Abstract:
An optical fiber including a core and a cladding including an inner cladding layer and an outer cladding layer is provided. The refractive index of the core Δ1, the refractive index of the inner cladding layer Δ2, and the refractive index of the outer cladding layer Δ3 have a relationship denoted by the following expressions: Δ1max&gt;Δ2min and Δ1max&gt;Δ3, and 0.01%&lt;|Δ2min−Δ3|&lt;0.03%. An outer circumference radius r1 of the core, an outer circumferential radius r2 of the inner cladding layer, and an outer circumferential radius r3 of the outer cladding layer have a relationship denoted by the following expressions: r1&lt;r2&lt;r3, and 0.2≦r1/r2≦0.5. A cable cut-off wavelength λcc 1260 nm or less. A mode field diameter at a wavelength of 1310 nm is 8.6 μm or more and 9.5 μm or less.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation application based on a PCT Patent Application No. PCT/JP2015/077080, filed Sep. 25, 2015, whose priority is claimed on Japanese Patent Application No. 2014-195937 filed Sep. 26, 2014 and Japanese Patent Application No. 2014-195938 filed Sep. 26, 2014, the entire contents of which are hereby incorporated by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to an optical fiber. 
     Description of the Related Art 
     An optical fiber has been installed even on the inside of buildings, houses, or the like according to the spread of Fiber To The Home (FTTH). According to this, an optical fiber has attracted attention in which an excessive loss, so-called bending loss (a macro bend loss) which occurs at the time of imparting bending properties, is reduced. 
     By using an optical fiber having a low bending loss, prevention of instantaneous interruption of a signal due to the loss which occurs at the time of bending the optical fiber, a reduction in installation costs due to handling simplification, and the like have been expected. 
     ITU-T Recommendation G.657 is used as the standard of an optical fiber in which the bending loss is reduced compared to a standard single mode optical fiber (SSMF) while being based on ITU-T Recommendation G.652 which is the standard of the standard single mode optical fiber (SSMF). 
     For example, the following methods have been proposed as a method of improving the bending loss. 
     (1) Increasing Refractive Index of Core 
     By increasing the refractive index of the core, a mode field diameter (MFD) decreases compared to S-SMF, and thus, containment of light with respect to the core is improved. Therefore, the bending loss of the optical fiber can be reduced. In this case, in order to match dispersion to G.652, it is preferable that so-called depressed refractive index profile in which the refractive index of the cladding near the core is reduced be adopted (for example, refer to Published Japanese Translation No. 2013-520711 of the PCT International. Publication and K. Okamoto and T. Okoshi, “Computer-aided synthesis of the optimum refractive index profile for a multimode fiber,” IEEE Trans. Microwave Theory Tech., vol. MTT-25, pp. 213-221, 1976). In addition, Published Japanese Translation No. 2013-520711 of the PCT International Publication shows that by adjusting the refractive index of an internal-layer cladding region, it is possible to maintain a balance between both of the characteristics, that is, the MFD and the bending loss. 
     A product corresponding to a bending radius up to 15 mm which is based on G.657.A1 is used as such a type of optical fiber. 
     (2) Adopting Refractive Index Profile having Trench-Shape 
     By adopting the trench-shape refractive index profile having a low refractive index portion at a location away from the core of the cladding, containment of the light with respect to the core can be improved and the bending loss can be reduced (for example, refer to Japanese Unexamined Patent Application, First Publication No. S63-43107). 
     A product corresponding to a bending radius up to 10 mm which is based on G.657.A2 or G.657.B2 and a product corresponding to a smaller bending radius up to 7.5 mm which is based on G.657.B3 are used as such a type of optical fiber. In addition, a product corresponding to a bending radius up to 7.5 mm which is based on G.657.B3 and of which other optical properties are based on the standard of G.657.A series are used as such a type of optical fiber. 
     (3) Forming Hole to Cladding 
     An optical fiber (for example, a hole-assisted fiber (HAF)) in which a hole along a longitudinal direction of the optical fiber is formed at a location away from the core of the cladding or an optical fiber in which a fine structure including a plurality of independent openings (for example, ClearCurve® manufactured by Corning Inc.) can improve containment of light with respect to the core. Therefore, the bending loss can be reduced (for example, refer to PCT International Publication No. WO2004/092793 and Published Japanese Translation No. 2009-543126 of the PCT International Publication). 
     A product corresponding to a bending radius up to 7.5 mm which is based on G.657.B3 is used as such a type of optical fiber. 
     In the above-described method, an optical fiber having a high refractive index of the core can have a lower bending loss. However, according to this, the mode field diameter decreases, and a connection loss with respect to SSMF increases. For this reason, there is a limit for reducing the bending loss. 
     In an optical fiber having a trench type refractive index profile, it is necessary to form the plurality of layers having a different refractive index, and thus, a manufacturing step of a preform becomes complicated. 
     In an optical fiber having a hole, a manufacturing step becomes complicated compared to an optical fiber having a solid structure. In addition, an advanced drawing technology is required, and thus, the manufacturing is not easily performed. 
     The present invention takes into consideration of the above circumstances and provides an optical fiber in which the bending loss can be reduced without increasing the connection loss and which is easy to manufacture. 
     SUMMARY OF THE INVENTION 
     It has been known that the refractive index of the cladding in a portion close to the core considerably affects optical properties of the optical fiber, but as a result of intensive studies of the present inventors, a refractive index profile which is able to reduce a bending loss without decreasing a mode field diameter has been found. 
     The present invention has been made based on the findings described above, and by adopting the above-described refractive index profile, the optical fiber has technical meaning from the viewpoint of making suppression of the connection loss at the time of being connected to the other optical fiber and a reduction in the bending loss compatible. 
     A first aspect of the present invention is an optical fiber including a core and a cladding formed on an outer periphery of the core. The cladding comprises at least an inner cladding layer adjacent to the core mid an outer cladding layer formed on the outer circumference side of the inner cladding layer, a refractive index of the core is Δ1 and a maximum refractive index of the core is Δ1max, a refractive index of the inner cladding layer is Δ2 and a minimum refractive index of the inner cladding layer is Δ2min, and a refractive index of the outer cladding layer is Δ3. The refractive index of the core, the refractive index of the inner cladding layer, and the refractive index of the outer cladding layer have a relationship denoted by Expressions (1) and (2).
 
