Abstract:
An embodiment of the invention relates to a MMF with a structure for enabling stable manufacture of the MMF suitable for wide-band multimode optical transmission, for realizing faster short-haul information transmission than before. In the MMF, when an input position of a DMD measurement pulse on an input end face is represented by a distance r from a center of a core with a radius a, a power of the DMD measurement pulse on an output end face with the input position r of the DMD measurement pulse being 0.8a is not more than 70% of a power of the DMD measurement pulse on the output end face with the input position r of the DMD measurement pulse being 0.

Description:
BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to a multimode optical fiber (hereinafter referred to as MMF: MultiMode optical Fiber) and an optical cable including the same. 
     Related Background Art 
     The MMF is widely used for short-haul information transmission like LAN (Local Area Network) because it is easy to establish fiber-fiber connection and it becomes feasible to readily construct a network by making use of low-demand-performance equipment. 
     Specifically, the MMF is used in relatively-short-haul communication networks with large communication capacity, e.g., communication in a data center. Particularly, it is believed that there will be increasing demands for MMFs satisfying OM3 (A1a.2) and OM4 (A1a.3) Standards of ISO/IEC11801, which are suitable for fast communication. The bandwidths as most important characteristics of the foregoing MMFs are generally evaluated by DMD (Differential Mode Delay) measurement as shown in IEC60793-1-49 ed2.0. 
     SUMMARY OF THE INVENTION 
     The Inventors conducted research on the conventional MMFs and found the problem as described below. 
     Namely, a refractive index profile of a core in a MMF (indicating refractive indices at respective portions on a straight line corresponding to the diameter of the core, which is perpendicular to the central axis of the MMF) has a dome shape called an α-power refractive index profile and the bandwidth as most important characteristic in the MMF rapidly varies even with slight variation in the α value which determines the shape of the foregoing α-power refractive index profile. Therefore, the broad-band MMFs satisfying the OM3 and OM4 Standards of ISO/IEC11801 have extremely small tolerance for the α-value variation, which is a major factor to determine production yield. 
     Specifically, if in a manufactured MMF the α value deviates from a designed optimum value (value by which the shape of the refractive index profile of the core is optimized for a predetermined wavelength), intermodal dispersion between the fundamental mode and a higher-order mode will increase. Namely, it can be confirmed by the DMD measurement that in a core cross section there is a large group delay difference between an inside region (hereinafter referred to as inside core region) and an outside region (hereinafter referred to as outside core region). Furthermore, an increase in the group delay difference between the inside core region and the outside core region means bandwidth degradation. 
     The present invention has been accomplished to solve the problem as described above and it is an object of the present invention to provide a MMF having a structure for enabling stable manufacture of the MMF suitable for wide-band multimode optical transmission, in order to realize faster short-haul information transmission than before. 
     It is noted that in the present specification, a simple expression of “optical fiber” without any particular note shall mean “multimode optical fiber (MMF).” The MMF according to an embodiment of the present invention concerns a GI (Graded Index) type MMF (hereinafter referred to as GI-MMF) and is definitely differentiated from the single-mode optical fiber (hereinafter referred to as SMF) for long-haul transmission by structure. The GI-MMF has a general structure composed of a high-refractive-index core and a low-refractive-index cladding. The MMF according to the embodiment of the present invention also includes a MMF having the structure common to the GI-MMF and provided with a trench part of a low refractive index located between the core and the cladding (referred to as BI-MMF: Bend-Insensitive MultiMode optical Fiber). The trench part has the lower refractive index than the cladding and provides the MMF with macro-bending resistance property. 
