Optical fiber and optical transport system

Abstract

The present invention relates to an optical fiber which can improve OSNR in an optical transmission system in which Raman amplification and an EDFA are combined. With respect to the optical fiber, a predetermined conditional formula is satisfied by an effective area Aeff.sub.1450 [m.sup.2] at a wavelength of 1450 nm, a transmission loss .sub.1450 [/km] at a wavelength of 1450 nm, and a transmission loss .sub.1550.sub._.sub.dB [dB/km] at a wavelength of 1550 nm. Further, with respect to the optical fiber, another predetermined conditional formula is satisfied by an effective area Aeff.sub.1550 [m.sup.2] at a wavelength of 1550 nm, and a transmission loss .sub.1550 [/km] at a wavelength of 1550 nm.

Claims

1. An optical transmission system comprising: an optical fiber transmission line using an optical fiber, the optical fiber comprising: a core extending along a predetermined axis; and a cladding provided on an outer periphery of the core, wherein each of the core and the cladding is configured to satisfy the following formula: $\frac{0.44}{{}_{1550\_dB}}<{\mathrm{Aeff}}_{1450}.Math.{}_{1450}<\frac{22}{{}_{1550\_dB}.Math.100-12}$ where Aeff.sub.1450 [m.sup.2] is an effective area at a wavelength of 1450 nm; .sub.1450 [/km] is a transmission loss at a wavelength of 1450 nm; and .sub.1550 dB [dB/km] is a transmission loss at a wavelength of 1550 nm; an Er-doped optical fiber amplifier which is configured to amplify signal light transmitted through the optical fiber transmission line; and a Raman amplifier which is configured to Raman-amplify the signal light transmitted through the optical fiber transmission line, wherein the following formula is satisfied: $\frac{0.11}{{\mathrm{Aeff}}_P.Math.{}_P}.Math.P_{\mathrm{Pump}}<{}_{\mathrm{SdB}}.Math.L-\frac{0.11}{{\mathrm{Aeff}}_P.Math.{}_P}.Math.P_{\mathrm{Pump}}<0.19L-0.028P_{\mathrm{Pump}}-1$ where Aeff.sub.p [m.sup.2] is an effective area of the optical fiber at a wavelength of pumping light for Raman amplification; .sub.p [/km] is a transmission loss of the optical fiber transmission line at the wavelength of the pumping light for Raman amplification; .sub.SdB [dB/km] is a transmission loss of the optical fiber transmission line at a signal light wavelength; L is a span length [km] of the optical fiber transmission line; and P.sub.pump [mW] is a pumping light power.

2. The optical fiber according to claim 1, wherein each of the core and the cladding is configured to satisfy the following formula:
Aeff.sub.1150.Math..sub.1150>2.2 where Aeff.sub.1550 [m.sup.2] is an effective area at a wavelength of 1550 nm; and .sub.1550 [km] is a transmission loss at a wavelength of 1550 nm.

3. The optical fiber according to claim 1, wherein the transmission loss .sub.1550.sub._.sub.dB at a wavelength of 1550 nm is 0.17 dB/km or less.

4. The optical fiber according to claim 1, wherein an effective area Aeff.sub.1550 at a wavelength of 1550 nm is 70 m.sup.2 to 160 m.sup.2.

5. The optical fiber according to claim 1, wherein a transmission loss .sub.1450.sub._.sub.dB at a wavelength of 1450 nm is 0.19 dB/km to 0.22 dB/km.

6. The optical fiber according to claim 1, wherein the effective area A.sub.eff1450 at a wavelength of 1450 nm is 60 m.sup.2 to 140 m.sup.2.

7. The optical fiber according to claim 1, wherein a relative refractive index difference of the core with respect to pure silica is 0.1% to +0.1%.

8. The optical fiber according to claim 7, wherein a relative refractive index difference of the core with respect to a reference area of the cladding is 0.18% to 0.45%, and a diameter of the core is 9 m to 15 m.