Δ1max&gt;Δ2min and Δ1max&gt;Δ3  (1)
 
0.01%&lt;|Δ2min−Δ3|&lt;0.03%  (2)
 
     An outer circumference radius r1 of the core, an outer circumferential radius r2 of the inner cladding layer, and an outer circumferential radius r3 of the outer cladding layer have a relationship denoted by Expressions (3) and (4).
 
 r 1&lt; r 2&lt; r 3  (3)
 
0.2≦ r 1/ r 2≦0.5  (4)
 
     A cable cut-off wavelength λcc satisfies Expression (5).
 
λ cc≦ 1260 nm  (5)
 
     A mode field diameter at a wavelength of 1310 nm satisfies Expression (6).
 
8.6 μm≦MFD≦9.5 μm  (6)
 
     A second aspect of the present invention is the optical fiber according to the first aspect, in which the refractive index of the core, the refractive index of the inner cladding layer, and the refractive index of the outer cladding layer have a relationship denoted by Expressions (1A) and (2A).
 
Δ1max&gt;Δ3&gt;Δ2min  (1A)
 
0.01%&lt;(Δ3−Δ2min)&lt;0.03%  (2A)
 
     A third aspect of the present invention is the optical fiber according to the second aspect, in which Δ1max further satisfies 0.33%≦Δ1max≦0.40%. 
     A fourth aspect of the present invention is the optical fiber according to any one of the first to third aspects, in which a loss increase at a wavelength of 1550 nm at the time of winding the optical fiber around a mandrel having a diameter of 15 mm 10 times is less than or equal to 0.25 dB, and a loss increase at a wavelength of 1625 nm at the time of winding the optical fiber around the mandrel having the diameter of 15 mm 10 times be less than or equal to 1.0 dB. 
     A fifth aspect of the present invention is the optical fiber according to any one of the first to fourth aspects, in which the outer cladding layer is formed of pure silica glass, and the inner cladding layer is formed of silica glass to which fluorine is added. 
     A sixth aspect of the present invention is the optical fiber according to any one of the first to fifth aspects, in which the outer cladding layer is formed of pure silica glass, and the inner cladding layer is formed of silica glass to which chlorine is added. 
     In addition, when Δ2&lt;Δ3, the inner cladding layer is preferably formed of, for example, the silica glass to which fluorine is added fluorine (F) is added. When Δ2&gt;Δ3, the inner cladding layer is preferably formed of, for example, the silica glass to which fluorine is added chlorine (Cl) is added. 
     A seventh aspect of the present invention is the optical fiber including a core and a cladding formed on an outer periphery of the core. The cladding includes at least an inner cladding layer adjacent to the core, a trench portion adjacent to the outer circumference side of the inner cladding layer, and an outer cladding layer formed on the outer circumference side of the trench portion. A refractive index of the core is Δ1 and a maximum refractive index of the core is Δ1max, a refractive index of the inner cladding layer is Δ2 and a minimum refractive index of the inner cladding layer is Δ2min, a refractive index of the trench portion is Δ3 and a minimum refractive index of the inner cladding layer is Δ3min, and a refractive index of the outer cladding laser is Δ4. The refractive index of the core, the refractive index of the inner cladding layer, the refractive index of the trench portion, and the refractive index of the outer cladding layer have a relationship denoted by Expressions (11)-(13).
 
Δ1max&gt;Δ2&gt;Δ3min  (11)
 
Δ1max&gt;Δ4&gt;Δ3min  (12)
 
0.01%&lt;(Δ4−Δ3min)&lt;0.03%  (13)
 
     An outer circumference radius r1 of the core, an outer circumferential radius r2 of the inner cladding layer, an outer circumferential radius r3 of the trench portion, and an outer circumferential radius r4 of the outer cladding layer have a relationship denoted by Expressions (14-16).
 
 r 1≦ r 2&lt; r 3&lt; r 4  (14)
 
1≦ r 2/ r 1≦5  (15)
 
1&lt; r 3/ r 2≦2  (16)
 
     A cable cut-off wavelength λcc satisfies Expression (17).
 
λ cc≦ 1260 nm  (17)
 
     A mode field diameter at a wavelength of 1310 nm satisfies Expression (18).
 
8.6 μm≦MFD≦9.5 μm  (18)
 
     An eighth aspect of the present invention is the optical fiber according to seventh aspect, in which a loss increase at a wavelength of 1550 nm at the time of winding the optical fiber around a mandrel having a diameter of 15 mm 1.0 times is less than or equal to 0.25 dB, and a loss increase at a wavelength of 1625 nm at the time of winding the optical fiber around the mandrel having the diameter of 15 mm 10 times be less than or equal to 1.0 dB. 
     A ninth aspect of the present invention is the optical fiber according to seventh or eighth aspect, in which the outer cladding layer is formed of pure silica glass, and the trench portion is formed of silica glass to which fluorine is added. 
     According to the aspects of the present invention described above, by adjusting a reflective index difference between the inner cladding layer and the outer cladding laser and a ratio of an outer circumference radius of the core and an outer circumference radius of the inner cladding layer, the connection loss at the time of being connected to the other optical fiber (for example, a general single mode optical fiber (SSMF)) is able to be suppressed to be low, and the bending loss is able to be reduced. 
     According to the aspects of the present invention described above, by adjusting a reflective index difference between the trench portion and the outer cladding layer and a ratio of an outer circumference radius of the core, an outer circumference radius of the inner cladding layer, and an outer circumference radius of the trench portion, the connection loss at the time of being connected to the other optical fiber (for example, a general single mode optical fiber (SSMF)) is able to be suppressed to be low, and the bending loss is able to be reduced. 
     In addition, according to the aspects of the present invention described above, the manufacturing method of the related art is able to be used without being considerably changed, and thus, the optical fiber is able to be easily manufactured, and the manufacturing costs are able to be made low. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a cross-sectional view schematically showing an optical fiber according to the first embodiment. 
         FIG. 2A  is a drawing schematically showing a refractive index profile of the optical fiber shown in  FIG. 1 . 
         FIG. 2B  is a drawing schematically showing a refractive index profile of an optical fiber of Comparative Example. 
         FIG. 3  is a cross-sectional view schematically showing an optical fiber according to the second embodiment. 
         FIG. 4  is a drawing schematically showing a refractive index profile of the optical fiber shown in  FIG. 3 . 
         FIG. 5  is a cross-sectional view schematically showing an optical fiber according to the third embodiment. 
         FIG. 6  is a drawing schematically showing a refractive index profile of the optical fiber shown in  FIG. 5 . 
         FIG. 7  is a drawing schematically showing a refractive index profile of the optical fiber according to another embodiment. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Hereinafter, the present invention will be described on the basis of preferred embodiments and with reference to the drawings. 
     First Embodiment 
       FIG. 1  shows schematic configuration of an optical fiber  10  according to a first embodiment of the present invention. 
     The optical fiber  10  includes a core  1  disposed on the center portion, and a cladding  4  disposed on the outer circumference side (the outer circumference) of the core  1  to be concentric with the core  1 . 
     The cladding  4  includes an inner cladding layer  2  adjacent to the outer circumference side (the outer circumference) of the core  1 , and an outer cladding layer  3  formed on the outer circumference side (the outer circumference) of the inner cladding layer  2 . 
       FIG. 2A  schematically shows a refractive index profile of the optical fiber  10 . 
     The refractive index of the core  1  is defined as Δ1, and the maximum refractive index of the core  1  is defined as Δ1max. 
     The refractive index of the inner cladding layer  2  is defined as Δ2, and the minimum refractive index of the inner cladding layer  2  is defined as Δ2min. 
     The refractive index of the outer cladding layer  3  is defined as Δ3. 
     The maximum refractive index Δ1max of the core  1  is the refractive index of the core  1  which is maximized in a diameter direction range from the center of the core  1  to the outer circumference of the core  1 . In the refractive index profile shown in  FIG. 2A , the refractive index Δ1 of the core  1  is constant without depending on the position in the diameter direction, and thus, the refractive index Δ1 is identical to the maximum refractive index Δ1max in the entire range. 
     The minimum refractive index Δ2min of the inner cladding layer  2  is the refractive index of the inner cladding laser  2  which is minimized in a diameter direction range from the inner circumference of the inner cladding laser  2  to the outer circumference of the inner cladding layer  2 . In the refractive index profile shown in  FIG. 2A , the refractive index Δ2 of the inner cladding layer  2  is constant without depending on the position in the diameter direction, and thus, the refractive index Δ2 is identical to the minimum refractive index Δ2min in the entire range. 
     In the optical fiber  10 , Expression (1) described below is established.
 