     A MMF according to an embodiment of the present invention, when configured as a GI-MMF, comprises: an input end face; an output end face opposed to the input end face; a core extending from the input end face to the output end face; and a cladding provided on an outer peripheral surface of the core. A MMF according to an embodiment of the present invention, when configured as a BI-MMF, comprises: an input end face; an output end face opposed to the input end face; a core extending from the input end face to the output end face; a cladding provided on an outer peripheral surface of the core; and a trench part provided between the core and the cladding. In both of the GI-MMF and the BI-MMF, the core has an outer diameter 2a and has an α-power refractive index profile. The trench part in the BI-MMF has a lower refractive index than the cladding. Particularly, in the embodiment of the invention, each of the GI-MMF and the BI-MMF is configured as follows: in the DMD measurement, when an input position of a measurement pulse on the input end face is represented by a distance r from a center of the core, a power of the measurement pulse on the output end face with the input position r of the measurement pulse being 0.8a is not more than 70% of a power of the measurement pulse on the output end face with the input position r being 0. The power of the measurement pulse can be confirmed by the DMD measurement and in the present specification the power of the measurement pulse means a time integral value of a measuring device for measuring the pulse intensity per given time (e.g., an integral value of an oscilloscope waveform on the vertical axis of pulse intensity and the horizontal axis of time). 
     Each of embodiments according to the present invention will become more fully understood from the detailed description given hereinbelow and the accompanying drawings. These embodiments are presented by way of illustration only, and thus are not to be considered as limiting the present invention. 
     Further scope of applicability of the present invention will become apparent from the detailed description given hereinafter. However, it should be understood that the detailed description and specific examples, while indicating preferred embodiments of the invention, are given by way of illustration only, and it is apparent that various modifications and improvements within the scope of the invention would be obvious to those skilled in the art from this detailed description. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  to  FIG. 1C  are drawings showing various configuration examples of optical cables according to the embodiment of the invention. 
         FIG. 2  is a drawing showing a schematic configuration of a device for performing the DMD measurement (DMD measurement device). 
         FIG. 3A  to  FIG. 3D  are drawings for explaining the principle of the DMD measurement by the device shown in  FIG. 2 . 
         FIG. 4A  and  FIG. 4B  are drawings showing a cross-sectional structure and a refractive index profile of a GI-MMF according to the embodiment of the invention. 
         FIG. 5A  and  FIG. 5B  are drawings showing a cross-sectional structure and a refractive index profile of a BI-MMF according to the embodiment of the invention. 
         FIG. 6A  to  FIG. 6C  are graphs showing a refractive index profile, theoretical values of pulse power in the DMD measurement, and measured values of pulse power in the DMD measurement, of a GI-MMF sample according to a comparative example. 
         FIG. 7  is a drawing for explaining a preform manufacturing step in processes for manufacturing the GI-MMF and BI-MMF according to the embodiment of the invention. 
         FIG. 8  is a drawing for explaining a drawing step in the processes for manufacturing the GI-MMF and BI-MMF according to the embodiment of the invention. 
         FIG. 9  is graphs showing measured values of pulse power in the DMD measurement with the GI-MMF sample of the embodiment of the invention and the GI-MMF sample of the comparative example. 
         FIG. 10  is graphs showing relations of the α value to determine the shape of the refractive index profile in the core versus EMB (effective modal bandwidth), with the GI-MMF samples of the embodiment of the invention and the GI-MMF of the comparative example. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     Each of embodiments of the present invention will be described below in detail with reference to the accompanying drawings. The same elements will be denoted by the same reference signs in the description of the drawings, without redundant description. 
       FIG. 1A  to  FIG. 1C  show various configuration examples of optical cables according to the embodiment of the invention, wherein  FIG. 1A  shows a cross-sectional structure of an optical cable including a MMF as an example of the optical cable according to the embodiment of the invention.  FIG. 1B  shows an optical cord in which a connector is attached to a tip portion of a MMF, as another example of the optical cable according to the embodiment of the invention, and the optical cord of this kind is also included in the optical cable according to the embodiment of the invention.  FIG. 1C  is a drawing showing a schematic configuration of an optical cable including a plurality of MMFs, as still another example of the optical cable according to the embodiment of the invention. 
