Abstract
The present invention is to provide a multi-core optical fiber that can expand its transmission wavelength band, and extend its transmission distance by reducing crosstalk, and also provide a method for designing the multi-core optical fiber. A multi-core optical fiber according to the present invention includes: four cores that are arranged in a square lattice pattern in a longitudinal direction; and a cladding region that is formed around the outer peripheral portions of the cores and has a lower refractive index than the cores, the absolute value of the relative refractive index difference between the cores and the cladding region being represented by A. In the multi-core optical fiber, the diameter of the cladding region is 125+1 m, the cutoff wavelength is 1.45 m or shorter, the mode field diameter MFD at a wavelength of 1.55 m is 9.5 to 10.0 m, the bending loss at a wavelength of 1.625 m and with a bending radius of 30 mm is 0.1 dB/100 turns or smaller, and the inter-core crosstalk at the wavelength of 1.625 m is 47 dB/km or smaller.
Claims
1. A multi-core optical fiber comprising: four cores that are arranged in a square lattice pattern in a longitudinal direction; and a cladding region that is formed around outer peripheral portions of the cores and has a lower refractive index than the cores, an absolute value of a relative refractive index difference between the cores and the cladding region being represented by A, wherein a diameter of the cladding region is 1251 m, a cutoff wavelength is less than or equal to 1.45 m, a mode field diameter MFD at a wavelength of 1.55 m is 9.5 to 10.0 m, a bending loss at a wavelength of 1.625 m and with a bending radius of 30 mm is less than or equal to 0.1 dB/100 turns, and inter-core crosstalk at the wavelength of 1.625 m is less than or equal to 47 dB/km.
2. The multi-core optical fiber according to claim 1, wherein a shortest distance from a center of each of the four cores to an outer periphery of the cladding region is longer than or equal to 33 m, and a radius a of each of the four cores and the relative refractive index difference between each of the four cores and the cladding region is within a range expressed by Mathematical Expression C1:
[Mathematical Expression C1]
0.0004a.sup.20.003a+0.00910.0005a.sup.20.0032a+0.0094, 0.0874a.sup.2, and 0.0101a.sup.758(C1).
3. The multi-core optical fiber according to claim 1, further comprising a coating layer that surrounds the cladding region, wherein a diameter including the coating layer is 20020 m.
4. A multi-core optical fiber comprising: four cores that are arranged in a square lattice pattern in a longitudinal direction; first cladding regions that surround the respective cores; and a second cladding region that surrounds all of the four first cladding regions, wherein a refractive index is the highest in the cores, is the second highest in the second cladding region, and is the lowest in the first cladding regions, a relative refractive index difference between the cores and the first cladding regions is less than or equal to 0.8%, a ratio between a diameter of the cores and a diameter of the first cladding regions is within a range of 2.0 to 3.0, a diameter of a cladding region including the first cladding regions and the second cladding region is 1251 m, a cutoff wavelength is less than or equal to 1.45 m, a mode field diameter MFD at a wavelength of 1.55 m is 9.5 to 11.4 m, a bending loss at a wavelength of 1.625 m and with a bending radius of 30 mm is less than or equal to 0.1 dB/100 turns, and inter-core crosstalk at the wavelength of 1.625 m is less than or equal to 54 dB/km.
5. The multi-core optical fiber according to claim 4, wherein a radius a of the cores, a relative refractive index difference between the cores and the first cladding regions, and a relative refractive index difference 2 between the cores and the second cladding region satisfy conditions expressed by Mathematical Expressions C2 to C4:
[Mathematical Expression C2]
0.0003a.sup.20.0024a+0.00790.0005a.sup.20.0032a+0.0094(C2)
[Mathematical Expression C3]
(0.0013MFD.sup.20.0296MFD+0.1735)(a.sub.2/a).sup.2+(0.0129MFD.sup.2+0.2885MFD1.6141)(a.sub.2/a)+(0.0419MFD.sup.20.9096MFD+4.9388)0.0015MFD+0.0223(C3)
[Mathematical Expression C4]
(0.0026MFD.sup.20.0573MFD+0.31)(a.sub.2/a).sup.2+(0.0124MFD.sup.2+0.2683MFD1.4515)(a.sub.2/a)+(0.0141MFD.sup.20.3045MFD+1.6488) .sub.2(0.002MFD.sup.20.0422MFD+0.2215)(a.sub.2/a).sup.2+(0.0098MFD.sup.2+0.205MFD1.0734)(a.sub.2/a)+(0.012MFD.sup.20.2533MFD+1.3312)(C4) where, a2 represents a radius (m) of the first cladding, and MFD represents a desired mode field diameter (m).
6. The multi-core optical fiber according to claim 4, further comprising third cladding regions that are formed in the first cladding regions, have a refractive index substantially equal to a refractive index of the second cladding region, and surround the cores.
7. The multi-core optical fiber according to claim 4, further comprising a coating layer that surrounds the cladding region, wherein a diameter including the coating layer is 20020 m.
Description
BRIEF DESCRIPTION OF DRAWINGS
(1) FIG. 1 is a diagram for explaining the structure of a multi-core optical fiber according to the present invention.