Δ1max&gt;Δ2min and Δ1max&gt;Δ3  (1)
 
     As shown in Expression (1), the maximum refractive index Δ1max of the core  1  is greater than the minimum refractive index Δ2min of the inner cladding layer  2  and the refractive index Δ3 of the outer cladding layer  3 . 
     In addition, in the optical fiber  10 , the minimum refractive index Δ2min of the inner cladding layer  2  is less than the refractive index Δ3 of the outer cladding layer  3 . 
     In the optical fiber  10 , Expression (2) described below is further established.
 
0.01%&lt;|Δ2min−Δ3|&lt;0.03%  (2)
 
     Expression (2) indicates that the absolute value of a difference between the minimum refractive index Δ2min of the inner cladding layer  2  and the refractive index Δ3 of the outer cladding layer  3  is greater than 0.01% and less than 0.03%. 
     When the absolute value of the difference between Δ2min and Δ3 is excessively small, the bending loss may not be sufficiently reduced. In contrast, when the absolute value of the difference between Δ2min and Δ3 is excessively large, the mode field diameter decreases, and a connection loss at the time of being connected to the other optical fiber (for example, a general single mode optical fiber (SSMF)) may increase. 
     In the optical fiber  10 , it is possible to reduce the bending loss by setting the absolute value of the difference between Δ2min and Δ3 to be greater than 0.01%. In addition, it is possible to optimize the mode field diameter (MFD) and to suppress the connection loss to be Sow at the time of being connected to the other optical fiber by setting the absolute value of the difference between Δ2min and Δ3 to be less than 0.03%. 
     In the optical fiber  10  of the first embodiment. Expression (1A) described below is established with respect to a magnitude relationship of Δ1max, Δ2min, and Δ3.
 
Δ1max&gt;Δ3&gt;Δ2min  (1A)
 
     As shown in Expression (1A), the maximum refractive index Δ1max of the core  1  is greater than the refractive index Δ3 of the outer cladding layer  3 . 
     The refractive index Δ3 of the outer cladding layer  3  is greater than the minimum refractive index Δ2min of the inner cladding layer  2 . 
     Δ3 is greater than Δ2min, and thus Expression (2) described above is able to be described as follows.
 
0.01%&lt;(Δ3−Δ2min)&lt;0.03%  (2A)
 
     Expression (2A) indicates that a difference between the refractive index Δ3 of the outer cladding layer  3  and the minimum refractive index Δ2min of the inner cladding layer  2  is greater than 0.01% and less than 0.03%. 
     The outer circumferential radii of the core  1 , the inner cladding layer  2 , and the outer cladding layer  3  are respectively defined as r1, r2, and r3. 
     The outer circumference radius r1 of the core  1 , the outer circumferential radius r2 of the inner cladding layer  2 , and the outer circumferential radius r3 of the outer cladding layer  3  have a relationship denoted by Expression (3) described below.
 
 r 1&lt; r 2&lt; r 3  (3)
 
     A ratio r1/r2 of the outer circumference radius r1 of the core  1  to the outer circumferential radius r2 of the tuner cladding layer  2  is in a range denoted by Expression (4) described below.
 
0.2≦ r 1/ r 2≦0.5  (4)
 
     When r1/r2 is excessively small, she mode field diameter decreases, the connection loss at the time of being connected to the other optical fiber (for example, SSMF) may increase. In contrast, when r1/r2 is excessively large, the bending loss may increase. 
     In the optical fiber  10 , r1/r2 is adjusted to be greater than or equal to 0.2, and thus, the mode field diameter is able to be optimized, and the connection loss at the time of being connected to the other optical fiber is able to be suppressed to be low. r1/r2 is adjusted to be less than or equal to 0.5, and thus, the bending loss is able to be reduced. 
     In the optical, fiber  10 , a cable cut-off wavelength λcc (i.e., a cut-off wavelength λc 22m  of 22 m) is adjusted to be less than or equal to 1260 nm. That is, Expression (5) described below is established.
 
λ cc≦ 1260 nm  (5)
 
     Accordingly, the regulation of ITU-T Recommendation G.652 is able to be satisfied. 
     The cut-off wavelength λcc, for example, is able to be measured by a measurement method disclosed in ITU-T Recommendation G.650. 
     In the optical fiber  10 , the refractive index and the outer circumferential radius described above are adjusted, and thus, the mode field diameter (MFD) at a wavelength of 1310 nm is greater than or equal 8.6 μm and less than or equal to 9.5 μm. That is, Expression (6) described below is established.
 