     Specifically, the optical cable  1 A in  FIG. 1A  includes a MMF  100  (glass part comprised of silica glass) according to the embodiment of the invention, which extends along the optical axis AX 1 , and a resin coat  130 , which is coated during drawing of an optical fiber preform. The MMF  100  has an input end face  100   a , and an output end face  100   b  (cf.  FIG. 3A ) opposed to the input end face  100   a , and these MMF  100  and resin coat  130  constitute a coated optical fiber  200 . The optical cable  1 A is further provided with a cable jacket  300  disposed on the outer periphery of the coated optical fiber  200 . The cable jacket  300  is composed of one or more resin layers. 
     The optical cable  1 B in  FIG. 1B  has a form of an optical cord and in the example of  FIG. 1B  the optical cable  1 A in  FIG. 1A  is applied to a part of the optical cord. Namely, the optical cable  1 B is an optical cord provided with the optical cable  1 A and with a connector  11  attached to a tip portion of the MMF  100  from which the cable jacket  300  has been removed. The optical cable  1 B having this structure is optically connected to another optical cord through a sleeve  12  for position alignment. Namely, as shown in  FIG. 1B , the connector  11  of the optical cord being the optical cable  1 B is inserted through one slot into the sleeve  12  along a direction indicated by an arrow S 1  in the drawing. On the other hand, a connector of another optical cord is also inserted through the other slot into the sleeve  12  along a direction indicated by an arrow S 2 . In this manner, optical connection is achieved between the MMF  100  in the optical cord of optical cable  1 B and the MMF in the other optical cord. 
     Furthermore, the optical cable according to the embodiment of the invention also includes the optical cable  1 C including the plurality of MMFs  200 A to  200 N as shown in  FIG. 1C . The optical cable  1 C may have a tape shape in which the plurality of MMFs  200 A to  200 N are integrally fixed by a cable coating (resin) while being arranged on the same plane, and an optical cord wherein connectors are attached to these MMFs  200 A to  200 N is also included in the optical cable  1 C. 
     The MMF  100  according to the embodiment of the invention has a configuration for effectively suppressing the bandwidth degradation of the MMF  100  due of deviation of the shape of the refractive index profile of the core from the ideal shape. Specifically, the configuration lowers the dependence of the bandwidth of the MMF on the shape of the refractive index profile of the core and, even with increase in the group delay difference between the inside core region and the outside core region, the power of propagating light is attenuated in the outside core region, so as to suppress influence on the transmission bandwidth. This suppression effect can be confirmed by the DMD measurement to compare power at respective portions on the output end face  100   b  of the MMF  100 . 
     In general, in the case of the MMF wherein the α value for defining the shape of the α-power refractive index profile of the core deviates from an optimum value at a use wavelength, intermodal dispersion between the fundamental mode and a higher-order mode becomes larger. However, even if there is a higher-order mode which causes great intermodal dispersion with the fundamental mode, it cannot be a factor to degrade the bandwidth unless the higher-order mode propagates up to a receiver because of leakage or attenuation in a process of propagation in the MMF. Even if such a higher-order mode reaches the receiver, the degree of the bandwidth degradation will be insignificant if the arriving higher-order mode is sufficiently attenuated. Furthermore, when the α value deviates from the optimum value, a mode propagating in the outside core region is more likely to demonstrate greater intermodal dispersion with the fundamental mode. If the MMF demonstrates noticeable leakage or attenuation of modes propagating in the outside core region, the bandwidth degradation will be reduced even with some deviation of the α value of the core profile from the optimum value, thereby gaining the advantage of maintaining the quality of wide-band multimode optical transmission. Furthermore, the optimum α value also varies depending on the use wavelength. For this reason, the transmission bandwidth also has dependence on the wavelength of propagating light and the MMF as described above must be able to maintain a wide bandwidth enough for use. This means that it becomes easier to manufacture the MMFs satisfying the OM3 (A1a.2) and OM4 (A1a.3) Standards of ISO/IEC11801, suitable for fast communication. 
     In passing, the MMF satisfying the OM3 Standard refers to a fiber that has the bandwidth called Effective Modal Bandwidth (EMB), of not less than 2000 MHz·km and the bandwidths in all-mode excitation (OFL (Over Filled Launch) bandwidth defined by International Standards IEC60793-1-41) of not less than 1500 MHz·km at 850 nm and not less than 500 MHz·km at 1300 nm. In the OM3 Standard, the MMF needs to satisfy the three conditions (OM3-1 to OM3-3) below.
 
