Polarization maintaining fiber

Abstract

Provided is a polarization maintaining fiber that, if bent so that the direction of the bending radius coincides with the fast axis, can suppress bending loss better than conventional fibers. The ratio between the radius r1 of a core (11) and the inner peripheral radius r2 of a low refractive index layer (12), r2 / r1, satisfies 1.0 ≤ r2 / r1 ≤ 2.4; the difference between the outer peripheral radius r3 of the low refractive index layer (12) and the inner peripheral radius r2 of the low refractive index layer (12), r3−r2, satisfies r3−r2 ≥ 3.0 μm; the relative refractive index difference Δ3 of the low refractive index layer (12) with respect to a cladding (14) satisfies Δ3 ≤ −0.25%; and 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, and the fiber cutoff wavelength is 1.34 μm or more.

Description

Polarization-Maintaining Fiber

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

[0002] Optical fibers having polarization-maintaining properties, i.e., polarization-maintaining fibers, are widely used. In recent years, polarization-maintaining fibers have been increasingly used in datacom devices such as CPO (Co-packaged Optics) switch modules and coherent optical transceivers. Patent Document 1, for example, is an example of a document disclosing polarization-maintaining fibers.

[0003] In ordinary optical fibers without polarization-maintaining properties, for example, to satisfy ITU-T G.657.A2, a standard for optical fibers for telecommunications, a low-refractive-index layer (such as a trench layer) is provided surrounding the core to minimize bending loss when the bending radius is set to 7.5 mm. In such optical fibers, the ratio r2 / r1 of the core radius r1 to the inner radius r2 of the low-refractive-index layer tends to be set to r2 / r1≧2.5. Following this example, a low-refractive-index layer that satisfies r2 / r1≧2.5 is also provided in polarization-maintaining fibers.

[0004] Japanese Patent Application Publication No. 2018-159926

[0005] A polarization-maintaining fiber having a pair of stress-applying parts arranged to sandwich the core has the property that it is more difficult to reduce bending loss when the bending radius direction is aligned with the fast axis direction (the direction perpendicular to the arrangement direction of the stress-applying parts) than when the fiber is bent so that the bending radius direction is aligned with the slow axis direction (the direction in which the stress-applying parts are arranged). This is because when the fiber is bent so that the bending radius direction is aligned with the slow axis direction, the stress-applying parts are likely to act to confine light in the core due to the relative refractive index difference between the stress-applying parts and the cladding, etc., whereas when the fiber is bent so that the bending radius direction is aligned with the fast axis direction, the stress-applying parts are less likely to act to confine light in the core, unlike the above circumstances.

[0006] One aspect of the present invention has been made in view of the above problems, and its object is to realize a polarization-maintaining fiber that can suppress bending loss more than conventional fibers when the fiber is bent so that the bending radius direction coincides with the fast axis.

[0007] 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≦2.4; 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 r3−r2≧3.0 μm; a relative refractive index difference Δ3 of the low refractive index layer with respect to the cladding satisfies Δ3≦−0.25%; and when light having a wavelength of 1.55 μm propagates through the core, the mode field diameter of the light is 9.2 μm or less, and the fiber cutoff wavelength is 1.34 μm or more.

[0008] According to one aspect of the present invention, it is possible to realize a polarization-maintaining fiber that can suppress bending loss more than ever before when the fiber is bent so that the bending radius direction coincides with the fast axis.

[0009] 1 is a cross-sectional view showing a transverse section of a polarization-maintaining fiber according to an embodiment of the present invention. A graph showing the refractive index profile n(r) on the slow axis and the refractive index profile n(r) on the fast axis of the polarization-maintaining fiber is also shown. A graph showing the relative refractive index difference profile 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. For an optical fiber having a core and a cladding surrounding the core, (1) the refractive index profile n(r) when no bending is applied, (2) the equivalent refractive index profile n′(r) when bending with a bending radius of 7.5 mm, and (3) the equivalent refractive index profile n′(r) when bending with a bending radius of 2.0 mm are shown.

[0010] As mentioned above, in recent years, there has been an increasing number of cases in which polarization-maintaining fibers are incorporated into datacom devices. For such polarization-maintaining fibers, it is required to suppress the bending loss at a bending radius of 2.0 mm more than conventional fibers (for example, to 1.0 dB or less). A polarization-maintaining fiber provided with a low-refractive-index layer that satisfies r2 / r1≧2.5 can sufficiently suppress the bending loss at a bending radius of 2.0 mm when bent so that the bending radius coincides with the slow axis direction.

[0011] However, in a polarization-maintaining fiber provided with a low-refractive-index layer satisfying r2 / r1≧2.5, when the fiber is bent so that the bending radius coincides with the fast axis direction, the bending loss increases when the bending radius is set to 2.0 mm. Therefore, even in a polarization-maintaining fiber bent so that the bending radius coincides with the slow axis direction, the bending loss increases when the fiber is bent so that the bending radius coincides with the fast axis direction by even 0.1 turns per turn due to twisting, making it difficult to reduce the bending loss when the bending radius is set to 2.0 mm compared to conventional fiber configurations. To reduce the possibility of such problems occurring, it is important to realize a polarization-maintaining fiber that can reduce the bending loss when the fiber is bent so that the bending radius coincides with the fast axis compared to conventional fiber configurations. Below, a polarization-maintaining fiber that can reduce the bending loss when the fiber is bent so that the bending radius coincides with the fast axis compared to conventional fiber configurations is described.

[0012] (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.

[0013] 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.

[0014] 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.

[0015] 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. The low-refractive-index layer 12 in 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 consists 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 parts, and parts that contact the stress-applying parts 131 and 132. The low refractive index layer 12 may be separated from the stress-applying parts as long as it satisfies conditions 1 to 5 described below.

[0016] 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 portions 131, 132 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 portion 131 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.

[0017] 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 leakage of light 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 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.

[0018] Furthermore, the shortest distance r4 from the center of the core 11 to the stress-applying portions 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 portions 131 and 132 outside the mode field, making it possible to suppress an increase in transmission loss that may occur due to boron oxide added to the stress-applying portions 131 and 132.

[0019] 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.

[0020] 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.

[0021] 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.

[0022] 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, 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, 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, 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 more. This can suppress an increase in transmission loss that may occur due to boron oxide added to the stress-applying portions 131 and 132 .

[0023] 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.

[0024] 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, 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, 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, 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, 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, 132.

[0025] 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.

[0026] 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.

