Polarization-maintaining fiber

Abstract

Provided is a polarization-maintaining fiber capable of inhibiting bending loss and reducing the value of MPI further than in conventional products. In the present invention, the ratio r2 / r1 of the inner circumferential radius r2 of a low refractive index layer (12) to the radius r1 of a core (11) satisfies 1.0≤r2 / r1≤3.0, the difference r3-r2 between the outer circumferential radius r3 of the low refractive index layer (12) and the inner circumferential radius r2 of the low refractive index layer (12) satisfies 4.0 μm≤r3-r2≤6.0 μm, the relative refractive index difference Δ3 of the low refractive index layer (12) with respect to a cladding (14) satisfies -0.38%≤Δ3≤-0.27%, and, when light having a wavelength of 1.55 μm propagates through the core (11), the mode field diameter of the light is at most 9.2 μm, and the fiber cutoff wavelength is at most 1.45 μm.

Description

Polarization-Maintaining Fiber

[0001] The present invention relates to polarization-maintaining fibers.

[0002] Optical fibers having a polarization-maintaining function, that is, polarization-maintaining fibers, are widely used. For example, Patent Document 1 discloses polarization-maintaining fibers.

[0003] Japanese Patent Application Publication No. 2018-159926

[0004] Optical modules such as optical transceivers often use polarization-maintaining fibers with a low-refractive-index layer (trench layer or depressed layer) surrounding the core, because the low-refractive-index layer surrounding the core has the effect of minimizing bending loss when the polarization-maintaining fiber is bent at a small bending radius.

[0005] However, in polarization-maintaining fibers, which tend to have shorter fiber lengths than optical fibers for communication applications, there is a concern that a phenomenon called MPI (Multi Path Interference) may occur, causing fluctuations in the power of light propagating through the polarization-maintaining fiber and degrading transmission characteristics. Therefore, in polarization-maintaining fibers, it is more important than ever to suppress bending loss and the value of MPI.

[0006] One aspect of the present invention has been made in view of the above problems, and its purpose is to realize a polarization-maintaining fiber that can suppress bending loss and the MPI value more than conventional ones.

[0007] A polarization-maintaining fiber according to a first aspect comprises a core, a low-refractive-index layer surrounding the core, a pair of stress-applying portions arranged at positions sandwiching the core, and a cladding that contains the core, the low-refractive-index layer, and the pair of stress-applying portions, wherein a ratio r2 / r1 of a radius r1 of the core to an inner radius r2 of the low-refractive-index layer satisfies 1.0≦r2 / r1≦3.0, a difference r3−r2 between an outer radius r3 of the low-refractive-index layer and the inner radius r2 of the low-refractive-index layer satisfies 4.0 μm≦r3−r2≦6.0 μm, a relative refractive index difference Δ3 of the low-refractive-index layer with respect to the cladding satisfies −0.38%≦Δ3≦−0.27%, a mode field diameter of light with a wavelength of 1.55 μm propagating through the core is 9.2 μm or less, and a fiber cutoff wavelength is 1.45 μm or less.

[0008] According to one aspect of the present invention, it is possible to realize a polarization-maintaining fiber that can suppress bending loss and MPI values ​​more effectively than ever before.

[0009] 1A is a cross-sectional view showing the transverse cross section of a polarization-maintaining fiber according to an embodiment of the present invention. Graphs showing the refractive index distribution n(r) on the slow axis and the refractive index distribution n(r) on the fast axis of the polarization-maintaining fiber are also shown. Graphs showing the relative refractive index difference distribution Δ(r) on the fast axis of the polarization-maintaining fiber shown in FIG. 1. (a) is a perspective view showing the polarization-maintaining fiber shown in FIG. 1 when bent so that the fast axis direction is in the direction of the bending radius, and (b) is a perspective view showing the polarization-maintaining fiber shown in FIG. 1 when bent so that the slow axis direction is in the direction of the bending radius.

[0033] FIG. 1B is a block diagram showing the configuration of a measurement system for measuring MPI. (a) is a graph showing the wavelength dependence of the power of light generated by a light source in the measurement system shown in FIG. 4. (b) is a graph showing the wavelength dependence of the power of light measured by a power meter in the measurement system shown in FIG. 4. Graphs showing the electric field distribution of the LP01x mode of the first dummy fiber and the electric field distributions of the LP11ax and LP11bx modes of the polarization-maintaining fiber in the measurement system shown in FIG. 4. 1A illustrates a case where an axial misalignment occurs in the slow axis direction, and FIG. 1B illustrates a case where an axial misalignment occurs in the fast axis direction, where FIG. 1A is a diagram for explaining the definition of the angle between two axes, and FIG. 1B is a diagram for explaining the definition of the angle between two directions.

[0010] In polarization-maintaining fibers, which tend to have shorter fiber lengths than optical fibers used for communications, there is a concern that a phenomenon called MPI (multipath interference) may occur, causing fluctuations in the power of light propagating through the polarization-maintaining fiber and resulting in degraded transmission characteristics. This MPI is particularly likely to occur when the polarization-maintaining fiber has a low refractive index layer. Assume that a preceding optical fiber is connected to one end of the polarization-maintaining fiber while being misaligned, and a following optical fiber is connected to the other end of the polarization-maintaining fiber while being misaligned. In this case, at the connection point between the one end of the polarization-maintaining fiber and the end of the preceding optical fiber, a portion of the light in the LP01 mode guided through the preceding optical fiber couples to the LP11 mode of the polarization-maintaining fiber, and at the connection point between the other end of the polarization-maintaining fiber and the end of the following optical fiber, a portion of the light in the LP11 mode guided through the polarization-maintaining fiber couples to the LP01 mode of the following optical fiber. In this case, interference occurs between (1) light that is guided in the upstream optical fiber as the LP01 mode, guided in the polarization-maintaining fiber as the LP11 mode, and guided in the downstream optical fiber as the LP01 mode, and (2) light that is guided in the upstream optical fiber as the LP01 mode, guided in the polarization-maintaining fiber as the LP01 mode, and guided in the downstream optical fiber as the LP01 mode. The phenomenon that causes this interference, or the physical quantity derived from the fluctuation range of the light intensity with respect to the wavelength of the light guided in the polarization-maintaining fiber, is called MPI. If the fiber length of the polarization-maintaining fiber is short, the total amount of confinement loss of the LP11 mode is small, and the light in the LP11 mode is guided from one end to the other without being lost. At the connection point between the other end of the polarization-maintaining fiber and the end of the downstream optical fiber, part of the light in the LP11 mode guided in the polarization-maintaining fiber is likely to be coupled to the LP01 mode of the downstream optical fiber. Therefore, the shorter the fiber length of the polarization-maintaining fiber, the greater the effect of MPI.

[0011] It is known that an MPI value exceeding −30 dB can cause a deterioration in the communication quality of a polarization-maintaining fiber. Therefore, it is important for polarization-maintaining fibers to be able to suppress bending loss and the MPI value more than ever before.

[0012] Hereinafter, a polarization-maintaining fiber that can suppress bending loss and MPI values ​​more effectively than conventional fibers will be described.

[0013] (Configuration of Polarization-Maintaining Fiber) The configuration of a polarization-maintaining fiber 1 according to one embodiment of the present invention will be described with reference to Fig. 1. Fig. 1 is a cross-sectional view showing a transverse section of the polarization-maintaining fiber 1. Here, the transverse section refers to a section perpendicular to the central axis of the polarization-maintaining fiber 1. Note that Fig. 1 also shows the refractive index distribution on the fast axis FA and the slow axis SA of the polarization-maintaining fiber 1.

[0014] As shown in Fig. 1, the polarization-maintaining fiber 1 includes a core 11, a low-refractive index layer 12, a pair of stress-applying portions 131 and 132, and a cladding 14. The polarization-maintaining fiber 1 is a so-called PANDA (Polarization-maintaining AND Absorption-reducing) polarization-maintaining fiber. In a cross section of the polarization-maintaining fiber 1, an axis passing through the center of the core 11 and extending in the arrangement direction of the stress-applying portions 131 and 132 is a slow axis SA, and an axis passing through the center of the core 11 and perpendicular to the arrangement direction of the stress-applying portions 131 and 132 is a fast axis FA. The polarization-maintaining fiber 1 may further include a coating (not shown) that covers the outer surface of the cladding 14.

[0015] The core 11 is a columnar region extending in the longitudinal direction of the polarization-maintaining fiber 1. The refractive index n1 of the core 11 is set to be higher than the refractive index n2 of the cladding 14, which will be described later. That is, the relative refractive index difference of the core 11 with respect to the cladding 14, Δ1 [%] = 100 × (n1 ２ -n2 ２ ) / (2 × n1 ２) takes a positive value. The core 11 is made of, for example, silica glass doped with an up-dopant. Examples of the up-dopant include germanium, aluminum, and phosphorus. In this embodiment, the cross-sectional shape of the core 11 is a circle with a radius r1. However, the cross-sectional shape of the core 11 is not limited to a circle in the strict sense, and may be any shape that can be approximated by a circle. When the cross-sectional shape of the core 11 is non-circular, the radius r1 of the core 11 is half the average value of the radii (equivalent to diameters) of the core 11 in a direction perpendicular to the central axis of the core 11.

[0016] The low-refractive-index layer 12 is a cylindrical region extending in the longitudinal direction of the polarization-maintaining fiber 1, and is disposed so as to surround the core 11. The refractive index n3 of the low-refractive-index layer 12 is set lower than the refractive index n2 of the cladding 14, which will be described later. That is, the relative refractive index difference of the low-refractive-index layer 12 with respect to the cladding 14, Δ3 [%] = 100 × (n3 ２ -n2 ２ ) / (2 × n3 ２ ) takes a negative value. The low-refractive-index layer 12 is made of, for example, silica glass doped with a down dopant. Examples of down dopants include fluorine and boron oxide. In this embodiment, the cross-sectional shape of the low-refractive-index layer 12 is annular (ring-shaped) with an inner radius r2 and an outer radius r3. However, the cross-sectional shape of the low-refractive-index layer 12 is not limited to a strict ring shape as long as it can be approximated by a ring shape. When the cross-sectional shape of the low-refractive-index layer 12 is non-annular, the inner radius r2 of the low-refractive-index layer 12 is half the average value of the inner diameters (corresponding to inner diameters) in a direction perpendicular to the central axis of the core 11, and the outer radius r3 of the low-refractive-index layer 12 is half the average value of the outer diameters (outer diameters) in a direction perpendicular to the central axis of the core 11.

[0017] The low refractive index layer 12 of this embodiment is in contact with each of the stress-applying portions 131 and 132. Therefore, the outer periphery of the low refractive index layer 12 is made up of a part of a circle having an outer periphery with a diameter larger than the shortest distance from the central axis of the core 11 to the stress-applying portion, and portions in contact with the stress-applying portions 131 and 132. Note that the low refractive index layer 12 may be separated from the stress-applying portions as long as it satisfies conditions 1 to 5 described below.

