Abstract
The present invention relates to an MMF with a structure for relaxing wavelength dependence of transmission bandwidth. In the MMF, a doping amount of a dopant for control of refractive index is adjusted, so as to make each of an OFL bandwidth at a wavelength of 850 nm and an OFL bandwidth at a wavelength of at least one of 980 nm, 1060 nm, and 1300 nm become not less than 1500 MHz.Math.km, make the OFL bandwidth at the wavelength of at least one of 980 nm, 1060 nm, and 1300 nm become wider than the OFL bandwidth at the wavelength of 850 nm, and effectively suppress increase in transmission loss.
Claims
1. A multimode optical fiber comprising: a core extending along a predetermined axis, the core having a diameter of 25 to 65 m and a GI refractive index profile whose shape is determined by value falling within a range of 1.8 to 2.2, the core containing both of a refractive-index increase agent and a first refractive-index decrease agent: and a cladding provided on an outer peripheral surface of the core and containing a second refractive-index decrease agent, a maximum relative refractive index difference between the core and the cladding falling within a range of 0.8 to 2.4%, the maximum relative refractive index difference being constituted of a first relative refractive index difference resulting from the refractive-index increase agent with reference to pure silica and a second relative refractive index difference resulting from each of the first and second refractive-decrease agents with reference to the pure silica, wherein component ratios of the first and second relative refractive index differences are set, while fixing the value, so as to satisfy both of following first and second conditions while transmission loss in a wavelength range of 850 nm to 1300 nm is not more than 4.0 dB/km: the first condition being defined as a condition that an OFL bandwidth at a wavelength of 850 nm is not less than 1500 MHz-km and an OFL bandwidth at a wavelength of at least one of 980 nm, 1060 nm, and 1300 nm is not less than 1500 MHz-km; and the second condition being defined as a condition that the OFL bandwidth at the wavelength of at least one of 980 nm, 1060 nm, and 1300 nm is wider than the OFL bandwidth at the wavelength of 850 nm, and wherein the refractive-index increase agent contains any one of GeO.sub.2, P.sub.2O.sub.5 and Cl, and each of the first and second refractive-index decrease agents contains any one of B.sub.2O.sub.3 and F.
2. The multimode optical fiber according to claim 1, wherein the cladding is comprised of silica glass doped with the second refractive-index decrease agent, or, a material other than the silica glass.
3. The multimode optical fiber according to claim 1, having chromatic dispersion falling within the range of 100 to +100 ps/nm/km, in the wavelength range of 850 nm to 1300 nm.
4. The multimode optical fiber according to claim 1, having the transmission loss of not more than 2.4 dB/km, in the wavelength range of 850 nm to 1300 nm.
5. The multimode optical fiber according to claim 1, wherein in a cross section of the multimode optical fiber perpendicular to the predetermined axis, the second relative refractive index difference in the core monotonically decreases along a radial direction from a center of the core, while maintaining the shape of the GI refractive index profile determined by the value.
6. The multimode optical fiber according to claim 1, wherein the core is doped with GeO.sub.2 as the refractive-index increase agent and each of the first and second refractive-index decrease agent is B.sub.2O.sub.3, and wherein in a cross section of the multimode optical fiber perpendicular to the predetermined axis, the first relative refractive index difference in the core monotonically decreases along a radial direction from a center of the core, while maintaining the shape of the GI refractive index profile determined by the value.
7. The multimode optical fiber according to claim 1, wherein the core is doped with GeO.sub.2 as the refractive-index increase agent and the first and second refractive index decrease agent is B.sub.2O.sub.3, and wherein in a cross section of the multimode optical fiber perpendicular to the predetermined axis, the second relative refractive index difference in the core monotonically decreases along a radial direction from a center of the core, while maintaining the shape of the GI refractive index profile determined by the value.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
(1) FIG. 1A is a cross section showing an example of the structure of the MMF according to the embodiment of the invention and FIG. 1B an example of its refractive index profile (GI refractive index profile).
(2) FIG. 2A and FIG. 2B are examples of refractive index profiles of sectional structures applicable to a peripheral region around the core in the MMF shown in FIG. 1A.
(3) FIG. 3A is a drawing showing a doping amount change along the radial direction of the MMF, of GeO.sub.2 added in the core of an MMF as a comparative example (GI MMF having a GI refractive index profile), FIG. 3B a refractive index profile formed by doping with GeO.sub.2, and FIG. 3C a refractive index profile along the radial direction of the MMF, of the MMF according to the comparative example.