[0027] 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."

[0028] 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.

[0029] When r4<r2 is satisfied, as will be seen from the examples described below, the polarization crosstalk can be suppressed to -33.0 dB or less under the following conditions: a fiber length of 2 m, a bending radius of 2.0 mm, and the polarization-maintaining fiber 1 is wound around the mandrel one turn so that the slow axis SA of the polarization-maintaining fiber 1 is perpendicular to the surface of the mandrel (see Examples 3 and 4). The polarization crosstalk required for optical devices such as telecom optical devices, datacom optical devices, and other communication optical devices, as well as amplifier and sensor optical devices, is approximately -30.0 dB under the above conditions. Therefore, a polarization-maintaining fiber 1 with the polarization crosstalk suppressed to -33 dB or less can be suitably used in these 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.

[0030] On the other hand, when the inner radius r2 of the low refractive index layer 12 coincides with the radius 11 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."

[0031] 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.

[0032] (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.

[0033] 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.

[0034] 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.

[0035] 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 .

[0036] 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.

[0037] The bending loss of the polarization-maintaining fiber 1 is measured in accordance with IEC 60793-1-47. Specifically, 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 before the polarization-maintaining fiber 1 is wound are measured as a reference, and the bending loss of the light per turn is calculated from the difference between these two powers. The mandrel is a rod-shaped jig with a perfectly circular cross section. Light with a wavelength of 1.55 μm guided through the core 11 is used to measure the bending loss. The bending loss is measured for both the case where the fast axis direction is aligned with the bending radius, as shown in FIG. 3A, and the case where the slow axis direction is aligned with 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, and when the direction of the slow axis of the polarization-maintaining fiber is perpendicular to the surface of the mandrel. From the above, in other words, the bending loss per turn of light with a wavelength of 1.55 μm when the bending radius is 2.0 mm and the fiber is bent so that the fast axis direction is in the direction of the bending radius, and the bending loss per turn of light with a wavelength of 1.55 μm 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 are measured. The "direction of the bending radius" mentioned above means the direction in which the slow axis SA or fast axis of the polarization-maintaining fiber 1 is oriented perpendicular to the surface of the mandrel when the polarization-maintaining fiber 1 is wound helically (or non-helically) around the mandrel, and the "direction of the bending radius" explained below will have the same meaning as above. Furthermore, the "bending radius" mentioned above is not limited to 2.0 mm, and may be, for example, any value between 2.0 and 2.5 mm.

[0038] The fiber cutoff wavelength of the polarization-maintaining fiber 1 is measured in accordance with IEC 60793-1-44. That is, when the fiber is cut to a length of 2 m and wound once around a mandrel with a diameter of 280 mm, the wavelength at which the higher-order mode is attenuated by 19.3 dB is measured as the fiber cutoff wavelength. 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.

[0039] The polarization crosstalk of the polarization-maintaining fiber 1 is measured using the power ratio method in accordance with IEC 60793-1-61. Specifically, the polarization crosstalk is measured when the polarization-maintaining fiber 1 cut to 2 m is wound once around a mandrel with a radius of 2.0 mm. Here, the mandrel is a rod-shaped jig with a perfectly circular cross section. For example, light with a wavelength of 1.55 μm is used to measure the polarization crosstalk. The polarization crosstalk is measured using a polarization-maintaining fiber cut to 2 m. The polarization crosstalk is measured by bending the polarization-maintaining fiber 1 so that its slow axis direction is aligned with the bending radius, as shown in FIG. 3B. In other words, the polarization crosstalk is measured by winding the polarization-maintaining fiber 1 around the mandrel so that the direction of 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] 4 is a graph showing the following refractive index profiles for an optical fiber having a core and a cladding surrounding the core: (1) a refractive index profile n(r) when no bending is applied, (2) an equivalent refractive index profile n'(r) when bending with a bending radius of 7.5 mm, and (3) an equivalent refractive index profile n'(r) when bending with a bending radius of 2.0 mm. As is well known, the equivalent refractive index n'(r) of a bent optical fiber is given by n'(r) = n(r) × (1 + r / R), where n(r) is the refractive index of the unbent optical fiber, r is an arbitrary position in the radial direction of the optical fiber, and R is the bending radius.

[0044] When the bending radius is 2.0 mm, in the region close to the core (r<2.6 × core radius), the equivalent refractive index is high and the electric field density is high, resulting in active electric field radiation. In the region far from the core (r≧2.6 × core radius), although the equivalent refractive index is even higher than in the region close to the core, the electric field density is low, resulting in slight electric field radiation. This indicates that by providing a low refractive index layer in the region close to the core, bending loss when the bending radius is 2.0 mm can be effectively suppressed.

[0045] Furthermore, when the bending radius is 7.5 mm, in the region close to the core (r<2.6 × core radius), although the electric field density is high, the equivalent refractive index is low, so almost no electric field radiation occurs. In the region far from the core (r≧2.6 × core radius), although the equivalent refractive index is high, the electric field density is low, so although electric field radiation occurs more than in the region close to the core, it is slight. This indicates that by providing a low refractive index layer in the region far from the core, bending loss when the bending radius is 7.5 mm can be effectively suppressed.

[0046] Taking the above points into consideration and taking into account the examples described later, the polarization-maintaining fiber 1 is configured to satisfy at least the following conditions.

[0047] (Condition 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 satisfies 1.0≦r2 / r1≦2.4.

[0048] (Condition 2) 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 satisfies r3-r2≧3.0 μm.

[0049] (Condition 3) The relative refractive index difference Δ3 of the low refractive index layer 12 with respect to the cladding 14 satisfies Δ3≦−0.25%.

[0050] (Condition 4) When light having a wavelength of 1.55 μm propagates through the core, the mode field diameter of the light is 9.2 μm or less.

[0051] (Condition 5) The fiber cutoff wavelength is 1.34 μm or more.

[0052] A polarization-maintaining fiber 1 that satisfies the above conditions can suppress bending loss when the bending radius is 2.0 mm or approximately 2.0 mm, particularly bending loss when the fiber is bent so that the fast axis direction is the direction of the bending radius (hereinafter also referred to as "bending loss in the fast axis direction") more than conventional fiber loss. Here, the above bending radius of approximately 2.0 mm does not mean that the bending radius is limited to 2.0 mm, but rather that equivalent effects can be obtained even with bending radii anywhere from 2.0 to 2.5 mm. Furthermore, the term "bending radius of approximately 2.0 mm" described below may also be used to mean any bending radius between 2.0 and 2.5 mm.