[0018] The stress-applying portions 131 and 132 are each a columnar region extending in the longitudinal direction of the polarization-maintaining fiber 1. The stress-applying portions 131 and 132 are arranged so as to sandwich the core 11. The refractive index n4 of the stress-applying portions 131 and 132 is set lower than the refractive index n2 of the cladding 14, which will be described later. The stress-applying portions 131 and 132 are made of, for example, silica glass doped with a down dopant. The down dopant can be, for example, boron oxide (B ２ O ３ ) and the like. In this embodiment, the cross-sectional shape of the stress-applying portions 131, 132 is circular. However, the cross-sectional shape of the stress-applying portions 131, 132 is not limited to circular. For example, the cross-sectional shape of the stress-applying portion 131 may be elliptical with the arrangement direction of the stress-applying portions 131, 132 as the minor axis direction, or may be elliptical with the arrangement direction of the stress-applying portions 131, 132 as the major axis direction. The cross-sectional shape of the stress-applying portions 131, 132 may be crescent or non-circular. The cross-sectional shape of the stress-applying portions 131, 132 may be an isosceles trapezoid with the upper base (shorter base) facing the core 11. In this case, one or both of the upper base and the lower base (longer base) of the stress-applying portions 131, 132 may be arc-shaped, bulging away from the core 11. The polarization-maintaining fiber 1 in which the stress-applying portions 131, 132 have an isosceles trapezoidal shape is sometimes called a “bow-tie polarization-maintaining fiber.” In this way, the polarization-maintaining fiber 1 is not limited to the above-mentioned PANDA polarization-maintaining fiber, and may be a bow-tie polarization-maintaining fiber.

[0019] The relative refractive index difference of the stress-applying portions 131 and 132 with respect to the outer region of the cladding 14 is Δ4=(n4 ２ -n2 ２ ) / (2 × n4 ２) is preferably −0.70% or less. This allows the stress-applying portions 131, 132 to function as low-refractive-index layers in the slow axis SA direction along which the stress-applying portions 131, 132 are arranged, thereby further suppressing light leakage from the core 11. Furthermore, the polarization-maintaining function can be suitably achieved. Furthermore, the relative refractive index difference Δ4 of the stress-applying portions 131, 132 with respect to the cladding 14 is preferably −0.90% or more. This can lead to a sufficiently small amount of boron oxide added, thereby suppressing deliquescence of the stress-applying portions 131, 132, which may occur when the concentration of boron oxide is too high. From the above, from the viewpoint of achieving both the effect of a relative refractive index difference Δ4 of −0.70% or less and the effect of a relative refractive index difference Δ4 of −0.90% or more, it is preferable that the relative refractive index difference Δ4 be −0.90% or more and −0.70% or less. The definition of the outer region of the cladding 14 will be described later.

[0020] Furthermore, the shortest distance r4 from the center of the core 11 to the stress-applying parts 131 and 132 is preferably 1.05 times or more half the mode field diameter of the light guided through the core 11. This places the stress-applying parts 131 and 132 outside the mode field, thereby suppressing an increase in transmission loss that can occur when material mismatch exists inside the mode field.

[0021] The shortest distance from the center of the core 11 to the stress-applying portion 131 refers to the distance from the center of the core 11 to the point included in the stress-applying portion 131 that is closest to the core 11. Similarly, the shortest distance from the center of the core 11 to the stress-applying portion 132 refers to the distance from the center of the core 11 to the point included in the stress-applying portion 132 that is closest to the core 11. Furthermore, the shortest distance between the core 11 and the stress-applying portion 131 refers to the distance from the point included in the core 11 that is closest to the stress-applying portion 131 to the point included in the stress-applying portion 131 that is closest to the core 11. Similarly, the shortest distance between the core 11 and the stress-applying portion 132 refers to the distance from the point included in the core 11 that is closest to the stress-applying portion 132 to the point included in the stress-applying portion 132 that is closest to the core 11.

[0022] The cladding 14 is a columnar region extending in the longitudinal direction of the polarization-maintaining fiber 1 and contains the core 11, the low-refractive-index layer 12, and the stress-applying portions 131 and 132. The central axis of the cladding 14 coincides or substantially coincides with the central axis of the core 11 and the central axis of the low-refractive-index layer 12. The refractive index of the cladding 14 is lower than that of the core 11 and higher than that of the low-refractive-index layer 12 and the stress-applying portions 131 and 132. The cladding 14 is made of, for example, silica glass. In this embodiment, the cross-sectional shape of the cladding 14 is circular. However, the cross-sectional shape of the cladding 14 is not limited to a circle. For example, the cross-sectional shape of the cladding 14 may be an ellipse whose minor axis is the arrangement direction of the stress-applying portions 131 and 132, or may be an ellipse whose major axis is the arrangement direction of the stress-applying portions 131 and 132.

[0023] The diameter of the cladding 14 is preferably 79 μm or more and 126 μm or less. More specifically, the diameter of the cladding 14 is preferably 125 μm ± 1 μm, i.e., 124 μm or more and 126 μm or less, and more preferably 125 μm. In this case, a polarization-maintaining fiber 1 having a diameter roughly equivalent to that of standard optical fibers used in communications infrastructure can be realized. Alternatively, the diameter of the cladding 14 is preferably 80 μm ± 1 μm, i.e., 79 μm or more and 81 μm or less, and more preferably 80 μm. In this case, a polarization-maintaining fiber 1 that can be mounted at high density and requires a small installation area when housed in an optical transceiver or applied to a sensor can be realized. Furthermore, since the rigidity of the polarization-maintaining fiber 1 can be kept small, a decrease in the mechanical strength of the polarization-maintaining fiber 1 when twisted can be reduced. Note that ±1 μm in the diameter of the cladding 14 is an acceptable error that does not significantly affect the optical and mechanical properties of the polarization-maintaining fiber 1. For example, ±1 μm for a cladding 14 diameter of 125 μm corresponds to the tolerance for the cladding diameter specified in the standard optical fiber specification (ITU-T). Furthermore, ±1 μm for the cladding diameter of an optical fiber with a cladding diameter of 80 μm may also correspond to the above tolerance value. Note that the diameter of the cladding 14 when the cross-sectional shape of the cladding 14 is non-circular is, for example, the average value of the diameter of the cladding 14 in a direction perpendicular to the central axis of the cladding 14.

[0024] When the diameter of the cladding 14 is 125 μm±1 μm, the shortest distance r4 from the center of the core 11 to the stress-applying portions 131 and 132 is preferably 10.0 μm or less. This allows sufficient stress to be applied to the core 11, thereby favorably achieving the polarization-maintaining function. Furthermore, compared to when the shortest distance r4 is greater than 10.0 μm, the stress-applying portions 131 and 132, which have a lower refractive index than the cladding 14, are closer to the core 11. This can further enhance the function of the stress-applying portions 131 and 132 as low-refractive-index layers in the slow axis SA direction, thereby further suppressing light leakage from the core 11. Furthermore, the shortest distance between the core 11 and the stress-applying portion 131 or the shortest distance between the core 11 and the stress-applying portion 132 can be expressed as the difference r4-r1 between the shortest distance r4 and the radius r1 of the core 11, and is preferably 0.5 μm or greater. This can suppress an increase in transmission loss that may occur due to boron oxide added to the stress-applying portions 131 and 132 .

[0025] Furthermore, when the diameter of the cladding 14 is 125 μm±1 μm, the diameter of the stress-applying portions 131, 132 is preferably 30.0 μm or more. This allows sufficient stress to be applied to the core 11, thereby favorably achieving the polarization-maintaining function. In this case, the diameter of the stress-applying portions 131, 132 is preferably 40.0 μm or less. This allows the stress-applying portions 131, 132 to be favorably disposed inside the cladding 14, which has a diameter of 125 μm±1 μm. From the above perspective, from the viewpoint of achieving both the effect of the stress-applying portions 131, 132 having a diameter of 40.0 μm or less and the effect of the stress-applying portions 131, 132 having a diameter of 30.0 μm or more, the diameter of the stress-applying portions 131, 132 is preferably 30.0 μm or more and 40.0 μm or less.

[0026] On the other hand, when the diameter of the cladding 14 is 80 μm±1 μm, the shortest distance r4 from the center of the core 11 to the stress-applying portions 131 and 132 is preferably 10.0 μm or less. This allows sufficient stress to be applied to the core 11, thereby favorably achieving the polarization-maintaining function. Furthermore, compared to when the shortest distance r4 is greater than 10.0 μm, the stress-applying portions 131 and 132, which have a lower refractive index than the cladding 14, are closer to the core 11. This can further enhance the function of the stress-applying portions 131 and 132 as low-refractive-index layers in the slow axis SA direction, thereby further suppressing light leakage from the core 11. Furthermore, the difference r4-r1 between the shortest distance from the center of the core 11 to the stress-applying portions 131 and 132 and the radius r1 of the core 11 is preferably 0.5 μm or more. This can suppress an increase in transmission loss that may occur when boron oxide is added to the stress-applying portions 131 and 132.

[0027] Furthermore, when the diameter of the cladding 14 is 80 μm±1 μm, the diameter of the stress-applying portions 131, 132 is preferably 22.0 μm or more. This allows sufficient stress to be applied to the core 11, thereby favorably achieving the polarization-maintaining function. In this case, the diameter of the stress-applying portions 131, 132 is preferably 27.0 μm or less. This allows the stress-applying portions 131, 132 to be favorably disposed inside the cladding 14, which has a diameter of 80 μm±1 μm. From the above, from the viewpoint of achieving both the effect of the stress-applying portions 131, 132 having a diameter of 27.0 μm or less and the effect of the stress-applying portions 131, 132 having a diameter of 22.0 μm or more, the diameter of the stress-applying portions 131, 132 is preferably 22.0 μm or more and 27.0 μm or less.

[0028] The inner radius r2 of the low refractive index layer 12 may be (1) larger than the radius r1 of the core 11, or (2) equal to the radius r1 of the core 11.

[0029] When the inner radius r2 of the low-refractive-index layer 12 is larger than the radius r1 of the core 11, i.e., when the low-refractive-index layer 12 is spaced apart from the core 11, the cladding 14 has a region inside the low-refractive-index layer 12 (hereinafter also referred to as the "inner region") and a region outside the low-refractive-index layer 12 (hereinafter also referred to as the "outer region"). In this case, the inner region of the cladding 14 covers the outer surface of the core 11, the low-refractive-index layer 12 covers the outer surface of the inner region of the cladding 14, and the outer region of the cladding 14 covers the outer surface of the low-refractive-index layer 12. Such a low-refractive-index layer 12 is also called a "trench layer."

[0030] In this case, it is preferable that the shortest distance r4 from the center of the core 11 to the stress-applying portion 131 satisfies r4<r2. It is also preferable that the shortest distance r4 from the center of the core 11 to the stress-applying portion 132 satisfies r4<r2. The low-refractive-index layer 12 containing a down dopant (such as fluorine) has a lower viscosity and is softer than the cladding 14 containing no dopant. When r4≧r2 is satisfied, the low-refractive-index layer 12 is interposed between the stress-applying portions 131 and 132 and the core 11 on the slow axis SA, and therefore is unable to impart sufficient stress to the core 11. As a result, the polarization crosstalk characteristics are likely to deteriorate. On the other hand, when r4<r2 is satisfied, the low-refractive-index layer 12 is not interposed between the stress-applying portion 131 and the core 11 on the slow axis SA, and therefore is able to reliably impart stress to the core 11. As a result, the polarization crosstalk is less likely to deteriorate.