9. The optical fiber according to claim 1, wherein a fiber cutoff wavelength is 1600 nm or less.

10. The optical fiber according to claim 9, wherein the cladding includes: an inner cladding surrounding the outer peripheral surface of the core; and an outer cladding surrounding an outer peripheral surface of the inner cladding, wherein a refractive index of the outer cladding is smaller than a refractive index of the core and is greater than a refractive index of the inner cladding.

11. The optical fiber according to claim 10, wherein a ratio b/a of a diameter 2a of the core to an outer diameter 2b of the inner cladding is 3.0 to 5.0.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) FIGS. 1A and 1B are diagrams showing an configuration of an optical transmission system 1 which uses Raman amplification and an EDFA in combination and showing a signal light power diagram in one span.

(2) FIG. 2 is a table which summarizes specifications of each of samples of an optical fiber according to a present embodiment and comparative examples.

(3) FIG. 3 is a table which summarizes specifications of each of the samples of an optical fiber according to the present embodiment and the comparative examples.

(4) FIG. 4 is a table which summarizes specifications of each of the samples of an optical fiber according to the present embodiment and the comparative examples.

(5) FIG. 5 is a diagram showing an example of a refractive index profile applicable to an optical fiber according to the present embodiment.

(6) FIG. 6 is a diagram showing another example of a refractive index profile applicable to an optical fiber according to the present embodiment.

(7) FIGS. 7A to 7F are diagrams showing a modified example of a refractive index profile of a core of an optical fiber according to the present embodiment.

(8) FIG. 8 is a graph showing dependence of each of Aeff.sub.1450.Math..sub.1450, 22/(.sub.1550.sub._.sub.dB10012), and 0.44/.sub.1550.sub._.sub.dB on .sub.1450.sub._.sub.dB under predetermined conditions.

(9) FIG. 9 is a graph showing dependence of each of Aeff.sub.1450.Math..sub.1450, 22/(.sub.1550.sub._.sub.dB10012), and 0.44/.sub.1550.sub._.sub.dB on Aeff.sub.1450 under predetermined conditions.

DESCRIPTION OF EMBODIMENTS

Description of an Embodiment of the Present Invention

(10) First, practical aspects of the present invention will be listed and described.

(11) As a first aspect of the present embodiment, the optical fiber includes a core extending along a predetermined axis and a cladding provided on an outer periphery of the core. In particular, each of the core and the cladding is configured to satisfy the above Formula (1), when an effective area at a wavelength of 1450 nm is Aeff.sub.150 [m.sup.2], a transmission loss at a wavelength of 1450 nm is .sub.1450 [/km], and a transmission loss at a wavelength of 1550 nm is .sub.1550.sub._.sub.dB [dB/km]. Note that the suffix dB of the transmission loss represents decibel display [dB/km] (.sub.dB=10log.sub.10(e)) of the transmission loss [/km].

(12) As a second aspect applicable to the above first aspect, each of the core and the cladding may be configured to satisfy the following Formula (2), when the effective area at a wavelength of 1550 nm is Aeff.sub.1550 [m.sup.2], and the transmission loss at a wavelength of 1550 nm is .sub.1550 [/km].
Aeff.sub.1550.Math..sub.1550>2.2(2)

(13) As a third aspect applicable to at least any one of the above first and second aspects, it is preferable that a transmission loss .sub.1550.sub._.sub.dB at a wavelength of 1550 nm be 0.17 dB/km or less. Further, as a fourth aspect applicable to at least any of one the above first to third aspects, it is preferable that an effective area Aeff.sub.1550 at a wavelength of 1550 nm be 70 m.sup.2 to 160 m.sup.2.

(14) As a fifth aspect applicable to at least any one of the above first to fourth aspects, it is preferable that a relative refractive index difference of the core with respect to pure silica be 0.1% to +0.1%.

