YTTERBIUM-DOPED OPTICAL FIBER Technical Field [0001] The present invention relates to an ytterbium-doped optical fiber for light amplification to which ytterbium is doped. More specifically, the present invention relates to an ytterbium-doped optical fiber in which deterioration in output, known as "photodarkening", and non-linear optical effects are inhibited. Priority is claimed on Japanese Patent Application No. 2008-283165, filed on November 4, 2008, the contents of which are incorporated herein by reference. Background Art [0002] A fiber for light amplification has a configuration in which a rare-earth element or the like is doped to a core and/or a clad of an optical fiber having an axisymmetric waveguide structure, and is used as a photoactive medium for fiber amps, fiber lasers or the like. In particular, a fiber laser using an Yb-doped optical fiber containing ytterbium (Yb) as a rare-earth element as an optical fiber for light amplification can obtain output light with high beam quality and high power output. Further, such a fiber laser has an oscillation wavelength of output light of about 1 μm which is substantially equal to that of Nd-YAG, one kind of conventional high output laser. For this reason, an Yb-doped optical fiber is expected to be practically applied as a laser medium for high output light sources applied to material processing such as welding, marking and cutting. [0003] In fiber-type optical amplifiers or fiber lasers, a phenomenon called "photodarkening" is known. This is a phenomenon in which the transmission loss of optical fibers caused by excited light or signal light propagating in fibers is increased. When such transmission loss increases, the gain of the optical fiber, in which a rare-earth element is doped and which is an amplification media, deteriorates. That is, the output of fiber-type optical amplifiers or fiber lasers is deteriorated over time, thus causing problems from the viewpoint of reliability. [0004] Generally, in a case where high output laser light is propagated to optical fibers, light of a wavelength different from the laser light is generated and amplified, whereby it is known that so-called "stimulated Raman scattering" is generated. As a result, problems, such as deterioration in the strength of the propagated laser output light and widening of the spectrum range of the laser light occur. That is, it is preferable that optical fibers are designed to prevent the appearance of non-linear optical effects, exemplified by stimulated Raman scattering. [0005] Several methods for inhibiting photodarkening have been disclosed to date. For example, a method for inhibiting photodarkening by applying a specific manufacturing method called "direct nanoparticle deposition (DND)" has been disclosed (for example, see Non-Patent Document 1). [0006] Further, a method for inhibiting photodarkening by adding a high concentration of aluminum to optical fibers has been disclosed (for example, see Non-Patent Document 2). Further, a method for inhibiting photodarkening by adding a high concentration of phosphorus to optical fibers has been disclosed (for example, see Non-Patent Document 3). [0007] Further, the following information has been disclosed in regard to the refractive index of silica glass. It is disclosed that an increase in refractive index of the core can be inhibited by adding a combination of aluminum oxide (A1203) and diphosphorus pentoxide (P2O5) to a preform made of silica glass (Si02) (for example, see Non-Patent Document 4 and 5). In particular, it is disclosed that as the concentrations (mol%) of aluminum oxide and diphosphorus pentoxide added are approximated to equal amounts, the refractive index approximates the refractive index of pure silicon dioxide. [0008] Further, an optical fiber, in which rare-earth elements, germanium, aluminum and phosphorus are added to a core thereof, is disclosed in Patent Document 1. This Patent Document 1 discloses that the difference in refractive index between the core and the clad is decreased and recrystallization of rare-earth elements is inhibited by adding these elements to the core. [Reference] [Patent Document] [0009] [Patent Document 1] Japanese Unexamined Patent Application, First Publication No. Hll-112070 [Non Patent Document] [0010] [Non-Patent Document 1] S. Tammela et al., The Potential of Direct Nanoparticle Deposition for the Next Generation of Optical Fibers, The Proceeding of SPIE Photonics West 2006, Vol. 6116-16 (2006) [Non-Patent Document 2] T. Kitabayashi et. al., Population Inversion Factor Dependence of Photodarkening of Yb-doped Fibers and Its Suppression by Highly Aluminum Doping, The Proceedings of OFC 2006, OThC5(2006) [Non-Patent Document 3] M. Engholm et. al., Preventing photodarkening in ytterbium-doped high power fiber laser; correlation to the UV-transparency of the core glass, The Proceeding of Optics Express Vol. 16, 1260-1268 (2008) [Non-Patent Document 4] D. S. Lipatov et. al., Optical Properties of Highly Al203and P2O5 Doped Silica Hosts for Large Mode Area Fiber Lasers and Amplifiers, the proceedings of ECOC2007, Poster Session P020. [Non-Patent Document 5] DiGIOVANNI et. al., Structure