8.6 μm≦MFD≦9.5 μm  (6)
 
     The mode field diameter is in the range of Expression (6), and thus, the connection loss at the time of being connected to the other optical fiber (for example, S-SMF) is able to be suppressed to be low. 
     In the optical fiber  10 , the mode field diameter is in the range of Expression (6), and thus, the regulation of ITU-T G.652 is satisfied. 
     In the optical fiber  10 , it is preferable that a loss increase at a wavelength of 1550 nm at the time of winding the optical fiber  10  around a cylindrical mandrel having a diameter of 15 mm 10 times be less than or equal to 0.25 dB. 
     In addition, it is preferable that the loss increase at a wavelength of 1.625 nm at the time of winding the optical fiber  10  around the cylindrical mandrel having a diameter of 15 mm 10 times be less than or equal to 1.0 dB. 
     The core  1 , for example, is able to be configured of silica glass of which the refractive index increases by adding a dopant such as germanium (Ge). 
     The inner cladding layer  2 , for example, is able to be configured of silica glass of which the refractive index decreases by adding a dopant such as fluorine (F). The inner cladding layer  2 , for example, may be configured of silica glass of which the refractive index increases by adding a dopant such as chlorine (Cl). 
     The outer cladding layer  3 , for example, is able to be configured of pure silica glass. In the outer cladding layer  3 , the refractive index may be adjusted by adding a dopant (for example, Ge, F, and the like). 
     Each layer configuring the optical fiber  10  is able to be formed by a known method such as a modified chemical vapor deposition method, a plasma chemical vapor deposition method, a vapor-phase axial deposition method, and an outside vapor deposition method, or a combination thereof. 
     For example, in a case where the modified chemical vapor deposition method is adopted, the optical fiber preform is able to be prepared as follows. 
     A glass deposition layer which becomes the inner cladding layer  2  is formed on the inside of a silica glass tube (for example, a glass tube formed of pure silica glass) which becomes the outer cladding layer  3 , for example, by using a raw material containing a dopant such as fluorine (F). The refractive index of the inner cladding layer  2  is able to be adjusted by the added amount of the dopant. 
     Next, a glass deposition layer which becomes the core  1  is formed on the inside of the glass deposition layer described above, for example, by using a raw material containing a dopant such as germanium (Ge). Furthermore, the core  1  is able to be formed by using a core rod which is separately prepared. 
     The silica glass tube in which the glass deposition layer is formed becomes the optical fiber preform through a transparency step, a solidification step, and the like. The optical fiber preform is subjected to fiber drawing, and thus, the optical, fiber  10  shown in  FIG. 1  is able to be obtained. 
     The chemical vapor deposition method is preferable front the viewpoint of accurately adjusting the refractive index profile by adding a dopant. 
     The vapor-phase axial deposition method and the outside vapor deposition method are also able to be applied to manufacture the optical fiber  10 . The vapor-phase axial deposition method and the outside vapor deposition method have advantages such as high productivity. 
     In the optical fiber  10 , a difference in the refractive indices between the inner cladding layer  2  and the outer cladding layer  3  is in the range described above (refer to Expression (2)), and a ratio of the outer circumferential radius of the core  1  and the outer circumferential radius of the inner cladding layer  2  in the range described above (refer to Expression (4)), and thus, the connection loss at the time of being connected to the other optical fiber is able to be suppressed to be low, and the bending loss is able to be reduced. 
     It has been known that the refractive index of the cladding in a portion close to the core considerably affects optical properties of the optical fiber, but as a result of intensive studies of the present inventor, a refractive index profile has been found in which the bending loss is able to be reduced without decreasing the mode field diameter. 
     By adopting the refractive index profile, the optical fiber  10  has technical meaning from the viewpoint of making suppression of the connection loss at the time of being connected to the other optical fiber and a reduction in the bending loss compatible. 
     In the optical fiber  10 , the difference in the refractive indices between the inner cladding layer  2  and the outer cladding layer  3  is small, and thus, the refractive index of the inner cladding layer  2  and the outer cladding layer  3  is able to be easily and accurately adjusted by using the manufacturing method of the related art (for example, a general manufacturing method of S-SMF) without considerably changing the method. 
     In addition, the difference in the refractive indices between the inner cladding layer  2  and the outer cladding layer  3  is small, and thus, constraint based on the manufacturing method decreases. For example, not only the chemical vapor deposition method which is considered to be suitable for adjusting the refractive index profile but also the vapor-phase axial deposition method and the outside vapor deposition method are able to be adopted. 
     Accordingly, the optical fiber  10  is able to be easily manufactured, and manufacturing costs are able to be made low. 
     In the optical fiber  10 , the difference in the refractive indices between the inner cladding layer  2  and the outer cladding layer  3  is small, and thus, the added amount of the dopant such as fluorine (F) and chlorine (Cl) for forming fee inner cladding layer  2  is able to be reduced. 
     Raw material gas (for example, SiF 4 ) used in a dope such as fluorine (F) is expensive, and thus, raw material costs are able to be suppressed and manufacturing costs are able to be made low by reducing the amount of the dopant added. 
     As shown in  FIG. 2A , in the optical fiber  10 , the minimum refractive index Δ2min of the inner cladding layer  2  is less than the refractive index Δ3 of the outer cladding layer  3 , and thus it is possible to make containment of the light with respect to the core  1  excellent and to reduce the bending loss. 
     More specifically, when Δ2 is small, it is preferable in terms of for example, costs other than the characteristics. Generally, in order to form a low refractive region, it is necessary to add a dopant such as fluorine (F) described above which reduces the refractive index, and material costs increases. However, in the present application, since the adding amount of the fluorine is remarkably small, the cost reduction can be expected. In addition, when Δ2 is small, it is preferable in terms of a transmission loss. The dopant added to the inner cladding layer  2  diffuses into the core portion under a high temperature environment such as the sintering process and the drawing process of a preform of the optical fiber. Since the Raleigh scattering coefficient which is a dominant factor of the transmission loss increases with the increase of the content of the dopant, the transmission loss decreases when the fluorine diffuses into the core portion. However, in the present application, since the adding amount of the fluorine is remarkably small, it is not necessary to consider influence on the transmission loss. 
     Here, the results of the simulation regarding the refractive index difference of the inner cladding layer  2  shown in  FIG. 1  are shown. Table 1 shows calculation results of characteristics when each parameter shown in  FIG. 2A  is set. 
     