[0031] On the other hand, when the inner radius r2 of the low refractive index layer 12 is the same as the radius r1 of the core 11, that is, when the low refractive index layer 12 is not spaced apart from the core 11, the low refractive index layer 12 covers the outer surface of the core 11, and the cladding 14 covers the outer surface of the low refractive index layer 12. Such a low refractive index layer 12 is also called a "depressed layer."

[0032] In this embodiment, the center of the circle forming the outer periphery of the core 11, the center of the circle forming the inner periphery of the low-refractive-index layer 12, and the center of the circle forming the outer periphery of the low-refractive-index layer 12 each coincide with the center of the circle forming the outer periphery of the cladding 14. However, the present invention is not limited to this. That is, the center of the circle forming the outer periphery of the core 11, the center of the circle forming the inner periphery of the low-refractive-index layer 12, and the center of the circle forming the outer periphery of the low-refractive-index layer 12 may each be included in the center of the cladding 14. Therefore, when the diameter of the cladding 14 satisfies the range of 79 μm to 126 μm, the center of the circle forming the outer periphery of the core 11, the center of the circle forming the inner periphery of the low-refractive-index layer 12, and the center of the circle forming the outer periphery of the low-refractive-index layer 12 may each be included in the center of the cladding 14. Here, the center of the cladding 14 refers to the inner region of a circle with a radius of 0.6 μm, the center of which coincides with the center of the circle forming the outer periphery of the cladding 14.

[0033] (Method for Measuring the Specifications of a Polarization-Maintaining Fiber) A method for measuring the specifications of the polarization-maintaining fiber 1 will be described with reference to Fig. 2. Fig. 2 is a graph showing the relative refractive index difference distribution Δ(r) at an arbitrary position r on the fast axis FA of the polarization-maintaining fiber 1.

[0034] First, the refractive index distribution n(r) on the fast axis FA is measured by an interference method. Next, the relative refractive index difference distribution Δ(r) on the fast axis FA is calculated from the refractive index distribution n(r) on the fast axis FA. For example, the relative refractive index difference Δ(r) is calculated by dividing the refractive index of pure silica glass by a reference value n ref Alternatively, the refractive index of the outer region of the cladding 14 is set to a reference value n ref Then, Δ(r) = 100 × [n(r) ２ -n ref ２ ] / (2×n(r) ２ ) can be calculated from the relative refractive index distribution Δ(r) on the fast axis FA. max and the minimum value Δ min Ask for.

[0035] Next, Δ(r)≧0.5×Δ maxis regarded as the core 11, and the radius of the region is taken as the radius r1 of the core 11. Also, Δ(r)≦0.5×Δ min The region that satisfies the above condition is regarded as the low refractive index layer 12, and the inner radius of the region is the inner radius r2 of the low refractive index layer 12, and the outer radius of the region is the outer radius r3 of the low refractive index layer 12.

[0036] Next, the relative refractive index difference Δ(r) of the core 11 with respect to the outer region of the cladding 14 is calculated as the relative refractive index difference Δ1 of the core 11 with respect to the outer region of the cladding 14, and the average value of the relative refractive index difference Δ(r) in the region satisfying Δ(r)≧0.9×Δmax is calculated. Furthermore, the relative refractive index difference Δ2 of the inner region of the cladding 14 with respect to the outer region of the cladding 14 is calculated as the average value of the relative refractive index difference Δ(r) in the region satisfying r1≦r≦r2. Furthermore, the relative refractive index difference Δ3 of the low refractive index layer 12 with respect to the outer region of the cladding 14 is calculated as the average value of the relative refractive index difference Δ(r) in the region satisfying r2≦r≦r3. Meanwhile, the relative refractive index difference Δ4 of the stress-applying portions 131, 132 with respect to the outer region of the cladding 14 is calculated as the average value of the relative refractive index difference in the region satisfying 50% or less of the minimum value of the refractive index distribution in the slow axis direction, based on the distribution of the relative refractive index differences of the stress-applying portions along the slow axis direction, as in FIG. 2 .

[0037] The mode field diameter of the polarization-maintaining fiber 1 is measured using the variable aperture method in accordance with IEC 60793-1-45. To measure the mode field diameter, light with a wavelength of 1.55 μm that is guided through the core 11 is used. Therefore, the "mode field diameter" and "mode field diameter at a wavelength of 1.55 μm" described below refer to the mode field diameter of light with a wavelength of 1.55 μm when that light propagates through the core.

[0038] The bending loss of the polarization-maintaining fiber 1 is measured in accordance with IEC 60793-1-47. That is, when the polarization-maintaining fiber 1 is wound around a mandrel with a radius of 2.0 mm once (when the bending radius is 2.0 mm), the power of the light in the LP01 mode from the light source and the power of the light in the LP01 mode from the light source in a state before the polarization-maintaining fiber 1 is wound are measured as a reference, and the bending loss per turn is calculated from the difference between these two powers. The mandrel is a rod-shaped jig with a perfectly circular cross section. To measure the bending loss, light with a wavelength of 1.55 μm guided through the core 11 is used. The bending loss is measured when the fiber is bent so that the fast axis direction is in the direction of the bending radius, as shown in FIG. 3A, and when the slow axis direction is in the direction of the bending radius, as shown in FIG. 3B. In other words, the bending loss is measured when the polarization-maintaining fiber is wound around the mandrel such that the direction of the slow axis of the polarization-maintaining fiber is perpendicular to the surface of the mandrel. In other words, the bending loss of light with a wavelength of 1.55 μm per turn is measured when the bending radius is 2.0 mm and the fiber is bent so that the slow axis direction is in the direction of the bending radius. Note that the "direction of the bending radius" refers to the direction in which the slow axis SA of the polarization-maintaining fiber 1 is perpendicular to the surface of the mandrel when the polarization-maintaining fiber 1 is wound around the mandrel in a spiral (or non-spiral) shape. The "direction of the bending radius" described below has the same meaning as described above. The "bending radius" is not limited to 2.0 mm, and may be, for example, between 2.0 and 2.5 mm.

[0039] The fiber cutoff wavelength of the polarization-maintaining fiber 1 is measured in accordance with IEC 60793-1-44. That is, in a polarization-maintaining fiber 1 cut to a fiber length of 2 m and wound once around a mandrel with a diameter of 280 mm, the fiber cutoff wavelength is the wavelength at which the higher-order mode is attenuated by 19.3 dB, and the fiber cutoff wavelength is measured based on the above conditions. The mandrel is a rod-shaped jig with a perfectly circular cross section. Here, the polarization-maintaining fiber 1 is wound around the mandrel so that the slow axis SA of the polarization-maintaining fiber 1 is perpendicular to the surface of the mandrel.

[0040] The diameter of the cladding 14 was measured by the transmitted near-field method based on IEC60793-1-20.

[0041] The distance from the central axis of the core to the stress-applying portion was obtained by measuring the fiber end face with an optical microscope.

[0042] The diameters of the stress-applying portions 131 and 132 were obtained by measuring the fiber end faces with an optical microscope.

[0043] (Method for Measuring MPI of Polarization-Maintaining Fiber) Next, a method for measuring MPI (Multi Path Interference) of a polarization-maintaining fiber will be described with reference to FIGS.

[0044] FIG. 4 is a block diagram showing the configuration of the MPI measurement system 100.

[0045] The measurement system 100 includes a polarization-maintaining fiber 1 to be measured, a light source 101, a polarizer 102, a first dummy fiber 103, a second dummy fiber 104, and a power meter 105. The fiber length of the polarization-maintaining fiber 1 to be measured is not particularly limited and may be, for example, 100 mm or more. In the examples and comparative examples described below, the fiber is cut to 0.3 m. Considering the MPI at a fiber length of 0.3 m, when measuring MPI at fiber lengths longer than 0.3 m, it is preferable to set the MPI threshold to an index smaller than the threshold at 0.3 m. When measuring MPI at fiber lengths shorter than 0.3 m, the MPI threshold may be set to an index larger than the MPI threshold at 0.3 m. The lengths of the first dummy fiber 103 and the second dummy fiber 104 must be long enough to eliminate unwanted higher-order modes, e.g., 5 m or more.

[0046] The light source 101 generates light having a wavelength ranging from 1530 nm to 1565 nm, for example. The light source 101 is configured to be able to change the wavelength of the generated light in 0.1 nm steps while maintaining the power of the generated light constant. The light generated by the light source 101 is input to a polarizer 102. The polarizer 102 selectively transmits linearly polarized light contained in the light output from the light source 101. The linearly polarized light transmitted through the polarizer 102 is input to a first dummy fiber 103. Note that the linearly polarized light transmitted through the polarizer 102 and input to the first dummy fiber 103 is, for example, linearly polarized light whose polarization direction (the vibration direction of the electric field) is parallel to the slow axis SA of the first dummy fiber 103. Furthermore, in the measurement system 100, the polarization extinction ratio of the linearly polarized light output from the first dummy fiber 103 and input to the polarization-maintaining fiber 1 is −25 dB or less. That is, in the measurement system 100, linearly polarized light having a polarization extinction ratio equivalent to that of laser light emitted from a commonly used optical device is input to the polarization-maintaining fiber 1, and linearly polarized light having a sufficient polarization extinction ratio value is input to the polarization-maintaining fiber 1.

[0047] The first dummy fiber 103 is connected to one end face of the polarization-maintaining fiber 1, and the second dummy fiber 104 is connected to the other end face of the polarization-maintaining fiber 1. The dummy fibers 103, 104 may be connected to the polarization-maintaining fiber 1 by fusion splicing or by connector connection. The dummy fibers 103, 104 are optical fibers that satisfy the condition that the connection loss in the LP01 mode when connected to the polarization-maintaining fiber 1 without axial misalignment is 0.05 dB or less, and these dummy fibers 103, 104 are used in a state where they are spirally wound around a cylindrical mandrel with a diameter of 150 mm.

[0048] The optical fiber used as the first dummy fiber 103 is an optical fiber having a polarization-maintaining function (for example, a PANDA-type or bowtie-type polarization-maintaining fiber). Splicing the first dummy fiber 103 and the polarization-maintaining fiber 1 without any axial misalignment means that the centers of the cores of the first dummy fiber 103 and the cores 11 of the polarization-maintaining fiber 1 are aligned, and the angle between the slow axis of the first dummy fiber 103 and the slow axis SA of the polarization-maintaining fiber 1 is 4° or less.