and properties of silica containing aluminum and phosphorus near the A1P04 join, Journal of Non-Crystalline Solids 113 (1989) 58-64. Disclosure of the Invention Problem that the Invention is to solve [0011] However, in accordance with the method disclosed in Non-Patent Document 1, photodarkening can be reliably inhibited, but cannot fundamentally realize sufficient dehydration. For this reason, there is a problem in that the transmission loss caused by hydroxyl groups is great. Further, the method has the difficulty of increasing the size of preforms and of a low yield. Accordingly, the method is not good for reducing optical fiber manufacturing costs. [0012] The method disclosed in Non-Patent Document 2 requires the addition of a large amount of aluminum in order to sufficiently inhibit photodarkening. As a result, there is a problem in that the refractive index of the optical fiber core increases. Optical fibers, to which rare-earth elements are added, used in fiber-type optical amplifiers or fiber lasers are generally used under the conditions of single mode transmission or a low number of modes of transmission. Accordingly, in a case where the refractive index of the core is high, it is necessary to make the diameter of the core relatively small. A small core diameter means that the effective core cross-sectional area (Aeff) of the optical fiber becomes small and thus the power density of the propagating light becomes high, whereby non-linear optical effects are liable to occur. That is, wavelength conversion occurs due to the non-linear optical effects and there is a problem in that the desired output light cannot be obtained. [0013] The method disclosed in Non-Patent Document 3 requires the addition of a large amount of phosphorus in order to sufficiently inhibit photodarkening. However, since phosphorus is a dopant for increasing a refractive index, the refractive index of the core increases. Accordingly, when an attempt is made to transmit light in single mode transmission or a low number of modes of transmission using the optical fiber obtained by this method, there is a problem in that the non-linear optical effects mentioned above readily occur. [0014] The refractive index of an optical fiber which contains aluminum and phosphorus and contains silica glass as a main component is reviewed in Non-Patent Document 4 and 5 in detail. However, the refractive index of an optical fiber which contains ytterbium, aluminum and phosphorus and contains silica glass as a main component is not reviewed in Non-Patent Document 4 and 5. Meanwhile, it is known that optical fibers in which the cores contain ytterbium and other rare-earth elements are useful for application in fiber-type optical amplifiers or fiber lasers. [0015] Patent Document 1 does not mention the inhibition of photodarkening. There is a concern that photodarkening cannot be sufficiently inhibited simply by adding the elements to the core in the concentration range mentioned in Patent Document 1. [0016] The present invention has been made in view of the above problems and it is an object to provide ytterbium-doped optical fiber which inhibits photodarkening, as well as suppressing an increase of the refractive index of the core and thus is capable of inhibiting non-linear optical effects. Means for solving the Problem [0017] The present invention adopts the followings approaches to solve the problems and thus accomplish the object. (1) The ytterbium-doped optical fiber of the present invention includes a core containing at least ytterbium, aluminum and phosphorous and a clad surrounding the core, wherein a molar concentration of diphosphorus pentoxide with respect to phosphorus in the core is equal to a molar concentration of aluminum oxide with respect to aluminum in the core, wherein a ratio of a molar concentration of diphosphorus pentoxide with respect to phosphorus in the core to the molar concentration of ytterbium oxide with respect to ytterbium in the core is higher than or equal to 10 and lower than or equal to 30, and wherein a relative refractive index difference between the core and the clad is higher than or equal to 0.05% and lower than or equal to 0.30%. [0018] (2) Preferably, the core and the clad are composed of a glass containing silica glass as a base. [0019] (3) Preferably, assuming the molar concentration of ytterbium oxide in the core is a, a satisfies an equation of 0.05<0.5<0.30. [0020] (4) The ytterbium-doped optical fiber of the present invention includes a core containing at least ytterbium, aluminum and phosphorous and a clad surrounding the core, wherein a ratio of a molar concentration of diphosphorus pentoxide with respect to phosphorus in the core to a molar concentration of ytterbium oxide with respect to ytterbium in the core is higher than or equal to 10 and lower than or equal to 30, wherein a relative refractive index difference between the core and the clad is higher than or equal to 0.05% and lower than or equal to 0.30%, and assuming the molar concentration of ytterbium oxide is a, a molar concentration of aluminum oxide with respect to aluminum in the core is p, and the molar concentration of diphosphorus