EMB (850 nm)≧2000 MHz·km  (OM3-1)
 
OFL bandwidth (850 nm)≧1500 MHz·km  (OM3-2)
 
OFL bandwidth (1300 nm)≧500 MHz·km  (OM3-3)
 
     In the OM4 Standard, the MMF needs to satisfy the three conditions (OM4-1 to OM4-3) below.
 
EMB (850 nm)≧4700 MHz·km  (OM4-1)
 
OFL bandwidth (850 nm)≧3500 MHz·km  (OM4-2)
 
OFL bandwidth (1300 nm)≧500 MHz·km  (OM4-3)
 
     It is known as an example that about a hundred modes propagate in the MMF with the core diameter of 50 μm and the relative refractive-index difference Δ core  of about 1% at the core center, but there is no specific index for measuring leakage or attenuation of individual modes. Then the Inventors considered that it should be effective to evaluate a radial distribution of pulse power on the output end face of MMF in the DMD measurement, as an index to figure out a level of leakage or attenuation of higher-order modes. Specifically, the MMF  100  according to the embodiment of the invention, which is either the GI-MMF or the BI-MMF, has a characteristic light power distribution which can be confirmed by the DMD measurement. Namely, the MMF according to the embodiment of the invention is characterized in that when an input position of a measurement pulse on the input end face is represented by a distance r from the center of the core with the diameter 2a, the power of the measurement pulse on the output end face with the input position r of the measurement pulse being 0.8a is not more than 70% and preferably not more than 40% of the power of the measurement pulse on the output end face with the input position r of the measurement pulse being 0. It is noted in the present specification that in the core with the diameter 2a, a region where the distance r from the core center falls within the range of 0.8a to a corresponds to the outside core region. In the aforementioned example, the region with the core radii from 20 μm to 25 μm is the outside core region and the region surrounded by the outside core region is the inside core region. 
     As preferred optical characteristics at the wavelength 850 nm of the MMF  100  according to the embodiment of the invention, the OFL bandwidth is not less than 1500 MHz·km and the EMB is not less than 2000 MHz·km. As more preferred optical characteristics at the wavelength 850 nm, the OFL bandwidth is not less than 3500 MHz·km and the EMB is not less than 4700 MHz·km. As preferred optical characteristics at both of the wavelength 850 nm and the wavelength 950 nm of the MMF according to the embodiment of the invention, the EMB at the wavelength 850 nm is not less than 4700 MHz·km and the EMB at the wavelength 950 nm is not less than 2700 MHz·km. As a preferred optical characteristic at any one of the wavelengths 980 nm, 1060 nm, and 1300 nm of the MMF  100  according to the embodiment of the invention, the OFL bandwidth is not less than 1500 MHz·km. As a more preferred optical characteristic at any one of the wavelengths 980 nm, 1060 nm, and 1300 nm, the OFL bandwidth is not less than 3500 MHz·km. 
     For obtaining the optical characteristics as described above, the MMF  100  according to the embodiment of the invention has a structure for attenuating light propagating at least through the outside core region in the core, or, for leaking such outside propagating light from the core into the cladding. Various means can be applied to the structure for selectively attenuating or leaking the outside propagating light in the core and a preferred example of such structure is, for example, a structure in which at least a part of a glass region surrounding the outer peripheral surface of the core and being different from the core is doped with a transition metal element. 
     (DMD Measurement) 
     The DMD measurement will be described below in detail using the accompanying drawings.  FIG. 2  is a drawing showing a schematic configuration of a DMD measurement device.  FIGS. 3A to 3D  are drawings for explaining the principle of the DMD measurement. 
     The DMD measurement device in  FIG. 2  is a device that measures pulse responses of the MMF while giving offsets in the radial direction of the MMF to a very limited excitation spot on the input end face of the MMF as an object to be measured.  FIG. 2  shows the optical cable  1 A including the MMF  100  of the measured object, as an example. 
     The DMD measurement device, as shown in  FIG. 2 , is provided with a light source  501 , a variable light attenuator  502 , an SMF (excitation fiber)  503 , a fiber center aligner  504 , a control unit  505 , an oscilloscope  506 , and an O/E converter  506   a . The light source  501  outputs a measurement pulse. The variable light attenuator  502  regulates the light quantity of the measurement pulse from the light source  501 . The SMF  503 , as shown in  FIG. 3A , guides the measurement pulse from the variable light attenuator  502  so as to apply the measurement pulse from an output end face  503   a  to a predetermined position on the input end face  100   a  of the MMF  100  (included in the optical cable  1 A). The fiber center aligner  504  fixes the output end face  503   a  of the SMF  503  and the input end face  100   a  of the MMF  100  at respective predetermined positions. The control unit  505  controls the fiber center aligner  504  to adjust relative positions of the output end face  503   a  of the SMF  503  and the input end face  100   a  of the MMF  100 . The O/E converter  506   a  converts the intensity waveform of the measurement pulse from the output end face  100   b  of the MMF  100  into an electric signal. The oscilloscope  506  generates an intensity waveform of the measurement pulse, based on the electric signal from the O/E converter  506   a . The fiber center aligner  504  is provided with a stage  504 A to which a tip portion of the SMF  503  including the output end face  503   a  is fixed and with a stage  504 B to which a tip portion of the MMF  100  including the input end face  100   a  is fixed. The control unit  505  adjusts respective positions of the stages  504 A and  504 B of the fiber center aligner  504 , so as to give the offsets in the radial direction of the MMF  100  indicated by an arrow S 3  to the excitation spot (the input position of the measurement pulse) on the input end face  100   a  of the MMF  100 . 