(15) As a sixth aspect applicable to at least any one of the above first to fifth aspects, it is preferable that a transmission loss .sub.1450.sub._.sub.dB at a wavelength of 1450 nm is 0.19 to 0.22 dB/km or less. Further, as a seventh aspect applicable to at least any one of the above first to sixth aspects, it is preferable that an effective area Aeff.sub.1450 at a wavelength of 1450 nm be 60 m.sup.2 to 140 m.sup.2.

(16) As an eighth aspect applicable to at least any one of the above first to seventh aspects, it is preferable that a relative refractive index difference of the core with respect to a reference area of the cladding be 0.18 to 0.45% and that a diameter of the core be 9 m to 15 m. Note that, in the present specification, when the cladding is configured with a single layer, the whole cladding is the reference area; however, when the cladding is configured with a plurality of layers, the outermost layer of the layers constituting the cladding is defined as the reference area.

(17) As a ninth aspect applicable to at least any one of the above first to eighth aspects, it is preferable that a fiber cutoff wavelength be 1600 nm or less. Further, as a tenth aspect applicable to at least any one of the above first to ninth aspects, the cladding may be configured, as described above, with an inner cladding surrounding an outer periphery of the core and an outer cladding surrounding the outer periphery of the inner cladding. In this configuration, it is preferable that a refractive index of the outer cladding be smaller than the refractive index of the core and be greater than the refractive index of the inner cladding. As an eleventh aspect applicable to at least any one of the above first to tenth aspects, it is preferable that the ratio b/a of a diameter 2a of the core to an outer diameter 2b of the inner cladding be 3.0 to 5.0.

(18) Further, an optical transmission system according to the present embodiment includes: an optical fiber transmission line using an optical fiber according to any of the above first to eleventh aspects; an Er-doped optical fiber amplifier which is configured to amplify signal light transmitted through the optical fiber transmission line; and a Raman amplifier which is configured to Raman-amplify the signal light transmitted through the optical fiber transmission line. In particular, the optical transmission system satisfies the following Formula (3), when the effective area of the above optical fiber at a wavelength of the pumping light for Raman amplification is Aeff.sub.P [m.sup.2], the transmission loss of the above optical fiber transmission line at the wavelength of the pumping light for Raman amplification is .sub.P [1/km] ([1/km] and [/km] represent the same unit), a transmission loss of the above optical fiber transmission line at a signal light wavelength is .sub.SdB [dB/km], a span length of the above optical fiber transmission line is L [km], and a power of pumping light for Raman amplification is P.sub.Pump [mW].

(19) $\begin{array}{cc}\frac{0.11}{{\mathrm{Aeff}}_P.Math.{}_P}.Math.P_{\mathrm{Pump}}<{}_{\mathrm{SdB}}.Math.L-\frac{0.11}{{\mathrm{Aeff}}_P.Math.{}_P}.Math.P_{\mathrm{Pump}}<0.19L-0.028P_{\mathrm{Pump}}-1& \left(3\right)\end{array}$

Details of the Embodiment of the Invention of the Present Application

(20) Hereinafter, a description will be given in detail on specific configurations of an optical fiber according to the present embodiment and an optical transmission system including the optical fiber with reference to the accompanying drawings. Note that, the present invention is not limited to these examples, and it is intended that the present invention is defined by the scope of the claims and includes all modifications within the meaning and scope equivalent to the claims.

(21) An optical transmission system according to the present embodiment includes the configuration shown in the above-described FIG. 1A, and the optical fiber according to the present embodiment is applicable, as an optical fiber transmission line, to the optical fiber 40 of the optical transmission system 1 shown in FIG. 1A. Further, FIG. 1B shows a signal light power diagram in one span when pumping light for Raman amplification is made to propagate in the one span (a repeater section on which the optical fiber 40 is deployed) of the optical fiber transmission line in the direction opposite to the propagation direction of the signal light. In the optical transmission system 1 of FIG. 1A, the signal light obtains a Raman gain of G.sub.R [dB] during propagation through the optical fiber 40 deployed on each span. Further, the signal light obtains an EDFA gain of G.sub.E [dB] by the EDFA 21 disposed on the span's output end. Such a configuration completely compensates the transmission loss of the signal light caused in the one span.