pentoxide is y, a, (3 and y satisfy an equation of 0.05<(P-y)x0.19+<0.5<0.30 in a case where p>y. [0021] (5) In the case of (4), p and y satisfy an equation of l<(p/y)<3. [0022] (6) The ytterbium-doped optical fiber of the present invention includes a core containing at least ytterbium, aluminum and phosphorous and a clad surrounding the core, wherein a ratio of a molar concentration of diphosphorus pentoxide with respect to phosphorus in the core to a molar concentration of ytterbium oxide with respect to ytterbium in the core is higher than or equal to 10 and lower than or equal to 30, wherein a relative refractive index difference between the core and the clad is higher than or equal to 0.05% and lower than or equal to 0.30%, and assuming the molar concentration of ytterbium oxide is a, a molar concentration of aluminum oxide with respect to aluminum in the core is p, and the molar concentration of diphosphorus pentoxide is y, a, P and y satisfy an equation of 0.05<(y-P)x0.04+a><0.5<0.30, in a case where p < y. [0023] (7) Preferably, in the case of (6), P and y satisfy an equation of 0.56<(p/y) The ytterbium-doped optical fiber (hereinafter, simply referred to as an "Yb-doped optical fiber") of the present invention includes a core and a clad surrounding the core, wherein the core contains at least ytterbium (Yb), aluminum (Al) and phosphorous (P). Further, a ratio of a molar concentration of diphosphorus pentoxide (P2O5) with respect to phosphorus in the core (hereinafter, simply referred to as a "concentration of diphosphorus pentoxide")to a molar concentration of ytterbium oxide (Yb203) with respect to ytterbium in the core (hereinafter, simply referred to as "concentration of ytterbium oxide") is higher than or equal to 10 and lower than or equal to 30. The relative refractive index difference between the core and the clad is higher than or equal to 0.05% and lower than or equal to 0.30%. [0029] Ytterbium is a dopant having a light amplification action. Aluminum is a dopant having an increase action on refractive index and an inhibitory action on crystallization of silica glass. Phosphorous is a dopant having photodarkening inhibitory action and an increase action on refractive index. [0030] Phosphorous in the core has an inhibitory action on photodarkening. However, in a case where the refractive index of the core is a desired low value in an optical fiber in which the core contains only ytterbium and phosphorus, silica glasses are crystallized. For this reason, this optical fiber cannot be used as an optical fiber for light amplification. However, by further adding aluminum to the core, photodarkening can be inhibited and crystallization of silica glasses can be inhibited, even if the refractive index of the core is lowered to a desired level. The reason for the inhibitory action of aluminum in regard to the crystallization of silica glasses is considered to be because ytterbium and phosphorus are dispersed in silica glasses. [0031] The present invention can prevent photodarkening by setting a ratio of a molar concentration of diphosphorus pentoxide (P2O5) with respect to phosphorus in the core to a molar concentration of ytterbium oxide (Yb2O3) with respect to ytterbium in the core within a specific range. [0032] From the aforementioned viewpoints, the ratio of a molar concentration of diphosphorus pentoxide (P2O5) with respect to phosphorus in the core to a molar concentration of ytterbium oxide (Yb203) with respect to ytterbium in the core is preferably higher than or equal to 10 and lower than or equal to 30, more preferably higher than or equal to 15 and lower than or equal to 20. When the molar concentration ratio is less than 10, the amount of loss increase due to photodarkening rapidly increases. On the other hand, when the molar concentration ratio is higher than 30, the background loss value rapidly becomes large. Generally, when the background loss value becomes large, in the case where the Yb-doped optical fiber is applied to a fiber laser, the fiber laser exhibits a deteriorated energy conversion efficiency. [0033] Further, assuming the molar concentration of ytterbium oxide in the core is a, the molar concentration of aluminum oxide with respect to aluminum in the core (hereinafter, simply referred to as "concentration of aluminum oxide") is p, and the molar concentration of diphosphorus pentoxide in the core is y, p=y. In this case, preferably, the equation of 0.05<0.5<0.30 is satisfied, more preferably, the equation of 0.08<0.5<0.20 is satisfied, and most preferably, the equation of 0.10<0.5<0.15 is satisfied. In the equations, "0.5" is a contribution ratio (variation ratio) in which 1 mol% ytterbium oxide contributes to an increase in the refractive index of the core. [0034] Ytterbium oxide increases the refractive index of the core in proportion to the molar concentration. In this regard, aluminum oxide and diphosphorus pentoxide together offset an increase in the refractive index of core. Accordingly, in the case where the molar concentration (p) of aluminum oxide in the core is equal to the molar concentration (y) of diphosphorus pentoxide in the core (P=y), only ytterbium oxide varies