       
         
               
               
             
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
             
             
               
                   
                 Example 
               
             
          
           
               
                 Parameter 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
               
                 Δ1 [%] 
                 0.37 
                 0.36 
                 0.35 
                 0.33 
                 0.36 
                 0.38 
                 0.34 
               
               
                 Δ2 [%] 
                 −0.03 
                 −0.03 
                 −0.03 
                 −0.03 
                 −0.02 
                 −0.02 
                 −0.02 
               
               
                 Δ3 [%] 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
               
               
                 r1/r2 
                 0.20 
                 0.40 
                 0.50 
                 0.20 
                 0.40 
                 0.20 
                 0.40 
               
               
                 r2 [μm] 
                 43.0 
                 22.5 
                 18.0 
                 47.0 
                 22.0 
                 43.0 
                 23.0 
               
               
                 MFD at 1.31 μm [μm] 
                 8.74 
                 8.98 
                 9.06 
                 9.35 
                 8.96 
                 8.74 
                 9.27 
               
               
                 cable cut-off wavelength 
                 1221 
                 1234 
                 1235 
                 1255 
                 1238 
                 1245 
                 1260 
               
               
                 λcc [nm] 
               
               
                 Bending loss (R = 15 mm) 
                 0.008 
                 0.009 
                 0.032 
                 0.006 
                 0.023 
                 0.003 
                 0.062 
               
               
                 at 1.55 μm [dB/10 turn] 
               
               
                 Bending loss (R = 15 mm) 
                 0.084 
                 0.069 
                 0.328 
                 0.047 
                 0.23 
                 0.024 
                 0.661 
               
               
                 at 1.625 μm [dB/10 turn] 
               
               
                 Dispersion at 1.31 μm 
                 0.348 
                 0.747 
                 0.577 
                 0.074 
                 0.411 
                 0.317 
                 0.744 
               
               
                 [ps/km/nm] 
               
               
                   
               
             
          
           
               
                   
                 Example 
               
             
          
           
               
                 Parameter 
                 8 
                 9 
                 10 
                 11 
                 12 
                 13 
                 14 
               
               
                   
               
               
                 Δ1 [%] 
                 0.37 
                 0.34 
                 0.39 
                 0.33 
                 0.36 
                 0.33 
                 0.40 
               
               
                 Δ2 [%] 
                 −0.01 
                 −0.01 
                 −0.01 
                 −0.01 
                 −0.04 
                 −0.04 
                 −0.04 
               
               
                 Δ3 [%] 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
               
               
                 r1/r2 
                 0.40 
                 0.20 
                 0.25 
                 0.29 
                 0.20 
                 0.33 
                 0.25 
               
               
                 r2 [μm] 
                 21.5 
                 43.5 
                 32.0 
                 32.0 
                 45.0 
                 28.5 
                 35.0 
               
               
                 MFD at 1.31 μm [μm] 
                 8.88 
                 9.14 
                 8.59 
                 9.40 
                 8.98 
                 9.34 
                 8.57 
               
               
                 cable cut-off wavelength 
                 1252 
                 1202 
                 1252 
                 1255 
                 1238 
                 1227 
                 1260 
               
               
                 λcc [nm] 
               
               
                 Bending loss (R = 15 mm) 
                 0.011 
                 0.20 
                 0.005 
                 0.25 
                 0.012 
                 0.082 
                 0.001 
               
               
                 at 1.55 μm [dB/10 turn] 
               
               
                 Bending loss (R = 15 mm) 
                 0.087 
                 0.94 
                 0.036 
                 0.930 
                 0.145 
                 0.82 
                 0.005 
               
               
                 at 1.625 μm [dB/10 turn] 
               
               
                 Dispersion at 1.31 μm 
                 0.128 
                 0.055 
                 −0.223 
                 0.532 
                 0.809 
                 1.193 
                 0.830 
               
               
                 [ps/km/nm] 
               
               
                   
               
             
          
         
       
     
     Based on the calculation results described above, if Δ1, r2, and r1/r2 are set appropriately when Δ2 has a range of −0.01% to −0.04%, an optical fiber which comply with G.657.A can be realized (i.e., MFD at the wavelength of 1310 nm is 8.6-9.5 μm), the cable cut-off wavelength λcc is less than or equal to 1260 nm, a loss increase (bending loss) at a wavelength of 1550 (1625) nm at the time of winding the optical fiber around a mandrel having a diameter of 15 mm 10 times be less than or equal to 0.25 (1.0) dB). In other words, when Δ2 has a range of −0.01% to −0.04%, it is found that both of the MFD and the bending loss can be increased. 
     As a comparative example, results of the case where the inner cladding layer does not present are shown. Table 2 shows calculation results of the characteristics when each parameter of the refractive index profile where the inner cladding layer shown in  FIG. 2B  is not present is set. 
     
       
         
               
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
             
             
               
                   
                   
               
               
                   
                 Comparative Example 
               
             
          
           
               
                 Parameter 
                 1 
                 2 
                 3 
               
               
                   
               
             
          
           
               
                 Δ1 [%] 
                 0.37 
                 0.36 
                 0.34 
               
               
                 r1 [μm] 
                 4.17 
                 4.25 
                 4.40 
               
               
                 MFD at 1.31 μm [μm] 
                 8.82 
                 8.98 
                 9.27 
               
               
                 λcc [nm] 
                 1256 
                 1261 
                 1263 
               
               
                 Bending loss (R = 15 mm) at 
                 0.185 
                 0.131 
                 0.469 
               
               
                 1.55 μm [dB/10 turn] 
               
               
                 Bending loss (R = 15 mm) at 
                 1.226 
                 1.944 
                 5.947 
               
               
                 1.625 μm [dB/10 turn] 
               
               
                 Dispersion at 1.31 μm 
                 −0.341 
                 −0.178 
                 0.084 
               
               
                 [ps/km/nm] 
               
               
                   
               
             
          
         
       
     