[0049] The optical fiber used as the second dummy fiber 104 may be an optical fiber having a polarization-maintaining function (for example, a PANDA-type or bowtie-type polarization-maintaining fiber). In this case, splicing the second dummy fiber 104 and the polarization-maintaining fiber 1 without any axial misalignment means splicing the second dummy fiber 104 and the polarization-maintaining fiber 1 so that the centers of the cores of the second dummy fiber 104 and the centers of the cores 11 of the polarization-maintaining fiber 1 overlap, and so that the slow axis of the second dummy fiber and the slow axis SA of the polarization-maintaining fiber 1 overlap.

[0050] The connection loss in LP01 mode can be measured using, for example, the narrowband ECL / PM technique described in ITU-T G. 650.1. In a bowtie polarization-maintaining fiber, the slow axis direction is parallel to the arrangement direction of the stress-applying portions, and the fast axis direction is perpendicular to the arrangement direction of the stress-applying portions.

[0051] The linearly polarized light that has passed through the polarizer 102 is input to the first dummy fiber 103. Here, the linearly polarized light output from the polarizer 102 is guided through the first dummy fiber 103 while maintaining its polarization direction. Thereafter, the linearly polarized light that has been guided through the first dummy fiber 103 is input to the polarization-maintaining fiber 1. Here, the linearly polarized light output from the first dummy fiber 103 is guided through the polarization-maintaining fiber 1 while maintaining its polarization direction. Thereafter, the linearly polarized light that has been guided through the polarization-maintaining fiber 1 is input to the second dummy fiber 104. Here, the linearly polarized light output from the polarization-maintaining fiber 1 is guided through the second dummy fiber 104 while maintaining its polarization direction. Thereafter, the light that has been guided through the second dummy fiber 104 is input to the power meter 105. The power meter 105 measures the power of the light output from the second dummy fiber 104.

[0052] The splice between the first dummy fiber 103 and the polarization-maintaining fiber 1, and the splice between the polarization-maintaining fiber 1 and the second dummy fiber 104 are performed in a state where there is an axial misalignment so as to satisfy the following conditions 1 to 3.

[0053] Condition 1: The connection loss of the LP01 mode at the connection point between the end of the first dummy fiber 103 and the end of the polarization-maintaining fiber 1 is 0.4 dB or more and 0.6 dB or less.

[0054] Condition 2: The connection loss of the LP01 mode at the connection point between the end of the second dummy fiber 104 and the end of the polarization-maintaining fiber 1 is 0.4 dB or more and 0.6 dB or less.

[0055] Condition 3: The average of the connection loss in the LP01 mode at the connection point between the end of the first dummy fiber 103 and the end of the polarization-maintaining fiber 1 and the connection loss in the LP01 mode at the connection point between the end of the second dummy fiber 104 and the end of the polarization-maintaining fiber 1 is 0.5 dB.

[0056] Specific examples of optical parameter conditions for the first dummy fiber 103, the polarization-maintaining fiber 1, and the second dummy fiber 104 that satisfy the above condition 3 include the following (1) and (2): (1) the difference in mode field diameter between the first dummy fiber 103 and the polarization-maintaining fiber 1 is 1.0 μm or less, and the difference in mode field diameter between the second dummy fiber 104 and the polarization-maintaining fiber 1 is 1.0 μm or less. (2) the ratio of the major axis to the minor axis of the mode field of the first dummy fiber 103 and the ratio of the major axis to the minor axis of the mode field of the polarization-maintaining fiber 1 are each 1.2 or more, and the ratio of the major axis to the minor axis of the mode field of the second dummy fiber 104 and the ratio of the major axis to the minor axis of the mode field of the polarization-maintaining fiber 1 are each 1.2 or more.

[0057] Therefore, part of the light in the LP01 mode guided through the first dummy fiber 103 is coupled to the LP11 mode of the polarization-maintaining fiber 1 due to the axial misalignment at the connection point between the end of the first dummy fiber 103 and the end of the polarization-maintaining fiber 1. Also, part of the light in the LP11 mode guided through the polarization-maintaining fiber 1 is coupled to the LP01 mode of the second dummy fiber 104 due to the axial misalignment at the connection point between the end of the polarization-maintaining fiber 1 and the end of the second dummy fiber 104. Therefore, interference occurs between (1) light that is guided in the first dummy fiber 103 as the LP01 mode, guided in the polarization-maintaining fiber 1 as the LP01 mode, and guided in the second dummy fiber 104 as the LP01 mode, and (2) light that is guided in the first dummy fiber 103 as the LP01 mode, guided in the polarization-maintaining fiber 1 as the LP11 mode, and guided in the second dummy fiber 104 as the LP01 mode. Because of this interference, when the wavelength of the light generated by the light source 101 is swept, the power of the light measured by the power meter 105 changes periodically.

[0058] FIG. 5A is a graph showing the wavelength dependence of the power of light generated by the light source 101. FIG. 5B is a graph showing the wavelength dependence of the power of light measured by the power meter 105. The power of light generated by the light source 101 is constant as shown in FIG. 5A. On the other hand, the power of light measured by the power meter 105 changes periodically as shown in FIG. 5B. The wavelength sweep range is determined to be larger than the change period of the power of light measured by the power meter 105 (e.g., more than twice the change period). The wavelength sweep step is determined to be smaller than the change period of the power of light measured by the power meter 105 (e.g., less than 1 / 10 of the change period). In the measurement system 100, the wavelength sweep range is set to the C-band (1530 nm or more and 1565 nm or less). This is because the polarization-maintaining fiber 1 is intended to be used in various optical devices. The above-mentioned "optical device" specifically refers to optical devices such as (1) telecom optical devices such as transceivers for intercity networks and submarine networks, and optical devices for datacom such as CPO (Co-packaged Optics) modules (CPO switch modules, etc.) and pluggable transceivers (coherent optical transceivers, etc.), (2) optical devices for amplifiers, and (3) optical devices for sensors. The "optical device" described below will be used in the same sense as the optical devices in (1) to (3) above.

[0059] The MPI is calculated according to the following formula (1), following the method described as the narrowband ECL / PM technique in ITU-T G. 650.1: In formula (1), PTP represents the difference between the maximum and minimum values ​​of the optical power measured by the power meter 105 when the wavelength of the light generated by the light source 101 is swept.

[0060] In the measurement system 100, (1) a first measurement is performed in which the first dummy fiber 103 and the polarization-maintaining fiber 1 are connected in a state where there is an axial misalignment in the slow axis direction, and the intensity of light output from the second dummy fiber 104 is measured using the power meter 105 while the wavelength of light generated by the light source 101 is swept from 1530 nm to 1565 nm in 0.1 nm steps, and (2) a second measurement is performed in which the first dummy fiber 103 and the polarization-maintaining fiber 1 are connected in a state where there is an axial misalignment in the fast axis direction, and the intensity of light output from the second dummy fiber 104 is measured using the power meter 105 while the wavelength of light generated by the light source 101 is swept from 1530 nm to 1565 nm in 0.1 nm steps. Then, in each of the first and second measurements, the MPI is calculated using the above formula (1) from the wavelength dependence of the light intensity measured by the power meter 105.

[0061] Note that, with respect to the splice between the first dummy fiber 103 and the polarization-maintaining fiber 1, "a state in which there is an axial misalignment in the slow axis direction" refers to a state in which the following conditions 4a and 4b are satisfied. Also, with respect to the splice between the first dummy fiber 103 and the polarization-maintaining fiber 1, "a state in which there is an axial misalignment in the fast axis direction" refers to a state in which the following conditions 5a and 5b are satisfied. Note that in the following description, an xy coordinate system is used as an xy coordinate system fixed to the end face of the first dummy fiber 103, with (1) the center of the core of the first dummy fiber 103 as the origin of coordinates, (2) an axis that passes through the center of the core of the first dummy fiber 103 and is parallel to the slow axis of the first dummy fiber 103 as the x-axis, and (3) an axis that passes through the center of the core of the first dummy fiber 103 and is parallel to the fast axis of the first dummy fiber 103 as the y-axis. Furthermore, with respect to the splice between the second dummy fiber 104 and the polarization-maintaining fiber 1, a "state in which there is an axial misalignment in the slow axis direction" refers to a state in which the following conditions 4a' and 4b' are satisfied. Furthermore, with respect to the splice between the second dummy fiber 104 and the polarization-maintaining fiber 1, a "state in which there is an axial misalignment in the fast axis direction" refers to a state in which the following conditions 5a' and 5b' are satisfied. In the following description, an x-y coordinate system is used as an x-y coordinate system fixed to the end face of the second dummy fiber 104, with (1) the center of the core of the second dummy fiber 104 as the origin of coordinates, (2) an axis that passes through the center of the core of the second dummy fiber 104 and is parallel to the slow axis of the second dummy fiber 104 as the x-axis, and (3) an axis that passes through the center of the core of the second dummy fiber 104 and is parallel to the fast axis of the second dummy fiber 104 as the y-axis.

[0062] Condition 4a: At the end face of the first dummy fiber 103 on the polarization-maintaining fiber 1 side, the angle formed by the direction from the center of the core of the first dummy fiber 103 toward the center (point overlapping with) of the core 11 of the polarization-maintaining fiber 1 and the slow axis (x-axis) direction of the first dummy fiber 103 is 15° or less. That is, when the coordinates of the point overlapping with the center of the core 11 of the polarization-maintaining fiber 1 at the end face of the first dummy fiber 103 are (x, y), |tan －１ (y / x)|≦15° is satisfied.

[0063] Condition 4b: At the end face of the first dummy fiber 103 on the polarization-maintaining fiber 1 side, the angle formed by the slow axis (x-axis) of the first dummy fiber 103 and the slow axis SA of the polarization-maintaining fiber 1 (a straight line overlapping with the slow axis SA) is 4° or less.

[0064] Condition 5a: At the end face of the first dummy fiber 103 on the polarization-maintaining fiber 1 side, the angle formed by the direction from the center of the core of the first dummy fiber 103 toward the center (point overlapping with) of the core 11 of the polarization-maintaining fiber 1 and the fast axis (y-axis) direction of the first dummy fiber 103 is 15° or less. That is, when the coordinates of the point overlapping with the center of the core 11 of the polarization-maintaining fiber 1 at the end face of the first dummy fiber 103 are (x, y), |tan －１ (x / y)|≦15° is satisfied.

[0065] Condition 5b: At the end face of the first dummy fiber 103 on the polarization-maintaining fiber 1 side, the angle formed by the slow axis (x-axis) of the first dummy fiber 103 and (a straight line overlapping) the slow axis SA of the polarization-maintaining fiber 1 is 4° or less.

[0066] Condition 4a': At the end face of the second dummy fiber 104 on the polarization-maintaining fiber 1 side, the angle formed by the direction from the center of the core of the second dummy fiber 104 toward the center (point overlapping with) of the core 11 of the polarization-maintaining fiber 1 and the slow axis (x-axis) direction of the second dummy fiber 104 is 15° or less. That is, when the coordinates of the point overlapping with the center of the core 11 of the polarization-maintaining fiber 1 at the end face of the second dummy fiber 104 are (x, y), |tan －１ (y / x)|≦15° is satisfied.