(2) FIG. 2 is a chart for explaining the relationship between structural parameters and optical characteristics of multi-core optical fibers according to the present invention.
(3) FIG. 3 is a chart for explaining the relationship among the mode field diameter (MFD), the required cladding thickness (minimum OCT), and crosstalk (XT) in a multi-core optical fiber according to the present invention.
(4) FIG. 4 is a diagram for explaining the structure of a multi-core optical fiber according to the present invention.
(5) FIG. 5 is charts for explaining the structural conditions for a multi-core optical fiber according to the present invention.
(6) FIG. 6 is charts for explaining the structural conditions for a multi-core optical fiber according to the present invention.
(7) FIG. 7 is a chart for explaining the structural conditions for a multi-core optical fiber according to the present invention.
(8) FIG. 8 is a chart for explaining the structural conditions for a multi-core optical fiber according to the present invention.
(9) FIG. 9 is a chart for explaining the structural conditions for a multi-core optical fiber according to the present invention.
(10) FIG. 10 is a chart for explaining the structural conditions for a multi-core optical fiber according to the present invention.
(11) FIG. 11 is a chart for explaining the structural conditions for a multi-core optical fiber according to the present invention.
(12) FIG. 12 is a chart for explaining the structural conditions for a multi-core optical fiber according to the present invention.
(13) FIG. 13 is a chart for explaining the structural conditions for a multi-core optical fiber according to the present invention.
(14) FIG. 14 is a diagram for explaining the structure of a multi-core optical fiber according to the present invention.
(15) FIG. 15 is a diagram for explaining the structure of a multi-core optical fiber according to the present invention.
(16) FIG. 16 is a flowchart for explaining a design method according to the present invention.
(17) FIG. 17 is a flowchart for explaining a design method according to the present invention.
DESCRIPTION OF EMBODIMENTS
(18) Embodiments of the present invention will be described below, with reference to the accompanying drawings. The embodiments described below are examples of the present invention, and the present invention is not limited to these embodiments. Note that like components are denoted by like reference numerals in this specification and the drawings.
First Embodiment
(19) FIG. 1 is a diagram for explaining the structure of a multi-core optical fiber 301 according to this embodiment. FIG. 1 (a) is a cross-sectional view of the multi-core optical fiber 301. FIG. 1 (b) is a diagram for explaining the refractive index distribution near a core of the multi-core optical fiber 301. The multi-core optical fiber 301 is an MCF that has a cladding 11 of 1251 m in diameter, and four cores 12. Here, the four cores 12 have substantially the same refractive index distributions, which are of a step index (SI) type or are refractive index distributions equivalent thereto. Here, a represents a core radius, and A represents a relative refractive index difference between the cores 12 and the cladding 11. When all the cores 12 have refractive index distributions of the SI type or equivalent to the SI type, the mass productivity and the yield of the multi-core optical fiber 301 can be significantly increased.
(20) FIG. 2 is a characteristics chart illustrating the relationship between structural parameters and optical characteristics of MCFs. In this characteristics chart, the abscissa axis indicates the core radius a, and the ordinate axis indicates the relative refractive index difference .
(21) Solid lines indicate core structures for obtaining predetermined mode field diameters (MFDs). In this chart, structures in which the MFDs at a wavelength of 1.55 m are 9.5 m, 10.0 m, and 11.4 m are shown.
(22) The dashed lines indicate core structures for obtaining predetermined cutoff wavelengths c. In this chart, structures in which the cutoff wavelengths c are 1.45 m, 1.48 m, 1.51 m, and 1.53 m are shown. The dotted line indicates a core structure for obtaining a predetermined bending loss (ab). In this chart, a structure in which the bending loss c at a wavelength of 1.625 m and a bending radius of 30 mm is 0.1 dB/100 turns is shown.
(23) Note that FIG. 2 is a characteristics chart obtained through numerical calculation (optical characteristics analysis of optical fibers, using a finite element method). Specifically, this chart is created by numerically calculating the MFD, the cutoff wavelength c, and the bending loss ab while changing the MCF core radius a and the relative refractive index difference , and plotting structures having the same value (MFD=9.5 m, for example) in a graph.
(24) In the case of the SI type, optical characteristics can be uniquely determined once the core structure is determined. For example, to obtain an MCF that has an MED (=9.5 m [wavelength: 1.55 m]), a bending loss ab (=0.1 dB/100 turns), and a cutoff wavelength c of 1.45 m or shorter, which are equivalent to those of an SMF, the core structure should be designed to have a core radius a and a relative refractive index difference that fall within a region surrounded by the solid lines, the dashed lines, and the dotted line of the respective numerical values in FIG. 2.
(25) Specifically, to obtain an MFD of 9.5 m or greater at a wavelength of 1.55 m, the solid line expressed by
[Mathematical Expression 1]
0.0005a.sup.20.0032a+0.0094(1)
is adopted. Also, to set the cutoff wavelength c to 1.45 m or shorter, the dashed line expressed by
[Mathematical Expression 2]
0.0874a.sup.2(2)
is adopted. Further, to obtain a bending loss of 0.1 dB/100 turns or smaller at a wavelength of 1.625 m and a bending radius of 30 mm, the dotted line expressed by
[Mathematical Expression 3]
0.0101a.sup.758(3)
is adopted.
