Multi-core optical fiber

Abstract

The multi-core optical fiber (1) comprises a plurality of cores (2), a first cladding (3), and a second cladding (4). The refractive index of the second cladding (4) is lower than that of the core (2) and higher than that of the first cladding (3). The transmission loss at a wavelength of 1550 nm is 0.22 dB / km or less. When the effective cross-sectional area of ​​the core (2) at a wavelength of 1550 nm is Aeff [μm2], the center-to-center distance between two adjacent cores (2) in a cross section perpendicular to the fiber axis is Λ [μm], and the relative refractive index difference of the core (2) based on the refractive index of the first cladding (3) is Δcore [%], then Aeff1 = 18.6 - 4.63ln(Δcore) + 1.24Λ + 24.1 [ln(Δcore)]. 2 -6.05×10 -3 Λ 2 Using Aeff1 defined as -0.858Λln(Δcore), the following condition 1a is satisfied. 0.35[%]≦Δcore[%]≦1.00[%] 25[μm]≦Λ[μm]≦50[μm] 0.80Aeff1≦Aeff≦1.35Aeff1

Description

[Technical field]

[0001] The present disclosure relates to a multi-core optical fiber. This application claims priority to Japanese Application No. 2023-012598 filed on January 31, 2023, and incorporates by reference all the contents of said Japanese application. [Background technology]

[0002] Non-Patent Documents 1 to 3 describe that the smaller the effective area (hereinafter also referred to as Aeff) of each core of a multi-core optical fiber (hereinafter also referred to as MCF), the stronger the light confinement in each core can be, and the lower the inter-core power coupling coefficient (hereinafter also referred to as PCC) and inter-core crosstalk (hereinafter also referred to as XT). Non-Patent Document 1 describes a step-index (hereinafter also referred to as SI) type MCF, Non-Patent Document 2 describes a trench-assisted type MCF, and Non-Patent Document 3 describes a hole-assisted type MCF. In a non-coupled type MCF that uses individual cores as independent optical spatial channels, reducing the PCC reduces the inter-core XT and improves the signal quality of each core. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] T. Hayashi et al., “Design strategy of uncoupled multicore fiber enabling high spatial capacity transmission”, SUM2013, MC2. 4 [Non-Patent Document 2] JH Chang et al., “Achievable capacity improvement by using multi-level modulation format in trench-assisted multi-core fiber system”, OPTICS EXPRESS 14262 Vol.21, No.12, 17 June 2013 [Non-Patent Document 3] F. Ye et al., “Capacity of Space-Division Multiplexing with Heterogeneous Multi-Core Fibers”, 2013 18th OECC / PS FC [Non-Patent Document 4] H. Yoshikawa et al., “Analysis of Two-Core Single-Mode Optical Fibers for Subscriber Lines”, Electronics and Communications in Japan, Part 2, Vol.72, No.8, P.45-53, 1989 [Non-Patent Document 5] RJ Black et al., “Developments in the theory of equivalent-step-index fibers”, J. Opt. Soc. Am. A,vol.1, No.11, p.1129-1131, November 1984 Summary of the Invention

[0004] The MCF of the present disclosure is a common depressed type MCF used for parallel propagation, and includes multiple cores, a common first cladding surrounding each of the multiple cores, and a second cladding surrounding the first cladding. The refractive index of the second cladding is lower than that of the cores and higher than that of the first cladding. The transmission loss at a wavelength of 1550 nm is 0.22 dB / km or less. The effective cross-sectional area of ​​the core at a wavelength of 1550 nm is defined as Aeff [μm 2], the center-to-center distance between two adjacent cores in the cross section perpendicular to the fiber axis is Λ [μm], and the relative refractive index difference of the core based on the refractive index of the first cladding is Δcore [%]. Aeff1=18.6-4.63ln(Δcore)+1.24Λ+24.1[ln(Δcore)] 2 -6.05×10 -3 Λ 2 -0.858Λln(Δcore) Using Aeff1 defined as: 0.35[%]≦Δcore[%]≦1.00[%] 25[μm]≦Λ[μm]≦50[μm] 0.80Aeff1≦Aeff≦1.35Aeff1 [Brief description of the drawings]

[0005] [Figure 1] Figure 1 is a graph showing the relationship between PCC and Aeff of each core. [Diagram 2] FIG. 2 is a diagram showing a cross section perpendicular to the fiber axis of an MCF according to an embodiment and a refractive index profile. [Diagram 3] FIG. 3 is a graph showing the relationship between the core radius and the relative refractive index difference of the core with respect to the refractive index of the first cladding. [Figure 4] Figure 4 is a graph showing the relationship between PCC and Aeff of each core. [Diagram 5] Figure 5 is a plot showing how much h increases depending on how much Aeff deviates from Aeff1. [Figure 6] FIG. 6 is a plot showing how much h increases depending on how much Aeff deviates from Aeff1. [Figure 7] FIG. 7 is a diagram showing a cross section perpendicular to the fiber axis of an MCF according to a modified example and a refractive index profile. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0006] [Problem that this disclosure aims to solve] The inventors discovered that in a so-called common depressed MCF, if Aeff is made too small, the PCC between cores becomes large. A common depressed MCF is an MCF that includes multiple cores, a common first cladding that surrounds the multiple cores, and a second cladding that surrounds the first cladding, and the refractive index of the second cladding is lower than that of the cores and higher than that of the first cladding.

[0007] An object of the present disclosure is to provide a common depressed MCF capable of reducing inter-core XT.

[0008] [Effects of this disclosure] According to the present disclosure, it is possible to provide a common depressed MCF capable of reducing inter-core XT.