     Specifically, in the DMD measurement, as shown in  FIG. 3A , the fiber center aligner  504  adjusts the relative positions of the output end face  503   a  of the SMF  503  extending along the optical axis AX 2  and the input end face  100   a  of the MMF  100  extending along the optical axis AX 1 , according to an instruction signal from the control unit  505 . Namely, the measurement pulse P in  having the intensity peak at the core center (coincident with the optical axis AX 2 ) is output from the output end face  503   a  of the SMF  503 , as shown in  FIG. 3C . On the other hand, on the input end face  100   a  of the MMF  100 , as shown in  FIG. 3D , the intensity peak of the measurement pulse P in  is given the offset in the radial direction (direction indicated by the arrow S 3  in  FIG. 3A ) from the core center (coincident with the optical axis AX 1 ). Intensity waveform of the measurement pulse P out  on the output end face  100   b  of the MMF  100  is converted into an electric signal by the O/E converter  506   a  and the electric signal is taken into the oscilloscope  506  to obtain an intensity distribution  507  of the measurement pulse PA as shown in  FIG. 3A . The intensity distribution  507  is composed of oscilloscope waveforms of the measurement pulse P out  corresponding to respective input positions of P in , where time is represented by the horizontal axis and core radial position of input of the measurement pulse P in  by the vertical axis. An oscilloscope waveform with each P in  input position is the shape as shown in  FIG. 3B  (where the vertical axis represents intensity and the horizontal axis represents time) and in the present specification an integral value (area) of this oscilloscope waveform means the power of the measurement pulse P out  on the output end face  100   b  of the MMF  100 . 
     (MMF of First Embodiment) 
       FIG. 4A  is a drawing showing a cross-sectional structure of a GI-MMF  100 A according to the first embodiment and  FIG. 4B  is a refractive index profile thereof. This GI-MMF  100 A is applicable to any one of the optical cables  1 A to  1 C shown in  FIGS. 1A to 1C . 
     The GI-MMF  100 A, as shown in  FIG. 4A , is provided with a core  110 A extending along the optical axis AX 1  and a cladding  120 A provided on the outer periphery of the core  110 A. In the GI-MMF  100 A shown in  FIG. 4A , the core  110 A is doped with GeO 2  for adjusting the shape of the refractive index profile and has the maximum refractive index n1. The cladding  120 A is pure silica or a glass region doped with an impurity for adjustment of refractive index and has the refractive index n2 (n2&lt;n1) lower than the maximum refractive index n1 of the core  110 A. 
     The refractive index profile  150 A of the GI-MMF  100 A shown in  FIG. 4B  indicates the refractive indices at respective portions on a line L 1  (coincident with the radial direction of the GI-MMF  100 A) perpendicular to the optical axis AX 1  and, more specifically, a region  151 A indicates the refractive indices at respective portions of the core  110 A along the line L 1  and a region  152 A does the refractive indices at respective portions of the cladding  120 A along the line L 1 . 
     Particularly, the region  151 A in the refractive index profile  150 A in  FIG. 4B  has a dome shape in which the refractive index becomes maximum at the center of the core  110 A where the refractive index n(r) coincides with the optical axis AX 1  (a position where the optical axis AX 1  intersects with the cross section of the GI-MMF  100 A), as expressed by Expression (1) below (α-power refractive index profile). The n(r) is the refractive index of the core  110 A with the radius a (or the diameter 2a) and represents the refractive index at the position r away in the radial direction from the center of the core  110 A. Therefore, concentrations of GeO 2  doped for adjustment of refractive index also steeply decrease from the center of the core  110 A toward the adjacent cladding  120 A. The α value for defining this dome shape is from 1.8 to 2.2. The relative refractive-index difference Δ core  of the center of the core  110 A to the cladding  120 A (which corresponds to the maximum relative refractive-index difference of the core  110 A to the cladding  120 A) is from 0.8 to 2.4%. The diameter of the core  110 A is from 25 to 65 μm. In the present specification, the same core structure also applies to the structure of the core in each of embodiments, comparative example, and others described below. The relative refractive-index difference Δ core  of the core  110 A (refractive index n1) to the cladding  120 A (refractive index n2) is defined by Expression (2) below. The following definition of the relative refractive-index difference is also applied to the other embodiments. 
     