(26) Next, a method for detecting the upper limit of MFDs and the required cladding thickness (minimum OCT) is described. The minimum OCT means the shortest distance between the center of the outermost core and the outer periphery of the cladding, where the excessive loss is 0.01 dB/km or smaller at a wavelength of 1.625 m. FIG. 3 is a diagram for explaining the relationship among the cutoff wavelength c, the MFD, the minimum OCT, and the crosstalk XT in the multi-core optical fiber 301. Here, the crosstalk XT is the value at a wavelength of 1.625 m, and the MFD is at a wavelength of 1.55 m. FIG. 3 is a characteristics chart obtained through numerical calculation (optical characteristics analysis of optical fibers, using a finite element method). Specifically, this chart is created by numerically calculating the crosstalk XT, the minimum OCT, and the cutoff wavelength c while changing the MFD of the MCF, and plotting structures having the cutoff wavelength c of the same value (c=1.45 m, for example) in a graph.
(27) As can be seen from the solid lines in FIG. 3, the minimum OCT becomes greater, as the MFD becomes greater. As can be seen from the dashed lines in FIG. 3, the XT becomes greater, as the FD becomes greater. On the other hand, where the cutoff wavelength c is shortened, the minimum OCT becomes greater (solid line), but the XT is substantially constant (dashed line). Here, if a QPSK signal is transmitted 1000 km or greater, the required XT is-47 dB/km. As can be seen from the dashed line in FIG. 3, MFD needs to be 10 m or smaller (the upper limit MFD=10 m) in order to set the cutoff wavelength c to 1.45 m or shorter at XT=47 dB/km. Further, from the solid lines in FIG. 3, to set the MFD to 10 m and the cutoff wavelength c to 1.45 m or shorter, it is necessary to set the minimum OCT to 33 m or greater (the thickness of the cladding 11 from the center of a core 12 to the outer periphery of the MCF is 33 m or greater).
(28) FIG. 2 also shows a curve (Mathematical Expression 4) having an upper limit MFD=10 m as calculated from FIG. 3.
[Mathematical Expression 4]
0.0004a.sup.20.003a+0.0091(4)
(29) In FIG. 2, the core radius a and the relative refractive index difference included in the region surrounded by the curve of MFD=9.5 m, the curve of MED=10 m, the curve of cutoff wavelength c=1.45 m, and the curve of bending loss b=0.1 dB/100 turns, and the minimum OCT of 33 m calculated from FIG. 3 are the design values of the multi-core optical fiber 301.
(30) That is, the multi-core optical fiber 301 characteristically includes: the cladding 11 that has a diameter of 125+1 m in a cross-section; and the four cores 12 that are arranged in a square lattice pattern in the cladding in the cross-section, wherein the shortest distance (minimum OCT) from the center of a core 12 to the outer periphery of the cladding 11 in the cross-section is 33 m or longer, and the relationship between the radius a of the cores 12 and the absolute value of the relative refractive index difference between the cores 12 and the cladding 11 satisfies Mathematical Expressions 1 to 4.
(31) A method for designing the multi-core optical fiber 301 is as illustrated in FIG. 16. That is, the design method includes: determining the cutoff wavelength, the upper limit value of crosstalk, the mode field diameter, and the bending loss of the multi-core optical fiber as specification values (step S11); detecting a corresponding mode field diameter corresponding to the upper limit value of crosstalk of the specification values, from a relationship chart (a second ordinate axis in FIG. 3) between the mode field diameter and the crosstalk at the cutoff wavelength of the specification values (step S12); detecting the minimum OTC corresponding to the corresponding mode field diameter, from a relationship chart (a first ordinate axis in FIG. 3) between the mode field diameter at the cutoff wavelength of the specification values and the shortest distance (minimum OTC) from the center of the core to the outer periphery of the cladding in a cross-section of the multi-core optical fiber (step S13); drawing a first curve satisfying the mode field diameter among the specification values, a second curve satisfying the cutoff wavelength among the specification values, a third curve satisfying the bending loss among the specification values, and a fourth curve satisfying the corresponding mode field diameter in an optical characteristics chart (FIG. 2) of the radius a of the core and the absolute value of the relative refractive index difference between the core and the cladding (step S14); detecting the radius a of the core and the absolute value of the relative refractive index difference included in the region surrounded by the first curve, the second curve, the third curve, and the fourth curve in the optical characteristics chart (step S15); and setting the detected minimum OTC, radius a of the core, and absolute value of the relative refractive index difference as design values of the multi-core optical fiber (step S16).
Second Embodiment
(32) FIG. 4 is a diagram for explaining the structure of a multi-core optical fiber 302 according to this embodiment. FIG. 4 (a) is a cross-sectional view of the multi-core optical fiber 302. FIG. 4 (b) is a diagram for explaining the refractive index distribution near a core of the multi-core optical fiber 302. The cladding diameter and the number of cores of the multi-core optical fiber 302 are 125+1 m and four cores, which are the same as those of the multi-core optical fiber 301 in FIG. 1, and the respective cores have substantially the same refractive index distributions.