     In the comparative example, despite an upper limit of die cable cut-off wavelength of 1260 nm and the bending-loss-enhanced refractive index, the bending loss does not satisfy the standard of G.657.A1. Also based on the results of the comparative example, it is also found that an optical fiber with high performance can be realized by providing the inner cladding-portion within an appropriate refractive index range. 
     Second Embodiment 
       FIG. 3  shows a schematic configuration of an optical fiber  20  according to a third embodiment of the present invention. 
     The optical fiber  20  includes the core  1  disposed on the center portion, and a cladding  14  disposed on the outer circumference side (the outer circumference) of the core  1  to be concentric with the core  1 . 
     The cladding  14  includes the inner cladding layer  12  adjacent to the outer circumference side (the outer circumference) of the core  1 , and the outer cladding layer  13  formed on the outer circumference side (the outer circumference) of the inner cladding layer  12 . 
       FIG. 14  schematically shows a refractive index profile of the optical fiber  20 , 
     The refractive index of the core  1  is defined as Δ1, and the maximum refractive index of the core  1  is defined as Δ1max. The refractive index of the inner cladding layer  12  is defined as Δ2, and the minimum refractive index of the inner cladding layer  12  is defined as Δ2min. The refractive index of the outer cladding layer  13  is defined as Δ3. 
     In the optical fiber  20 , Expression (7) described below is established as with the optical fiber  10  of the first embodiment.
 
Δ1max&gt;Δ2min and Δ1max&gt;Δ3  (7)
 
     The optical fiber  20  is different from the optical fiber  10  of the first embodiment in that the minimum refractive index Δ2min of the inner cladding layer  12  is adjusted to be greater than the refractive index Δ3 of the outer cladding layer  13 . 
     In the optical fiber  20 , Expression (8) described below is established as with the optical fiber  10  of the first embodiment.
 
0.01%&lt;|Δ2min−Δ3|&lt;0.03%  (8)
 
     The absolute value of the difference between the Δ2min and Δ3 is adjusted to be in the range of Expression (8) described above, and thus, the mode field diameter (MFD) is able to be optimized, the connection loss at the time of being connected to the other optical fiber is able to be suppressed to be low, and the bending loss is able to be reduced. 
     The outer circumference radius r1 of the core  1 , the outer circumferential radius r2 of the inner cladding layer  12 , and the outer circumferential radius r3 of the outer cladding layer  13  have relationships denoted by Expressions (9) and (10) described below, as with the optical fiber  10  of the first embodiment.
 
 r 1&lt; r 2&lt; r 3  (9)
 
0.2≦ r 1/ r 2≦0.5  (10)
 
     r1/r2 is adjusted to be greater than or equal to 0.2, and thus the mode field diameter is able to be optimized, the connection loss at the time of being connected to the other optical fiber is able to be suppressed to be low, and the bending loss is able to be reduced. 
     In the optical fiber  20 , a cable cut-off wavelength λcc (i.e., a cut-off wave length λc 22m  of 22 m) is adjusted to be less than or equal to 1260 nm, as with the optical fiber  10  of the first embodiment. 
     In addition, the mode field diameter (MFD) at a wavelength of 1310 nm is greater than or equal to 8.6 μm and less than or equal to 9.5 μm. 
     In the optical fiber  20 , it is preferable that the loss increase at a wavelength of 1550 nm at the time of winding the optical fiber  20  around a cylindrical mandrel having a diameter of 15 mm 10 times be less than or equal to 0.25 dB. In addition, it is preferable that the loss increase at a wavelength of 1625 nm at the time of winding the optical fiber  20  around the cylindrical mandrel having a diameter of 15 mm 10 times be less than or equal to 1.0 dB. 
     The core  1 , for example, is able to be configured of silica glass of which the refractive, index increases by adding a dopant such as germanium (Ge). 
     The inner cladding layer  2 , for example, is able to be configured of pure silica glass, in the inner cladding layer  2 , for example, the refractive index may be adjusted by adding a dopant such as chlorine (Cl). 
     The outer cladding layer  3 , for example, is able to be configured of pure silica glass. The outer cladding layer  3 , for example, may be configured of silica glass of which the refractive index decreases by adding a dopant such as fluorine (F). 
     The optical fiber  20  is able to be manufactured by a modified chemical vapor deposition method, a plasma chemical vapor deposition method, a vapor-phase axial deposition method, an outside vapor deposition method, and the like, as with the optical fiber  10  of the first embodiment. 
     For example, in a case where the modified chemical vapor deposition method is adopted, the optical fiber preform is able to be prepared as follows. 
     A glass deposition layer which becomes the inner cladding layer  2  is formed on the inside of a silica glass tube (for example, a silica, glass tube containing a dopant such as fluorine (F)) which becomes the outer cladding layer  3  by using a raw material such as pure silica glass. 
     Next, a glass deposition layer which becomes the core  1  is formed on the inside of the glass deposition layer, for example, by using a raw material, containing a dopant such as germanium (Ge). Furthermore, the core  1  is able to be formed by using a core rod which is separately prepared. 
     The silica glass tube in which the glass deposition, layer is formed, becomes the optical fiber preform through a transparency step, a solidification step, and the like. The optical fiber preform is subjected to fiber drawing, and thus, the optical fiber  20  shown in  FIG. 3  is able to be obtained. 
     In the optical fiber  20 , a difference in the refractive indices between the inner cladding layer  12  and the outer cladding layer  13  is in the range described above, and a ratio of the outer circumferential radius of the core  1  and the outer circumferential radius of the inner cladding layer  12  is in the range described above, and thus, the connection loss at the time of being connected to the other optical fiber is able to be suppressed to be low, and the bending loss is able to be reduced. 
     In the optical fiber  20 , the manufacturing method of the related art is able to be used without being considerably changed, and thus, the optical fiber  20  is able to be easily manufactured, and the manufacturing costs are able to be made low. 
     As described above, the preferred embodiments of the present invention have been described, but the second embodiment and the third embodiment are examples of the present invention, and addition, omission, substitution, and other changes are able to be performed without departing from the range of the present invention. 
     For example, in the optical fibers  10  and  20  shown in  FIG. 1  and  FIG. 3 , the clads  4  and  14  are formed of two cladding layers (the inner cladding layer and the outer cladding layer), and the cladding may include layers other than the inner cladding layer and the outer cladding layer. 
     Third Embodiment 
       FIG. 5  shows a schematic configuration of an optical fiber  30  according to a third embodiment of the present invention. 
     The optical fiber  30  includes a core  21  disposed on the center portion, and a cladding  25  disposed on the outer circumference side (the outer circumference) of the core  21  to be concentric with the core  21 . 
     The cladding  25  includes an inner cladding portion  22  adjacent to the outer circumference side (the outer circumference) of the core  21 , a trench  23  formed to be adjacent to the outer circumference side (the outer circumference) of the inner cladding portion  22 , and an outer cladding portion  24  formed on the outer circumference side (the outer circumference) of the trench  23 . 
       FIG. 6  schematically shows a refractive hides profile of the optical fiber  30 . 
     The refractive index of the core  21  is defined as Δ1, and the maximum refractive index of the core  21  is defined as Δ1max. 
     The refractive index of the inner cladding portion  22  is defined as Δ2, and the minimum refractive index of the inner cladding portion  22  is defined as Δ2min. 
     The refractive index of the trench  23  is defined as Δ3, and the minimum refractive index of the trench  23  is defined as Δ3min. 
     The refractive index of the outer cladding portion  24  is defined as Δ4. 
     The maximum refractive index Δ1max of the core  21  is the refractive index of the core  21  which is maximized in a diameter direction range from the center of the core  21  to the outer circumference of the core  21 . In the refractive index profile shown in  FIG. 6 , the refractive index Δ1 of the core  21  is constant without depending on the position of the diameter direction, and thus, the refractive index Δ1 is identical to the maximum refractive index Δ1max in the entire range. 
     The minimum refractive index Δ2min of the inner cladding portion  22  is the refractive index of the inner cladding portion  22  which is minimized in a diameter direction range from the inner circumference of the inner cladding portion  22  to the outer circumference of the inner cladding portion  22 . In the refractive index profile shown in  FIG. 6 , the refractive index Δ2 of the inner cladding portion  22  is constant without depending on the position of the diameter direction, and thus, the refractive index Δ2 is identical to the minimum refractive index Δ2min in the entire range. 
     The minimum refractive index Δ3min of the trench  23  is the refractive index of the trench  23  which is minimized in a diameter direction range from the inner circumference of the trench  23  to the outer circumference of the trench  23 . In the refractive index profile shown in  FIG. 6 , the refractive index Δ3 of the trench  23  is constant without depending on the position of the diameter direction, and thus, the refractive index Δ3 is identical to the minimum refractive index Δ3min in the entire range. 
     In the optical fiber  30 , Expression (11) described below is established.
 