       
         
           
             
               
                 
                   
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     (MMF of Second Embodiment) 
       FIG. 5A  is a drawing showing a cross-sectional structure of a BI-MMF  100 B according to the second embodiment and  FIG. 5B  is a refractive index profile thereof. This BI-MMF  100 B is applicable to any one of the optical cables  1 A to  1 C shown in  FIGS. 1A to 1C . 
     The BI-MMF  100 B, as shown in  FIG. 5A , is provided with a core  110 B extending along the optical axis AX 1 , a cladding  120 B provided on the outer periphery of the core  110 B, and a trench part  130 B provided between the core  110 B and the cladding  120 B. In the BI-MMF  100 B shown in  FIG. 5A , the core  110 B is doped with GeO 2  for adjusting the shape of the refractive index profile and has the maximum refractive index n1. The trench part  130 B is doped with a refractive index decreasing agent such as fluorine, for providing the BI-MMF  100 B with macro-bending resistance property and has the refractive index n3 (&lt;n1). The cladding  120 B is pure silica or a glass region doped with an impurity for adjustment of refractive index and has the refractive index n2 lower than the maximum refractive index n1 of the core  110 B and higher than that of the trench part  130 B (n3&lt;n2&lt;n1). 
     The refractive index profile  150 B of the BI-MMF  100 B shown in  FIG. 5B  indicates the refractive indices at respective portions on a line L 2  (coincident with the radial direction of the BI-MMF  100 B) perpendicular to the optical axis AX 1  and, more specifically, a region  151 B indicates the refractive indices at respective portions of the core  110 B along the line L 2 , a region  152 B does the refractive indices at respective portions of the cladding  120 B along the line L 2 , and a region  153 B does the refractive indices at respective portions of the trench part  130 B along the line L 2 . 
     Particularly, the region  151 B in the refractive index profile  150 B in  FIG. 5B  has the α-power refractive index profile given by the aforementioned Expression (1). The refractive index n(r) is the refractive index of the core  110 B with the radius a and represents the refractive index at the position r away in the radial direction from the center of the core  110 B. Therefore, concentrations of GeO 2  doped for adjustment of refractive index also steeply decrease from the center of the core  110 B toward the adjacent trench part  130 B. The α value for defining the shape of this α-power refractive index profile is from 1.8 to 2.2. The relative refractive-index difference Δ core  of the center of the core  110 B to the cladding  120 B, which is defined by the foregoing Expression (2), is from 0.8 to 2.4%. The diameter of the core  110 B is from 25 to 65 μm. The foregoing core structure is the same as the structure of the core in the first embodiment ( FIGS. 4A and 4B ). The relative refractive-index difference Δ trench  of the trench part  130 B (refractive index n3) to the cladding  120 A (refractive index n2) is defined by Expression (3) below. 
     
       
         
           
             
               
                 