[0009] [Description of the embodiments of the present disclosure] First, the embodiments of the present disclosure will be listed and described. (1) The MCF according to the first aspect of the present disclosure is a common depressed type MCF used for parallel propagation, and includes multiple cores, a common first cladding surrounding each of the multiple cores, and a second cladding surrounding the first cladding. The refractive index of the second cladding is lower than that of the cores and higher than that of the first cladding. The transmission loss at a wavelength of 1550 nm is 0.22 dB / km or less. The effective cross-sectional area of ​​the core at a wavelength of 1550 nm is Aeff [μm 2 ], the center-to-center distance between two adjacent cores in the cross section perpendicular to the fiber axis is Λ [μm], and the relative refractive index difference of the core based on the refractive index of the first cladding is Δcore [%]. Aeff1=18.6-4.63ln(Δcore)+1.24Λ+24.1[ln(Δcore)] 2 -6.05×10 -3 Λ 2 -0.858Λln(Δcore) Aeff1 [μm 2 ] to satisfy condition 1a below. 0.35[%]≦Δcore[%]≦1.00[%] 25[μm]≦Λ[μm]≦50[μm] 0.80Aeff1≦Aeff≦1.35Aeff1 In this MCF, the first cladding functions as a common depressed region. Since the PCC between two adjacent cores (hereinafter also referred to as parallel propagation PCC) can be reduced when signal light is propagated in parallel, the XT between two adjacent cores (hereinafter also referred to as parallel propagation XT) can be reduced when signal light is propagated in parallel. The increase in the parallel propagation PCC and parallel propagation XT can be suppressed to 3 dB or less from the minimum value.

[0010] (2) In (1) above, condition 1a may be further defined by the following formula: 0.83Aeff1≦Aeff≦1.18Aeff1 In this case, the increase in the parallel propagation PCC and parallel propagation XT can be suppressed to 1 dB or less from the minimum value.

[0011] (3) In (1) above, condition 1a may be further defined by the following formula: 0.90Aeff1≦Aeff≦1.12Aeff1 In this case, the increase in the parallel propagation PCC and parallel propagation XT can be suppressed to 0.5 dB or less from the minimum value.

[0012] (4) In (1) above, condition 1a may be further defined by the following formula: 0.95Aeff1≦Aeff≦1.05Aeff1 In this case, the increase in the parallel propagation PCC and parallel propagation XT can be suppressed to 0.1 dB or less from the minimum value.

[0013] (5) The MCF according to the second aspect of the present disclosure is a common depressed type MCF used for parallel propagation, and includes multiple cores, a common first cladding surrounding each of the multiple cores, and a second cladding surrounding the first cladding. The refractive index of the second cladding is lower than that of the cores and higher than that of the first cladding. The transmission loss at a wavelength of 1550 nm is 0.22 dB / km or less. The effective cross-sectional area of ​​the core at a wavelength of 1550 nm is Aeff [μm 2 ], the center-to-center distance between two adjacent cores in the cross section perpendicular to the fiber axis is Λ [μm], and the relative refractive index difference of the core based on the refractive index of the first cladding is Δcore [%]. Aeff1=18.6-4.63ln(Δcore)+1.24Λ+24.1[ln(Δcore)] 2 -6.05×10 -3 Λ 2 -0.858Λln(Δcore) Aeff1 [μm 2 ] to satisfy condition 2a below. 0.30[%]≦Δcore[%]≦0.35[%] 20[μm]≦Λ[μm]≦25[μm] 0.88Aeff1≦Aeff≦1.35Aeff1 In this MCF, the first cladding functions as a common depressed band. Since the parallel propagation PCC can be reduced, the parallel propagation XT can be reduced. The parallel propagation PCC and parallel propagation XT can be suppressed to an increase of 3 dB or less from the minimum value.

[0014] (6) In (5) above, condition 2a may be further defined by the following formula: 0.90Aeff1≦Aeff≦1.18Aeff1 In this case, the increase in the parallel propagation PCC and parallel propagation XT can be suppressed to 1 dB or less from the minimum value.

[0015] (7) In (5) above, condition 2a may be further defined by the following formula: 0.92Aeff1≦Aeff≦1.12Aeff1 In this case, the increase in the parallel propagation PCC and parallel propagation XT can be suppressed to 0.5 dB or less from the minimum value.

[0016] (8) In (5) above, condition 2a may be further defined by the following formula: 0.96Aeff1≦Aeff≦1.05Aeff1 In this case, the increase in the parallel propagation PCC and parallel propagation XT can be suppressed to 0.1 dB or less from the minimum value.

[0017] (9) The MCF according to a third aspect of the present disclosure is a common depressed type MCF used for counter propagation, and includes a plurality of cores, a common first cladding surrounding each of the plurality of cores, and a second cladding surrounding the first cladding. The refractive index of the second cladding is lower than that of the cores and higher than that of the first cladding. The transmission loss at a wavelength of 1550 nm is 0.22 dB / km or less. The effective cross-sectional area of ​​the core at a wavelength of 1550 nm is Aeff [μm 2 ], the center-to-center distance between two adjacent cores in the cross section perpendicular to the fiber axis is Λ [μm], and the relative refractive index difference of the core based on the refractive index of the first cladding is Δcore [%]. Aeff2=19.2-3.01ln(Δcore)+1.40Λ+25.6[ln(Δcore)] 2 -7.72×10 -3 Λ 2 -0.980Λln(Δcore) Aeff2 [μm 2 ] to satisfy condition 1b below. 0.35[%]≦Δcore[%]≦1.00[%] 25[μm]≦Λ[μm]≦50[μm] 0.75Aeff2≦Aeff≦1.36Aeff2 In this MCF, the first cladding functions as a common depressed region. Since the PCC between two adjacent cores (hereinafter also referred to as counter-propagating PCC) can be reduced when the signal light is counter-propagated, the XT between two adjacent cores (hereinafter also referred to as counter-propagating XT) can be reduced when the signal light is counter-propagated. The increase in the counter-propagating PCC and counter-propagating XT can be suppressed to 3 dB or less from the minimum value.

[0018] (10) In (9) above, condition 1b may be further defined by the following formula: 0.85Aeff2≦Aeff≦1.18Aeff2 In this case, the increase in counter-propagation PCC and counter-propagation XT can be suppressed to 1 dB or less from the minimum value.