[0053] As examples, 18 types of polarization-maintaining fibers 1 were manufactured and their specifications were measured. As a comparative example, one type of polarization-maintaining fiber was manufactured and its specifications were measured. The measurement results are shown in Tables 1 and 2 below.

[0054] Furthermore, for the polarization-maintaining fibers 1 according to Examples 1, 3, and 4, the polarization crosstalk when wound once around a mandrel with a radius of 2.0 mm was measured using light with a wavelength of 1.55 μm, with the direction of the slow axis SA of the polarization-maintaining fiber 1 perpendicular to the surface of the mandrel. As a result, the polarization crosstalk of the polarization-maintaining fibers 1 according to Examples 1, 3, and 4 was −27 dB, −33 dB, and −38 dB, respectively. Furthermore, the (r4−r1) / r1 ratio (distance from the core center to the stress-applying portion / core radius) according to Examples 1, 3, and 4 was 1.1, 1.2, and 1.3, respectively, and the (r4−r1) / r1 ratio according to Examples 3 and 4 was 1.2 or greater and 1.3 or less. Furthermore, the ratio of the stress-applying portion diameter to the cladding radius according to Examples 1, 3, and 4 was all 0.62.

[0055] The polarization-maintaining fibers 1 according to Examples 1 to 18 all satisfy the above-mentioned conditions 1 to 5. As a result, in the polarization-maintaining fibers 1 according to Examples 1 to 18, the bending loss in the fast axis direction per turn at a wavelength of 1.55 μm can be suppressed to 5.70 dB or less. In this case, even if the bending loss condition is such that a small bending radius of about 2.0 mm is required as one target value 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 satisfy the conditions to the extent that it can be applied to the optical device, etc.

[0056] On the other hand, the polarization-maintaining fiber according to Comparative Example 1 satisfies the above-mentioned conditions 2 to 4, but does not satisfy the above-mentioned condition 1. As a result, the polarization-maintaining fiber according to Comparative Example 1 cannot suppress the bending loss in the fast axis direction per turn at a wavelength of 1.55 μm to 5.70 dB or less.

[0057] If a twist occurs at a location away from the bending section, the ends of the bending section (the beginning and end of the bend) are susceptible to the twist. Therefore, even if an attempt is made to wind one turn in the slow axis direction, the end of the bending section may bend in the fast axis direction. A typical case is when 0.9 turns of bending in the slow axis direction and 0.1 turns of bending in the fast axis direction are applied. If the bending loss per turn in the fast axis direction is 5.7 dB and the bending loss per turn in the slow axis direction is 0.18 dB, the bending loss per turn is (5.7 dB × 0.1) + (1.8 dB × 0.9) = 0.73 dB, which is kept below 1 dB. Therefore, even if the bending loss conditions are such that a small bending radius of about 2.0 mm is required as a guideline for the target values ​​of 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 meet the conditions to the extent that it can be applied to the optical device.

[0058] In the polarization-maintaining fiber 1 according to Example 1, the ratio r2 / r1 is 1.0, and in the polarization-maintaining fiber 1 according to Example 6, the ratio r2 / r1 is 2.4. In the polarization-maintaining fibers 1 according to the other Examples, the ratio r2 / r1 is greater than 1.0 and smaller than 2.4. This means that if the ratio r2 / r1 is 1.0 or greater and 2.4 or less, the bending loss in the fast axis direction can be suppressed to 5.70 dB or less.

[0059] In the polarization-maintaining fibers 1 according to Examples 9 and 18, the difference r3 - r2 is 3.0 μm. In the polarization-maintaining fibers 1 according to the other Examples, the difference r3 - r2 is greater than 3.0 μm. The larger the difference r3 - r2, i.e., the thicker the low-refractive-index layer 12, the stronger the light confinement effect, and therefore the smaller the bending loss in the fast axis direction. This means that if the difference r3 - r2 is 3.0 μm or greater, the bending loss in the fast axis direction per turn at a wavelength of 1.55 μm can be suppressed to 5.70 dB or less.

[0060] Note that the larger the difference r3-r2, the stronger the light confinement effect, and therefore the smaller the bending loss in the fast axis direction. However, if the difference r3-r2 is increased while maintaining the mode field diameter and cutoff wavelength, the relative refractive index difference Δ1 of the core 11 becomes smaller, resulting in an increase in bending loss in the slow axis direction. To suppress bending loss in the slow axis direction more than conventional methods, it is preferable that the difference r3-r2 be 8.0 μm or less. In fact, in Examples 1 to 18, by setting the difference r3-r2 to 8.0 μm or less, the bending loss in the slow axis direction per turn at a wavelength of 1.55 μm was suppressed to 0.18 dB or less. Furthermore, in Examples 1 to 14 and 16 to 18, by setting the difference r3-r2 to 8.0 μm or less, the bending loss in the slow axis direction per turn at a wavelength of 1.55 μm was suppressed to 0.15 dB or less. This enables the polarization-maintaining fiber 1 to be applied to optical devices requiring even smaller bending loss. In Examples 1 to 14 and 16 to 18, r3-r2≧3.0 μm is satisfied, in other words, 3.0 μm≦r3-r2≦8.0 μm is satisfied.

[0061] Furthermore, in the polarization-maintaining fibers 1 according to Examples 10 and 11, the relative refractive index difference Δ3 is −0.25%. In the polarization-maintaining fibers 1 according to the other Examples, the relative refractive index difference Δ3 is a value smaller than −0.25%. The smaller the relative refractive index difference Δ3, the stronger the light confinement effect, and therefore the smaller the bending loss in the fast axis direction. Therefore, this means that if the relative refractive index difference Δ3 is −0.25% or less, the bending loss in the fast axis direction can be more reliably suppressed to 5.70 dB or less.