(22) First, a description will be given on a gain G.sub.R and an ASE noise power P.sub.ASE.sub._.sub.Raman of the Raman amplification. The gain G.sub.R [dB] which the signal light obtains by the Raman amplification for one span is expressed by the following Formula (4). In the formula, g.sub.R [10.sup.14 m/W] is Raman gain coefficient, Aeff.sub.P [m.sup.2] is an effective area at a pumping light wavelength, Leff.sub.P [km] is an effective length at a pumping light wavelength, and P.sub.Pump [mW] is a power of input pumping light.

(23) $\begin{array}{cc}{G}_R\left[\mathrm{dB}\right]=10\log \left[\exp \left(\frac{g_R}{{\mathrm{Aeff}}_P}.Math.L_{\mathrm{effP}}.Math.P_{\mathrm{Pump}}\right)\right]\frac{0.11}{{\mathrm{Aeff}}_P.Math.{}_P}.Math.P_{\mathrm{Pump}}& \left(4\right)\end{array}$

(24) The following Formula (5) represents Leff.sub.P, when a repeater interval (span length) is represented by L [km], and a transmission loss at a pumping light wavelength is represented by .sub.P [1/km]. In the case that L is sufficiently long (some ten kilometers or more), Leff.sub.P can be approximated by the following Formula (6).
Leff.sub.P=[1exp(.sub.PL)]/.sub.P(5)
Leff.sub.P1/.sub.P(6)

(25) The value g.sub.R is determined substantially by material of the core, and in the case of a pure silica core fiber, in which substantially no impurity is added to the core, g.sub.R is about 2.6 [10.sup.14 In/W] and approximately constant.

(26) Further, the following Formula (7) represents an ASE (Amplified Spontaneous Emission) noise power P.sub.ASE.sub._.sub.Raman [mW] caused by Raman amplification. In the formula, h=6.6310.sup.34 [Js] is Planck's constant, is a light frequency and is about 194 THz, is a noise band and is, for example, about 12.5 GHz, and NF.sub.R is a noise figure of the Raman amplification.
P.sub.ASE.sub._.sub.Raman=h.Math.NF.sub.R.Math.(G.sub.R1)(7)

(27) Next, a description will be given on a gain G.sub.E and an ASE noise power P.sub.ASE.sub._.sub.EDFA of the EDFA. If it is assumed that the transmission loss in one span is completely compensated by the Raman amplification and the EDFA, the gain G.sub.E [dB] to be obtained by the EDFA is expressed by the following Formula (8), in which the Raman amplification gain is substituted from the span total loss. In the formula, .sub.SdB [dB/km] is a transmission loss at the signal light wavelength.

(28) $\begin{array}{cc}{G}_E\left[\mathrm{dB}\right]={}_{\mathrm{SdB}}.Math.L-G_R\left[\mathrm{dB}\right]{}_{\mathrm{SdB}}.Math.L-\frac{0.11}{{\mathrm{Aeff}}_P.Math.{}_P}.Math.P_{\mathrm{Pump}}& \left(8\right)\end{array}$

(29) Further, the ASE noise power P.sub.ASE.sub._.sub.EDFA [mW] caused by the EDFA is expressed by the following Formula (9). In the formula, NF.sub.E is a noise figure of the EDFA and is generally about 5 to 6 dB.
P.sub.ASE.sub._.sub.EDFA=h.Math.NF.sub.E.Math.(G.sub.E1)(9)