[0067] Condition 4b': At the end face of the second dummy fiber 104 on the polarization-maintaining fiber 1 side, the angle formed between the slow axis (x-axis) of the second dummy fiber 104 and the slow axis SA of the polarization-maintaining fiber 1 (a straight line overlapping with the slow axis SA) is 4° or less.

[0068] Condition 5a': At the end face of the second dummy fiber 104 on the polarization-maintaining fiber 1 side, the angle formed by the direction from the center of the core of the second dummy fiber 104 toward the center (point overlapping with) of the core 11 of the polarization-maintaining fiber 1 and the fast axis (y-axis) direction of the second dummy fiber 104 is 15° or less. That is, when the coordinates of the point overlapping with the center of the core 11 of the polarization-maintaining fiber 1 at the end face of the second dummy fiber 104 are (x, y), |tan －１ (x / y)|≦15° is satisfied.

[0069] Condition 5b': At the end face of the second dummy fiber 104 on the polarization-maintaining fiber 1 side, the angle formed between the slow axis (x-axis) of the second dummy fiber 104 and the slow axis SA of the polarization-maintaining fiber 1 (a straight line overlapping with the slow axis SA) is 4° or less.

[0070] Consider the case where the polarization direction (direction of the electric field) of the linearly polarized light guided through the first dummy fiber 103 is parallel to the x-axis, i.e., the light guided through the first dummy fiber 103 is in the LP01x mode. In this case, the first measurement can evaluate the MPI when part of the light in the LP01x mode guided through the first dummy fiber 103 couples with the LP11ax mode of the polarization-maintaining fiber 1. Furthermore, the second measurement can evaluate the MPI when part of the light in the LP01x mode guided through the first dummy fiber 103 couples with the LP11bx mode of the polarization-maintaining fiber 1.

[0071] In fact, in the first measurement, the first dummy fiber 103 and the polarization-maintaining fiber 1 are connected with an axial misalignment in the slow axis direction. Therefore, most of the light in the LP01x mode guided through the first dummy fiber 103 is coupled to the LP11ax mode of the polarization-maintaining fiber 1 without coupling to the LP11bx mode of the polarization-maintaining fiber 1. This is because, in this case, as shown in (a) of FIG. 6 , the overlap integral between the electric field distribution of the light in the LP01x mode of the first dummy fiber 103 and the electric field distribution of the light in the LP11bx mode of the polarization-maintaining fiber 1 is small, while the overlap integral between the electric field distribution of the light in the LP11ax mode of the polarization-maintaining fiber 1 and the electric field distribution of the light in the LP11ax mode of the polarization-maintaining fiber 1 is large. Therefore, the first measurement can evaluate the MPI when the light in the LP01x mode guided through the first dummy fiber 103 is coupled to the LP11ax mode of the polarization-maintaining fiber 1.

[0072] On the other hand, in the second measurement, the first dummy fiber 103 and the polarization-maintaining fiber 1 are connected with an axial misalignment in the fast axis direction. Therefore, most of the light in the LP01x mode guided through the first dummy fiber 103 is coupled to the LP11bx mode of the polarization-maintaining fiber 1 without coupling to the LP11ax mode of the polarization-maintaining fiber 1. This is because, in this case, as shown in (b) of FIG. 6 , the overlap integral between the electric field distribution of the light in the LP01x mode of the first dummy fiber 103 and the electric field distribution of the light in the LP11ax mode of the polarization-maintaining fiber 1 is small, while the overlap integral between the electric field distribution of the light in the LP11bx mode of the polarization-maintaining fiber 1 and the electric field distribution of the light in the LP11bx mode of the polarization-maintaining fiber 1 is large. Therefore, the second measurement makes it possible to evaluate the MPI when most of the light in the LP01x mode guided through the first dummy fiber 103 is coupled to the LP11bx mode of the polarization-maintaining fiber 1.

[0073] (Characteristics of Polarization-Maintaining Fiber) In a polarization-maintaining fiber 1 having a low refractive index layer 12, the total amount of confinement loss of the LP11 mode is reduced, and therefore, light in the LP11 mode excited at one end face (the connection point with the first dummy fiber 103) is more likely to remain without being lost and reach the other end face (the connection point with the second dummy fiber 104). Due to this mechanism, even when the fiber length is short, the total amount of confinement loss of the LP11 mode is reduced, and therefore, light in the LP11 mode is more likely to remain without being lost and reach the other end face, and therefore, the MPI value is more likely to increase. For this reason, in a polarization-maintaining fiber 1 having a low refractive index layer 12, it is more important than ever to suppress the MPI value. Furthermore, in a polarization-maintaining fiber 1 that is expected to be used in a variety of applications, it is more important than ever to suppress bending loss.

[0074] The value of MPI is related to the value of the cutoff wavelength. This is because the cutoff wavelength, like the MPI, is a physical quantity that reflects the magnitude of light in a higher-order mode at an arbitrary wavelength in the polarization-maintaining fiber 1. Therefore, the inventors of the present application investigated the relationship between the cutoff wavelength and MPI in the polarization-maintaining fiber 1. As a result, they found that by setting the fiber cutoff wavelength to 1.45 μm or less, the value of MPI caused by axial misalignment in at least one direction can be suppressed to −30 dB or less.

[0075] Here, the MPI value caused by axial misalignment in at least one direction or the MPI value caused by axial misalignment in an arbitrary direction (direction D) refers to the MPI value measured in the above-described measurement system 100 when the first dummy fiber 103 and the polarization-maintaining fiber 1 are spliced ​​together in an axially misaligned state so as to satisfy the following conditions a and b and the above conditions 1 to 3, or when the second dummy fiber 104 and the polarization-maintaining fiber 1 are spliced ​​together in an axially misaligned state so as to satisfy the following conditions a' and b' and the above conditions 1 to 3. Note that when direction D is the slow axis direction, the following conditions a and b coincide with the above conditions 4a and 4b, and when direction D is the fast axis direction, the following conditions a and b coincide with the above conditions 5a and 5b.

[0076] Condition a: At the end face of the first dummy fiber 103, the angle formed by the direction from the center of the core of the first dummy fiber 103 toward the center (or the point where it overlaps) of the core 11 of the polarization-maintaining fiber 1 and direction D is 15° or less.

[0077] Condition b: At the end face of the first dummy fiber 103, the angle formed by the slow axis (x-axis) of the first dummy fiber 103 and the slow axis SA of the polarization-maintaining fiber 1 (a straight line overlapping with the slow axis SA) is 4° or less.

[0078] Condition a': At the end face of the second dummy fiber 104, the angle formed by the direction from the center of the core of the second dummy fiber 104 toward the center (or the point where it overlaps) of the core 11 of the polarization-maintaining fiber 1 and direction D is 15° or less.

[0079] Condition b': At the end face of the second dummy fiber 104, the angle formed by the slow axis (x-axis) of the second dummy fiber 104 and (a line overlapping with) the slow axis SA of the polarization-maintaining fiber 1 is 4° or less.

[0080] Here, for the polarization-maintaining fiber 1, the cutoff wavelength can be specified using the fiber cutoff wavelength condition when the fiber length is 2 m instead of the cutoff wavelength condition when the fiber length is 0.3 m, for the reasons explained below. As described above, the MPI is measured using a polarization-maintaining fiber 1 cut to 0.3 m. On the other hand, the fiber cutoff wavelength is measured using a polarization-maintaining fiber 1 cut to 2 m and wound once around a mandrel with a diameter of 280 mm. As such, the fiber length of the polarization-maintaining fiber 1 used for measurement differs from that of the fiber cutoff wavelength. Therefore, the value of the MPI cannot be specified solely based on the condition for the fiber cutoff wavelength. This is because the wavelength at which the higher-order mode is attenuated by 19.3 dB in a polarization-maintaining fiber 1 cut to 0.3 m correlates with the MPI when measured at a fiber length of 0.3 m, and in a polarization-maintaining fiber 1 having a low refractive index layer 12, the wavelength at which the higher-order mode is attenuated by 19.3 dB in a polarization-maintaining fiber 1 cut to 0.3 m is different from the fiber cutoff wavelength (the wavelength at which the higher-order mode is attenuated by 19.3 dB in a polarization-maintaining fiber cut to 2 m).

[0081] However, in the polarization-maintaining fiber 1, the conditions for satisfying the MPI value of −30 dB or less and the bending loss value of 0.20 dB or less, described below, can be specified using the fiber cutoff wavelength condition instead of the cutoff wavelength condition when the fiber length is cut to 0.3 m. This is because, whether the fiber length is 0.3 m or 2 m, the conditions for the structure of the low-refractive-index layer 12 and the mode field diameter condition that can suppress the MPI value to −30 dB or less and the bending loss value to 0.20 dB or less, described below, remain the same, excluding manufacturing errors. Here, the cutoff wavelength when the fiber length is cut to 0.3 m is not determined by an international standard and is therefore a parameter that is not generally measured, whereas the fiber cutoff wavelength is determined by an international standard and is therefore a parameter that is generally measured. Therefore, when the conditions for the fiber cutoff wavelength are used to specify the polarization-maintaining fiber 1, the values ​​of the MPI and bending loss described above are easily determined, making it easier to determine whether the MPI value is −30 dB or less and the bending loss value is 0.20 dB or less, described below. Therefore, the conditions for the fiber cutoff wavelength are specified as the conditions for satisfying an MPI value of −30 dB or less and a bending loss value of 0.20 dB or less, which will be described later, in the polarization-maintaining fiber 1. More specifically, the conditions for the structure of the low-refractive-index layer 12 are: (1) the ratio r2 / r1 of the radius r1 of the core 11 to the inner radius r2 of the low-refractive-index layer 12, (2) the difference r3-r2 between the outer radius r3 of the low-refractive-index layer 12 and the inner radius r2 of the low-refractive-index layer 12, and (3) the relative refractive index difference Δ3 of the low-refractive-index layer 12 with respect to the cladding 14.

[0082] Based on the above, the inventors of the present application investigated what conditions, such as those related to the fiber cutoff wavelength and the structure of the low-refractive-index layer 12, must be satisfied to suppress the MPI caused by axial misalignment in at least one direction to −30 dB or less, and to suppress the bending loss of light with a wavelength of 1.55 μm per turn to 0.20 dB or less when the bending radius is 2.0 mm or approximately 2.0 mm and when the fiber is bent so that the slow-axis direction is in the direction of the bending radius (hereinafter also referred to as “bending loss in the slow-axis direction”). As a result, they found that when the conditions related to the structure of the low-refractive-index layer 12 satisfy the following conditions A, B, and C, and further satisfy the following condition D, the MPI caused by axial misalignment in at least one direction can be suppressed to −30 dB or less.

[0083] Condition A: The ratio r2 / r1 of the radius r1 of the core 11 to the inner radius r2 of the low refractive index layer 12 satisfies 1.0≦r2 / r1≦3.0.

[0084] Condition B: The difference r3-r2 between the outer radius r3 of the low refractive index layer 12 and the inner radius r2 of the low refractive index layer 12 satisfies 4.0 μm≦r3-r2≦6.0 μm.