Δ1max&gt;Δ2&gt;Δ3min  (11)
 
     As shown in Expression (11), the maximum refractive index Δ1max of the core  21  is greater than the refractive index Δ2 of the inner cladding portion  22 . 
     The refractive index Δ2 of the inner cladding layer  22  is greater than Δ3min of the trench  23 . 
     In the optical fiber  30 , Expression (12) described below is further established.
 
Δ1max&gt;Δ4&gt;Δ3min  (12)
 
     As shown, in Expression (12), the maximum refractive index Δ1max of the core  21  is greater than the refractive index Δ4 of the outer cladding portion  24 . 
     The refractive index Δ4 of the outer cladding portion  24  is greater than Δ3min of the trench  23 . 
     In the optical fiber  30 , Expression (13) described below is further established.
 
0.01%&lt;(Δ4−Δ3min)&lt;0.03%  (13)
 
     Expression (13) indicates dial a difference between the refractive index Δ4 of the outer cladding portion  24  and the minimum refractive index Δ3min of the trench  23  is greater than 0.01% and less than 0.03%. 
     When the difference between Δ4 and Δ3min is excessively small, the bending loss may not be sufficiently reduced. In contrast, the difference between Δ4 and Δ3min is excessively large, the mode field diameter decreases, and the connection loss at the time of being connected to the other optical fiber (for example, a general single mode optical fiber (S-SMF)) may increase. 
     In the optical fiber  30 , the difference between Δ4 and Δ3min is in a range of greater than 0.01%, and thus, the bending loss is able so be reduced. In addition, the difference between Δ4 and Δ3min is less than 0.03%, and thus, the mode field diameter (MFD) is able to be optimized, and the connection loss at the time of being connected to the other optical fiber is able to be suppressed to be low. 
     The outer circumferential radii of the core  21 , the inner cladding portion  22 , the trench  23 , and the outer cladding portion  24  are respectively r1, r2, r3, and r4. 
     The outer circumference radius r1 of the core  21 , the outer circumferential radius r2 of the inner cladding layer  22 , the outer circumferential radius r3 of the trench  23 , and the outer circumferential radius r4 of the outer cladding layer  24  have a relationship denoted by Expression (14) described below.
 
 r 1≦ r 2&lt; r 3&lt; r 4  (14)
 
     A ratio r2/r1 of the outer circumferential radios r2 of the inner cladding layer  22  to the outer circumference radius r1 of the core  21  is in a range denoted by Expression (15) described below.
 
1≦ r 2/ r 1≦5  (15)
 
     When r2/r1 is excessively small, the bending loss may increase. In contrast, when r2/r1 is excessively large, the mode field diameter decreases, and the connection loss at the time of being connected to the other optical fiber (for example, SSMF) may increase. 
     In the optical fiber  30 , r2/r1 is greater than or equal to 1, and thus, it is possible to reduce the bending loss. r2/r1 is less than or equal to 5, the mode field diameter is able to be optimized, and the connection loss at the time of being connected to the other optical fiber is able to be suppressed to be low. 
     A ratio r3/r2 of the outer circumferential radius r3 of the trench  23  to the outer circumferential radius r2 of the inner cladding layer  22  is in a range denoted by Expression (16) described below.
 
1&lt; r 3/ r 2≦2  (16)
 
     When r3/r2 is excessively small, the bending loss may increase. In contrast, when r3/r2 is excessively large, the mode field diameter decreases, and the connection loss at the time of being connected to the other optical fiber (for example, SSMF) may increase. 
     In the optical fiber  30 , r3/r2 is greater than 1, and thus, it is possible to reduce the bending loss. r3/r2 is less than or equal to 2, and thus, the mode field diameter is able to be optimized, and the connection loss at the time of being connected to the other optical fiber is able to be suppressed to be low. 
     In the optical fiber  30 , the cut-off wavelength λcc is less than or equal to 1260 nm. 
     That is, Expression (17) described below is established.
 
λ cc≦ 1260 nm  (17)
 
     Accordingly, the regulation of ITU-T Recommendation G.652 is able to be satisfied. 
     The cut-off wavelength λcc, for example, is able to be measured by a measurement method disclosed in ITU-T Recommendation G.650. 
     In the optical fiber  30 , the refractive index and the outer circumferential radius described above are adjusted, and thus the mode field diameter (MFD) at a wavelength of 1310 nm is greater than or equal to 8.6 μm and less than or equal to 9.5 μm. That is. Expression (18) described below is established.
 