[0019] (11) In (9) above, condition 1b may be further defined by the following formula: 0.89Aeff2≦Aeff≦1.12Aeff2 In this case, the increase in counter-propagation PCC and counter-propagation XT can be suppressed to 0.5 dB or less from the minimum value.

[0020] (12) In (9) above, condition 1b may be further defined by the following formula: 0.95Aeff2≦Aeff≦1.05Aeff2 In this case, the increase in counter-propagation PCC and counter-propagation XT can be suppressed to 0.1 dB or less from the minimum value.

[0021] (13) The MCF according to a fourth aspect of the present disclosure is a common depressed type MCF used for counter propagation, and includes a plurality of cores, a common first cladding surrounding each of the plurality of cores, and a second cladding surrounding the first cladding. The refractive index of the second cladding is lower than that of the cores and higher than that of the first cladding. The transmission loss at a wavelength of 1550 nm is 0.22 dB / km or less. The effective cross-sectional area of ​​the core at a wavelength of 1550 nm is Aeff [μm 2], the center-to-center distance between two adjacent cores in the cross section perpendicular to the fiber axis is Λ [μm], and the relative refractive index difference of the core based on the refractive index of the first cladding is Δcore [%]. Aeff2=19.2-3.01ln(Δcore)+1.40Λ+25.6[ln(Δcore)] 2 -7.72×10 -3 Λ 2 -0.980Λln(Δcore) Aeff2 [μm 2 ] to satisfy condition 2b below. 0.30[%]≦Δcore[%]≦0.35[%] 20[μm]≦Λ[μm]≦25[μm] 0.84Aeff2≦Aeff≦1.36Aeff2 In this MCF, the first cladding functions as a common depressed band. Since the counter-propagating PCC can be reduced, the counter-propagating XT can be reduced. The increase of the counter-propagating PCC and the counter-propagating XT can be suppressed to 3 dB or less from the minimum value.

[0022] (14) In (13) above, condition 2b may be further defined by the following formula: 0.88Aeff2≦Aeff≦1.18Aeff2 In this case, the increase in counter-propagation PCC and counter-propagation XT can be suppressed to 1 dB or less from the minimum value.

[0023] (15) In (13) above, condition 2b may be further defined by the following formula: 0.90Aeff2≦Aeff≦1.12Aeff2 In this case, the increase in counter-propagation PCC and counter-propagation XT can be suppressed to 0.5 dB or less from the minimum value.

[0024] (16) In (13) above, condition 2b may be further defined by the following formula: 0.95Aeff2≦Aeff≦1.05Aeff2 In this case, the increase in counter-propagation PCC and counter-propagation XT can be suppressed to 0.1 dB or less from the minimum value.

[0025] (17) In any of the above (1) to (16), when the core radius is ra [μm], the cable cutoff wavelength is λcc [nm], and the relative refractive index difference of the core based on the refractive index of the first cladding is Δcore [%], condition 3, condition 4, condition 5, or condition 6 may be satisfied. Condition 3 is defined by the following formula: λcc[nm]≦1260[nm] ra[nm]≧2.51(Δcore) -0.605 [μm] Condition 4 is defined by the following formula: λcc[nm]≦1360[nm] ra[nm]≧2.71(Δcore) -0.607 [μm] Condition 5 is defined by the following formula: λcc[nm]≦1460[nm] ra[nm]≧2.92(Δcore) -0.609 [μm] Condition 6 is defined by the following formula: λcc[nm]≦1530[nm] ra[nm]≧3.06(Δcore) -0.611 [μm] In this case, the confinement of the signal light in each core can be strengthened.

[0026] (18) In any of (1) to (17) above, the fiber may further include a third cladding surrounded by the first cladding, and the third cladding may be positioned on a line segment connecting the centers of two adjacent cores in a cross section perpendicular to the fiber axis, spaced apart from each of the two adjacent cores, and the refractive index of the third cladding may be lower than the refractive index of the first cladding. In this case, the inter-core PCC and inter-core XT can be further reduced.

[0027] (19) In the above (18), the third cladding may have a circular shape in a cross section perpendicular to the fiber axis. In this case, the MCF can be manufactured more easily.

[0028] (20) In any of the above (1) to (19), the multiple cores, the first cladding, and the second cladding may include silica-based glass. In this case, low transmission loss can be achieved in the wavelength band from 1260 nm to 1625 nm used in optical communications, and high manufacturability can also be achieved.

[0029] [Details of the embodiment of the present disclosure] Specific examples of the MCF according to the present embodiment will be described with reference to the drawings as necessary. Note that the present disclosure is not limited to these examples, but is intended to include all modifications within the scope of the claims and meaning equivalent to the claims. In the description of the drawings, the same elements are given the same reference numerals, and duplicated descriptions are omitted.

[0030] In an SI type (more precisely, matched cladding type) MCF as described in Non-Patent Document 1, for example, in order to transmit an optical signal by operating each core in a single mode at a wavelength of 1550 nm, the cable cutoff wavelength (hereinafter also referred to as λcc) of each core is set to 1530 nm or less. In this case, in order to reduce the inter-core PCC and inter-core XT, it is desirable to make λcc as long as possible and to strengthen the confinement of light in the core. By reducing the inter-core PCC and inter-core XT, it is possible to increase the core density (the number of cores per cross-sectional area) on the cross section of the MCF while maintaining the quality of the transmission signal.

[0031] Figure 1 is a graph showing the relationship between the PCC between two adjacent cores at a wavelength of 1550 nm and the Aeff of each core when the λcc of each core is fixed at 1530 nm. The vertical axis of Figure 1 shows the PCC between the cores [ / km]. The horizontal axis of Figure 1 shows the Aeff [μm 2FIG. 1 shows the cases where the center-to-center spacing Λ of the cores is 25 μm, 30 μm, 35 μm, 40 μm, 45 μm, and 50 μm.