[0085] Condition C: The relative refractive index difference Δ3 of the low refractive index layer 12 with respect to the cladding 14 (the outer region of the cladding 14; hereinafter, sometimes simply referred to as the cladding 14) satisfies −0.38%≦Δ3≦−0.27%.

[0086] Condition D: The fiber cutoff wavelength is 1.45 μm or less.

[0087] It is known that the impact of MPI on transmission quality is sufficiently small if the MPI value is −30 dB or less. Therefore, by satisfying the above conditions A, B, and C, it is possible to realize a polarization-maintaining fiber 1 in which degradation of transmission quality due to MPI does not occur, or, even if degradation of transmission quality due to MPI does occur, the degree of degradation is sufficiently small.

[0088] The value of the bending loss in the slow axis direction depends on the strength of light confinement in the core 11 as well as the structure of the low refractive index layer 12. Therefore, the inventors took up the mode field diameter as a quantity representing the strength of light confinement in the core 11, and investigated what conditions the mode field diameter must satisfy to suppress the bending loss in the slow axis direction to 0.20 dB or less. As a result, they found that the bending loss in the slow axis direction can be suppressed to 0.20 dB or less when the above conditions A, B, and C regarding the structure of the low refractive index layer 12 are satisfied and further when the following condition E regarding the mode field diameter is satisfied.

[0089] Condition E: When light having a wavelength of 1.55 μm propagates through the core 11, the mode field diameter of the light is 9.2 μm or less.

[0090] Based on the above, the inventors of the present application have found that by satisfying the above conditions A, B, C, D, and E, it is possible to suppress the MPI caused by axial misalignment in at least one direction to −30 dB or less, and to suppress the bending loss in the slow axis direction to 0.20 dB or less. In this case, even if the bending loss conditions and strict MPI conditions are met when a bending radius of 2.0 mm or a small bending radius of approximately 2.0 mm is required as one target value for the optical device described above, it is possible to realize a polarization-maintaining fiber 1 that can meet the conditions to the extent that it is applicable to the optical device, for example, when the polarization-maintaining fiber 1 is housed in the optical device. Here, the bending radius of approximately 2.0 mm is not limited to 2.0 mm, and it means that equivalent effects can be obtained even with a bending radius of 2.0 to 2.5 mm. Furthermore, in the following description, the term "bending radius of approximately 2.0 mm" may be used interchangeably with a bending radius of 2.0 to 2.5 mm.

[0091] (Preferred Form of Polarization-Maintaining Fiber) In the polarization-maintaining fiber 1, it is preferable that both the MPI value caused by axial misalignment with respect to the fast axis direction and the MPI value caused by axial misalignment with respect to the slow axis direction are −30 dB or less. Of the MPI value caused by axial misalignment with respect to the fast axis direction and the MPI value caused by axial misalignment with respect to the slow axis direction, one is the best MPI value, and the other is the worst MPI value. Therefore, when both the MPI value caused by axial misalignment with respect to the fast axis direction and the MPI value caused by axial misalignment with respect to the slow axis direction are −30 dB or less, the MPI value caused by axial misalignment in any direction can be more reliably suppressed to −30 dB or less. Therefore, even if the strict MPI conditions required as one guideline for the target values ​​of the above-mentioned optical devices are met, for example, when the polarization-maintaining fiber 1 is housed in the optical device, it is possible to realize a polarization-maintaining fiber 1 that can meet the conditions to a degree that makes it applicable to the optical device, etc.

[0092] Furthermore, in the polarization-maintaining fiber 1, it is preferable that one or both of the MPI value caused by axial misalignment with respect to the fast axis direction and the MPI value caused by axial misalignment with respect to the slow axis direction are −35 dB or less. This makes it possible to realize a polarization-maintaining fiber 1 that can satisfy the conditions to the extent that it is applicable to optical devices used in high-speed communication systems, which require stricter MPI conditions, among the optical devices described above. It is more preferable that both the MPI value caused by axial misalignment with respect to the fast axis direction and the MPI value caused by axial misalignment with respect to the slow axis direction are −35 dB or less. This makes it possible to more reliably suppress the MPI value caused by axial misalignment in any direction to −35 dB or less. This makes it possible to realize a polarization-maintaining fiber 1 that can more reliably satisfy the conditions to the extent that it is applicable to optical devices used in high-speed communication systems, which require stricter MPI conditions, among the optical devices described above.

[0093] In addition, in the polarization-maintaining fiber 1, it is preferable that one or both of the MPI value caused by axial misalignment with respect to the fast axis direction and the MPI value caused by axial misalignment with respect to the slow axis direction be −40 dB or less, and it is even more preferable that both of the MPI value caused by axial misalignment with respect to the fast axis direction and the MPI value caused by axial misalignment with respect to the slow axis direction be −40 dB or less. This makes it possible to realize a polarization-maintaining fiber 1 that can satisfy the conditions to a degree that makes it applicable to optical devices used in higher-speed communication systems that require even stricter MPI conditions.

[0094] When the polarization-maintaining fiber 1 is bent, coupling of higher-order modes to the radiation mode, which reduces the MPI, and coupling of the fundamental mode to the higher-order modes, which increases the MPI, can occur. Here, when the bending loss is small, coupling of higher-order modes to the radiation mode becomes more prevalent than coupling of the fundamental mode to the higher-order modes, and bending reduces the MPI. Therefore, if the bending loss is sufficiently small, it is more preferable that, for example, both the MPI value caused by axial misalignment with respect to the fast axis direction and the MPI value caused by axial misalignment with respect to the slow axis direction are −40 dB or less when bending is applied. Here, bending refers to, for example, cutting the polarization-maintaining fiber 1 to a fiber length of 0.3 m and bending it so that the slow axis direction is in the direction of the bending radius and the bending radius is 2.0 mm. This makes it possible to more reliably suppress the MPI value caused by axial misalignment in any direction to −40 dB or less when bending is applied. Therefore, it is possible to realize a polarization-maintaining fiber 1 that can meet the conditions applicable to optical devices used in high-speed communication systems, which require even stricter MPI conditions.

[0095] Furthermore, the coupling of higher-order modes to radiation modes, which is a factor in reducing MPI, becomes more active as the relative refractive index difference Δ3 of the low-refractive index layer 12 with respect to the cladding 14 increases (as the refractive index valley in the low-refractive index layer 12 becomes shallower). Therefore, by increasing the relative refractive index difference Δ3 of the low-refractive index layer 12 with respect to the cladding 14, it is possible to realize a polarization-maintaining fiber 1 in which one or both of the MPI value caused by axial misalignment in the fast axis direction and the MPI value caused by axial misalignment in the slow axis direction are sufficiently small.

[0096] In view of this, in the polarization-maintaining fiber 1, it is preferable that the relative refractive index difference Δ3 of the low-refractive-index layer 12 with respect to the cladding 14 satisfies −0.37%≦Δ3≦−0.27%. This makes it possible to minimize the MPI values, so that both the MPI values ​​caused by axial misalignment in the fast axis direction and the MPI values ​​caused by axial misalignment in the slow axis direction are −30 dB or less, as shown in Examples 2 and 3 in Table 1 described later. Therefore, even if the strict MPI conditions required as one of the target values ​​for the optical device described above are met, it is possible to realize a polarization-maintaining fiber 1 that satisfies the conditions applicable to the optical device, for example, when the polarization-maintaining fiber 1 is housed in the optical device. Alternatively, it is possible to minimize the MPI values, so that at least one of the MPI values ​​caused by axial misalignment in the fast axis direction and the MPI values ​​caused by axial misalignment in the slow axis direction is −40 dB or less, as shown in Examples 2 and 3 in Table 1 described later. This makes it possible to realize a polarization-maintaining fiber 1 that can meet the conditions to the extent that it can be applied to optical devices used in high-speed communication systems that require even stricter MPI conditions.

[0097] In light of the examples described below, in the polarization-maintaining fiber 1, if the fiber cutoff wavelength is 1.45 μm or less and the fiber cutoff wavelength is 1.40 μm or greater, as described above, the MPI caused by axial misalignment in at least one direction can be more reliably suppressed to −30 dB or less, and the bending loss in the slow axis direction can be more reliably suppressed to 0.20 dB or less. This is because, as described above, the fiber cutoff wavelength of 1.45 μm or less can suppress the MPI sufficiently small, and the fiber cutoff wavelength of 1.40 μm or greater can suppress the bending loss sufficiently small. Therefore, even if the bending loss condition and strict MPI condition are met in a case where a small bending radius of about 2.0 mm is required as one target value for the above-mentioned optical device, for example, when the polarization-maintaining fiber 1 is housed in the optical device, it is possible to realize a polarization-maintaining fiber 1 that can more reliably satisfy the conditions to a degree that makes it applicable to the optical device, etc.

[0098] Furthermore, it is preferable that the mode field diameter at a wavelength of 1.55 μm in the polarization-maintaining fiber 1 is 9.0 μm or less. This makes it possible to keep the bending loss low, to a value of less than 0.10 dB, to two decimal places or less, as shown in Examples 1 and 3 in Table 1 described below. Therefore, even if the bending loss condition is such that a small bending radius of about 2.0 mm is required as one of the target values ​​for the optical device described above, for example, when the polarization-maintaining fiber 1 is housed in the optical device, it is possible to realize a polarization-maintaining fiber 1 that can more reliably satisfy the conditions to the extent that it can be applied to the optical device, etc.

[0099] Furthermore, in the polarization-maintaining fiber 1, it is preferable that the relative refractive index difference Δ1 of the core 11 with respect to the cladding 14 satisfies 0.30%≦Δ1. By making the relative refractive index difference Δ1 0.30% or greater, bending loss can be more reliably suppressed. Therefore, even if the bending loss condition is met when a small bending radius of about 2.0 mm is required as one of the target values ​​for the optical device described above, for example, when the polarization-maintaining fiber 1 is housed in the optical device, it is possible to realize a polarization-maintaining fiber 1 that can more reliably satisfy the conditions to the extent that it can be applied to the optical device, etc.

[0100] Furthermore, in the polarization-maintaining fiber 1, the relative refractive index difference Δ1 of the core 11 with respect to the cladding 14 preferably satisfies Δ1≦0.38%. A relative refractive index difference Δ1 of 0.38% or less can reduce splice loss. Therefore, even if the strict splice loss condition required as one of the target values ​​for the optical device described above is met, for example, when the polarization-maintaining fiber 1 is housed in the optical device or spliced ​​with other optical fibers, a polarization-maintaining fiber 1 that can more reliably satisfy the conditions applicable to the optical device or other optical fibers can be realized. Alternatively, as described above, in addition to the mode field diameter at a wavelength of 9.2 μm or less, it is preferable that the mode field diameter at a wavelength of 1.55 μm be 8.8 μm or more. In reality, the mode field diameter of the optical waveguide to which the polarization-maintaining fiber is connected is often 8.8 μm or more but not more than 9.6 μm, taking into account manufacturing errors. This is because the mode field diameter of the single mode fiber connected to the optical waveguide is often 8.8 μm or more and 9.6 μm or less when manufacturing errors are taken into consideration. Therefore, from the perspective of reducing the connection loss with the optical waveguide, the mode field diameter of the polarization-maintaining fiber 1 is 8.8 μm or more, which makes it possible to suppress the connection loss.