[0062] Note that the smaller the relative refractive index difference Δ3 of the low-refractive index layer 12, the stronger the light confinement effect, and therefore the smaller the bending loss in the fast axis direction. However, if the relative refractive index difference Δ3 of the low-refractive index layer 12 is reduced while maintaining the mode field diameter and cutoff wavelength, the relative refractive index difference Δ1 of the core 11 becomes smaller, resulting in an increase in bending loss in the slow axis direction. In order to suppress bending loss in the slow axis direction more than conventional techniques, the relative refractive index difference Δ of the low-refractive index layer 12 is preferably −0.43% or more. In fact, in Examples 1 to 18, by setting the relative refractive index difference Δ of the low-refractive index layer 12 to −0.43% or more, the bending loss in the slow axis direction per turn at a wavelength of 1.55 μm was suppressed to 0.18 dB or less. Furthermore, in Examples 1 to 14 and 16 to 18, by setting the relative refractive index difference Δ of the low-refractive index layer 12 to −0.43% or more, the bending loss in the slow axis direction per turn at a wavelength of 1.55 μm was suppressed to 0.15 dB or less. This makes it possible to realize a polarization-maintaining fiber 1 that can satisfy the conditions for application to the optical device, etc., when used when bending the polarization-maintaining fiber 1 further in the slow axis direction and when the polarization-maintaining fiber 1 is housed in the optical device, etc., described above, which requires a smaller bending loss value. Note that in Examples 1 to 14 and 16 to 18, Δ3≧−0.43% is satisfied, in other words, −0.43%≦Δ3≦−0.25% is satisfied.

[0063] Furthermore, in the polarization-maintaining fibers 1 according to Examples 2, 6, and 18, the mode field diameter at a wavelength of 1.55 μm is 9.2 μm. In the polarization-maintaining fibers 1 according to the other Examples, the mode field diameter at a wavelength of 1.55 μm is smaller than 9.2 μm. A small mode field diameter means strong light confinement, and therefore small bending loss in the fast axis direction. This means that if the mode field diameter is 9.2 μm or less, the bending loss per turn in the fast axis direction at a wavelength of 1.55 μm can be suppressed to 5.70 dB or less.

[0064] In all the embodiments, the mode field diameter at a wavelength of 1.55 μm is 8.5 μm or greater. In this case, the larger mode field diameter compared to a case where the mode field diameter is less than 8.5 μm can make it easier for light propagating from another optical fiber or optical device to be incident on the polarization-maintaining fiber at the splice point with the other optical fiber or optical device. This can reduce splice loss. Therefore, even if the strict splice loss requirement, which is one of the target values ​​for the optical device described above, is met, it is possible to realize a polarization-maintaining fiber 1 that can more reliably satisfy the conditions for application to the optical device or the other optical fiber, for example, when the polarization-maintaining fiber 1 is housed in the optical device or spliced ​​with the other optical fiber. Considering the beam size and focusing lens of the laser light source used in an optical transceiver (such as a coherent optical transceiver) operating at a wavelength of 1.55 μm, a mode field diameter of 8.9 μm or greater is preferable in order to reduce splice loss to a level that allows operation when applied to the optical transceiver.

[0065] Furthermore, in the polarization-maintaining fiber 1 according to Example 16, the fiber cutoff wavelength is 1.34 μm. In the polarization-maintaining fibers 1 according to the other Examples, the fiber cutoff wavelength is greater than 1.34 μm. A longer cutoff wavelength means stronger light confinement, and therefore smaller bending loss in the fast axis direction. This means that if the fiber cutoff wavelength is 1.34 μm or greater, the bending loss per turn in the fast axis direction at a wavelength of 1.55 μm can be suppressed to 5.70 dB or less.

[0066] In all the examples, the fiber cutoff wavelength is 1.44 μm or less. When the fiber length is short, for example, 1 m or less, the cutoff wavelength may shift toward the longer wavelength side. Therefore, to reduce the possibility that a shift in the cutoff wavelength toward the longer wavelength side due to the fiber length will cause the cutoff wavelength to exceed the operating wavelength and make single-mode transmission at the operating wavelength difficult, it is preferable that there be a certain margin between the operating wavelength and the upper limit of the cutoff wavelength measured at a fiber length of 2 m. Therefore, when the cutoff wavelength is, for example, 1.44 μm or less as described above, even if the cutoff wavelength shifts toward the longer wavelength side when the fiber length is short as described above, the cutoff wavelength can be prevented from exceeding the operating wavelength. Therefore, the possibility that single-mode transmission at the operating wavelength will become difficult can be reduced.

[0067] 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 Δ1≧0.13%. In the polarization-maintaining fiber 1 according to Example 15, the relative refractive index difference Δ1 of the core 11 is 0.13%. Furthermore, in the polarization-maintaining fibers 1 according to the other Examples, the relative refractive index difference Δ of the core 11 is greater than 0.13%. The larger the relative refractive index difference Δ1, the stronger the light confinement effect, and therefore the smaller the bending loss in the fast axis direction. Therefore, this means that if the relative refractive index difference Δ1 of the core 11 satisfies Δ1≧0.13%, the bending loss in the fast axis direction per turn at a wavelength of 1.55 μm can be more reliably suppressed to 5.70 dB or less.

[0068] In all the examples, the relative refractive index difference Δ1 of the core 11 with respect to the cladding 14 satisfies Δ1≦0.41%. In this case, it is possible to prevent the mode field diameter of light propagating through the core 11 from becoming too small, and to suppress light loss at the connection point with other optical fibers or optical devices. Therefore, even if the strict connection loss condition required as one of the target values ​​of the above-mentioned optical devices is met, for example, when the polarization-maintaining fiber 1 is housed in the optical device or connected to another optical fiber, 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 or the other optical fiber.

[0069] 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 1.0≦r2 / r1≦1.8. In fact, the polarization-maintaining fibers 1 according to Examples 1 to 5 and 7 to 18 satisfy 1.0≦r2 / r1≦1.8. If 1.0≦r2 / r1≦1.8 is satisfied, the bending loss in the fast axis direction per turn at a wavelength of 1.55 μm can be more reliably suppressed to 5.70 dB or less.

[0070] Furthermore, in the polarization-maintaining fiber 1, it is preferable that 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 r3-r2≧5.0 μm, the relative refractive index difference Δ3 of the low-refractive-index layer 12 with respect to the cladding 14 satisfies Δ3≦−0.30%, the ratio r2 / r1 of the radius r1 of the core 11 and the inner radius r2 of the low-refractive-index layer 12 satisfies 1.0≦r2 / r1≦1.8, the mode field diameter at a wavelength of 1.55 μm is 9.0 μm or less, and the fiber cutoff wavelength is 1.39 μm or more.

[0071] A polarization-maintaining fiber 1 that satisfies these conditions can suppress the bending loss in the fast axis direction per turn at a wavelength of 1.55 μm to 5.70 dB or less, similar to the polarization-maintaining fiber 1 of Example 1 and polarization-maintaining fibers that can achieve equivalent effects.