(33) The multi-core optical fiber 302 includes the cores 12, first cladding regions 11-1 surrounding the cores 12, and a second cladding region 11-2 surrounding the first cladding regions 11-1, and the refractive index becomes lower in the order of the cores 12, the second cladding region 11-2, and the first cladding regions 11-1. With such a structure, control on optical confinement can be enhanced, and the range of MED and the transmission distance illustrated in FIG. 3 can be improved.
(34) FIG. 5 shows an example of the structural conditions for obtaining a predetermined MFD, cutoff wavelength, and XT in the multi-core optical fiber 302. FIG. 5 is characteristics charts obtained through numerical calculation (optical characteristics analysis of optical fibers, using a finite element method). Specifically, these charts are created by numerically calculating a relative refractive index difference 42, the crosstalk XT, and the cutoff wavelength c while changing the relative refractive index difference of the MCF for each MED, and plotting structures having the same cutoff wavelength (c=1.45 m) and the same crosstalk (XT=54 dB/km) in a graph. In FIGS. 5(a) to 5(c), MED at a wavelength of 1.55 m is set to 10.1 m, 10.7 m, and 11.3 m, respectively, and a2/a is calculated as 3.0 in each case.
(35) The cutoff wavelength c can be set to 1.45 m or shorter in the region closer to the origin than the dashed line in FIG. 5. Further, the core position (the position in a radial direction from the center of the MCF) is set so that the excessive loss is 0.01 dB/km or less at a wavelength of 1.625 m. In the region on the opposite side of the origin from the solid line in FIG. 5, the XT at a wavelength of 1.625 m is-54 dB/km or less. Under this crosstalk XT condition, the signal format can be extended up to 16 QAM with a transmission distance of 1000 km, and the transmission distance can be extended up to about 5000 km with a QPSK signal.
(36) As can be seen from FIGS. 5(a) to 5(c), the structural conditions for obtaining the cutoff wavelength of 1.45 m or shorter are that an upper limit value max (the maximum value of the dashed line with respect to the abscissa axis) of the relative refractive index difference is set for each MED, and the upper limit value max decreases with increase in MED.
(37) Further, the lower limit value min of the relative refractive index difference and the range of the relative refractive index difference 2 (2max-2min) for achieving the crosstalk XT of 54 dB/km or less are determined from the intersection of the solid line and the dashed line.
(38) That is, it is safe to say that FIG. 5 is charts for explaining the ranges of the relative refractive index differences and 2 for achieving the cutoff wavelength c of 1.45 m or shorter and the crosstalk XT of 54 dB/km or less with each MED.
(39) FIG. 6 also shows an example of the structural conditions for obtaining a predetermined MED, cutoff wavelength, and XT in the multi-core optical fiber 302. FIG. 6 is also characteristics charts obtained through numerical calculation (optical characteristics analysis of optical fibers, using a finite element method). Specifically, these charts are created by numerically calculating a relative refractive index difference 42, the crosstalk XT, and the cutoff wavelength c while changing the relative refractive index difference of the MCF for each MFD, and plotting structures having the same cutoff wavelength (c=1.45 m) and the same crosstalk (XT=54 dB/km) in a graph. In FIGS. 6(a) to 6(c), a2/a is set to 3.0, 2.5, and 2.0, respectively, and MED at a wavelength of 1.55 m is calculated to be 10.1 m. Note that FIG. 6(a) shows the same contents as FIG. 5(a).
(40) Here, the maximum value of the relative refractive index difference on the ordinate axis is 0.8%. This is because it is normally difficult to lower the refractive index of the cladding by 0.8% or more with respect to the refractive index of the core, in a case where the core is formed with pure quartz glass. Here, as illustrated in FIGS. 6(b) and 6(c), Amax is 0.8% or greater when a2/a is 2 or 2.5. However, there is little point in appealing the A of 0.8% or greater for the above reason, and is not shown in these drawings.
(41) As illustrated in FIGS. 6(a) to 6(c), Amin becomes greater, as a2/a is made smaller. On the other hand, it is apparent that the range of the relative refractive index difference 2 (2max-2min) decreases.
(42) The following can be seen from FIGS. 5 and 6.
(43) ((1) Amax is determined from the structural condition of a.sub.2/a=3.0 (a2/a=2.5 or 2.0 is meaningless, because the value exceeds 0.8%).
(44) ((2) The ranges of min and 2 can be defined as functions of a.sub.2/a and MED.
(45) FIG. 7 is a chart for explaining the relationship between MFD of the multi-core optical fiber 302 and the range of 4. Here, a2/a=3.0, with the above (1) being taken into consideration. The upper limit value (Amax) and the lower limit value (Amin) of A shown in FIG. 5 are expressed by functions of MED at a wavelength of 1.55 m. As shown in FIG. 7, Amax decreases linearly with respect to MED as in the expression shown below.
[Mathematical Expression 5]
0.0015MFD+0.0223(6)
(46) The maximum MFD that satisfies c of 1.45 m or shorter, and XT of 54 dB/km or less (the conditions described above with reference to FIG. 5) is MED=11.4 m, which is the intersection of Amax and Amin. FIG. 2 also shows the curve (Mathematical Expression 6) of the maximum MFD.