[0101] Furthermore, in the polarization-maintaining fiber 1, it is preferable that the ratio r2 / r1 of the radius r1 of the core 11 to the inner radius r2 of the low-refractive-index layer 12 satisfies 2.4<r2 / r1≦3.0. As a result, when the mode field diameter and cutoff wavelength of the polarization-maintaining fiber 1 are the same, it is easier to increase Δ1 when 2.4<r2 / r1≦3.0 than when 2.4≦r2 / r1, and therefore the bending loss in the slow axis direction can be more reliably suppressed to 0.20 dB or less.

[0102] As described above, the fiber cutoff wavelength is the wavelength at which the higher-order mode is attenuated by 19.3 dB in a polarization-maintaining fiber 1 cut to 2 m and wound once around a mandrel with a diameter of 280 mm. When the fiber length is shorter than 2 m, the wavelength at which the higher-order mode is attenuated by 19.3 dB (cutoff wavelength) tends to shift toward longer wavelengths. Therefore, when the fiber length is shorter than 2 m, the wavelength at which the higher-order mode is attenuated by 19.3 dB may exceed the operating wavelength, i.e., single-mode transmission at the operating wavelength may become difficult. To reduce this possibility, it is preferable to provide a certain margin between the fiber cutoff wavelength and the operating wavelength. For example, if the fiber cutoff wavelength is shorter than 1.34 μm, a margin of approximately 0.2 μm can be provided between the fiber cutoff wavelength and the lower limit of the C-band (1530 nm or more and 1565 nm or less). Therefore, even if the cutoff wavelength shifts toward longer wavelengths due to a fiber length shorter than 2 m, the cutoff wavelength can be prevented from exceeding the operating wavelength. This reduces the possibility that single-mode transmission becomes difficult at the wavelength used.

[0103] As examples, three types of polarization-maintaining fibers 1 were manufactured and their specifications were measured. As comparative examples, two types of polarization-maintaining fibers were manufactured and their specifications were measured. The measurement results are shown in Table 1 below.

[0104] The polarization-maintaining fibers 1 according to Examples 1 to 3 satisfy the above-mentioned conditions A to E. As a result, the polarization-maintaining fibers 1 according to Examples 1 to 3 can suppress the value of MPI caused by axial misalignment in the slow axis direction to −30 dB or less, and can suppress the value of bending loss in the slow axis direction to 0.20 dB or less.

[0105] On the other hand, the polarization-maintaining fiber according to Comparative Example 1 satisfies the above-mentioned conditions A to C and E, but the fiber cutoff wavelength is greater than 1.45 μm, and it does not satisfy condition D. As a result, in the polarization-maintaining fiber according to Comparative Example 1, the value of MPI caused by axial misalignment with respect to the slow axis direction and the value of MPI caused by axial misalignment with respect to the fast axis direction cannot be suppressed to −30 dB or less.

[0106] Furthermore, the polarization-maintaining fiber according to Comparative Example 2 satisfies the above-mentioned conditions A, D, and E, but the difference r3-r2 is greater than 6.0 μm, so the above-mentioned condition B is not satisfied, and the relative refractive index difference Δ3 is greater than −0.27%, so the above-mentioned condition C is not satisfied. In particular, the relative refractive index difference Δ3 is −0.03%, a value close to zero. As a result, the polarization-maintaining fiber according to Comparative Example 2 cannot suppress the bending loss in the slow axis direction to 0.20 dB or less.

[0107] In the polarization-maintaining fibers 1 according to Examples 2 and 3, both the MPI value caused by axial misalignment in the fast axis direction and the MPI value caused by axial misalignment in the slow axis direction are −30 dB or less. Therefore, the MPI value caused by axial misalignment in any direction can be suppressed to −30 dB or less.

[0108] In addition, in the polarization-maintaining fibers 1 according to Examples 1 and 2, either the value of the MPI caused by the axial misalignment in the fast axis direction or the value of the MPI caused by the axial misalignment in the slow axis direction is −35 dB or less. In other words, in the polarization-maintaining fibers 1 according to Examples 1 and 2, the value of the MPI caused by the axial misalignment in the slow axis direction is −35 dB or less. In addition, in the optical fiber 1 according to Example 3, both the value of the MPI caused by the axial misalignment in the fast axis direction and the value of the MPI caused by the axial misalignment in the slow axis direction are −35 dB or less.

[0109] In addition, in the polarization-maintaining fibers 1 according to Examples 2 and 3, either the value of the MPI caused by axial misalignment in the fast axis direction or the value of the MPI caused by axial misalignment in the slow axis direction is −40 dB or less. In other words, in the polarization-maintaining fibers 1 according to Examples 2 and 3, the value of the MPI caused by axial misalignment in the slow axis direction is −40 dB or less.

[0110] In the polarization-maintaining fibers according to Examples 1, 2, and 3, when the fiber is cut to a length of 0.3 m, the bending radius is 2.0 mm, and the fiber is bent so that the slow axis direction is in the same direction as the bending radius, the MPI value caused by misalignment with respect to the slow axis direction is −40 dB or less. In the polarization-maintaining fiber according to Example 3, when the fiber is cut to a length of 0.3 m, the bending radius is 2.0 mm, and the fiber is bent so that the slow axis direction is in the same direction as the bending radius, the MPI value caused by misalignment with respect to the fast axis direction and the MPI value caused by misalignment with respect to the slow axis direction are both −40 dB or less.

[0111] Furthermore, in the polarization-maintaining fibers 1 according to Examples 2 and 3, the relative refractive index difference Δ3 of the low-refractive-index layer 12 with respect to the cladding 14 satisfies −0.37%≦Δ3≦−0.27%. As a result, in the polarization-maintaining fibers 1 according to Examples 2 and 3, the MPI value caused by axial misalignment in the fast axis direction and the MPI value caused by axial misalignment in the slow axis direction are both −30 dB or less.

[0112] Furthermore, the polarization-maintaining fibers 1 according to Examples 1, 2, and 3 have a fiber cutoff wavelength of 1.40 μm or more. As a result, the polarization-maintaining fibers 1 according to Examples 1, 2, and 3 have a bending loss value in the slow axis direction of 0.20 dB or less.

[0113] In addition, in the polarization-maintaining fibers 1 according to Examples 1 to 3, the relative refractive index difference Δ1 of the core 11 with respect to the cladding 14 satisfies 0.30%≦Δ1.

[0114] In the polarization-maintaining fibers 1 according to Examples 1 to 3, the relative refractive index difference Δ1 of the core 11 with respect to the cladding 14 satisfies Δ1≦0.38%. In the polarization-maintaining fibers 1 according to Examples 1 to 3, the mode field diameter at a wavelength of 1.55 μm is 8.8 μm or more.

[0115] In the polarization-maintaining fiber 1 according to Example 3, the ratio r2 / r1 of the radius r1 of the core 11 to the inner radius r2 of the low refractive index layer 12 satisfies 2.4<r2 / r1≦3.0.

[0116] (Supplementary Notes on Terminology) The definition of the angle formed by two axes will be explained with reference to FIG. 7(a).

[0117] When two axes A1 and A2 intersect, four angles are generated around the intersection point, and the magnitude of these four angles is one of two angles θ1 and θ2. In this specification, the magnitude of the angle formed by the two axes A1 and A2 refers to the smaller angle θ1 of these two angles θ1 and θ2.

[0118] The definition of the angle between two directions will be explained with reference to FIG.

[0119] When the two directions D1 and D2 are expressed as vectors, two angles are generated around the starting point, and the magnitude of these two angles is one of two angles θ1 and θ2. In this specification, the magnitude of the angle formed by the two directions D1 and D2 refers to the smaller angle θ1 of these two angles θ1 and θ2.

[0120] (Summary) Some of the aspects of the present invention described above are listed below.

[0121] A polarization-maintaining fiber according to a first aspect comprises a core, a low-refractive-index layer surrounding the core, a pair of stress-applying portions arranged at positions sandwiching the core, and a cladding that contains the core, the low-refractive-index layer, and the pair of stress-applying portions, wherein a ratio r2 / r1 of a radius r1 of the core to an inner radius r2 of the low-refractive-index layer satisfies 1.0≦r2 / r1≦3.0, a difference r3−r2 between an outer radius r3 of the low-refractive-index layer and the inner radius r2 of the low-refractive-index layer satisfies 4.0 μm≦r3−r2≦6.0 μm, a relative refractive index difference Δ3 of the low-refractive-index layer with respect to the cladding satisfies −0.38%≦Δ3≦−0.27%, a mode field diameter of light with a wavelength of 1.55 μm propagating through the core is 9.2 μm or less, and a fiber cutoff wavelength is 1.45 μm or less.

[0122] A polarization-maintaining fiber according to Aspect 2 is the polarization-maintaining fiber according to Aspect 1, characterized in that when the bending radius is 2.0 mm and the fiber is bent so that the slow axis direction is in the direction of the bending radius, the bending loss per turn for light with a wavelength of 1.55 μm is 0.20 dB or less. Note that the phrase "the bending loss per turn for light with a wavelength of 1.55 μm when the fiber is bent so that the slow axis direction is in the direction of the bending radius" can be rephrased as "the bending loss per turn of a polarization-maintaining fiber bent so that the slow axis direction is in the direction of the bending radius, measured using light with a wavelength of 1.55 μm."

[0123] A polarization-maintaining fiber according to aspect 3 is the polarization-maintaining fiber according to aspect 1 or 2, characterized in that the value of MPI (Multi Path Interference) caused by axial misalignment in at least one direction is −30 dB or less.

[0124] The MPI caused by the axial misalignment in at least one direction can be measured, for example, by the following measurement method.

[0125] A measurement method for measuring MPI caused by axial misalignment in a specific direction using a fiber connector having a polarization-maintaining fiber cut to a fiber length of 0.3 m, a first dummy fiber having one end face connected to one end face of the polarization-maintaining fiber, and a second dummy fiber having one end face connected to the other end face of the polarization-maintaining fiber, wherein the first dummy fiber is a polarization-maintaining fiber that has a connection loss of 0.05 dB or less when connected to the polarization-maintaining fiber such that the center of the core of the first dummy fiber and the center of the core of the polarization-maintaining fiber overlap at the one end face of the first dummy fiber and the angle formed by the slow axis of the first dummy fiber and the slow axis of the polarization-maintaining fiber is 4° or less, the second dummy fiber is a polarization-maintaining fiber that, when connected to the polarization-maintaining fiber, has a connection loss of 0.05 dB or less such that the center of the core of the second dummy fiber and the center of the core of the polarization-maintaining fiber overlap at the one end face of the second dummy fiber and the angle formed by the slow axis of the first dummy fiber and the slow axis of the polarization-maintaining fiber is 4° or less; the first dummy fiber and the second dummy fiber are connected to the polarization-maintaining fiber so as to satisfy the following conditions 1, 2, and 3; the first dummy fiber is further connected to the polarization-maintaining fiber so as to satisfy the following conditions a and b; and the second dummy fiber is further connected to the polarization-maintaining fiber so as to satisfy the following conditions a' and b'; the measurement method comprises the steps of inputting linearly polarized light from the other end face of the first dummy fiber while sweeping its wavelength, and measuring the power of light output from the other end face of the second dummy fiber; The difference between the maximum and minimum values ​​of the optical power measured in the measurement step is defined as PTP, and the value of the MPI is calculated as MPI [dB] = 20 log [(10^ （ＰＴＰ／２０） -1) / (10^ （ＰＴＰ／２０） and calculating the value of the α-to-β ratio in accordance with the formula (1).