                   
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     (Evaluation) 
     The following will describe the evaluation results of the higher-order mode removal function in the outside core region and the bandwidth stability with two samples of GI-MMF  100 A (embodiment samples) as MMF  100  of the embodiment of the invention and a sample of GI-MMF according to a comparative example (comparative sample) which were prepared for the evaluation. Although the below description explains the samples of GI-MMF, the same evaluation results would be expected with the BI-MMF shown in  FIGS. 5A and 5B  because the shape of the core is the same. For this reason, the evaluation on the BI-MMF will be omitted in the following description. 
     First,  FIG. 6A  is a refractive index profile of the GI-MMF of the comparative sample. As shown in  FIG. 6A , the comparative sample has the core radius of 25 μm (the core diameter of 50 μm). The relative refractive-index difference Δ core  of the core center to the cladding is 1.07% and the α value for defining the shape of the α-power refractive index profile in the core is 2.06. 
     The graph of  FIG. 6B  shows the calculation results of the DMD measurement for the comparative sample having the structure as described above and theoretical values of relative pulse power in the DMD measurement against core radii. The graph of  FIG. 6C  shows the actual measurement results of the DMD measurement of the comparative sample and measured values of pulse power in the DMD measurement against core radii. In  FIGS. 6B and 6C , the DMD pulse powers (pulse powers measured by the DMD measurement and powers of the measurement pulse on the output end face of the MMF as measured object) are expressed by relative values. Namely, while with incidence of the measurement pulse to the core center (core radius of 0 μm) on the input end face of the comparative sample the power of the measurement pulse on the output end face of the comparative sample (reference value) is defined as 1, the powers of the measurement pulse on the output end face of the sample with incidence of the measurement pulse to the positions other than the core center are expressed by relative values to the foregoing reference value. 
     As seen from  FIGS. 6B and 6C , the comparative sample demonstrates approximate agreement between the theoretical values shown in  FIG. 6B  and the measured values shown in  FIG. 6C . The theoretical values in  FIG. 6B  are values calculated from coupling ratios from incidence pulse to guided modes and leaky modes of the measurement pulse injected into the comparative sample in execution of the DMD measurement. The reason why the DMD pulse powers become lower in the outside core region (region with the core radii from 20 μm to 25 μm) is that the coupling ratios from guided modes to leaky modes become higher for the measurement pulse injected into the outside core region (outside propagating light). 
     On the other hand, each of the GI-MMFs  100 A prepared as embodiment sample 1 and embodiment sample 2 has the cross-sectional structure and refractive index profile shown in  FIGS. 4A and 4B  and their basic structure is the same as the GI-MMF  100 A of the above comparative sample. Namely, each of the GI-MMFs  100 A of embodiment samples 1 and 2 has the core radius of 25 μm (the core diameter of 50 μm). The relative refractive-index difference Δ core  of the core center to the cladding  120 A is 1.07% and the α value for defining the shape of the α-power refractive index profile in the core  110 A is 2.06. However, each of the embodiment samples 1 and 2 is different from the comparative sample in that each embodiment sample has the structure for attenuating the light propagating at least through the outside core region with the core radii of 20 μm to 25 μm in the core  110 A, or, for leaking such outside propagating light from the core to the cladding. Specifically, a preferred structure is one in which a transition metal element is doped in at least a part of the glass region surrounding the outer peripheral surface of the core  110 A and being different from the core  110 A. In each of the prepared embodiment samples 1 and 2, the cladding is doped with a small amount of Cu; in the embodiment sample 1 the Cu dopant amount in the cladding  120 A is 4 ppb; in the embodiment sample 2 the Cu dopant amount into the cladding  120 A is 13 ppb. In the case of the BI-MMF  100 B in  FIGS. 5A and 5B , the glass region doped with the transition metal element includes the trench part  130 B, as well as the cladding  120 B. 
     Doping of Cu into the cladding  120 A in the GI-MMFs  100 A of embodiment samples 1, 2 is carried out during a step of manufacturing a cladding part in an optical fiber preform for GI-MMFs  100 A. Namely, the optical fiber preform for GI-MMFs  100 A is manufactured by producing a glass region (core rod) to become the core  110 A and thereafter performing deposition of glass fine particles onto the core rod (step ST 1 ), dehydration (step ST 2 ), sintering (step ST 3 ), and elongation (step ST 4 ) according to the flowchart shown in  FIG. 7 , and then the optical fiber preform with the shape of optical fiber is drawn into fiber. The glass region corresponding to the trench part  130 B in the BI-MMF  100 B is also manufactured along the flowchart of  FIG. 7 .  FIG. 8  is a drawing for explaining the drawing step for obtaining the GI-MMF  100 A and the BI-MMF  100 B. 
     Specifically, the doping of Cu into the cladding  120 A is carried out in the process of forming the glass region (cladding part) to become the cladding  120 A, on the outer peripheral surface of the prepared core rod. In this process of manufacturing the glass region to become the cladding  120 A, fine particles of silica glass are first deposited by VAD (Vapor Phase Axial Deposition) or by OVD (Outside Vapor Deposition) (step ST 1 ). The resulting porous preform is subjected to dehydration (step ST 2 ) and sintering (step ST 3 ) in a dehydration/sintering furnace and on that occasion, a Cu piece as dopant source is intentionally put in the dehydration/sintering furnace, whereby Cu can be mixed in the glass region to become the cladding  120 A. Thereafter, the intermediate preform obtained through the dehydration (step ST 2 ) and sintering (step ST 3 ) is elongated to a predetermined outside diameter, thereby obtaining an optical fiber preform  800  for the embodiment samples 1, 2. In the example of  FIG. 8 , the resultant optical fiber preform  800  is the optical fiber preform for GI-MMF  100 A and this is composed of a glass region  810  to become the core  110 A, and a glass region  820  to become the cladding  120 A. In the optical fiber preform for BI-MMF  100 B, a region between a dashed line in  FIG. 8  and the outer periphery of the glass region  810  corresponds to a glass region to become the trench part. 