the refractive index of the core. Accordingly, when a, P and y satisfy the equation of 0.05<0.5<0.30 in a case where p=y, a great effect whereby photodarkening as well as crystallization of glasses can be efficiently inhibited can be obtained. When a><0.5 is lower than 0.05, that is, when the difference in refractive index between the core and the clad is lower than 0.05, bend loss or loss due to external stress to the optical fiber is great and is not practical. Meanwhile, when a><0.5 is higher than 0.30, that is, when the difference in refractive index between the core and the clad is higher than 0.30, due to the exhibition of non-linear optical effects exemplified by stimulated Raman scattering, wavelength conversion is apt to occur and the desired output light cannot be obtained. [0035] Further, assuming the molar concentration of ytterbium oxide in the core is a, the molar concentration of aluminum oxide in the core is p, and the molar concentration of diphosphorus pentoxide in the core is y, the equation of p>y is possible. In this case, preferably, the equation of 0.05<(P-y)x0.19+a><0.5<0.30 is satisfied, and more preferably, the equation of 0.08<(P-y)x0.19+ax0.5<0.20 is satisfied. In the equations, "0.5" is a contribution ratio (variation ratio) in which 1 mol% ytterbium oxide contributes to an increase in the refractive index of the core and "0.19" is a contribution ratio (variation ratio) in which 1 mol% aluminum oxide contributes to an increase in the refractive index of the core. [0036] In the case where the molar concentration (P) of aluminum oxide in the core is higher than the molar concentration (y) of diphosphorus pentoxide in the core (p>y), the refractive index of the core increases in proportion to the excess molar concentration of aluminum oxide. In addition, ytterbium oxide also increases the refractive index of the core. Accordingly, the increase in the refractive index of the core due to the excess aluminum oxide and ytterbium oxide satisfies an additive property. Accordingly, when a, p and y satisfy the equation of 0.05<(p-y)x0.19+ax0.5<0.30 in a case where p>y, a great effect whereby photodarkening as well as crystallization of glasses can be efficiently inhibited can be obtained. When (p-y)x0.19+ax0.5 is lower than 0.05, that is, when the difference in refractive index between the core and the clad is lower than 0.05, bend loss or loss due to external stress to the optical fiber is great and is not practical. Meanwhile, when (P-y)x0.19+ax0.5 is higher than 0.30, that is, when the difference in refractive index between the core and the clad is higher than 0.30, due to the exhibition of non-linear optical effects exemplified by stimulated Raman scattering, wavelength conversion is apt to occur and the desired output light cannot be obtained. In this case, preferably, β and y satisfy the equation of K(p/y)<3. When p/y is higher than 3, in some cases, the relative refractive index difference between the core and the clad is higher than 0.30. For this reason, the desired output light mentioned above cannot be obtained. [0037] Further, assuming the molar concentration of ytterbium oxide in the core is a, the molar concentration of aluminum oxide in the core is p, and the molar concentration of diphosphorus pentoxide in the core is y, the equation of P<0.5<0.30. 4. An ytterbium-doped optical fiber comprising a core containing at least ytterbium, aluminum and phosphorous and a clad surrounding the core, wherein a ratio of a molar concentration of diphosphorus pentoxide with respect to phosphorus in the core to a molar concentration of ytterbium oxide with respect to ytterbium in the core is higher than or equal to 10 and lower than or equal to 30, wherein a relative refractive index difference between the core and the clad is higher than or equal to 0.05% and lower than or equal to 0.30%, and assuming the molar concentration of ytterbium oxide is a, a molar concentration of aluminum oxide with respect to aluminum in the core is p, and the molar concentration of diphosphorus pentoxide is y, a, P and y satisfy an equation of 0.05<(P-y)x0.19+ax0.5<0.30 in a case where p>y. 5. The ytterbium-doped optical fiber according to claim 4, wherein p and y satisfy an equation of l<(p/y)<3. 6. An ytterbium-doped optical fiber comprising a core containing at least ytterbium, aluminum and phosphorous and a clad surrounding the core, wherein a ratio of a molar concentration of diphosphorus pentoxide with respect to phosphorus in the core to a molar concentration of ytterbium oxide with respect to ytterbium in the core is higher than or equal to 10 and lower than or equal to 30, wherein a relative refractive index difference between the core and the clad is higher than or equal to 0.05% and lower than or equal to 0.30%, and assuming the molar concentration of ytterbium oxide is a, a molar concentration of aluminum oxide with respect to aluminum in the core is P, and the molar concentration of diphosphorus pentoxide is y, a, P and y satisfy an equation of 0.05<(y-p)x0.04+ax0.5<0.30, in a case where p < y. 7. The ytterbium-doped optical fiber according to claim 6, wherein P and y satisfy an equation of 0.56<(p/y)