[Mathematical Expression 6]
0.0003a.sup.20.0024a+0.0079(6)
(47) In the MCF structure in FIG. 4, the shape of the electrical field distribution (MDF) is dominantly determined by the radius a of the cores 12 and the relative refractive index difference between the cores 12 and the first claddings 11-1. Accordingly, the conditions for the radius a of the cores 12 and the relative refractive index difference can be found from FIG. 2.
(48) That is, in a case where a2/a=3.0, the core radius a and the relative refractive index difference included in the region surrounded by the curve of MFD=9.5 m and the curve of MFD=11.4 m in FIG. 2 are design values of the multi-core optical fiber 302 calculated from MDF. Note that, in the MCF structure in FIG. 4, the cutoff wavelength c and the bending loss ab vary with the relative refractive index difference 42, and therefore, the dashed lines and the dotted line in FIG. 2 are not taken into consideration.
(49) Hereinafter, the ranges of the core radius a and the relative refractive index difference calculated from FIG. 2 are limited as follows.
(50) ((a) The upper limit value max of the relative refractive index difference
(51) Mathematical Expression 5 expresses the variation of Amax with respect to MED when a2/a=3.0, and another expression is satisfied in a case where a2/a has a different value. However, as can be determined from FIGS. 5 and 6, when a2/a is smaller than 3.0, Amax becomes greater and exceeds 0.8%. As described above, a structure in which A exceeds 0.8% is not realistic. Therefore, if Mathematical Expression 5 (the straight line in FIG. 7) in a case where a2/a=3.0 is defined as the upper limit value of 4, the result of Mathematical Expression 5 can be used even when a2/a has a different value.
(52) ((b) The lower limit value min of the relative refractive index difference
(53) As illustrated in FIG. 6, Amin becomes greater, as a2/a becomes smaller than 3.0. That is, as for min, when a2/a is smaller than 3.0, the curve shown in FIG. 7 rises. Therefore, the result of Mathematical Expression 5 cannot be used in a case where a2/a has a different value (the curve of Amin varies for each value of a.sub.2/a).
(54) FIG. 8 is a chart for explaining that the curve of Amin (a curve in FIG. 7) varies with each value of a.sub.2/a. Specifically, FIG. 8 is a chart illustrating the variation of Amin with respect to a2/a of the multi-core optical fiber 302 for each MFD at a wavelength of 1.55 m. As illustrated in FIGS. 5 and 6, Amin varies with a2/a and MFD. Here, the variation of Amin is expressed by functions of a2/a and MED from FIG. 8.
(55) FIG. 9 illustrates the respective coefficients (k1, k2, and k3) expressed by functions of MFD in a case where the relationship between a2/a and Amin shown in FIG. 8 is approximated by a quadratic function (k1x.sup.2+k2x+k3; x being a2/a). From these results, the lower limit min of is calculated according to the expression shown below.
[Mathematical Expression 7]
(0.0013MFD.sup.20.0296MFD)+0.1735)(a.sub.2/a).sup.2+(0.0129MFD.sup.2+0.2885MFD1.6141)(a.sub.2/a)+(0.0419MFD.sup.20.9096MFD+4.9388)(7)
(56) That is, the curve of min in FIG. 7 varies with a2/a. The maximum value of MFD (which is 11.4 when a2/a=3.0) also varies with a2/a.
(57) Further, the multi-core optical fiber 302 also has the parameter of 2.
(58) (c) The Upper Limit Value 2Max of the Relative Refractive Index Difference 2
(59) FIG. 10 is a chart for explaining that 2max varies with each value of a.sub.2/a (2max varies among FIGS. 6(a) to 6(c)). Specifically, FIG. 10 is a chart illustrating the variation of 2max with respect to a2/a of the multi-core optical fiber 302 for each MED at a wavelength of 1.55 m. As illustrated in FIGS. 5 and 6, 2_max varies with a2/a and MFD. Here, the variation of 2max is expressed by functions of a.sub.2/a and MED from FIG. 10.
(60) FIG. 11 illustrates the respective coefficients (k1, k2, and k3) expressed by functions of MFD in a case where the relationship between a2/a and 2max shown in FIG. 10 is approximated by a quadratic function (k1x.sup.2+k2x+k3; x being a2/a). From these results, the upper limit 2max of 2 is calculated according to the expression shown below.
[Mathematical Expression 8]
.sub.2(0.002MFD.sup.20.0422MFD+0.2215)(a.sub.2/a).sup.2+(0.0098MFD.sup.2+0.205MFD1.0734)(a.sub.2/a)+(0.012MFD.sup.20.2533MFD+1.3312)(8)
(d) The Lower Limit Value 2 Min of the Relative Refractive Index Difference 2
(61) FIG. 12 is a chart for explaining that 2 min varies with each value of a.sub.2/a (2min varies among FIGS. 6(a) to 6(c)). Specifically, FIG. 12 is a chart illustrating the variation of 2 min with respect to a2/a of the multi-core optical fiber 302 for each MFD at a wavelength of 1.55 m. As illustrated in FIGS. 5 and 6, 2min varies with a2/a and MFD. Here, the variation of 2min is expressed by functions of a2/a and MED from FIG. 12.