(30) Next, a description will be given on a phase shift amount caused by self-phase modulation and an allowable input signal light power. One of nonlinear phenomena generated in an optical fiber includes self-phase modulation. Because the self-phase modulation shifts the phase of the signal light and thus deteriorates transmission performance, it is necessary to keep the self-phase modulation to an allowable value or less in the optical transmission system. The following Formula (10) represents a phase shift amount .sub.SPM [rad], for one span, caused by self-phase modulation in the case of the optical transmission system not using Raman amplification. In the formula, n.sub.2 [10.sup.20 m.sup.2/W] is a nonlinear refractive index, [nm] is a wavelength, Aeff.sub.S [m.sup.2] is an effective area at a signal light wavelength, P.sub.sig [mW] is an input signal light power, and .sub.S [1/km] is a transmission loss at a signal light wavelength.

(31) $\begin{array}{cc}{}_{\mathrm{SPM}}=\frac{2}{}\frac{n_2}{{\mathrm{Aeff}}_S}{L}_{\mathrm{effS}}{P}_{\mathrm{Sig}}\frac{44}{}\frac{1}{{\mathrm{Aeff}}_S{}_S}{P}_{\mathrm{Sig}}& \left(10\right)\end{array}$

(32) When the repeater interval (span length) is represented by L [km], the following Formula (11) represents Leff.sub.S. In the case that L is sufficiently long (some ten kilometers or more), Leff.sub.S can be approximated by the following Formula (12).
Leff.sub.S=[1exp(.sub.SL)]/.sub.S(11)
Leff.sub.S1/.sub.S(12)

(33) The value n.sub.2 is substantially determined by material of the core, and in the case of a pure silica core fiber, in which substantially no impurity is added to the core, is 2.2 [10.sup.20 m.sup.2/W] and approximately constant.

(34) In the case that Raman amplification is used, a signal light power increases near the span's output end, and .sub.SPM also increases accordingly. However, for example, in the case that signal light with an input signal light power of 2 dBm/ch is transmitted through an SSMF with a span length of 100 km, the difference of .sub.SPM is as small as about 5% between the case of using Raman amplification with a pumping light power of 200 mW and the case of not using Raman amplification. Thus, the .sub.SPM can be represented approximately by the above Formula (10) even when Raman amplification is used.

(35) The .sub.SPM allowable in an optical transmission system is, for example, 1 rad as an accumulated value all through the transmission line from the transmitter to the receiver. For example, in the case of a transmission line constituted by 50 spans, the allowable .sub.SPM for one span is 0.02 rad. The maximum input signal light power P.sub.sig.sub._.sub.max [mW] with which the phase shift amount does not exceed a certain allowable amount .sub.SPM.sub._.sub.max [rad.] is expressed by the following Formula (13).

(36) $\begin{array}{cc}{P}_{\mathrm{Sig}\_\mathrm{ma}x}=\frac{}{44}{\mathrm{Aeff}}_S{}_S.Math.{}_{\mathrm{SPM}\_m\mathrm{ax}}& \left(13\right)\end{array}$

(37) Next, an optical fiber which improves OSNR will be described. The following Formula (14) represents the OSNR in the optical transmission system in which Raman amplification and an EDFA are combined, in the case that the input signal power is set to P.sub.sig.sub._.sub.max so that the phase shift amount caused by the self-phase modulation is an allowable amount .sub.SPM.sub._.sub.max.

(38) $\begin{array}{cc}\mathrm{OSNR}=\frac{P_{\mathrm{sig}\_\mathrm{ma}x}}{P_{\mathrm{ASE}\_\mathrm{EDFA}}+P_{\mathrm{ASE}\_\mathrm{Raman}}.Math.G_E}& \left(14\right)\end{array}$

(39) In general, in the optical transmission system in which Raman amplification and an EDFA are combined, the gain of the EDFA is greater than the gain of the Raman amplification. Further, because the noise characteristics of the EDFA are inferior to those of the Raman amplification (which means that the noise figure NF.sub.E is greater than the noise figure NF.sub.R), P.sub.ASE.sub._.sub.EDFA is greater than P.sub.ASE.sub._.sub.Raman. Therefore, in order to improve the OSNR, it is effective to keep P.sub.ASE.sub._.sub.EDFA small.