[0072] Furthermore, in the polarization-maintaining fiber 1, it is preferable that 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 r3-r2≧5.0 μm, the relative refractive index difference Δ3 of the low-refractive-index layer 12 with respect to the cladding 14 satisfies Δ3≦−0.30%, 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 1.2≦r2 / r1<1.6, the mode field diameter at a wavelength of 1.55 μm is 9.2 μm or less, and the fiber cutoff wavelength is 1.38 μm or more.

[0073] A polarization-maintaining fiber 1 that satisfies these conditions can suppress bending loss in the fast axis direction per turn at a wavelength of 1.55 μm to 4.60 dB or less, similar to the polarization-maintaining fibers 1 of Examples 2, 3, 12, 14, and 15 and polarization-maintaining fibers that can achieve equivalent effects.

[0074] Furthermore, in the polarization-maintaining fiber 1, it is preferable that 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 r3-r2≧5.0 μm, the relative refractive index difference Δ3 of the low-refractive-index layer 12 with respect to the cladding 14 satisfies Δ3≦−0.30%, 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 1.6≦r2 / r1<1.8, the mode field diameter at a wavelength of 1.55 μm is 9.0 μm or less, and the fiber cutoff wavelength is 1.36 μm or more.

[0075] A polarization-maintaining fiber 1 that satisfies these conditions can suppress the bending loss in the fast axis direction per turn at a wavelength of 1.55 μm to 3.76 dB or less, similar to the polarization-maintaining fibers 1 of Examples 4, 5, and 17 and polarization-maintaining fibers that can achieve equivalent effects.

[0076] Furthermore, in the polarization-maintaining fiber 1, it is preferable that 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 r3-r2≧5.0 μm, the relative refractive index difference Δ3 of the low-refractive-index layer 12 with respect to the cladding 14 satisfies Δ3≦−0.30%, 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 1.8<r2 / r1≦2.4, the mode field diameter at a wavelength of 1.55 μm is 9.2 μm or less, and the fiber cutoff wavelength is 1.41 μm or more.

[0077] A polarization-maintaining fiber 1 that satisfies these conditions can suppress the bending loss in the fast axis direction per turn at a wavelength of 1.55 μm to 4.72 dB or less, similar to the polarization-maintaining fiber 1 of Example 6 and polarization-maintaining fibers that can achieve equivalent effects.

[0078] Furthermore, in the polarization-maintaining fiber 1, it is preferable that 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 r3-r2≧8.0 μm, the relative refractive index difference Δ3 of the low-refractive-index layer 12 with respect to the cladding 14 satisfies Δ3≦−0.30%, the ratio r2 / r1 of the radius r1 of the core 11 and the inner radius r2 of the low-refractive-index layer 12 satisfies r2 / r1≦1.8, the mode field diameter at a wavelength of 1.55 μm is 9.1 μm or less, and the fiber cutoff wavelength is 1.38 μm or more.

[0079] A polarization-maintaining fiber 1 that satisfies these conditions can suppress the bending loss in the fast axis direction per turn at a wavelength of 1.55 μm to 3.42 dB or less, similar to the polarization-maintaining fiber 1 of Example 13 and polarization-maintaining fibers that can achieve equivalent effects.

[0080] Furthermore, in the polarization-maintaining fiber 1, it is preferable that 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 r3-r2≧5.0 μm, the relative refractive index difference Δ3 of the low-refractive-index layer 12 with respect to the cladding 14 satisfies Δ3≦−0.38%, the ratio r2 / r1 of the radius r1 of the core 11 and the inner radius r2 of the low-refractive-index layer 12 satisfies 1.4≦r2 / r1≦1.6, the mode field diameter at a wavelength of 1.55 μm is 9.1 μm or less, and the fiber cutoff wavelength is 1.34 μm or more.

[0081] A polarization-maintaining fiber 1 that satisfies these conditions can suppress the bending loss in the fast axis direction per turn at a wavelength of 1.55 μm to 2.50 dB or less, similar to the polarization-maintaining fiber 1 of Example 16 and polarization-maintaining fibers that can achieve equivalent effects.

[0082] 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 1.4≦r2 / r1≦2.4. In fact, the polarization-maintaining fibers 1 according to Examples 3 to 11, 13, and 16 to 18 satisfy 1.4≦r2 / r1≦2.4. If 1.4≦r2 / r1≦2.4 is satisfied, it is possible to obtain effects equivalent to those obtained when the above-mentioned condition r4<r2 is satisfied.

[0083] Furthermore, in the polarization-maintaining fiber 1, it is more 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 1.4≦r2 / r1≦1.8. In fact, the polarization-maintaining fibers 1 according to Examples 3 to 5, 7 to 11, 13, and 16 to 18 satisfy 1.4≦r2 / r1≦1.8. If 1.4≦r2 / r1≦1.8 is satisfied, it is possible to obtain both an effect equivalent to that obtained when the above-mentioned r4<r2 is satisfied and an effect of more reliably suppressing the bending loss in the fast axis direction per turn at a wavelength of 1.55 μm to 5.70 dB or less.

[0084] 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 1.4≦r2 / r1≦1.8, 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 r3−r2≧5.0 μm, the mode field diameter at a wavelength of 1.55 μm is 9.0 μm or less, and the fiber cutoff wavelength is 1.36 μm or more.

[0085] Consider Examples 10 and 11, in which the mode field diameter is 9.0 μm and the difference r3 - r2 is 5.0 μm. Example 11 shows that when the ratio r2 / r1 is 1.8, the bending loss in the fast axis direction can be suppressed to the target value of 5.70 dB or less if the cutoff wavelength is 1.36 μm or greater. Furthermore, Example 10 shows that when the ratio r2 / r1 is 1.4, the bending loss in the fast axis direction can be suppressed to 4.80 dB or less if the fiber cutoff wavelength is 1.39 μm or greater. In Example 10, there is a margin of 0.9 dB or more in the bending loss in the fast axis direction to the target value of 5.70 dB, so it is expected that the bending loss in the fast axis direction can be suppressed to the target value of 5.70 dB or less even if the cutoff wavelength is reduced to 1.36 μm. From the above, if the mode field diameter is 9.0 μm or less, the difference r3 - r2 satisfies r3 - r2 ≧ 5.0, the ratio r2 / r1 satisfies 1.4 ≦ r2 / r1 ≦ 1.8, and the cutoff wavelength is 1.36 μm or more, it is expected that the bending loss in the fast axis direction can be suppressed to the target value of 5.70 dB or less.