[0032] Although the value varies depending on the center-to-center distance between two adjacent cores, it can be seen that the smaller Aeff is, the more exponentially the PCC (represented by the symbol h) decreases. For SI-type and matched cladding-type cores, once λcc and Aeff are determined, the relative refractive index difference of the core based on the refractive index of the cladding, and the core radius are uniquely determined. This is because the design freedom is limited only by the relative refractive index difference of the core and the core radius.

[0033] Non-Patent Document 4 shows that even in a grade-index core, if the spot diameter and λcc are equivalent, the PCC is the same as that of an SI core. Therefore, it can be seen that in a grade-index core, as in the SI core, the smaller the Aeff, the lower the PCC h exponentially decreases.

[0034] Trench-assisted and hole-assisted MCFs offer more freedom in design. Therefore, the refractive index profile and the confinement of light in the core are not uniquely determined by λcc and Aeff alone. When the values ​​from the lowest refractive index of the trench or hole to the highest refractive index of the core are fixed, the smaller Aeff is, the higher the confinement of light in the core can be, and PCC h decreases exponentially, as shown in Non-Patent Documents 2 and 3.

[0035] Fig. 2 is a diagram showing a cross section perpendicular to the fiber axis and a refractive index profile of an MCF according to an embodiment. As shown in Fig. 2, an MCF 1 according to an embodiment includes a plurality of cores 2, a common first cladding 3, and a second cladding 4. The cores 2, the first cladding 3, and the second cladding 4 each contain silica-based glass. In the MCF 1, the transmission loss at a wavelength of 1550 nm is 0.22 dB / km or less. Silica-based glass is glass whose main component is silica, and contains 90% or more silica.

[0036] The cores 2 have the same circular shape in a cross section perpendicular to the fiber axis. The radius ra of each core 2 is, for example, 3 μm or more and 7 μm or less. Each core 2 extends along the fiber axis of the MCF 1. In this embodiment, the MCF 1 is a two-core optical fiber, and the number of cores 2 is two, but this is not limited to this. In a cross section perpendicular to the fiber axis, the two cores 2 are arranged to face each other across the central axis of the MCF 1. In a cross section perpendicular to the fiber axis, the two cores 2 are arranged at an equal distance from the central axis. In a cross section perpendicular to the fiber axis, the center-to-center distance Λ between two adjacent cores 2 is, for example, 30 μm or more and 50 μm or less.

[0037] The first cladding 3 is a common cladding surrounding the multiple cores 2. The first cladding 3 covers the outer peripheral surfaces of the multiple cores 2. In a cross section perpendicular to the fiber axis, the first cladding 3 has a circular shape. The second cladding 4 is a common cladding surrounding the first cladding 3. The second cladding 4 covers the outer peripheral surface of the first cladding 3. For example, the shortest distance between the interface between the first cladding 3 and the second cladding 4 and the center of the multiple cores 2 is 15 μm or more and 20 μm or less. In a cross section perpendicular to the fiber axis, the second cladding 4 has a circular shape. The radius of the second cladding 4 is, for example, 50 μm or more and 100 μm or less, or 62 μm or more and 63 μm or less.

[0038] The refractive index of the second cladding 4 is lower than that of the core 2 and higher than that of the first cladding 3. The relative refractive index difference of the second cladding 4 based on the refractive index of the first cladding 3 is 0.02% or more, the relative refractive index difference of the core 2 is 0.30% or more and 1.00% or less, and the difference between the relative refractive index difference of the core 2 and the relative refractive index difference of the second cladding 4 is 0.20% or more. The refractive index distribution in FIG. 2 is shown with the relative refractive index difference Δ based on the refractive index of the first cladding 3 as the vertical axis and the radial position r as the horizontal axis. The radial position r is 0 at the center of the fiber. The MCF1 is a common depressed type MCF. The first cladding 3 functions as a common depressed.

[0039] In MCF1, the effective cross-sectional area of ​​core 2 at a wavelength of 1550 nm is defined as Aeff [μm 2 ], the center distance between two adjacent cores 2 in the cross section perpendicular to the fiber axis is Λ [μm], and the relative refractive index difference of the core 2 based on the refractive index of the first cladding 3 is Δcore [%]. Aeff1 [μm 2 ] is defined, condition 1a or condition 2a is satisfied. Aeff1=18.6-4.63ln(Δcore)+1.24Λ+24.1[ln(Δcore)] 2 -6.05×10 -3 Λ 2 -0.858Λln(Δcore) Condition 1a and condition 2a are defined by the following equations. In the above formula, the unit of Aeff1 is [μm 2 ], the constant coefficients have the following units: 18.6 [μm 2 ]. -4.63[μm 2 ]. 1.24[μm]. 24.1[μm 2 -6.05×10 -3 [-(unitless)]. -0.858[μm]. That is, Aeff is the effective cross-sectional area [μm 2 ], Λ is the center interval in [μm], Δcore is the relative refractive index difference in [%], Aeff1 is in [μm 2 ] means the numerical value when (Condition 1a) 0.35[%]≦Δcore[%]≦1.00[%] 25[μm]≦Λ[μm]≦50[μm] 0.80Aeff1≦Aeff≦1.35Aeff1 (Condition 2a) 0.30[%]≦Δcore[%]≦0.35[%] 20[μm]≦Λ[μm]≦25[μm] 0.88Aeff1≦Aeff≦1.35Aeff1

[0040] Condition 1a may be further defined by any of the following expressions: 0.83Aeff1≦Aeff≦1.18Aeff1 0.90Aeff1≦Aeff≦1.12Aeff1 0.95Aeff1≦Aeff≦1.05Aeff1 Condition 2a may be further defined by any of the following expressions: 0.90Aeff1≦Aeff≦1.18Aeff1 0.92Aeff1≦Aeff≦1.12Aeff1 0.96Aeff1≦Aeff≦1.05Aeff1

