58 or more. The specified value of bending loss in the ITU-T G.652 recommendation is the same as the value mentioned above. Also, the cutoff wavelength in the ITU-T G.652 recommendation is shorter than the specified value in ITU-T G.654. ​​Therefore, the ratio R Δ By setting .gamma. to a value in the range of 0.58 to 0.77, the bending loss and cutoff wavelength specified in both recommendations can be obtained.

[0045] FIG. 11 shows the ratio R ａ 11 is a diagram showing the changes of the first curve G1L and the second curve G2U with respect to the ratio R ａ This analysis shows the change in the range of region R6 with respect to the number of cores. Δ According to a document (Japanese Patent No. 6560806) that discloses a technique related to unbonded MCF, the ratio R ａ By setting the ratio R to 3.0 or less, the leakage loss can be suppressed to 0.01 dB / km. ａ is the lower limit of

[0046] Therefore, the ratio R ａ has a value ranging from 1.0 to 3.0. As shown by the second curve G2U in FIG. 11, the ratio R ａ Therefore, for the second curve G2U, the ratio R ａ On the other hand, the bending loss can be calculated by the ratio R ａ As the coefficient A in Equation (1) increases, the graph shifts downward. ３ can be approximated by the following equation (7): ３ =-0.03R ａ +1.58 ... (7)

[0047] In this analysis, coefficient A １ and A ２ is the ratio R ａ By appropriately selecting the coefficients shown in this formula (7) and FIG. 6, an arbitrary ratio R ａ For example, based on the table of FIG. １ =0.028125,A ２ =-0.32781,B １ =0.034766, B ２ = -0.54278, coefficient A ３ is expressed by the formula (7), and the coefficient B ３ is expressed by Equation (6). In this case, the core radius a １ and the relative refractive index difference Δ １ is the possible ratio R ａ This can be applied to all cases where the number of cores is 12 or less under the condition.

[0048] 10 Multi-core optical fiber (C-MCF) 11 First cladding 11a Outer circumferential surface 12 Second cladding 13 Core 14 Boundary a １ Core radius a ２ Distance Δ １ Relative refractive index difference Δ ２ Relative refractive index difference R, R1 to R6 Region G1, G1L 1st curve G2, G2U 2nd curve G3 3rd curve

Claims

1. A coupled multi-core optical fiber comprising: a first cladding; a second cladding formed within said first cladding and having a lower refractive index than said first cladding; and a plurality of cores formed within said second cladding, each having a core radius and a refractive index higher than that of said first cladding by a relative refractive index difference, wherein said core radius and said relative refractive index difference have values ​​within a region surrounded by a first curve showing a predetermined bending loss under conditions in which a lower limit value of core spacing varies depending on the number of cores, a second curve showing a predetermined cutoff wavelength under conditions in which an upper limit value of core spacing varies depending on the number of cores, and a third curve showing a mode field diameter at a predetermined wavelength in a two-dimensional space represented by said core radius and said relative refractive index difference.

2. The coupled multi-core optical fiber according to claim 1, wherein the first cladding has an outer diameter of 125±1 μm, the bending loss is 0.1 dB / 100 turns, and the cutoff wavelength is 1530 nm.

3. The coupled multi-core optical fiber according to claim 2, wherein the first curve is approximated by the following Equation 1, and the second curve is approximated by the following Equation 2. Δ １ = A １ a １ ２ +A ２ a １ +A ３ ... (1) Δ １ =B １ a １ ２ +B ２ a １ +B ３ ... (2) a １ : Said core radius [μm] Δ １ a: the relative refractive index difference [%] between the first cladding and each of the cores ２ Δ: Distance from the outermost core of the plurality of cores to the boundary between the first cladding and the second cladding [μm] ２ : Relative refractive index difference between the second cladding and each of the cores [%] A １ =0.028125 A ２ =-0.32781 A ３ = 4.08R Δ ２ -5.10R Δ +4.00 B １ =0.034766B ２ =-0.54278B ３ = 7.5R Δ ２ -9.2R Δ +4.24 0.58≦R Δ ≦0.77 1.0≦R ａ ≦3.0 R Δ =Δ １ / Δ ２ R ａ = a ２ / a １ 4. The coupled multi-core optical fiber according to claim 2, wherein the first curve is defined by the following formula 1, and the second curve is defined by the following formula 2. Δ １ = A １ a １ ２ +A ２ a １ +A ３ ... (1) Δ １ =B １ a １ ２ +B ２ a １ +B ３ ... (2) a １ : Said core radius [μm] Δ １ a: the relative refractive index difference [%] between the first cladding and each of the cores ２ Δ: Distance from the outermost core of the plurality of cores to the boundary between the first cladding and the second cladding [μm] ２ : Relative refractive index difference between the second cladding and each of the cores [%] A １ =0.028125 A ２ =-0.32781 A ３ =-0.03R ａ +1.58 B １ =0.034766B ２ =-0.54278B ３ = 7.5R Δ ２ -9.2R Δ +4.24 0.58≦R Δ ≦0.77 1.0≦R ａ ≦3.0 R Δ =Δ １ / Δ ２ R ａ = a ２ / a １

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