     Next, as shown in  FIG. 8 , the resultant optical fiber preform  800  is drawn in a direction indicated by an arrow S 4  with one end thereof being heated, thereby manufacturing the MMF  100  corresponding to the GI-MMF  100 A or the BI-MMF  100 B. The outer peripheral surface of the manufactured MMF  100  is coated with the resin coat  130  by a resin coating device  830 , thereby obtaining the coated optical fiber  200 . 
       FIG. 9  is graphs showing relations of pulse input position (input position of the measurement pulse on the input end face of each sample) versus output end pulse power (power of the measurement pulse on the output end face in each sample) in the DMD measurement, as to the GI-MMFs  100 A of the respective embodiment samples 1, 2 as described above and the GI-MMF of the comparative sample. In  FIG. 9 , graph G 910  shows the output end pulse powers of the comparative sample, graph G 920  the output end pulse powers of the embodiment sample 1 in which the cladding is doped with the small amount of Cu, and graph G 930  the output end pulse powers of the embodiment sample 2 in which the cladding is doped with the larger amount of Cu than in the embodiment sample 1. It is noted that the output end pulse powers in  FIG. 9  are indicated by relative values as in  FIGS. 6B and 6C . Namely, while with incidence of the measurement pulse to the core center (core radius of 0 μm) on the input end face of each sample the power of the measurement pulse on the output end face of the sample (reference value) is defined as 1, the powers of the measurement pulse on the output end face of the sample with incidence of the measurement pulse to the positions other than the core center are expressed by relative values to the foregoing reference value. 
     As seen from this  FIG. 9 , the powers of the measurement pulse (outside propagating light) propagating in the outside core region (the region with the core radii of 20 μm to 25 μm) in both of the embodiment samples 1, 2 wherein the cladding  120 A is doped with Cu are obviously lower than those in the comparative sample. By comparison between embodiment sample 1 and embodiment sample 2, the powers of the measurement pulse propagating through the outside core region are lower in the embodiment sample 2 with the larger Cu dopant amount than in the embodiment sample 1. For example, in the case of the embodiment sample 1, the output end pulse powers with incidence of the measurement pulse into the outside core region (with the core radii of 20 μm to 25 μm) are not more than 70% of the foregoing reference value. In the case of the embodiment sample 2, the output end pulse powers with incidence of the measurement pulse into the outside core region are not more than 40% of the foregoing reference value. It is understood from this result that in both of the embodiment samples 1, 2 the light propagating through the outside core region is selectively weakened by action of Cu doped in the cladding  120 A. 
     Furthermore, in order to evaluate superiority of the embodiment of the invention in terms of bandwidth variation and production yield,  FIG. 10  shows the theoretical values of EMB at the wavelength 850 nm against multiple a values, as to the GI-MMFs  100 A of the respective embodiment samples 1, 2 and the GI-MMF of the comparative sample. In  FIG. 10 , graph G 1010  shows EMB of the comparative sample, graph G 1020  EMB of the embodiment sample 1 wherein the cladding is doped with the small amount of Cu, and graph G 1030  EMB of the embodiment sample 2 wherein the cladding is doped with the larger amount of Cu than in the embodiment sample 1. 
     The results shown in  FIG. 10  are the theoretical values calculated from the distribution states of output end pulse powers shown in  FIG. 9 , for each of the comparative sample, the embodiment sample 1, and the embodiment sample 2. The power distribution of measurement pulse calculated for the ordinary GI-MMF of the comparative sample ( FIG. 6B ) approximately agrees with the intensity distribution of measurement pulse actually measured and thus it is considered that the theoretical values shown in  FIG. 10  have no significant difference from measured values, either. The calculation of EMB at the wavelength 850 nm was done on the assumption that the refractive index profile of the core in each sample was the α-power refractive index profile and under each of the conditions of α=2.02, α=2.06, and α=2.1. 
     As seen from  FIG. 10 , the optimum value of the α value at the wavelength 850 nm is 2.06 in all the samples. At each a value, the bandwidth is expanded in the embodiment samples 1, 2 compared to the comparative sample. In the cases where the α value deviates from the optimum value (2.06) at the wavelength 850 nm, the comparative sample demonstrates significant degradation of bandwidth. On the other hand, the bandwidth degradation is relieved in each of the embodiment samples 1, 2 compared to the comparative sample. It is understood from this result that the MMF  100  (GI-MMF  100 A or BI-MMF  100 B) wherein the light propagating through the outside core region is largely attenuated is essentially superior in bandwidth stability to the comparative sample (ordinary GI-MMF). 
     In the MMF according to the embodiment of the invention, the power of light propagating through the outside region in the core cross section is steeply lowered with respect to the power of light propagating through the center of the core cross section. For this reason, in the case where the shape of the refractive index profile in the core deviates from the shape of the refractive index profile (or where the α value deviates from the optimum value in the manufactured MMF), even if the group delay difference between the inside core region and the outside core region is increased, the influence of the group delay difference of propagating light through the outside core region is suppressed on the transmission bandwidth and, as a result, the dependence of the transmission bandwidth of the MMF on the shape of the refractive index profile of the core is reduced. 
     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.