(40) As understood from the above Formula (9), P.sub.ASE.sub._.sub.EDFA increases linearly with respect to G.sub.E; therefore, in order to reduce P.sub.ASE.sub._.sub.EDFA, it is effective to keep G.sub.E small. In addition, by keeping G.sub.E small, it is possible to keep small a Raman ASE noise power P.sub.ASE.sub._.sub.Raman.Math.G.sub.E after being amplified by the EDFA.

(41) Here, assume the signal light wavelength to be 1550 nm, and assume the pumping light wavelength to be 1450 nm. The effective area at a wavelength of 1550 nm is represented by Aeff.sub.1550 [m.sup.2], the transmission loss at a wavelength of 1550 nm is represented by .sub.1550 [1/km] and .sub.1550.sub._.sub.dB [dB/km]. The effective area at a wavelength of 1450 nm is represented by Aeff.sub.1450 [m.sup.2], and the transmission loss at a wavelength of 1450 nm are represented by .sub.1450 [1/km] and .sub.1450.sub._.sub.dB [dB/km].

(42) In order to keep G.sub.E small, it is preferable that Condition 1 represented by the following Formula (15) be satisfied. By satisfying Condition 1, G.sub.E represented by the above Formula (8), in which L=100 km and P.sub.Pump=200 mW, is kept to be 12 dB or less. It is possible to reduce G.sub.E by 1 dB or more compared with a standard single mode fiber (Aeff.sub.1550=80 m.sup.2, Aeff.sub.1450=75 m.sup.2, .sub.1550.sub._.sub.dB=0.19 dB/km, .sub.1450=0.053/km, g.sub.R=2.710.sup.14 m/W). That is, it is possible to reduce P.sub.ASE.sub._.sub.EDFA by 1 dB or more and thus to improve the OSNR.

(43) $\begin{array}{cc}{\mathrm{Aeff}}_{1450}.Math.{}_{1450}<\frac{22}{{}_{1550\_dB}.Math.100-12}& \left(15\right)\end{array}$

(44) On the other hand, if G.sub.E is kept to be excessively small, G.sub.R increases to be comparable to G.sub.E. In such a case, P.sub.ASE.sub._.sub.Raman becomes large, and as a result, the OSNR is deteriorated. To address this issue, it is preferable that Condition 2 represented by the following Formula (16) be satisfied. By satisfying Condition 2, the above Formula (4) and the above Formula (8) lead to the relationship G.sub.R<G.sub.E; thus, it is possible to suppress the increase in P.sub.ASE.sub._.sub.Raman. As a result, the OSNR can be improved.

(45) $\begin{array}{cc}{\mathrm{Aeff}}_{1450}.Math.{}_{1450}>\frac{0.44}{{}_{1550\_dB}}& \left(16\right)\end{array}$

(46) Further, improving P.sub.sig.sub._.sub.max is effective in improving the OSNR. Therefore, the above Formula (13) shows that it is preferable that Aeff.sub.S.Math..sub.S be greater, and it is preferable that Condition 3 represented by the following Formula (17) be satisfied. By satisfying Condition 3, it is possible to make P.sub.sig.sub._.sub.max [mW] become 0.5 mW (3 dBm) or more when .sub.SPM.sub._.sub.max=0.02 rad, and it is thus possible to improve the OSNR.
Aeff.sub.1550.Math..sub.1550>2.2(17)

(47) FIGS. 2 to 4 are tables which summarize specifications of each of samples of the optical fiber according to the present embodiment and comparative examples. In the tables, comparative example 1 is a standard single mode fiber (SMF) compliant to ITU-T G.652. Comparative example 2 is a dispersion-shift fiber (DSF) compliant to ITU-T G.653.