(4) FIG. 4A to FIG. 4D are drawings showing wavelength characteristics of OFL bandwidths in MMFs of the comparative example.
(5) FIG. 5A is a drawing showing a doping amount change along the radial direction of the MMF, of GeO.sub.2 added in the core of the MMF according to the first embodiment (GI MMF having the GI refractive index profile), and a refractive index profile formed by doping with GeO.sub.2, FIG. 5B a drawing showing a doping amount change along the radial direction of the MMF of B.sub.2O.sub.3 added in both of the core and cladding of the MMF according to the first embodiment (GI MMF having the GI refractive index profile), and a refractive index profile formed by doping with B.sub.2O.sub.3, and FIG. 5C a refractive index profile along the radial direction of the MMF, of the MMF of the first embodiment.
(6) FIG. 6A is a drawing showing respective wavelength characteristics of OFL bandwidths in the MMF of the comparative example and the MMF of the first embodiment and FIG. 6B a table as a list of relationships between OFL bandwidth and wavelength shown in FIG. 6A.
(7) FIG. 7A is a drawing showing a doping amount change along the radial direction of the MMF, of GeO.sub.2 added in the core of the MMF according to the second embodiment (GI MMF having the GI refractive index profile), and a refractive index profile formed by doping with GeO.sub.2, FIG. 7B a drawing showing a doping amount change along the radial direction of the MMF, of B.sub.2O.sub.3 added in both of the core and cladding of the MMF according to the second embodiment (GI MMF having the GI refractive index profile), and a refractive index profile formed by doping with B.sub.2O.sub.3, and FIG. 7C a refractive index profile along the radial direction of the MMF, of the MMF of the second embodiment.
(8) FIG. 8 is graphs showing relationships between .sub.opt to minimize the inter-modal dispersion, among values defining the shape of GI refractive index profile, and wavelength, for various dopants for control of refractive index added in the core and combinations thereof.
(9) FIG. 9A is a drawing showing wavelength characteristics of OFL bandwidths, at various ratios to constitute a maximum relative refractive index difference in MMFs, of relative refractive index differences resulting from the dopants for control of refractive index added in the MMFs of the second embodiment, and FIG. 9B an enlarged view of region A shown in FIG. 9A.
DESCRIPTION OF EMBODIMENTS
Description of Embodiment of Present Invention
(10) An MMF according to the present invention has a core extending along a predetermined axis, and a cladding provided on an outer peripheral surface of the core.
(11) (1) As a first aspect, when a first condition is defined as a condition that an OFL bandwidth at a wavelength of 850 nm is not less than 1500 MHz.Math.km and an OFL bandwidth at a wavelength of at least one of 980 nm, 1060 nm, and 1300 nm is not less than 1500 MHz.Math.km and when a second condition is defined as a condition that the OFL bandwidth at the wavelength of at least one of 980 nm, 1060 nm, and 1300 nm is wider than the OFL bandwidth at the wavelength of 850 nm, a doping amount of a dopant for control of refractive index in a region corresponding to at least either of the core and the cladding, in the MMF is adjusted so as to satisfy both of the first condition and the second condition. Transmission loss in a wavelength range of 850 nm to 1300 nm is not more than 4.0 dB/km. In this case, it becomes feasible to achieve upgrades of the existing transmission systems, without need for replacement of the conventional MMFs with the MMF optimized for each operation wavelength, because the MMF of the first aspect achieves the relaxation of the wavelength dependence of the OFL bandwidth as a transmission bandwidth. On the assumption of the WDM transmission, if the MMF applied is one wherein the transmission bandwidth on the longer wavelength side is wider than that at 850 nm, it can derive the transmission characteristics enough for use of the WDM transmission system, on the longer wavelength side.
(12) (2) As a second aspect applicable to the first aspect, the cladding may be comprised of silica glass doped with the dopant for control of refractive index, or, a material other than the silica glass.
(13) (3) As a third aspect applicable to at least either one of the first and second aspects, the core may have a GI refractive index profile. In this case, the GI refractive index profile may be formed by doping the core with a plurality of dopants different from each other, as the dopant for control of refractive index.
(14) (4) As a fourth aspect applicable to at least any one of the first to third aspects, each of the plurality of dopants for control of refractive index preferably contains any one of GeO.sub.2, P.sub.2O.sub.5, B.sub.2O.sub.3, F, and Cl.