(62) FIG. 13 illustrates the respective coefficients (k1, k2, and k3) expressed by functions of MED in a case where the relationship between a2/a and 2 min shown in FIG. 12 is approximated by a quadratic function (k1x.sup.2+k2x+k3; x being a2/a). From these results, the lower limit 2 min of 2 is calculated according to the expression shown below.
[Mathematical Expression 9]
.sub.2(0.0026MFD.sup.20.0573MFD+0.31)(a.sub.2/a).sup.2+(0.0124MFD.sup.2+0.2683MFD1.4515)(a.sup.2/a)+(0.0141MFD.sup.20.3045MFD+1.6488)(9)
(63) As described above, in the structure of the multi-core optical fiber 302, the cutoff wave c (dashed lines) and the bending loss ab (dotted line) are not taken into consideration in FIG. 2, but the range of the relative refractive index difference 42 is limited according to Mathematical Expression 8 and Mathematical Expression 9, and the cutoff wavelength c is 1.45 m or shorter.
(64) That is, the multi-core optical fiber 302 characteristically includes: the cladding 11 that has a diameter of 125+1 m in a cross-section; and the four cores 12 that are arranged in a square lattice pattern in the cladding 11 in the cross-section, wherein the cladding 11 includes first claddings 11-1 surrounding the respective cores 12, and a second cladding 11-2 containing all the first claddings 11-1, the refractive index is the highest in the cores 12, and is the lowest in the first claddings 11-1, the relationship between the radius a (m) of the cores 12 and the absolute value of the relative refractive index difference between the cores 12 and the first claddings 11-1 satisfies Mathematical Expression C2, the absolute value of the relative refractive index difference satisfies Mathematical Expression C3, and the absolute value 2 of the relative refractive index difference between the second cladding 11-2 and the cores 12 satisfies Mathematical Expression C4.
[Mathematical Expression C2]
0.0003a.sup.20.0024a+0.00790.0005a.sup.20.0032a+0.0094(C2)
[Mathematical Expression C3]
(0.0013MFD.sup.20.0296MFD+0.1735)(a.sub.2/a).sup.2+(0.0129MFD.sup.2+0.2885MFD1.6141)(a.sub.2/a)+(0.0419MFD.sup.20.9096MPD+4.9388)0.0015MFD+0.0223(C3)
[Mathematical Expression C4]
(0.0026MFD.sup.20.0573MFD+0.31)(a.sub.2/a).sup.2+(0.0124MFD.sup.2+0.2683MFD1.4515)(a.sub.2/a)+(0.0141MFD.sup.20.3045MFD+1.6488) .sub.2(0.002MFD.sup.20.0422MFD+0.2215)(a.sub.2/a).sup.2+(0.0098MFD.sup.2+0.205MFD1.0734)(a.sub.2/a)+(0.012MFD.sup.20.2533MFD+1.3312)(C4)
(65) Here, a2 represents the radius (m) of the first claddings 11-1, and MED represents a desired mode field diameter (m).
(66) A method for designing the multi-core optical fiber 302 is as illustrated in FIG. 17. That is, the design method includes: determining the cutoff wavelength c, the upper limit value of crosstalk XT, the mode field diameter MFD, and the bending loss ab of the multi-core optical fiber 302 as specification values (step S21); drawing a region having a wavelength shorter than the cutoff wavelength of the specification values and crosstalk equal to or smaller than the upper limit value of the crosstalk of the specification values in a relationship chart (FIGS. 5 and 6) of the absolute value of the relative refractive index difference between the cores and the first claddings, the absolute value 2 of the relative refractive index difference between the cores and the second cladding, the mode field diameter MFD, and the ratio (a2/a) between the radius a of the cores and the radius a2 of the first claddings (step S22); detecting the maximum value max and the minimum value min of the absolute value of the relative refractive index difference between the cores and the first claddings included in the region in which the ratio (a2/a) between the radius of the cores and the radius of the first claddings has a provisionally determined value (steps S23 and S24; as for min, the relational expression between MED and a2/a can be expressed by Mathematical Expression 7); drawing the variation curves of max and min with respect to changes in MED in a graph of MFD and , and detecting the corresponding MFD when the variation curves intersect (step S25); drawing a first curve satisfying the mode field diameter of the specification values and a second curve satisfying the corresponding mode field diameter in an optical characteristics chart of the radius a of the cores and the absolute value of the relative refractive index difference between the cores and the claddings (step S26); detecting the radius a of the cores and the absolute value of the relative refractive index difference included in the region surrounded by the first curve and the second curve in the optical characteristics chart (step S27); calculating the range of the absolute value of the relative refractive index difference satisfying Mathematical Expression C3 among the absolute values of the relative refractive index differences included in the region surrounded by the first curve and the second curve (step S28); calculating the range of the absolute value 2 of the relative refractive index difference between the second cladding and the cores by plugging the absolute value & of the relative refractive index difference included in the region surrounded by the first curve and the second curve, and the provisionally determined ratio (a2/a) into Mathematical Expression C4 (step S29); and setting the detected radius a of the cores, ratio (a2/a), absolute value of the relative refractive index difference, and absolute value 2 of the relative refractive index difference between the second cladding and the cores, as design values of the multi-core optical fiber (step S30).