[0041] In MCF1, the effective cross-sectional area of ​​core 2 at a wavelength of 1550 nm is defined as Aeff [μm 2 ], the center distance between two adjacent cores 2 in the cross section perpendicular to the fiber axis is Λ [μm], and the relative refractive index difference of the core 2 based on the refractive index of the first cladding 3 is Δcore [%]. 2 ] is defined, condition 1b or condition 2b is met. Aeff2=19.2-3.01ln(Δcore)+1.40Λ+25.6[ln(Δcore)] 2 -7.72×10 -3 Λ 2 -0.980Λln(Δcore) In the above formula, the unit of Aeff2 is [μm 2 ], the constant coefficients have the following units: 19.2 [μm 2 ]. -3.01[μm 2 ]. 1.40[μm]. 25.6[μm 2 -7.72×10 -3 [-(unitless)]. -0.980[μm]. That is, Aeff is the effective cross-sectional area [μm 2 ], Λ is the center interval in [μm], Δcore is the relative refractive index difference in [%], Aeff2 is in [μm 2 ] means the numerical value when Condition 1b and condition 2b are defined by the following equations. (Condition 1b) 0.35[%]≦Δcore[%]≦1.00[%] 25[μm]≦Λ[μm]≦50[μm] 0.75Aeff2≦Aeff≦1.36Aeff2 (Condition 2b) 0.30[%]≦Δcore[%]≦0.35[%] 20[μm]≦Λ[μm]≦25[μm] 0.84Aeff2≦Aeff≦1.36Aeff2

[0042] Condition 1b may be further defined by any of the following expressions: 0.85Aeff2≦Aeff≦1.18Aeff2 0.89Aeff2≦Aeff≦1.12Aeff2 0.95Aeff2≦Aeff≦1.05Aeff2 Condition 2b may be further defined by any of the following expressions: 0.88Aeff2≦Aeff≦1.18Aeff2 0.90Aeff2≦Aeff≦1.12Aeff2 0.95Aeff2≦Aeff≦1.05Aeff2

[0043] In the common depressed type, λcc when only the waveguide structure including the core 2 and the common depressed (i.e., the first cladding 3) is considered is a value larger than the desired λcc. By adjusting the relative refractive index difference of the second cladding 4 based on the refractive index of the first cladding 3 and by adjusting the shortest distance between the center of the core 2 and the second cladding 4 in the cross section perpendicular to the fiber axis, λcc can be adjusted to a desired value. Therefore, the relative refractive index difference Δcore of the core 2 based on the radius ra of the core 2 and the common first cladding 3 can be freely set to a value independent of λcc. In addition, according to the MCF1, PCC h can be reduced when the same λcc is realized, compared to SI type, matched cladding type, and trench-assisted type MCFs.

[0044] In order to strengthen the confinement of each core 2, at least compared to the SI type and matched cladding type, it is desirable to set λcc, when considering only the waveguide structure portion including the core 2 and the common depressed (i.e., the first cladding 3), to a value larger than the upper limit of the desired λcc. To achieve this in a commonly depressed type MCF, it is desirable to satisfy condition 3, condition 4, condition 5, or condition 6 defined by the following formula, where ra [μm] is the radius of the core 2, λcc [nm] is the cable cutoff wavelength, and Δcore [%] is the relative refractive index difference of the core 2 based on the refractive index of the first cladding 3. (Condition 3) λcc[nm]≦1260[nm] ra[μm]≧2.51(Δcore) -0.605 [μm] (Condition 4) λcc[nm]≦1360[nm] ra[μm]≧2.71(Δcore) -0.607 [μm] (Condition 5) λcc[nm]≦1460[nm] ra[μm]≧2.92(Δcore) -0.609 [μm] (Condition 6) λcc[nm]≦1530[nm] ra[μm]≧3.06(Δcore) -0.611 [μm] MCF1 satisfies conditions 3, 4, 5, and 6. Here, λcc is a numerical value representing the cable cutoff wavelength in units of [nm], ra is a numerical value representing the radius in units of [μm], and Δcore is a numerical value representing the relative refractive index difference in units of [%]. In this case, the constant coefficients on the right-hand sides of conditions 3 to 6 are in units of [μm]. That is, in condition 3, it is 2.51 [μm], in condition 4, it is 2.71 [μm], in condition 5, it is 2.92 [μm], and in condition 6, it is 3.06 [μm].

[0045] FIG. 3 is a graph showing the relationship between the radius of the core and the relative refractive index difference of the core based on the refractive index of the first cladding. The vertical axis of FIG. 3 shows the radius of the core ra [μm]. The horizontal axis of FIG. 3 shows the relative refractive index difference of the core based on the refractive index of the first cladding [%]. FIG. 3 shows cases where λcc is 1.26 μm, 1.36 μm, 1.46 μm, and 1.53 μm. In other words, the lines shown in FIG. 3 correspond to cases where the equality of the two equations is satisfied for each of Condition 3, Condition 4, Condition 5, and Condition 6. The areas above these lines are desirable.

[0046] In many cases, the refractive index profile of an actual optical fiber is not strictly SI type. In that case, by calculating an equivalent SI type refractive index profile based on the ESI (Equivalent Step index) approximation described in Non-Patent Document 5, conditions 3, 4, 5, and 6 can be applied to an MCF having a non-SI type core. In this case, Δcore,s, which is Δcore in the ESI approximation, can be expressed by the following equation using the effective normalized frequency Veff described in Non-Patent Document 5, the core radius ρs in the ESI approximation, the wavelength λ, and the refractive index of the core n1.

number

[0047] Next, referring to Figure 4, we will explain the results of investigating the relationship between h and Aeff for each Δcore and for each Λ. Figure 4 is a graph showing the relationship between PCC and Aeff of each core. The vertical axis of Figure 4 shows the PCC [ / km] between cores. The horizontal axis of Figure 4 shows Aeff [μm 2 ] is shown. Figure 4 shows the cases where the core center distance Λ is 25 μm, 30 μm, 35 μm, 40 μm, 45 μm, and 50 μm. Figure 4 shows the case where Δcore is 0.40%. Although not shown in the figure, the relationship between h and Aeff was also investigated in the same way when Δcore was in the range of 0.30% to 1.00%.