(15) (5) As a fifth aspect applicable to at least any one of the first to fourth aspects, the MMF preferably has chromatic dispersion falling within the range of 100 to +100 ps/nm/km, in the wavelength range of 850 nm to 1300 nm. The WDM transmission can be one of candidates as means for realizing an increase in capacity of short-haul transmission. In this case, if chromatic dispersion occurs at each of communication wavelengths, it will lead to degradation of transmission quality. Therefore, it is preferred that the chromatic dispersion should fall within the foregoing range, in the wavelength range of 850 nm to 1300 nm which is expected to be used in future.
(16) (6) As a sixth aspect applicable to at least any one of the first to fifth aspects, the MMF preferably has the transmission loss of not more than 2.7 dB/km and more preferably has the transmission loss of not more than 2.4 dB/km, in the wavelength range of 850 nm to 1300 nm.
(17) (7) As a seventh aspect applicable to at least any one of the first to sixth aspects, the core and the cladding both are preferably doped with a common refractive-index decrease agent, as the dopant for control of refractive index. Furthermore, preferably, in a cross section of the multimode optical fiber perpendicular to the predetermined axis, a doping amount of the common refractive-index decrease agent in the core monotonically increases along a radial direction from a center of the core.
(18) (8) As an eighth aspect applicable to at least any one of the first to seventh aspects, the dopant for control of refractive index includes a refractive-index increase agent and a refractive-index decrease agent. In this case, preferably, the core is doped with GeO.sub.2 as the refractive-index increase agent and both of the core and the cladding are doped with B.sub.2O.sub.3 as the refractive-index decrease agent. Furthermore, preferably, in the cross section of the multimode optical fiber perpendicular to the predetermined axis, a doping amount of the refractive-index increase agent in the core monotonically decreases along the radial direction from the center of the core, in order to obtain a refractive index profile of a predetermined shape.
(19) (9) As a ninth aspect applicable to at least any one of the first to eighth aspects, the dopant for control of refractive index includes a refractive-index increase agent and a refractive-index decrease agent. In this case, preferably, the core is doped with GeO.sub.2 as the refractive-index increase agent and both of the core and the cladding are doped with B.sub.2O.sub.3 as the refractive-index decrease agent. Furthermore, preferably, in the cross section of the multimode optical fiber perpendicular to the predetermined axis, a doping amount of the refractive-index decrease agent in the core monotonically increases along the radial direction from the center of the core, in order to obtain a refractive index profile of a predetermined shape. Particularly, when the core is doped with the refractive-index increase agent and the refractive-index decrease agent as the dopant for control of refractive index, a sufficient maximum relative refractive index difference can be obtained without increase in respective doping amounts of the refractive-index increase agent and the refractive-index decrease agent and thus degradation of transmission characteristics in the MMF other than the transmission bandwidth, such as the chromatic dispersion and the transmission loss, can also be effectively suppressed.
Details of Embodiments of Present Invention
(20) Each of embodiments of the present invention will be described below in detail with reference to the accompanying drawings. In the description of the drawings, the same portions and the same elements will be denoted by the same reference signs, without redundant description. It should be noted that the present invention is by no means intended to be limited to these examples presented by way of illustration but is intended for inclusion of all changes within the meaning and scope of equivalence to the scope of claims, as described in the scope of claims.
(21) FIG. 1A is a cross section showing an example of the structure of the MMF according to the embodiment of the invention and FIG. 1B an example of its refractive index profile (GI refractive index profile). The MMF with the core having the GI refractive index profile as shown in FIG. 1B will be referred to hereinafter as GI-MMF.
(22) The GI-MMF 100, as shown in FIG. 1A, has a core 110 extending along an optical axis AX, and a cladding 120 provided on the outer periphery of the core 110. In this GI-MMF 100, at least one of the core 110 and the cladding 120 is doped with one or more dopants for control of refractive index (each dopant for control of refractive index will be referred to hereinafter as an index-control dopant). The core 110 has the diameter 2a and has a maximum refractive index n.sub.1 at its center (position intersecting with the optical axis AX). The cladding 120 has the diameter 2b. The cladding 120 is comprised of pure silica glass, silica glass doped with an index-control dopant, or a material other than the glass materials, and has a refractive index n.sub.0 (<n.sub.1).