(67) Note that, in a case where design values are not obtained in step S30, a2/a is changed, and the operation is then repeated starting from step S23.
Third Embodiment
(68) FIG. 14 is a diagram for explaining the structure of a multi-core optical fiber 303 according to this embodiment. FIG. 14 (a) is a cross-sectional view of the multi-core optical fiber 303. FIG. 14 (b) is a diagram for explaining the refractive index distribution near a core of the multi-core optical fiber 303. The cladding diameter and the number of cores of the multi-core optical fiber 303 are 125+1 m and four cores, which are the same as those of the multi-core optical fiber 301 in FIG. 1, and the respective cores have substantially the same refractive index distributions.
(69) The multi-core optical fiber 303 includes cores 12, third cladding regions 11-3 surrounding the cores 12, first cladding regions 11-1 surrounding the third cladding regions 11-3, and a second cladding region 11-2 surrounding the first cladding regions 11-1. The refractive index becomes lower in the order of the cores 12, the second cladding region 11-2, and the first cladding regions 11-1. The refractive index of the third cladding regions 11-3 is the same as the refractive index of the second cladding region 11-2.
(70) In the multi-core optical fiber 303, the refractive index of the cladding is higher than that of the multi-core optical fiber 302, and the number of parameters is larger. Accordingly, the multi-core optical fiber 303 can increase MED and reduce XT by larger amounts than the multi-core optical fiber 302. At this stage, if the ranges of a, a2, , and 2 are designed as described in the second embodiment, the same optical characteristics as those of the second embodiment can be achieved, which is preferable.
Fourth Embodiment
(71) FIG. 15 is a diagram for comparing cross-sectional structures of multi-core optical fibers. Normally, an optical fiber has a coating layer formed with resin or the like around glass (a cladding), so as to ensure mechanical reliability. FIG. 15(a) is a diagram for explaining a standard multi-core optical fiber that includes the coating layer and has a diameter of 250+15 m. FIG. 15(b) is a diagram for explaining a multi-core optical fiber that includes the coating layer and has a diameter of 200+20 m. It is known that mechanical reliability and loss characteristics can be maintained even in a case where the diameter including the coating layer is 200 #20 m. In the multi-core optical fibers (301 to 303) described above, the diameter including the coating layer is set to 200+20 m. Thus, a multi-core optical fiber having a smaller diameter can be mounted on an optical cable, and an optical cable with a high density and a large number of cores can be formed, which is preferable.
(72) [Supplementary Notes]
(73) The point of the present invention is that predetermined conditions are set for the refractive index distribution and the core position in an MCF of a standard cladding diameter, to expand the single-mode band and reduce crosstalk XT at the same time. Specific multi-core optical fibers of the present invention are as follows.
(74) A first multi-core optical fiber is a multi-core optical fiber that has the structure illustrated in FIG. 1, and characteristically includes: a cladding that has a diameter of 125+1 m in a cross-section; and four cores that are arranged in a square lattice pattern in the cladding in the cross-section, wherein the shortest distance from the center of the core to the outer periphery of the cladding in the cross-section is 33 m or longer, and the relationship between the radius a (m) of the core and the absolute value of the relative refractive index difference between the core and the cladding satisfies Mathematical Expression C1.
[Mathematical Expression C1]
0.0004a.sup.20.003a+0.00910.0005a.sup.20.0032a+0.0094, 0.0874a.sup.2, and 0.0101a.sup.758(C1)
(75) Meanwhile, a method for designing the first multi-core optical fiber includes: determining the cutoff wavelength, the upper limit value of crosstalk, the mode field diameter, and the bending loss of the multi-core optical fiber as specification values; detecting a corresponding mode field diameter corresponding to the upper limit value of crosstalk of the specification values, from a relationship chart (a second ordinate axis in FIG. 3) between the mode field diameter and the crosstalk at the cutoff wavelength of the specification values; detecting the minimum OTC corresponding to the corresponding mode field diameter, from a relationship chart (a first ordinate axis in FIG. 3) between the mode field diameter at the cutoff wavelength of the specification values and the shortest distance (minimum OTC) from the center of the core to the outer periphery of the cladding in a cross-section of the multi-core optical fiber; drawing a first curve satisfying the mode field diameter among the specification values, a second curve satisfying the cutoff wavelength among the specification values, a third curve satisfying the bending loss of the specification values, and a fourth curve satisfying the corresponding mode field diameter in an optical characteristics chart (the graph in FIG. 2) of the radius a of the core and the absolute value of the relative refractive index difference between the core and the cladding; detecting the radius a of the core and the absolute value of the relative refractive index difference included in the region surrounded by the first curve, the second curve, the third curve, and the fourth curve in the optical characteristics chart; and setting the detected minimum OTC, radius a of the core, and absolute value of the relative refractive index difference as design values of the multi-core optical fiber.