[0086] 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 1.5≦r2 / r1≦1.8, 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 r3−r2≧4.0 μm, the relative refractive index difference Δ3 of the low-refractive-index layer 12 with respect to the cladding 14 satisfies Δ3≦−0.30%, the mode field diameter at a wavelength of 1.55 μm is 9.1 μm or less, and the fiber cutoff wavelength is 1.39 μm or more.

[0087] Consider Examples 7 and 8, in which the mode field diameter is 9.1 μm, the difference r3 - r2 is 4.0 μm, and the relative refractive index difference Δ3 is -0.30%. Example 7 shows that when the ratio r2 / r1 is 1.5, the bending loss in the fast axis direction can be suppressed to the target value of 5.70 dB or less if the cutoff wavelength is 1.39 μm or greater. Example 8 also shows that when the ratio r2 / r1 is 1.8, the bending loss in the fast axis direction can be suppressed to 2.97 dB or less if the fiber cutoff wavelength is 1.43 μm or greater. In Example 7, there is a margin of 2.73 dB or more in the bending loss in the fast axis direction to the target value of 5.70 dB, so it is expected that the bending loss in the fast axis direction can be suppressed to the target value of 5.7 dB or less even if the cutoff wavelength is reduced to 1.39 μm. From the above, if the mode field diameter is 9.1 μm or less, the difference r3 - r2 satisfies r3 - r2 ≧ 4.0, the relative refractive index difference Δ3 satisfies Δ3 ≦ -0.30%, the ratio r2 / r1 satisfies 1.5 ≦ r2 / r1 ≦ 1.8, and the cutoff wavelength is 1.39 μm or more, it is expected that the bending loss in the fast axis direction can be suppressed to the target value of 5.70 dB or less.

[0088] 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 1.6≦r2 / r1≦1.8, the relative refractive index difference Δ3 of the low-refractive-index layer 12 with respect to the cladding 14 satisfies Δ3≦−0.40%, the mode field diameter at a wavelength of 1.55 μm is 9.1 μm or less, and the fiber cutoff wavelength is 1.38 μm or more.

[0089] Consider Examples 9 and 18, in which the mode field diameter is 9.1 μm and the relative refractive index difference Δ3 is −0.4%. Example 9 reveals that when the ratio r2 / r1 is 1.6, the bending loss in the fast axis direction can be suppressed to the target value of 5.70 dB or less if the cutoff wavelength is 1.38 μm or greater. Example 18 reveals that when the ratio r2 / r1 is 1.8, the bending loss in the fast axis direction can be suppressed to 4.43 dB or less if the fiber cutoff wavelength is 1.41 μm or greater. In Example 18, there is a margin of 1.27 dB or more in the bending loss in the fast axis direction to the target value of 5.70 dB, so it is expected that the bending loss in the fast axis direction can be suppressed to the target value of 5.70 dB or less even if the cutoff wavelength is reduced to 1.38 μm. From the above, if the mode field diameter is 9.1 μm or less, the relative refractive index difference Δ3 satisfies Δ3≦−0.4%, and the cutoff wavelength is 1.38 μm or more, it is expected that the bending loss in the fast axis direction can be suppressed to the target value of 5.70 dB or less.

[0090] As described above, the polarization crosstalk of the polarization-maintaining fibers 1 according to Examples 1, 3, and 4 was measured when the fibers were wound once around a mandrel with a radius of 2.0 mm, with the direction of the slow axis SA of the polarization-maintaining fiber 1 perpendicular to the surface of the mandrel, using light with a wavelength of 1.55 μm. As a result, the polarization crosstalk of the polarization-maintaining fibers 1 according to Examples 1, 3, and 4 was −27 dB, −33 dB, and −38 dB, respectively.

[0091] The polarization-maintaining fibers 1 according to Examples 3 and 4, in which the radius r1 of the core 11 satisfies r1≦4.7 μm, have polarization crosstalk smaller than −30 dB, whereas the polarization-maintaining fiber 1 according to Example 1, in which the radius r1 of the core 11 satisfies r1>4.7 μm, has polarization crosstalk larger than 30 dB. Furthermore, the polarization-maintaining fibers 1 according to Examples 3 and 4, in which the shortest distance r from the center of the core 11 to the stress-applying portions 131 and 132 satisfies r4<r2, have polarization crosstalk smaller than −30 dB, whereas the polarization-maintaining fiber 1 according to Example 1, in which the shortest distance r from the center of the core 11 to the stress-applying portions 131 and 132 satisfies r4>r2, has polarization crosstalk larger than −30 dB. The polarization crosstalk required for optical devices such as the above-mentioned optical devices for telecom, datacom, and amplifiers is often about −30 dB. Therefore, a polarization-maintaining fiber 1 in which the radius r1 of the core 11 satisfies r1≦4.7 μm, or a polarization-maintaining fiber 1 in which the shortest distance r4 from the center of the core 11 to the stress-applying portions 131 and 132 satisfies r4<r2, can be realized that is practically tolerant to polarization crosstalk even when applied to the above-mentioned optical devices.

[0092] (Summary) Some of the aspects of the present invention described above are listed below.

[0093] 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≦2.4, 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 r3−r2≧3.0 μm, a relative refractive index difference Δ3 of the low-refractive-index layer with respect to the cladding satisfies Δ3≦−0.25%, and when light with a wavelength of 1.55 μm propagates through the core, the mode field diameter of the light is 9.2 μm or less, and a fiber cutoff wavelength is 1.34 μm or more.

[0094] 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 fast 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 5.70 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 fast 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 fast axis direction is in the direction of the bending radius, measured using light with a wavelength of 1.55 μm."

[0095] A polarization-maintaining fiber according to aspect 3 is the polarization-maintaining fiber according to aspect 1 or 2, 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 0.18 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."

[0096] A polarization-maintaining fiber according to a fourth aspect is the polarization-maintaining fiber according to any one of the first to third aspects, characterized in that the relative refractive index difference Δ1 of the core with respect to the cladding satisfies Δ1≧0.13%.

[0097] A polarization-maintaining fiber according to Aspect 5 is the polarization-maintaining fiber according to any one of Aspects 1 to 4, characterized in that the relative refractive index difference Δ1 of the core with respect to the cladding satisfies Δ1≦0.41%.

[0098] A polarization-maintaining fiber according to Aspect 6 is the polarization-maintaining fiber according to any one of Aspects 1 to 5, characterized in that 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 3.0 μm≦r3-r2≦8.0 μm.