(23) The refractive index profile 150 of the GI-MMF 100, which is shown in FIG. 1B, indicates refractive indices of respective parts on a line L perpendicular to the optical axis AX (the line L coincides with a radial direction of the GI-MMF 100) and, more specifically, region 151 indicates refractive indices of respective parts of the core 110 along the line L, and region 152 refractive indices of respective parts of the cladding 120 along the line L.
(24) Particularly, the refractive index profile 150 of FIG. 1B has a refractive index profile n(r) expressed by Formula (1) below. The core 110 corresponding to the region 151 has the refractive index n(r) in a dome shape in which the refractive index is maximum at the center of the core 110 coincident with the optical axis AX (or at a position where the optical axis AX intersects with the cross section of the GI-MMF 100) (which is an -power refractive index profile). The refractive index n(r) of the core 110 defined in the range of 0ra represents the refractive index of the core 110 with the radius a (the diameter 2a) and refractive index at a position distant by r in the radial direction from the center of the core 110. Therefore, when the core 110 is doped with a refractive-index increase agent such as GeO.sub.2, P.sub.2O.sub.5, or Cl as an index-control dopant, a concentration of the foregoing refractive-index increase agent as exemplified sharply decreases from the center of the core 110 toward the cladding 120 (or monotonically decreases). Inversely, when the core 110 is doped with a refractive-index decrease agent such as B.sub.2O.sub.3 or F as an index-control dopant, a concentration of the refractive-index decrease agent sharply increases from the center of the core 110 toward the cladding 120 (or monotonically increases). The value to define this dome shape is from 1.8 to 2.2. A maximum relative refractive index difference between the core 110 and the cladding 120 (which corresponds to a relative refractive index difference between the refractive index of the cladding 120 and the maximum refractive index at the center of the core 110) is from 0.8 to 2.4%. The diameter of the core 110 is from 25 to 65 m. In the present specification, the structure of the core in the embodiments, comparative example, and others described below is the same as the above-described structure of the core. The maximum relative refractive index difference between the cladding 120 (ref active index n.sub.0) and the core 110 (maximum refractive index n.sub.1) is defined by Formula (2) below. The below definition of the relative refractive index difference is also applied to the other embodiments.
(25)
In the above formulae, represents the maximum relative refractive index difference of the core relative to the cladding, n.sub.1 the refractive index at the core center (maximum refractive index), n.sub.0 the refractive index of the cladding, r the distance from the core center, a the radius of the core, and the power to determine the shape of the profile.
(26) By use of the WKB approximation (Wentzel-Kramers-Brillouin approximation), the value to minimize the inter-modal dispersion of the MMF (.sub.opt) is expressed by Formula (3) below. The parameter y in Formula (3) is an amount indicative of wavelength dependence of the maximum relative refractive index difference , which is called Olshansky parameter, and is defined by Formula (4) below.
(27)
In the above formula, N.sub.1 represents the group index of the core and the transmission wavelength in vacuum.
(28) A trench portion having a refractive index n.sub.2 lower than the refractive index n.sub.0 of the cladding 120 may be provided around the core 110. FIGS. 2A and 2B are examples of refractive index profiles of sectional structures applicable to the peripheral portion around the core in the MMF shown in FIG. 1A. Namely, the trench portion may be provided between the core and the cladding, as shown in FIG. 2A. The trench portion may also be provided in the cladding as separated by a predetermined distance from the core, as shown in FIG. 2B. In this example of FIG. 2B, there is a part of the cladding located between the core and the trench portion. A relative refractive index difference .sub.trench between the trench portion and the cladding is obtained by replacing the refractive index n.sub.1 in the foregoing Formula (2) with n.sub.2.
(29) In the MMF having any one of the above-described sectional structures and refractive index profiles, as is considered to be applied to a transmission system for implementation of WDM transmission, its chromatic dispersion preferably falls within the range of 100 to +100 ps/nm/km, in the wavelength range of 850 nm to 1300 nm. The MMF of the present embodiment includes a mode of doping with multiple kinds of index-control dopants. For high-speed extended distance transmission of a signal, the fiber is desired to have all of the transmission loss, chromatic dispersion, and bandwidth at good levels. For example, even if the bandwidth is good but if the transmission loss is high, the signal will fail to propagate; if the chromatic dispersion is large, the signal waveform will degrade. For this reason, it is desirable to prevent the signal from being degraded by any other cause, while maintaining the bandwidth.