(76) Further, a second multi-core optical fiber is a multi-core optical fiber that has the structure illustrated in FIG. 4, and characteristically includes: a cladding that has a diameter of 125+1 m in a cross-section; and four cores that are arranged in a square lattice pattern in the cladding in the cross-section, wherein the cladding includes first claddings surrounding the respective cores, and a second cladding containing all the first claddings, the refractive index is the highest in the cores, and is the lowest in the first claddings, the relationship between the radius a (m) of the cores and the absolute value of the relative refractive index difference between the cores and the first claddings satisfies Mathematical Expression C2, the absolute value of the relative refractive index difference satisfies Mathematical Expression C3, and the absolute value 2 of the relative refractive index difference between the second cladding and the cores satisfies Mathematical Expression C4.
[Mathematical Expression C2]
0.0003a.sup.20.0024a+0.00790.0005a.sup.20.0032a+0.0094(C2)
[Mathematical Expression C3]
(0.0013MFD.sup.20.0296MFD+0.1735)(a.sub.2/a).sup.2+(0.0129MFD.sup.2+0.2885MFD1.6141)(a.sub.2/a)+(0.0419MFD.sup.20.9096MFD+4.9388)0.0015MFD+0.0223(C3)
[Mathematical Expression C4]
(0.0026MFD.sup.20.0573MFD+0.31)(a.sub.2/a).sup.2+(0.0124MFD.sup.2+0.2683MFD1.4515)(a.sub.2/a)+(0.0141MFD.sup.20.3045MFD+1.6488) .sub.2(0.002MFD.sup.20.0422MFD+0.2215)(a.sub.2/a).sup.2+(0.0098MFD.sup.2+0.205MFD1.0734)(a.sub.2/a)+(0.012MFD.sup.20.2533MFD+1.3312)(C4)
(77) Here, a2 represents the radius (m) of the first claddings, and MFD represents a desired mode field diameter (m).
(78) Further, a method for designing the second multi-core optical fiber includes: determining the cutoff wavelength, the upper limit value of crosstalk, the mode field diameter, and the bending loss of the multi-core optical fiber as specification values; drawing a region having a wavelength shorter than the cutoff wavelength of the specification values and crosstalk equal to or smaller than the upper limit value of the crosstalk of the specification values in a relationship chart (FIGS. 5 and 6) of the absolute value of the relative refractive index difference between the cores and the first claddings, the absolute value 2 of the relative refractive index difference between the cores and the second cladding, the mode field diameter MFD, and the ratio (a2/a) between the radius a of the cores and the radius a2 of the first claddings; detecting the maximum value max and the minimum value min of the absolute value of the relative refractive index difference between the cores and the first claddings included in the region in which the ratio (a2/a) between the radius of the cores and the radius of the first claddings has a provisionally determined value (as for min, the relational expression between MED and a2/a can be expressed by Mathematical Expression 7); drawing variation curves of max and min with respect to changes in MFD in a graph of MED and 4, and detecting the corresponding MFD when the variation curves intersect; drawing a first curve satisfying the mode field diameter of the specification values and a second curve satisfying the corresponding mode field diameter in an optical characteristics chart of the radius a of the cores and the absolute value of the relative refractive index difference between the cores and the claddings; detecting the radius a of the cores and the absolute value of the relative refractive index difference included in the region surrounded by the first curve and the second curve in the optical characteristics chart; calculating the range of the absolute value of the relative refractive index difference satisfying Mathematical Expression C3 among the absolute values & of the relative refractive index differences included in the region surrounded by the first curve and the second curve; calculating the range of the absolute value 2 of the relative refractive index difference between the second cladding and the cores by plugging the absolute value & of the relative refractive index difference included in the region surrounded by the first curve and the second curve, and the provisionally determined ratio (a2/a) into Mathematical Expression 9; and setting the detected radius a of the cores, ratio (a2/a), absolute value of the relative refractive index difference, and absolute value 2 of the relative refractive index difference between the second cladding and the cores, as design values of the multi-core optical fiber.
[Mathematical Expression C3]
(0.0013MFD.sup.20.0296MFD+0.1735)(a.sub.2/a).sup.2+(0.0129MFD.sup.2+0.2885MFD1.6141)(a.sub.2/a)+(0.0419MFD.sup.20.9096MFD+4.9388)0.0015MFD+0.0223(C3)
[Mathematical Expression C4]
(0.0026MFD.sup.20.0573MFD+0.31)(a.sub.2/a).sup.2+(0.0124MFD.sup.2+0.2683MFD1.4515)(a.sup.2/a)+(0.0141MFD.sup.20.3045MFD+1.6488).sub.2(0.002MFD.sup.20.0422MFD+0.2215)(a.sub.2/a).sup.2+(0.0098MFD.sup.2+0.205MFD)1.0734)(a.sub.2/a)+(0.012MFD.sup.20.2533MFD+1.3312)(C4)
(79) Here, a2 represents the radius (m) of the first claddings, and MED represents a desired mode field diameter (m).
(80) (Effects)
(81) The present invention can achieve low XT, while expanding the single-mode wavelength band to the S-band, for an MCF having a standard cladding diameter.
REFERENCE SIGNS LIST
(82) 11 cladding 11-1 first cladding 11-2 second cladding 11-3 third cladding 12 core 301 to 303 multi-core optical fiber