(48) FIG. 2 shows the characteristics of each of the samples of the optical fibers according to the present embodiment and the comparative examples, in other words, FIG. 2 shows: Aeff.sub.1550; Aeff.sub.1450; .sub.1550.sub._.sub.dB; .sub.1450.sub._.sub.dB; a fiber cutoff wavelength c; a bending loss, with a diameter 20 mm, at a wavelength of 1550 nm; Aeff.sub.1450.Math..sub.1450 (the left member of each of the above Formula (15) and the above Formula (16)); 22/(.sub.1550.sub._.sub.dB.Math.10012) (the right member of the above Formula (15)), 0.44/.sub.1550.sub._.sub.dB (the right member of the above Formula (16)); Aeff.sub.1550.Math..sub.1550 (the left member of the above Formula (17)); and whether Conditions 1 to 3 are satisfied. The optical fibers of samples 1 to 6 satisfy all of Conditions 1 to 3.

(49) FIG. 3 shows the transmission characteristics when the pumping light power is set to 200 mW and when the signal light is transmitted through the optical fiber transmission line with a span length 100 km for each of the samples of the optical fibers according to the present embodiment and the comparative examples. The OSNRs of the optical fibers of Samples 1 to 6 can be improved by 1.5 dB or more compared with the SMF.

(50) FIG. 4 shows construction parameters of each of the samples of the optical fibers according to the present embodiment and the comparative examples. FIG. 5 is a diagram showing a refractive index profile of an optical fiber of the embodiment. The optical fiber of the sample has: a core with a refractive index of n1 and a diameter 2a [m]; and a cladding surrounding the core.

(51) A relative refractive index difference of the core with respect to a refractive index n0 of pure silica is represented by 0 [%] (the following Formula (18)). The value 0 is preferably 0.1% to +0.1%. Condition 1 shows that it is preferable that .sub.1450 be smaller, and it is effective in lowering .sub.1450 to add substantially no impurity to the core through which most of the signal light power goes through.
0[%]=100(n1n0)/n1(18)

(52) More preferably, an optical fiber of the embodiment has: a core having a refractive index n1 and a diameter 2a [m] as the refractive index profile shown in FIG. 6; an inner cladding surrounding the core and having a refractive index n2 and a diameter of 2b [m]; and an outer cladding surrounding the inner cladding and having a refractive index n3. A relative refractive index difference of the core with respect to the outer cladding is represented by 1 [%] (the following Formula (19)). A relative refractive index difference of the inner cladding with respect to the outer cladding is represented by 2 [%] (the following Formula (20)).
1[%]=100(n1n3)/n1,(19)
2[%]=100(n2n3)/n2,(20)

(53) Further, it is preferable that the following Formula (21) be satisfied. Conditions 2 and 3 show that it is preferable that Aeff.sub.1450 and Aeff.sub.1550 be greater, and by using an optical fiber with such a refractive index profile, it is possible to increase Aeff to 100 m.sup.2 or more while keeping effective single mode conditions for the signal light and keeping the bending loss at a wavelength of 1550 nm to 20 dB/m or less when the optical fiber is wound to have a diameter of 20 mm.
n1>n3>n2(21)

(54) Here, the effective single mode conditions mean that the fiber cutoff wavelength c is 1600 nm or less. By satisfying the conditions, the cable cutoff wavelength can become the signal light wavelength or less (for example, C band: 1530 nm to 1565 nm).

(55) Further, as shown in FIGS. 7A to 7F, it is possible to variously deform the refractive index profile of the core of a sample (optical fiber) applicable to the optical fiber according to the present embodiment. In such cases, the average value of the refractive index of the core is regarded to be n1.

(56) FIG. 1A shows the configuration of the optical transmission system 1 equipped with the optical fiber transmission line using the optical fiber according to the present embodiment. In the optical transmission system 1, it is preferable that the following Formula (22) be satisfied, when the span length is represented by L [km], and the pumping light power is represented by P.sub.Pump [mW]. By satisfying Formula (22), the above Formula (8) shows that G.sub.E can be reduced by 1 dB or more in the optical transmission system 1 according to the present embodiment compared with the optical transmission system using a standard single mode fiber; therefore, it is possible to reduce P.sub.ASE.sub._.sub.EDFA by 1 dB or more and thus to improve the OSNR.