(30) (Wavelength Dependence of OFL Bandwidth)
(31) Next, the relaxation of the wavelength dependence of the OFL bandwidth in the MMF of the present embodiment will be described below using a comparative example.
(32) First, FIG. 3A is a drawing showing a doping amount change along the radial direction of the MMF, of GeO.sub.2 added in the core of the MMF according to the comparative example (GI MMF having a GI refractive index profile), FIG. 3B a refractive index profile formed by doping with GeO.sub.2, and FIG. 3C a refractive index profile along the radial direction of the MMF, of the MMF according to the comparative example.
(33) The MMF of the comparative example is a GI-MMF having the same sectional structure as the sectional structure shown in FIG. 1A, which has the core extending along the optical axis AX, and the cladding provided on the outer peripheral surface of the core. The outer diameter of the core (the diameter 2a) is 50 m and the outer diameter of the cladding is 125 m. The core is doped with GeO.sub.2 as an index-control dopant and a doping amount of GeO.sub.2 is set, as shown in. FIG. 3A, so that the doping amount monotonically decreases along the radial direction from the core center (position coincident with the optical axis AX in the cross section of the core). FIG. 3B shows the refractive index profile formed by doping with GeO.sub.2 and a relative refractive index difference .sub.GE resulting from GeO.sub.2 is 1%. On the other hand, since the cladding is comprised of pure SiO.sub.2, a resultant overall refractive index profile of the MMF according to this comparative example is a GI refractive index profile of the shape shown in FIG. 3C. In the GI refractive index profile of FIG. 3C, the maximum relative refractive index difference between the core and cladding is equal to the relative refractive index difference .sub.GE resulting from GeO.sub.2. It is noted herein that .sub.GE is given by setting n.sub.1 in the foregoing Formula (2) to the maximum refractive index at the core center and setting n.sub.0 to the refractive index of pure SiO.sub.2.
(34) Wavelength characteristics of the OFL bandwidths in MMFs having the structure as described above are shown in FIGS. 4A to 4D. The wavelength characteristic shown in FIG. 4A is expressed by a relationship between OFL bandwidth and wavelength in the MMF where the value to define the shape of the GI refractive index profile in the core is adjusted to .sub.opt at the wavelength of 0.85 m ( value with which the inter-modal dispersion becomes minimum at the wavelength of 0.85 m). The wavelength characteristic shown in FIG. 4B is expressed by a relationship between OFL bandwidth and wavelength in the MMF where the value to define the shape of the GI refractive index profile in the core is adjusted to .sub.opt at the wavelength of 0.98 m. The wavelength characteristic shown in FIG. 4C is expressed by a relationship between OFL bandwidth and wavelength in the MMF where the value to define the shape of the GI refractive index profile in the core is adjusted to .sub.opt at the wavelength of 1.06 m. The wavelength characteristic shown in FIG. 4D is expressed by a relationship between OFL bandwidth and wavelength in the MMF where the value to define the shape of the GI refractive index profile in the core is adjusted to .sub.opt at the wavelength of 1.30 m.
(35) As seen from these FIGS. 4A to 4D, the OFL bandwidth becomes sharply narrower at wavelengths off the designed wavelength. Namely, it is understood that the MMFs of the comparative example cannot secure a wide OFL bandwidth, in a wide wavelength range. In the MMF adjusted so that the bandwidth is good at 0.85 m, the bandwidth does not reach 1500 MHz.Math.km at any wavelength of 0.98 m, 1.06 m, and 1.30 m. It is also understood that in the MMF adjusted so that the bandwidth is good at any wavelength of 0.98 m, 1.06 m, and 1.30 m, the bandwidth at the wavelength of 0.85 m does not reach 1500 MHz.Math.km. As described above, it is difficult to obtain an MMF which can secure the bandwidth characteristic of 1500 MHz.Math.km in the current transmission systems (0.85 m) and which can also secure the bandwidth characteristic of 1500 MHz.Math.km in future transmission systems (systems using at least any one wavelength of 0.98 m, 1.06 m, and 1.30 m), by simple doping with GeO.sub.2 as a dopant.
First Embodiment
(36) In contrast to it, FIGS. 5A to 5C show the configuration of the MMF according to the first embodiment. This MMF of the first embodiment is a GI-MMF having the same sectional structure as the sectional structure shown in FIG. 1A, which has the core extending along the optical axis AX, and the cladding provided on the outer peripheral surface of the core. The outer diameter of the core (the diameter 2a) is 50 m and the outer diameter of the cladding 125 m.