[0048] From this result, it was found that h reaches a minimum value at different Aeff for each Λ. Aeff at which PCC h reaches a minimum value hmin in parallel propagation between two adjacent cores is approximated by the above-mentioned Aeff1. This approximation is valid at least in the range of Δcore between 0.30% and 1.00% and Λ between 20μm and 50μm. Parallel propagation refers to the direction of the signal light propagating through two adjacent cores being the same.

[0049] 5 and 6 are plots showing how much h increases when Aeff deviates from Aeff1. The horizontal axis of FIG. 5 and FIG. 6 shows Aeff / Aeff1. The vertical axis of FIG. 5 and FIG. 6 shows 10log 10 (h / hmin) is shown. hmin represents the minimum value of h for each combination of Δcore and Λ. In Fig. 5, values ​​are plotted for Δcore in the range of 0.35% to 1.00% and Λ in the range of 25μm to 50μm. In Fig. 6, values ​​are plotted for Δcore in the range of 0.30% to 1.00% and Λ in the range of 20μm to 50μm.

[0050] From Figure 5, the following can be confirmed: 0.80Aeff1≦Aeff≦1.35Aeff1 When this condition is satisfied, the increase in h compared to hmin is preferably kept to 3 dB or less in dB terms. 0.83Aeff1≦Aeff≦1.18Aeff1 When this condition is satisfied, the increase in h compared to hmin can be suppressed to 1 dB or less, which is more preferable. 0.90Aeff1≦Aeff≦1.12Aeff1 When the above condition is satisfied, the increase in h compared to hmin is suppressed to 0.5 dB or less, which is even more preferable. 0.95Aeff1≦Aeff≦1.05Aeff1 When the above condition is satisfied, the increase in h compared to hmin is suppressed to 0.1 dB or less, which is most desirable. This result corresponds to the above condition 1a.

[0051] From FIG. 6, it can be seen that the desirable lower limit of Aeff is particularly narrowed by extending the lower limit of Δcore to 0.30% and extending the lower limit of Λ to 20 μm. That is, 0.88Aeff1≦Aeff≦1.35Aeff1 When this condition is satisfied, the increase in h compared to hmin is preferably kept to 3 dB or less in dB terms. 0.90Aeff1≦Aeff≦1.18Aeff1 When this condition is satisfied, the increase in h compared to hmin is suppressed to 1 dB or less, which is more desirable. 0.92Aeff1≦Aeff≦1.12Aeff1 When the above condition is satisfied, the increase in h compared to hmin is suppressed to 0.5 dB or less, which is even more preferable. 0.96Aeff1≦Aeff≦1.05Aeff1 When the above condition is satisfied, the increase in h compared to hmin is suppressed to 0.1 dB or less, which is most desirable. This result corresponds to the above condition 2a.

[0052] As described in Non-Patent Document 1, by making the propagation directions of signal light between adjacent cores, i.e., two adjacent cores, opposite to each other, the PCC and XT between adjacent cores can be reduced. In this case, Aeff at which PCCbs, the PCC caused by Rayleigh backscattering, is at a minimum, or Aeff at which XTbs, the XT caused by Rayleigh backscattering, is at a minimum, i.e., Aeff at which PCC h is at a minimum hmin in counter propagation, is approximated by the above-mentioned Aeff2. This approximation is effective at least in the range of Δcore being 0.30% to 1.00% and Λ being 20 μm to 50 μm. Counter propagation refers to the opposite directions of signal light propagating through two adjacent cores.

[0053] From the above approximation by Aeff2, we can confirm the following: 0.75Aeff2≦Aeff≦1.36Aeff2 When the above equation is satisfied, the increase in PCCbs from its minimum value and the increase in XTbs from its minimum value are desirably suppressed to 3 dB or less in dB value. 0.85Aeff2≦Aeff≦1.18Aeff2 When the above equation is satisfied, the increase in PCCbs from its minimum value and the increase in XTbs from its minimum value can be suppressed to 1 dB or less, which is more preferable. 0.89Aeff2≦Aeff≦1.12Aeff2 When the above condition is satisfied, the increase in PCCbs from its minimum value and the increase in XTbs from its minimum value are suppressed to 0.5 dB or less in dB value, which is even more preferable. 0.95Aeff2≦Aeff≦1.05Aeff2 When the above condition is satisfied, the increase in PCCbs from its minimum value and the increase in XTbs from its minimum value are suppressed to 0.1 dB or less, which is most desirable. This result corresponds to the above condition 1b.

[0054] It can be seen that the desirable lower limit of Aeff is particularly narrowed by extending the lower limit of Δcore to 0.30% and extending the lower limit of Λ to 20 μm. 0.84Aeff2≦Aeff≦1.36Aeff2 When the above equation is satisfied, the increase in PCCbs from its minimum value and the increase in XTbs from its minimum value are desirably suppressed to 3 dB or less in dB value. 0.88Aeff2≦Aeff≦1.18Aeff2 When the above equation is satisfied, the increase in PCCbs from its minimum value and the increase in XTbs from its minimum value can be suppressed to 1 dB or less, which is more preferable. 0.90Aeff2≦Aeff≦1.12Aeff2 When the above condition is satisfied, the increase in PCCbs from its minimum value and the increase in XTbs from its minimum value are suppressed to 0.5 dB or less in dB value, which is even more preferable. 0.95Aeff2≦Aeff≦1.05Aeff2 When the above condition is satisfied, the increase in PCCbs from its minimum value and the increase in XTbs from its minimum value are suppressed to 0.1 dB or less, which is most desirable. This result corresponds to the above condition 2b.