[0099] A polarization-maintaining fiber according to Aspect 7 is the polarization-maintaining fiber according to any one of Aspects 1 to 6, characterized in that the relative refractive index difference Δ3 of the low refractive index layer with respect to the cladding satisfies −0.43%≦Δ3≦−0.25%.

[0100] A polarization-maintaining fiber according to an eighth aspect is the polarization-maintaining fiber according to any one of the first to seventh aspects, characterized in that the mode field diameter is 8.5 μm or more.

[0101] 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 fiber cutoff wavelength is 1.44 μm or less.

[0102] A polarization-maintaining fiber according to Aspect 10 is the polarization-maintaining fiber according to any one of Aspects 1 to 9, characterized in that the shortest distance r4 from the center of the core to the stress-applying portion satisfies r4<r2.

[0103] 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 shortest distance r4 from the center of the core to the stress-applying portion satisfies r4≦10.0 μm.

[0104] 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 relative refractive index difference Δ4 of the stress-applying portions with respect to the cladding satisfies Δ4≦−0.70%.

[0105] 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 diameter of the cladding is 79 μm or more and 126 μm or less.

[0106] 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 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≦1.8.

[0107] A polarization-maintaining fiber according to Aspect 15 is the polarization-maintaining fiber according to Aspect 1, characterized in that it satisfies any one of the following (A) to (F):

[0108] (A) 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 r3-r2≧5.0 μm, the relative refractive index difference Δ3 of the low refractive index layer with respect to the cladding satisfies Δ3≦−0.30%, the ratio r2 / r1 of the core radius r1 to the inner radius r2 of the low refractive index layer satisfies 1.0≦r2 / r1≦1.8, the mode field diameter is 9.0 μm or less, and the fiber cutoff wavelength is 1.39 μm or more.

[0109] (B) 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 r3-r2≧5.0 μm, the relative refractive index difference Δ3 of the low refractive index layer with respect to the cladding satisfies Δ3≦−0.30%, the ratio r2 / r1 of the core radius r1 to the inner radius r2 of the low refractive index layer satisfies 1.2≦r2 / r1<1.6, the mode field diameter is 9.2 μm or less, and the fiber cutoff wavelength is 1.38 μm or more.

[0110] (C) 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 r3-r2≧5.0 μm, the relative refractive index difference Δ3 of the low refractive index layer with respect to the cladding satisfies Δ3≦−0.30%, the ratio r2 / r1 of the core radius r1 to the inner radius r2 of the low refractive index layer satisfies 1.6≦r2 / r1<1.8, the mode field diameter is 9.0 μm or less, and the fiber cutoff wavelength is 1.36 μm or more.

[0111] (D) 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 r3-r2≧5.0 μm, the relative refractive index difference Δ3 of the low refractive index layer with respect to the cladding satisfies Δ3≦−0.30%, the ratio r2 / r1 of the core radius r1 to the inner radius r2 of the low refractive index layer satisfies 1.8<r2 / r1≦2.4, the mode field diameter is 9.2 μm or less, and the fiber cutoff wavelength is 1.41 μm or more.

[0112] (E) 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 r3-r2≧8.0 μm, the relative refractive index difference Δ3 of the low refractive index layer with respect to the cladding satisfies Δ3≦−0.30%, the ratio r2 / r1 of the core radius r1 to the inner radius r2 of the low refractive index layer satisfies r2 / r1≦1.8, the mode field diameter is 9.1 μm or less, and the fiber cutoff wavelength is 1.38 μm or more.

[0113] (F) 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 r3-r2≧5.0 μm, the relative refractive index difference Δ3 of the low refractive index layer with respect to the cladding satisfies Δ3≦−0.38%, the ratio r2 / r1 of the core radius r1 to the inner radius r2 of the low refractive index layer satisfies 1.4≦r2 / r1≦1.6, the mode field diameter is 9.1 μm or less, and the fiber cutoff wavelength is 1.34 μm or more.

[0114] A polarization-maintaining fiber according to Aspect 16 is the polarization-maintaining fiber according to any one of Aspects 1 to 13, 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 1.4≦r2 / r1≦2.4.

[0115] A polarization-maintaining fiber according to Aspect 17 is the polarization-maintaining fiber according to Aspect 16, 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 1.4≦r2 / r1≦1.8.

[0116] A polarization-maintaining fiber according to Aspect 18 is the polarization-maintaining fiber according to Aspect 17, characterized in that the ratio r2 / r1 of the core radius r1 to the inner radius r2 of the low refractive index layer satisfies 1.4≦r2 / r1≦1.8, 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 r3−r2≧5.0 μm, the mode field diameter is 9.0 μm or less, and the fiber cutoff wavelength is 1.36 μm or more.

[0117] A polarization-maintaining fiber according to Aspect 19 is the polarization-maintaining fiber according to Aspect 17, characterized in that a ratio r2 / r1 of the core radius r1 to the inner radius r2 of the low refractive index layer satisfies 1.5≦r2 / r1≦1.8, a 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 r3−r2≧4.0 μm, a relative refractive index difference Δ3 of the low refractive index layer with respect to the cladding satisfies Δ3≦−0.30%, the mode field diameter is 9.1 μm or less, and the fiber cutoff wavelength is 1.39 μm or more.

[0118] A polarization-maintaining fiber according to Aspect 20 is the polarization-maintaining fiber according to Aspect 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 1.6≦r2 / r1≦1.8, the relative refractive index difference Δ3 of the low refractive index layer with respect to the cladding satisfies Δ3≦−0.40%, the mode field diameter is 9.1 μm or less, and the fiber cutoff wavelength is 1.38 μm or more.

[0119] (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.

[0120] 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 said core; a pair of stress-applying portions arranged at positions sandwiching said core; and a cladding containing said core, said low-refractive index layer, and said pair of stress-applying portions; wherein a ratio r2 / r1 of a radius r1 of said core to an inner radius r2 of said low-refractive index layer satisfies 1.0≦r2 / r1≦2.4; a difference r3-r2 between an outer radius r3 of said low-refractive index layer and the inner radius r2 of said low-refractive index layer satisfies r3-r2≧3.0 μm; a relative refractive index difference Δ3 of said low-refractive index layer with respect to said cladding satisfies Δ3≦-0.25%; when light having a wavelength of 1.55 μm propagates through said core, the mode field diameter of said light is 9.2 μm or less; and a fiber cutoff wavelength is 1.34 μm or more.