(37) The core is doped with GeO.sub.2 as an index-control dopant and the doping amount of GeO.sub.2 is set, as shown in FIG. 5A, so that the doping amount monotonically decreases along the radial direction from the core center (position coincident with the optical axis AX in the cross section of the core). In the refractive index profile formed by doping with GeO.sub.2, which is shown in FIG. 5A, the relative refractive index difference .sub.GE resulting from GeO.sub.2 is given by setting n.sub.1 in above Formula (2) to the maximum refractive index at the core center and setting n.sub.0 to the refractive index of the cladding. On the other hand, the core and cladding are doped with B.sub.2O.sub.3 as an index-control dopant, uniformly in the radial direction. In the refractive index profile formed by doping with B.sub.2O.sub.3, which is shown in FIG. 5B, the relative refractive index difference .sub.B resulting from B.sub.2O.sub.3 is given by setting n.sub.1 in above Formula (2) to the refractive index of SiO.sub.2 doped with B.sub.2O.sub.3 and setting n.sub.0 to the refractive index of pure SiO.sub.2.
(38) When the predetermined regions are doped with one or more of the multiple kinds of index-control dopants as described above, the GI refractive index profile is obtained as the overall refractive index profile of the MMF of this first embodiment, as shown in the refractive index diagram FIG. 5C. In the GI refractive index profile of FIG. 5C, the maximum relative refractive index difference between the core and cladding is constituted of the relative refractive index difference .sub.GE resulting from GeO.sub.2 (=1%=.sub.GE) and thus the maximum relative refractive index difference of 1% is ensured as a whole of the GI refractive index profile.
(39) FIG. 6A shows a wavelength characteristic (graph G710) of the OFL bandwidth in the MMF of the comparative example and a wavelength characteristic (graph G720) of the OFL bandwidth in the MMF of the first embodiment, which are configured as described above. FIG. 6B is a table as a list of the relationships between OFL bandwidth and wavelength shown in FIG. 6A.
(40) In the examples of graphs G710 and G720 shown in FIG. 6A, the comparative example and the first embodiment both are represented by respective relationships between OFL bandwidth and wavelength in the MMFs where the value to define the shape of the GI refractive index profile in the core is adjusted to .sub.opt at the wavelength of 0.98 m. It is seen from FIGS. 6A and 6B that at all wavelengths, the OFL bandwidth of the first embodiment is wider than the OFL bandwidth of the comparative example. For example, at the wavelength of 0.85 m, the OFL bandwidth of the first embodiment is not less than 1.5 GHz.Math.km, whereas the OFL bandwidth of the comparative example is not more than 1.5 GHz.Math.km. As described above, it is understood that the MMF of the first embodiment ensures the wide OFL bandwidth in the wider wavelength range than the MMF of the comparative example does.
Second Embodiment
(41) Next, the structure of the MMF according to the second embodiment will be described using FIGS. 7A-7C, FIG. 8, and FIGS. 9A and 9B. This MMF of the second embodiment is also a GI-MMF having the same sectional structure as the sectional structure shown in FIG. 1A, which has the core extending the optical axis AX, and the cladding provided on the outer peripheral surface of the core. The outer diameter of the core (the diameter 2a) is 50 m and the outer diameter of the cladding 125 m. In this second embodiment, the core is doped with GeO.sub.2 as a refractive-index increase agent and the core and cladding are doped with B.sub.2O.sub.3 as a refractive-index decrease agent.
(42) The doping amount of GeO.sub.2 in the core is set, as shown in FIG. 7A, so that the doping amount monotonically decreases along the radial direction from the core center (position coincident with the optical axis AX in the cross section of the core). In the refractive index profile formed by doping with GeO.sub.2, which is shown in FIG. 7A, the relative refractive index difference .sub.GE resulting from GeO.sub.2 is given by setting n.sub.1 in above Formula (2) to the maximum refractive index at the core center and setting n.sub.0 to the refractive index of pure SiO.sub.2. On the other hand, the doping amount of B.sub.2O.sub.3 in the core is set, as shown in FIG. 7B, so that the doping amount monotonically increases along the radial direction from the core center (position coincident with the optical axis AX in the cross section of the core). As shown in FIG. 7B, the cladding is doped with B.sub.2O.sub.3, uniformly along the radial direction. In the refractive index profile formed by doping with B.sub.2O.sub.3, which is shown in FIG. 7B, the relative refractive index difference .sub.B resulting from B.sub.2O.sub.3 is given by setting n.sub.1 in above Formula (2) to the maximum refractive index at the core center and setting n.sub.0 to the refractive index of the cladding doped with B.sub.2O.sub.3.