[0126] Condition 1: The connection loss in the LP01 mode at the connection point between the end of the first dummy fiber and the end of the polarization-maintaining fiber is 0.4 dB or more and 0.6 dB or less.

[0127] Condition 2: The connection loss in the LP01 mode at the connection point between the end of the second dummy fiber and the end of the polarization-maintaining fiber is 0.4 dB or more and 0.6 dB or less.

[0128] Condition 3: The average of the connection loss in the LP01 mode at the connection point between the end of the first dummy fiber and the end of the polarization-maintaining fiber and the connection loss in the LP01 mode at the connection point between the end of the second dummy fiber and the end of the polarization-maintaining fiber is 0.5 dB.

[0129] Condition a: At one end face of the first dummy fiber, the angle formed between the direction from the center of the core of the first dummy fiber toward the center of the core of the polarization-maintaining fiber and the at least any direction is 15° or less.

[0130] Condition b: At the one end face of the first dummy fiber, the angle formed between the slow axis of the first dummy fiber and the slow axis of the polarization-maintaining fiber is 4° or less.

[0131] Condition a': At one end face of the second dummy fiber, the angle formed between the direction from the center of the core of the second dummy fiber toward the center of the core of the polarization-maintaining fiber and the at least any direction is 15° or less.

[0132] Condition b': At the one end face of the second dummy fiber, the angle formed between the slow axis of the second dummy fiber and the slow axis of the polarization-maintaining fiber is 4° or less.

[0133] A polarization-maintaining fiber according to Aspect 4 is the polarization-maintaining fiber according to Aspect 3, characterized in that both the value of MPI caused by axial misalignment with respect to the fast axis direction and the value of MPI caused by axial misalignment with respect to the slow axis direction are −30 dB or less.

[0134] A polarization-maintaining fiber according to Aspect 5 is the polarization-maintaining fiber according to Aspect 3, characterized in that one or both of the MPI value caused by axial misalignment with respect to the fast axis direction and the MPI value caused by axial misalignment with respect to the slow axis direction is −35 dB or less.

[0135] A polarization-maintaining fiber according to a sixth aspect is the polarization-maintaining fiber according to the fifth aspect, characterized in that both the value of MPI caused by axial misalignment with respect to the fast axis direction and the value of MPI caused by axial misalignment with respect to the slow axis direction are −35 dB or less.

[0136] A polarization-maintaining fiber according to Aspect 7 is the polarization-maintaining fiber according to Aspect 3, characterized in that either or both of the MPI value caused by axial misalignment with respect to the fast axis direction and the MPI value caused by axial misalignment with respect to the slow axis direction are −40 dB or less.

[0137] A polarization-maintaining fiber according to an eighth aspect is the polarization-maintaining fiber according to the third aspect, characterized in that, when the bending radius is 2.0 mm and the fiber is bent so that the slow-axis direction is in the direction of the bending radius, both the value of the MPI caused by the misalignment with respect to the fast-axis direction and the value of the MPI caused by the misalignment with respect to the slow-axis direction are −40 dB or less.

[0138] A polarization-maintaining fiber according to Aspect 9 is the polarization-maintaining fiber according to any one of Aspects 1 to 8, characterized in that the relative refractive index difference Δ3 of the low refractive index layer with respect to the cladding satisfies −0.37%≦Δ3≦−0.27%.

[0139] A polarization-maintaining fiber according to Aspect 10 is the polarization-maintaining fiber according to any one of Aspects 1 to 8, characterized in that the fiber cutoff wavelength is 1.40 μm or more.

[0140] A polarization-maintaining fiber according to an eleventh aspect is the polarization-maintaining fiber according to any one of the first to tenth aspects, characterized in that the relative refractive index difference Δ1 of the core with respect to the cladding satisfies 0.30%≦Δ1.

[0141] A polarization-maintaining fiber according to Aspect 12 is the polarization-maintaining fiber according to any one of Aspects 1 to 11, characterized in that the mode field diameter is 9.0 μm or less.

[0142] A polarization-maintaining fiber according to Aspect 13 is the polarization-maintaining fiber according to any one of Aspects 1 to 12, characterized in that the mode field diameter is 8.8 μm or more.

[0143] A polarization-maintaining fiber according to Aspect 14 is the polarization-maintaining fiber according to any one of Aspects 1 to 13, characterized in that the relative refractive index difference Δ1 of the core with respect to the cladding satisfies Δ1≦0.38%.

[0144] A polarization-maintaining fiber according to Aspect 15 is the polarization-maintaining fiber according to any one of Aspects 1 to 14, characterized in that the shortest distance r4 from the center of the core to the stress-applying portion satisfies r4≦10.0 μm.

[0145] A polarization-maintaining fiber according to Aspect 16 is the polarization-maintaining fiber according to any one of Aspects 1 to 15, characterized in that the relative refractive index difference Δ4 of the stress-applying portions with respect to the cladding satisfies Δ4≦−0.70%.

[0146] A polarization-maintaining fiber according to Aspect 17 is the polarization-maintaining fiber according to any one of Aspects 1 to 16, characterized in that the diameter of the cladding is 79 μm or more and 126 μm or less.

[0147] A polarization-maintaining fiber according to Aspect 18 is the polarization-maintaining fiber according to any one of Aspects 1 to 17, characterized in that the ratio r2 / r1 of the radius r1 of the core to the inner radius r2 of the low refractive index layer satisfies 2.4<r2 / r1≦3.0.

[0148] A polarization-maintaining fiber according to Aspect 19 is the polarization-maintaining fiber according to any one of Aspects 1 to 18, characterized in that the fiber cutoff wavelength is less than 1.34 μm.

[0149] (Additional Notes) The present invention is not limited to the above-described embodiments, and various modifications are possible within the scope of the claims. Embodiments obtained by appropriately combining the technical means disclosed in the above-described embodiments are also included in the technical scope of the present invention.

[0150] REFERENCE SIGNS LIST 1 Polarization-maintaining fiber 11 Core 12 Low refractive index layer 131 Stress-applying portion 132 Stress-applying portion 14 Cladding FA Fast axis SA Slow axis

Claims

1. A polarization-maintaining fiber comprising: a core; a low-refractive index layer surrounding the core; a pair of stress-applying portions arranged at positions sandwiching the core; and a cladding containing the core, the low-refractive index layer, and the pair of stress-applying portions; wherein the ratio r2 / r1 of the radius r1 of the core to the inner radius r2 of the low-refractive index layer satisfies 1.0≦r2 / r1≦3.0; the difference r3-r2 between the outer radius r3 of the low-refractive index layer and the inner radius r2 of the low-refractive index layer satisfies 4.0μm≦r3-r2≦6.0μm; the relative refractive index difference Δ3 of the low-refractive index layer with respect to the cladding satisfies -0.38%≦Δ3≦-0.27%; when light having a wavelength of 1.55μm propagates through the core, the mode field diameter of the light is 9.2μm or less; and the fiber cutoff wavelength is 1.45μm or less.

2. The polarization-maintaining fiber according to claim 1, characterized in that when the bending radius is 2.0 mm and when the fiber is bent so that the slow axis direction is in the direction of the bending radius, the bending loss per turn for light with a wavelength of 1.55 μm is 0.20 dB or less.

3. A polarization-maintaining fiber according to claim 1 or 2, characterized in that the value of MPI (Multi Path Interference) caused by axial misalignment in at least one direction is -30 dB or less.

4. A polarization-maintaining fiber according to claim 3, wherein both the value of MPI caused by axial misalignment in the fast axis direction and the value of MPI caused by axial misalignment in the slow axis direction are -30 dB or less.

5. A polarization-maintaining fiber according to claim 3, characterized in that either or both of the MPI value caused by axial misalignment in the fast axis direction and the MPI value caused by axial misalignment in the slow axis direction is -35 dB or less.

6. The polarization-maintaining fiber according to claim 5, wherein both the value of MPI caused by axial misalignment in the fast axis direction and the value of MPI caused by axial misalignment in the slow axis direction are -35 dB or less.

7. The polarization-maintaining fiber according to claim 3, wherein one or both of the MPI value caused by axial misalignment with respect to the fast axis direction and the MPI value caused by axial misalignment with respect to the slow axis direction is -40 dB or less.

8. The polarization-maintaining fiber according to claim 7, wherein, when the bending radius is 2.0 mm and the fiber is bent so that the slow axis direction is in the direction of the bending radius, both the MPI value caused by misalignment with respect to the fast axis direction and the MPI value caused by misalignment with respect to the slow axis direction are -40 dB or less.

9. A polarization-maintaining fiber according to any one of claims 1 to 8, characterized in that the relative refractive index difference Δ3 of said low refractive index layer with respect to said cladding satisfies -0.37%≦Δ3≦-0.27%.

10. A polarization-maintaining fiber according to any one of claims 1 to 8, characterized in that the fiber cutoff wavelength is 1.40 µm or more.

11. A polarization-maintaining fiber according to any one of claims 1 to 10, characterized in that the relative refractive index difference Δ1 of the core with respect to the cladding satisfies 0.30%≦Δ1.

12. A polarization-maintaining fiber according to any one of claims 1 to 11, characterized in that the mode field diameter is 9.0 µm or less.

13. A polarization-maintaining fiber according to any one of claims 1 to 12, characterized in that the mode field diameter is 8.8 µm or more.

14. A polarization-maintaining fiber according to any one of claims 1 to 13, characterized in that the relative refractive index difference Δ1 of the core with respect to the cladding satisfies Δ1≦0.38%.

15. A polarization-maintaining fiber according to any one of claims 1 to 14, characterized in that the shortest distance r4 from the center of the core to the stress-applying portion satisfies r4≦10.0 μm.

16. A polarization-maintaining fiber according to any one of claims 1 to 15, characterized in that the relative refractive index difference Δ4 of said stress-applying portions with respect to said cladding satisfies Δ4≦-0.70%.

17. A polarization-maintaining fiber according to any one of claims 1 to 16, characterized in that the diameter of the cladding is 79 µm or more and 126 µm or less.

18. A polarization-maintaining fiber according to any one of claims 1 to 17, characterized in that the ratio r2 / r1 of the radius r1 of the core to the inner radius r2 of the low refractive index layer satisfies 2.4<r2 / r1≦3.

0.

19. A polarization-maintaining fiber according to any one of claims 1 to 18, characterized in that the fiber cutoff wavelength is less than 1.34 µm.

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