8.6 μm≦MFD≦9.5 μm  (18)
 
     The mode field diameter is in the range of Expression (18), and thus, the connection loss at the time of being connected to the other optical fiber (for example, SSMF) is able to be suppressed to be low. 
     In the optical fiber  30 , the mode field diameter is in the range of Expression (18), and thus, the regulation of ITU-T G.652 is satisfied. 
     In the optical fiber  30 , it is preferable that the loss increase at a wavelength of 1550 nm at the time of winding, the optical fiber  30  around a cylindrical mandrel having a diameter of 15 mm 10 times be less than, or equal to 0.25 dB. 
     In addition, it is preferable that the loss increase at a wavelength of 1625 nm at the time of winding the optical fiber  30  around the cylindrical mandrel having a diameter of 15 mm 10 times be less than or equal to 1.0 dB. 
     The core  21 , for example, is able to be configured of silica glass of which the refractive index increases by adding a dopant such as germanium (Ge). 
     The inner cladding layer  22  and the trench  23 , for example, are able to be configured of silica glass of which the refractive index decreases by adding a dopant such as fluorine (F). 
     The outer cladding layer  24 , for example, is able to be configured of pure silica glass. In the outer cladding layer  24 , the refractive index may be adjusted by adding a dopant (for example, Ge, F, and the like). 
     Each layer configuring the optical fiber  30  is able to be formed by a known method such as a modified chemical vapor deposition method, a plasma chemical vapor deposition method, a vapor-phase axial deposition method, and an outside vapor deposition method, or a combination thereof. 
     For example, in a case where the modified chemical vapor deposition method is adopted, the optical fiber preform is able to be prepared as follows. 
     A glass deposition layer which becomes the trench  23  is formed on the inside of the silica glass tube (for example, a glass tube formed of pare silica glass) which becomes the outer cladding layer  24 , for example, by using a raw material containing a dopant such as fluorine (F). 
     A glass deposition layer which becomes the inner cladding layer  22  is formed on the inside of the glass deposition layer, for example, by using a raw material containing a dopant such as fluorine (F). 
     The refractive index of the trench  23  and the inner cladding layer  22  is able to be adjusted by the added amount of the dopant. 
     Next, a glass deposition layer which becomes the core  21  is formed on the inside of the glass deposition layer, for example, by using a raw material containing a dopant such as germanium (Ge). Furthermore, the core  21  is able to be formed by using a core rod which is separately prepared. 
     The silica glass tube in which the glass deposition layer is formed becomes the optical fiber preform through a transparency step, a solidification step, and the like. The optical fiber preform is subjected to fiber drawing, and thus, the optical fiber  30  shown in  FIG. 5  is able to be obtained. 
     The chemical vapor deposition method is preferable from the viewpoint of accurately adjusting the refractive index profile by adding a dopant. 
     The vapor-phase axial deposition method and the outside vapor deposition method are also able to be applied to manufacture the optical fiber  30 . The vapor-phase axial deposition method and the outside vapor deposition method have advantages such as high productivity. 
     In the optical fiber  30  a difference in the refractive indices between the trench  23  and the outer cladding layer  24  is in the range described above (refer to Expression (13), and a ratio of the outer circumferential radius of the core  21 , the outer circumferential radius of the inner cladding layer  22 , and the outer circumferential radius of the trench  23  is in the range described above (refer to Expressions (15) to (17)), and thus, the connection loss at the time of being connected to the other optical fiber is able to be suppressed to be low, and the bending loss is able to be reduced. 
     It has been known that the refractive index of the cladding in a portion close to the core considerably affects optical properties of the optical fiber, but as a result of intensive studies of the present inventor, a refractive index profile has been found in which the bending loss is able to be reduced without decreasing the mode field diameter. 
     By adopting the refractive index profile, the optical fiber  30  has technical meaning from the viewpoint of making suppression of the connection loss at the time of being connected to the other optical fiber and a reduction in the bending loss compatible. 
     In the optical fiber  30 , the difference in the refractive indices between the trench  23  and the outer cladding layer  24  is small, and thus, the refractive index of the trench  23  and the outer cladding layer  24  is able to be easily and accurately adjusted by using the manufacturing method of the related art (for example, a general manufacturing method of SSMF) without considerably changing the method. 
     In addition, the difference in the refractive indices between the trench  23  and the outer cladding layer  24  is small, and thus, constraint based on the manufacturing method decreases. For example, not only the chemical vapor deposition method which is considered to be suitable for adjusting the refractive index profile, but also the vapor-phase axial deposition method, and the outside vapor deposition method are able to be adopted. 
     Accordingly, the optical fiber  30  is able to be easily manufactured, and manufacturing costs are able to be made low. 
     In the optical fiber  30 , the difference in the refractive indices between the trench  23  and the outer cladding layer  24  is small, and thus, the added amount of the dopant such as fluorine (F) for forming the trench  23  is able to be reduced. 
     Raw material gas (for example, SiF 4 ) used in a dope such as fluorine (F) is expensive, and thus, raw material costs are able to be suppressed and manufacturing costs are able to be made low by reducing the added amount of the dopant. 
     As described above, the outer circumference radii r1 to r4 of the core  21 , the inner cladding layer  22 , the trench  23 , and the outer cladding layer  24  have a relationship denoted by Expression (14).
 
 r 1≦ r 2&lt; r 3&lt; r 4  (14)
 
     In the optical fiber  30  shown in  FIG. 5  and  FIG. 6 , r1, r2, and r3 are values different from each other, but the present invention includes a case of r1=r2 and r2≠r3. 
       FIG. 7  is a diagram of a refractive index profile of an optical fiber of a fifth embodiment of the present invention, and shows a case of r1=r2 and r2≠r3. 
     In the optical fiber, r1 is identical to r2, and thus the cladding  25  is formed only of the trench  23  and the outer cladding layer  24  formed on the outer circumference side of the trench  23 . 
     As described above, the fourth embodiment and the fifth embodiment of the present invention have been described, but the fourth embodiment and the fifth embodiment are examples of the present invention, and addition, omission, substitution, and other changes are able to be performed without departing from the range of the present invention. 
     For example, in the optical fiber  30  shown in  FIG. 5 , the cladding  25  is formed of three lasers (the inner cladding layer, the trench, and the outer cladding layer), but the cladding may include other layers.