(43) When the predetermined regions are doped with one or more of the multiple kinds of index-control dopants as described above, the GI refractive index profile is obtained as an overall refractive index profile of the MMF of the second embodiment, as shown in FIG. 7C. In the GI refractive index profile of FIG. 7C, the maximum relative refractive index difference between the core and cladding is constituted of the relative refractive index difference .sub.GE resulting from GeO.sub.2 and the relative refractive index difference .sub.B resulting from B.sub.2O.sub.3 (=1.0%=.sub.GE+.sub.B) and thus the maximum relative refractive index difference of 1% is ensured as a whole of the GI refractive index profile.
(44) When the core or the like is doped with multiple kinds of index-control dopants as in the above second embodiment, the wavelength dependence of .sub.opt demonstrates significant variation. FIG. 8 is graphs showing relationships between .sub.opt to minimize the inter-modal dispersion, among values defining the shape of the GI refractive index profile, and wavelength, for various index-control dopants added in the core and combinations thereof. In FIG. 8, graph G901 shows the relationship between .sub.opt and wavelength in the case where the core is doped with only B.sub.2O.sub.3 as an index-control dopant (=.sub.B=1.0%); graph G902 shows the relationship between .sub.opt and wavelength in the case where the core is doped with GeO.sub.2 and B.sub.2O.sub.3 as index-control dopants so as to constitute of .sub.GE=0.1% and .sub.B=0.9%; graph G903 shows the relationship between .sub.opt and wavelength in the case where the core is doped with GeO.sub.2 and B.sub.2O.sub.3 as index-control dopants so as to constitute of .sub.GE=0.2% and .sub.B=0.8%; graph G904 shows the relationship between .sub.opt and wavelength in the case where the core is doped with GeO.sub.2 and B.sub.2O.sub.3 as index-control dopants so as to constitute of .sub.GE=0.3% and .sub.B=0.7%; graph G905 shows the relationship between .sub.opt and wavelength in the case where the core is doped with GeO.sub.2 and B.sub.2O.sub.3 as index-control dopants so as to constitute of .sub.GE=0.4% and .sub.B=0.6%; graph G906 shows the relationship between .sub.opt and wavelength in the case where the core is doped with GeO.sub.2 and B.sub.2O.sub.3 as index-control dopants so as to constitute of .sub.GE=0.5% and .sub.B=0.5%; graph G907 shows the relationship between .sub.opt and wavelength in the case where the core is doped with GeO.sub.2 and B.sub.2O.sub.3 as index-control dopants so as to constitute of .sub.GE=0.6% and .sub.B=0.4%; graph G908 shows the relationship between .sub.opt and wavelength in the case where the core is doped with GeO.sub.2 and B.sub.2O.sub.3 as index-control dopants so as to constitute of .sub.GE=0.7% and .sub.B=0.3%; graph G909 shows the relationship between .sub.opt and wavelength in the case where the core is doped with GeO.sub.2 and B.sub.2O.sub.3 as index-control dopants so as to constitute of .sub.GE=0.8% and .sub.B=0.2%; graph G910 shows the relationship between .sub.opt and wavelength in the case where the core is doped with GeO.sub.2 and B.sub.2O.sub.3 as index-control dopants so as to constitute of .sub.GE=0.9% and .sub.B=0.1%; graph G911 shows the relationship between .sub.opt and wavelength in the case where the core is doped with only GeO.sub.2 as an index-control dopant (=.sub.GE=1.0%).
(45) It is understood that, by adjusting the number of the kinds of index-control dopants to be added in the core or the like, as described above, it is possible to form a plurality of OFL bandwidth peaks in the wavelength range of 0.85 m to 1.3 m (cf. FIG. 8). For this reason, it becomes feasible to ensure a wider OFL bandwidth than that of the conventional MMF (graph G911) throughout the wavelength range of 0.85 m to 1.3 m. Specifically, in the wavelength range of 0.85 m to 1.3 m, a change amount of .sub.opt is preferably not more than 0.1. In the examples shown in FIGS. 4A to 4D, the OFL, bandwidth becomes sharply narrower at wavelengths off the set wavelength of .sub.opt. Then, since a plurality of OFL bandwidth peaks can be formed with relaxation of the wavelength dependence of .sub.opt as described above, it also becomes easier to secure the sufficiently wider OFL bandwidth than that of the conventional MMF at the wavelengths off the set wavelength of .sub.opt.