(57) 0$\begin{array}{cc}{}_{\mathrm{SdB}}.Math.L-\frac{0.11}{{\mathrm{Aeff}}_P.Math.{}_P}.Math.P_{\mathrm{Pump}}<0.19L-0.028P_{\mathrm{Pump}}-1& \left(22\right)\end{array}$

(58) Further, in the optical transmission system 1 equipped with the optical fiber transmission line using the fiber according to the present embodiment, it is preferable that the following Formula (23) be satisfied. By satisfying Formula (23), the relationship G.sub.R<G.sub.E is satisfied based on the above Formula (4) and the above Formula (8); thus, it is possible to suppress the increase in P.sub.ASE.sub._.sub.Raman and thus to improve the OSNR.

(59) $\begin{array}{cc}\frac{0.11}{{\mathrm{Aeff}}_P.Math.{}_P}.Math.P_{\mathrm{Pump}}<{}_{\mathrm{SdB}}.Math.L-\frac{0.11}{{\mathrm{Aeff}}_P.Math.{}_P}.Math.P_{\mathrm{Pump}}& \left(23\right)\end{array}$

(60) Next, with reference to FIGS. 8 and 9, a description will be given on each of appropriate ranges of the transmission loss .sub.1450.sub._.sub.dB at a wavelength of 1450 nm and the effective area Aeff.sub.1450 at a wavelength of 1450 nm. Note that the prepared optical fibers (which have the refractive index profile shown in FIG. 5 or FIG. 6). Specifically, FIG. 8 is a graph showing the dependency of each of Aeff.sub.1450.Math..sub.145, 22/(.sub.1550.sub._.sub.dB10012), and 0.44/.sub.1550.sub._.sub.dB on .sub.1450.sub._.sub.dB under the conditions that Aeff.sub.1450 is made to be 73 m.sup.2 and .sub.1550.sub._.sub.dB is made to be .sub.1450.sub._.sub.dB0.045 [dB/km]. Further, FIG. 9 is a graph showing the dependency of each of Aeff.sub.1450.Math..sub.1450, 22/(.sub.1550.sub._.sub.dB10012), and 0.44/.sub.1550.sub._.sub.dB on Aeff.sub.1450 under the condition that .sub.1550.sub._.sub.dB is made to be 0.155 dB/km and .sub.1450 is made to be 0.045 dB/km.

(61) Note that Aeff.sub.1450.Math..sub.1450 is represented by graph G810 in FIG. 8 and graph G910 in FIG. 9, which are each the left member of each of the above Formula (15) and Formula (16). The member 22/(.sub.1550.sub._.sub.dB10012) is the right member of the above Formula (15), where the right member is represented by each of graph G820 in FIG. 8 and graph G920 in FIG. 9. Further, 0.44/.sub.1550.sub._.sub.dB is the right member of the above Formula (16), where the right member is represented by each of graph G830 in FIG. 8 and graph G930 in FIG. 9.

(62) As understood from FIG. 8, if .sub.1450.sub._.sub.dB is in the range from 0.19 to 0.22 dB/km, Condition 1 represented by the above Formula (15) and Condition 2 represented by the above Formula (16) are satisfied. On the other hand, as understood from FIG. 9, if Aeff.sub.1450 is in the range from 60 m.sup.2 to 140 m.sup.2, Condition 1 and Condition 2 respectively represented by the above Formula (15) and the above Formula (16) are both satisfied.

REFERENCE SIGNS LIST

(63) 1: Optical transmission system, 10: Transmitter, 20: Repeater, 21: EDFA, 22: Pumping light source for Raman-amplification, 30: Receiver, 40: Optical fiber