[0055] As described above, in the MCF 1 according to this embodiment, the first cladding 3 functions as a common depressed. In the MCF 1, by satisfying condition 1a or condition 2a, the parallel propagating PCC and the parallel propagating XT can be reduced. By satisfying condition 1b or condition 2b, the counter-propagating PCC and the counter-propagating XT can be reduced. That is, in the MCF 1, which is a common depressed type, the PCC and the XT can be reduced more than in the SI type or matched cladding type MCF. Moreover, by setting the Aeff of each core 2 in an appropriate range, the PCC and the XT can be suppressed to values ​​close to the minimum values. In addition, since the MCF 1 does not have a refractive index structure for enhancing the individual confinement of each core 2, unlike the trench-assisted type or the hole-assisted type, it is easy to manufacture and is capable of reducing the PCC and the XT.

[0056] Although the embodiments have been described above, the present disclosure is not necessarily limited to the above-described embodiments, and various modifications are possible without departing from the spirit and scope of the present disclosure.

[0057] FIG. 7 is a diagram showing a cross section perpendicular to the fiber axis and a refractive index profile of an MCF according to a modified example. As shown in FIG. 7, an MCF 1A according to a modified example is different from the MCF 1 shown in FIG. 2 in that it further includes a third cladding 5. The third cladding 5 is surrounded by the first cladding 3. In the cross section perpendicular to the fiber axis, the third cladding 5 is disposed on a line segment L connecting the centers of two adjacent cores 2, and is spaced apart from each of the two adjacent cores 2. The third cladding 5 does not cover any of the multiple cores 2. This can further reduce the PCC h between two adjacent cores 2.

[0058] The third cladding 5 has a circular shape in a cross section perpendicular to the fiber axis. This facilitates manufacturing. In this embodiment, the radius of the third cladding 5 is equal to the radius of the core 2, but may be different from the radius of the core 2. The third cladding 5 includes silica-based glass. The third cladding 5 has a refractive index lower than that of the first cladding 3, and functions as a low-refractive index pit. The relative refractive index difference of the third cladding 5 based on the refractive index of the first cladding 3 is, for example, −0.8% or more and −0.1% or less. In this modification, in a cross section perpendicular to the fiber axis, the third cladding 5 is located equidistant from the centers of the two cores 2, and the center of the third cladding 5 overlaps with the center of the MCF 1A.

[0059] The features and characteristics of the MCF disclosed herein can be measured by the following methods. The refractive indices of the core, first cladding, and second cladding can be measured, for example, by the refraction near-field method or the lateral interferometry. The transmission loss can be measured by applying the method described in ITU-T G.650.1 to each core of the MCF. The effective area can be measured, for example, by the method described in Appendix III of ITU-T G.650.2 (08 / 2015). The effective area of ​​two adjacent cores can be measured by the method described in Appendix III of ITU-T G.650.2 (08 / 2015). The center-to-center distance in a cross section perpendicular to the fiber axis can be measured, for example, by the refraction near-field method, the lateral interference method, or a microscope observation image (transmission near-field method) of the MCF cross section.

[0060] Although the above description has been given by taking an example of an uncoupled MCF, the present invention is not limited to this. Even in a coupled MCF (also called a randomly coupled MCF) that allows inter-core XT and increases core density, if the coupling between cores is too strong, the difficulty of the numerical calculation to compensate for inter-core XT increases. Therefore, by adopting a core structure that can reduce the inter-core PCC, the core density can be increased (the core interval can be narrowed). Therefore, in both the uncoupled MCF and the coupled MCF, the inter-core PCC and inter-core XT can be reduced while maintaining the individual optical characteristics of each core at the desired values ​​within the range of the economically feasible refractive index profile. [Explanation of symbols]

[0061] 1,1A…MCF 2. Core 3…First cladding 4…Second cladding 5…Third cladding ra...core radius L…Line segment Λ…Center-to-center distance of adjacent cores Δ…Relative refractive index difference

Claims

1. A common depressed type multi-core optical fiber used for parallel propagation, Multiple cores and a common first clad surrounding each of the cores; a second cladding surrounding the first cladding; the refractive index of the second cladding is lower than the refractive index of the core and higher than the refractive index of the first cladding; The transmission loss at a wavelength of 1550 nm is 0.22 dB / km or less. The effective cross-sectional area of ​​the core at a wavelength of 1550 nm is defined as Aeff [μm ２ ], the center-to-center distance between two adjacent cores in a cross section perpendicular to the fiber axis is Λ [μm], and the relative refractive index difference of the core based on the refractive index of the first cladding is Δcore [%], Aeff1 = 18.6 - 4.63ln(Δcore) + 1.24Λ + 24.1[ln(Δcore)]^2 - 6.05×10^(-3)Λ - 0.858Λln(Δcore) ２ -6.05×10 －３ Λ ２ -0.858Λln(Δcore) Aeff1 [μm ２ ], and satisfying the following condition 1a. 0.35%≦Δcore%≦1.00% 25 [μm]≦Λ[μm]≦50 [μm] 0.80Aeff1≦Aeff≦1.35Aeff1

2. The multi-core optical fiber according to claim 1 , wherein the condition 1a is further defined by the following formula: 0.83Aeff1≦Aeff≦1.18Aeff1

3. The multi-core optical fiber according to claim 1 , wherein the condition 1a is further defined by the following formula: 0.90Aeff1≦Aeff≦1.12Aeff1

4. The multi-core optical fiber according to claim 1 , wherein the condition 1a is further defined by the following formula: 0.95Aeff1≦Aeff≦1.05Aeff1