2. The polarization-maintaining fiber according to claim 1, characterized in that when the bending radius is 2.0 mm and the fast axis direction is in the direction of said bending radius, the bending loss per turn for light with a wavelength of 1.55 μm is 5.70 dB or less.

3. A polarization-maintaining fiber according to claim 1 or 2, 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 0.18 dB or less.

4. A polarization-maintaining fiber according to any one of claims 1 to 3, characterized in that the relative refractive index difference Δ1 of the core with respect to the cladding satisfies Δ1 ≥ 0.13%.

5. A polarization-maintaining fiber according to any one of claims 1 to 4, characterized in that the relative refractive index difference Δ1 of the core with respect to the cladding satisfies Δ1≦0.41%.

6. A polarization-maintaining fiber according to any one of claims 1 to 5, characterized in that 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 3.0 μm≦r3 - r2 ≦8.0 μm.

7. A polarization-maintaining fiber according to any one of claims 1 to 6, characterized in that the relative refractive index difference Δ3 of said low refractive index layer with respect to said cladding satisfies -0.43%≦Δ3≦-0.25%.

8. A polarization-maintaining fiber according to any one of claims 1 to 7, characterized in that the mode field diameter is 8.5 µm or more.

9. A polarization-maintaining fiber according to any one of claims 1 to 8, characterized in that the fiber cutoff wavelength is 1.44 µm or less.

10. A polarization-maintaining fiber according to any one of claims 1 to 9, characterized in that the shortest distance r4 from the center of the core to the stress-applying portion satisfies r4<r2.

11. A polarization-maintaining fiber according to any one of claims 1 to 10, characterized in that the shortest distance r4 from the center of the core to the stress-applying portion satisfies r4≦10.0 μm.

12. A polarization-maintaining fiber according to any one of claims 1 to 11, characterized in that the relative refractive index difference Δ4 of said stress-applying portions with respect to said cladding satisfies Δ4≦-0.70%.

13. A polarization-maintaining fiber according to any one of claims 1 to 12, characterized in that the diameter of the cladding is 79 µm or more and 126 µm or less.

14. A polarization-maintaining fiber according to any one of claims 1 to 13, 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 1.0≦r2 / r1≦1.

8.

15. A polarization-maintaining fiber according to claim 1, characterized in that it satisfies any one of the following (A) to (F): (A) 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 r3-r2≧5.0 μm, the relative refractive index difference Δ3 of the low refractive index layer with respect to the cladding satisfies Δ3≦-0.30%, the ratio r2 / r1 of the core radius r1 to the inner radius r2 of the low refractive index layer satisfies 1.0≦r2 / r1≦1.8, the mode field diameter is 9.0 μm or less, and the fiber cutoff wavelength is 1.39 μm or more. (B) 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 r3-r2≧5.0 μm, the relative refractive index difference Δ3 of the low refractive index layer with respect to the cladding satisfies Δ3≦−0.30%, the ratio r2 / r1 of the core radius r1 to the inner radius r2 of the low refractive index layer satisfies 1.2≦r2 / r1<1.6, the mode field diameter is 9.2 μm or less, and the fiber cutoff wavelength is 1.38 μm or more. (C) 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 r3-r2≧5.0 μm, the relative refractive index difference Δ3 of the low refractive index layer with respect to the cladding satisfies Δ3≦−0.30%, the ratio r2 / r1 of the core radius r1 to the inner radius r2 of the low refractive index layer satisfies 1.6≦r2 / r1<1.8, the mode field diameter is 9.0 μm or less, and the fiber cutoff wavelength is 1.36 μm or more. (D) 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 r3-r2≧5.0 μm, the relative refractive index difference Δ3 of the low refractive index layer with respect to the cladding satisfies Δ3≦−0.30%, the ratio r2 / r1 of the core radius r1 to the inner radius r2 of the low refractive index layer satisfies 1.8<r2 / r1≦2.4, the mode field diameter is 9.2 μm or less, and the fiber cutoff wavelength is 1.41 μm or more.(E) 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 r3-r2≧8.0 μm, the relative refractive index difference Δ3 of the low refractive index layer with respect to the cladding satisfies Δ3≦−0.30%, the ratio r2 / r1 of the core radius r1 to the inner radius r2 of the low refractive index layer satisfies r2 / r1≦1.8, the mode field diameter is 9.1 μm or less, and the fiber cutoff wavelength is 1.38 μm or more. (F) 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 r3-r2≧5.0 μm, the relative refractive index difference Δ3 of the low refractive index layer with respect to the cladding satisfies Δ3≦−0.38%, the ratio r2 / r1 of the core radius r1 to the inner radius r2 of the low refractive index layer satisfies 1.4≦r2 / r1≦1.6, the mode field diameter is 9.1 μm or less, and the fiber cutoff wavelength is 1.34 μm or more.

16. A polarization-maintaining fiber according to any one of claims 1 to 13, 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 1.4≦r2 / r1≦2.

4.

17. The polarization-maintaining fiber according to claim 16, wherein the ratio r2 / r1 of the radius r1 of the core to the inner radius r2 of the low refractive index layer satisfies 1.4≦r2 / r1≦1.

8.

18. A polarization-maintaining fiber according to claim 17, wherein the ratio r2 / r1 of the core radius r1 to the inner radius r2 of the low refractive index layer satisfies 1.4≦r2 / r1≦1.8, 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 r3-r2≧5.0 μm, the mode field diameter is 9.0 μm or less, and the fiber cutoff wavelength is 1.36 μm or more.

19. A polarization-maintaining fiber according to claim 17, wherein the ratio r2 / r1 of the core radius r1 to the inner radius r2 of the low refractive index layer satisfies 1.5≦r2 / r1≦1.8, 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 r3-r2≧4.0 μm, the relative refractive index difference Δ3 of the low refractive index layer with respect to the cladding satisfies Δ3≦-0.30%, the mode field diameter is 9.1 μm or less, and the fiber cutoff wavelength is 1.39 μm or more.

20. A polarization-maintaining fiber according to claim 17, characterized in that the ratio r2 / r1 of the core radius r1 to the inner radius r2 of the low refractive index layer satisfies 1.6≦r2 / r1≦1.8, the relative refractive index difference Δ3 of the low refractive index layer with respect to the cladding satisfies Δ3≦-0.40%, the mode field diameter is 9.1 μm or less, and the fiber cutoff wavelength is 1.38 μm or more.

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