(46) When n (2) kinds of index-control dopants are used for adjustment of the shape of the refractive index profile of MMF, each of these n kinds of index-control dopants is added in at least either of the core and the cladding. At this time, the maximum relative refractive index difference is constituted of relative refractive index differences .sub.1, .sub.2, .sub.3, . . . , .sub.n resulting from these n kinds of index-control dopants, as represented by Formula (5) below.
=.sub.1+.sub.2+.sub.3+ . . . +.sub.n(5)
(47) Next, for MMFs (GI-MMFs) of the second embodiment, which have the GI refractive index profile shown in FIG. 7C, relationships between constitutive ratios of index-control dopants and wavelength characteristics of OFL bandwidths will be described using FIG. 9A and FIG. 9B. FIG. 9A is a drawing showing wavelength characteristics of OFL bandwidths at various ratios to constitute the maximum relative refractive index difference in the MMFs, of the relative refractive index differences resulting from the index-control dopants added in the MMFs of the second embodiment, and FIG. 9B an enlarged view of region A shown in FIG. 9A.
(48) In FIGS. 9A and 9B, graph G1010 shows the wavelength characteristic of the OFL bandwidth in the case where the maximum relative refractive index difference is constituted of the relative refractive index difference .sub.GE=0% resulting from GeO.sub.2 and the relative refractive index difference .sub.B=1% resulting from B.sub.2O.sub.3; graph G1020 shows the wavelength characteristic of the OFL bandwidth in the case where is constituted of .sub.GE=0.1% and .sub.B=0.9%; graph G1030 shows the wavelength characteristic of the OFL bandwidth in the case where is constituted of .sub.GE=0.2% and .sub.B=0.8%; graph G1040 shows the wavelength characteristic of the OFL bandwidth in the case where is constituted of .sub.GE=0.3% and .sub.B=0.7%; graph G1050 shows the wavelength characteristic of the OFL bandwidth when is constituted of .sub.GE=0.4% and A.sub.B=0.6%; graph G1060 shows the wavelength characteristic of the OFL bandwidth when is constituted of .sub.GE=0.5% and .sub.B=0.5%; graph G1070 shows the wavelength characteristic of the OFL bandwidth in the case where is constituted of .sub.GE=0.6% and .sub.B=0.4%; graph G1080 shows the wavelength characteristic of the OFL bandwidth in the case where is constituted of .sub.GE=0.7% and .sub.B=0.3%; graph G1090 shows the wavelength characteristic of the OFL bandwidth in the case where is comprised of .sub.GE=0.8% and .sub.B=0.2%; graph G1100 shows the wavelength characteristic of the OFL bandwidth in the case where is constituted of .sub.GE=0.9% and .sub.B=0.1%; graph G1010 shows the wavelength characteristic of the OFL bandwidth in the MMF of the comparative example. The examples shown in. FIGS. 9A and 9B show the relationships between OFL bandwidth and wavelength in the MMFs where the value to define the shape of the GI refractive index profile in the core is adjusted to .sub.opt at the wavelength of 1060 nm. It is seen from FIGS. 9A and 9B that at all wavelengths, the OFL bandwidths of the second embodiment are wider than the OFL bandwidth of graph G1110 as the comparative example. The bandwidth at the wavelength of 0.85 m becomes wider with increase in .sub.B and exceeds 1.5 GHz.Math.km when .sub.B reaches 0.7%. The OFL bandwidth at a wavelength of at least one of 980 nm, 1060 nm, and 1300 nm is wider than the OFL bandwidth at the wavelength of 850 nm. As described above, it is understood that the MMFs of the second embodiment ensure the wide OFL bandwidth in the wider wavelength range than the MMF of the comparative example.
(49) From the above description of the present invention, it will be obvious that the invention may be varied in many ways. Such variations are not to be regarded as a departure from the spirit and scope of the invention, and all improvements as would be obvious to those skilled in the art are intended for inclusion within the scope of the following claims.