5. A common depressed type multi-core optical fiber used for parallel propagation, Multiple cores and a common first clad surrounding each of the cores; a second cladding surrounding the first cladding; the refractive index of the second cladding is lower than the refractive index of the core and higher than the refractive index of the first cladding; The transmission loss at a wavelength of 1550 nm is 0.22 dB / km or less. The effective cross-sectional area of ​​the core at a wavelength of 1550 nm is defined as Aeff [μm ２ ], the center-to-center distance between two adjacent cores in a cross section perpendicular to the fiber axis is Λ [μm], and the relative refractive index difference of the core based on the refractive index of the first cladding is Δcore [%], Aeff1 = 18.6 - 4.63 ln(Δcore) + 1.24Λ + 24.1[ln(Δcore)] ２ -6.05×10 －３ Λ ２ -0.858Λ ln(Δcore) Aeff1 [μm ２ ], and satisfying the following condition 2a. 0.30%≦Δcore%≦0.35% 20 [μm]≦Λ[μm]≦25 [μm] 0.88Aeff1≦Aeff≦1.35Aeff1

6. The multi-core optical fiber according to claim 5 , wherein the condition 2a is further defined by the following formula: 0.90Aeff1≦Aeff≦1.18Aeff1

7. The multi-core optical fiber according to claim 5 , wherein the condition 2a is further defined by the following formula: 0.92Aeff1≦Aeff≦1.12Aeff1

8. The multi-core optical fiber according to claim 5 , wherein the condition 2a is further defined by the following formula: 0.96Aeff1≦Aeff≦1.05Aeff1

9. A common depressed type multi-core optical fiber used for counter propagation, Multiple cores and a common first clad surrounding each of the cores; a second cladding surrounding the first cladding; the refractive index of the second cladding is lower than the refractive index of the core and higher than the refractive index of the first cladding; The transmission loss at a wavelength of 1550 nm is 0.22 dB / km or less. The effective cross-sectional area of ​​the core at a wavelength of 1550 nm is defined as Aeff [μm ２ ], the center-to-center distance between two adjacent cores in a cross section perpendicular to the fiber axis is Λ [μm], and the relative refractive index difference of the core based on the refractive index of the first cladding is Δcore [%], Aeff2 = 19.2 - 3.01 ln(Δcore) + 1.40Λ + 25.6[ln(Δcore)]² - 7.72×10⁻³Λ - 0.980Λln(Δcore) ２ - 7.72×10 －３ Λ ２ - 0.980Λln(Δcore) Aeff2 [μm ２ ], and satisfying the following condition 1b. 0.35%≦Δcore%≦1.00% 25 [μm]≦Λ[μm]≦50 [μm] 0.75Aeff2≦Aeff≦1.36Aeff2

10. The multi-core optical fiber according to claim 9 , wherein the condition 1b is further defined by the following formula: 0.85Aeff2≦Aeff≦1.18Aeff2

11. The multi-core optical fiber according to claim 9 , wherein the condition 1b is further defined by the following formula: 0.89Aeff2≦Aeff≦1.12Aeff2

12. The multi-core optical fiber according to claim 9 , wherein the condition 1b is further defined by the following formula: 0.95Aeff2≦Aeff≦1.05Aeff2

13. A common depressed type multi-core optical fiber used for counter propagation, Multiple cores and a common first clad surrounding each of the cores; a second cladding surrounding the first cladding; the refractive index of the second cladding is lower than the refractive index of the core and higher than the refractive index of the first cladding; The transmission loss at a wavelength of 1550 nm is 0.22 dB / km or less. The effective cross-sectional area of ​​the core at a wavelength of 1550 nm is defined as Aeff [μm ２ ], the center-to-center distance between two adjacent cores in a cross section perpendicular to the fiber axis is Λ [μm], and the relative refractive index difference of the core based on the refractive index of the first cladding is Δcore [%], Aeff2 = 19.2 - 3.01ln(Δcore) + 1.40Λ + 25.6[ln(Δcore)] - 7.72×10 ２ Λ －３ - 0.980Λln(Δcore) ２ ２ -7.72×10 －３ Λ ２ -0.980Λln(Δcore) Aeff2 [μm ２ ], and satisfying the following condition 2b. 0.30%≦Δcore%≦0.35% 20 [μm]≦Λ[μm]≦25 [μm] 0.84Aeff2≦Aeff≦1.36Aeff2

14. The multi-core optical fiber according to claim 13 , wherein the condition 2b is further defined by the following formula: 0.88Aeff2≦Aeff≦1.18Aeff2

15. The multi-core optical fiber according to claim 13 , wherein the condition 2b is further defined by the following formula: 0.90Aeff2≦Aeff≦1.12Aeff2

16. The multi-core optical fiber according to claim 13 , wherein the condition 2b is further defined by the following formula: 0.95Aeff2≦Aeff≦1.05Aeff2

17. 17. The multi-core optical fiber according to claim 1, wherein condition 3, condition 4, condition 5, or condition 6 is satisfied when a radius of the core is ra [μm], a cable cutoff wavelength is λcc [nm], and a relative refractive index difference of the core with respect to a refractive index of the first cladding is Δcore [%]. The condition 3 is defined by the following formula. λcc[nm]≦1260[nm] ra≧2.51(Δcore) －０．６０５ μm The condition 4 is defined by the following formula. λcc[nm]≦1360[nm] ra≧2.71(Δcore) －０．６０７ [μm] The condition 5 is defined by the following formula. λcc[nm]≦1460[nm] ra≧2.92(Δcore) －０．６０９ [μm] The condition 6 is defined by the following formula. λcc[nm]≦1530[nm] ra≧3.06(Δcore) －０．６１１ [μm]

18. Further comprising a third cladding surrounded by the first cladding, the third cladding is disposed on a line segment connecting centers of two adjacent cores in a cross section perpendicular to a fiber axis, and spaced apart from each of the two adjacent cores; The refractive index of the third cladding is lower than the refractive index of the first cladding. The multi-core optical fiber according to any one of claims 1 to 16.

19. In a cross section perpendicular to the fiber axis, the third cladding has a circular shape. The multi-core optical fiber according to claim 18.

20. the plurality of cores, the first cladding, and the second cladding include silica-based glass; The multi-core optical fiber according to any one of claims 1 to 16.

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