Abstract:
To determine the type of unknown optical fiber, an automatic fiber fusion-type splicer is used having movable clamps, electrodes, camera devices and background illumination, coupled to electronic circuits containing control, driver, and interface circuits. A fiber portion is imaged to allow the fiber core to be distinguished in the captured image, both when the fiber is cold and when it is heated. From a first fiber picture in a heated state, a first light intensity profile is determined along a line perpendicular to the fiber. The profile derivative is compared to derivatives of known light intensity profiles. Similar procedures are performed for the cold fiber. Based on the comparing operations, the type of the tested fiber is determined.

Description:
This application is the US national phase of international application PCT/SE01/01427, filed in English on Jun. 20, 2001, which designated the U.S. PCT/SE01/01427 claims priority from SE application 0002310-1, filed on Jun. 20, 2000. 
    
    
     TECHNICAL FIELD 
     The present invention relates to a method for evaluating an optical fiber, in particular for determining the general type of optical fiber to which a considered optical fibers belongs, to be used in an automatic fiber splicer for automatically selecting correct splicing parameters and also to a method of setting an optical system used in a splicer. 
     BACKGROUND 
     Equipment and methods for aligning and splicing silica based optical fibers has been developed and improved for many years. The most common method for performing an alignment of optical fibers to be spliced with an accuracy better than 0.2 micron and making accurate splice loss estimation has comprised advanced digital image processing of magnified pictures of the splicing position before, at and after the actual splicing of the fibers, these pictures produced by a camera system. The design of a compact optical system, capable of giving a sharp image of the spliced fibers and their cores before, during and after the splicing which in many cases is made by a fusion process, has been a critical task in developing fiber splicing machines having a high performance, see e.g. T. Haibara, M. Matsumoto, T. Tanifuji and M. Tokuda, “Monitoring method for axis alignment of single-mode fiber and splice loss estimation”, Optics Letters, Vol 6, No. 4, April 1983, O. Kawata, K. Hoshino, Y. Miyajima, M. Ohnishi and K. Ishihara, “A splicing and inspection technique for single-mode fibers using direct core monitoring”, J. Ligthwave Technology, Vol. LT-2, No. 2, April 1984, and T. Katagiri, M. Tachikura and I. Sankawa. “Optical microscope observation method of a single mode optical fiber core for precise core-axis alignment”, J. Ligthwave Technology, Vol. LT-2, No. 3, June 1984. 
     In a fusion splicer equipped with a digital camera system, the fibers to be spliced or being spliced or having been spliced are conventionally illuminated by a light source, normally a LED, located at a distance behind the fibers as seen from a lens system. The lens system is focused on some point in the fiber claddings or in the fiber cores and a magnified image of the fibers is created on a CCD matrix (Charge Coupled Device). The electric signal from the camera is A/D converted, and the digital picture is processed in a computer system. The measurement data from the pictures are then used for moving fibers to the desired accurate alignment and for estimating the splice loss. 
     The optical system of a fusion splicer can also be adapted to image the hot fibers during fusion, see e.g. German patent 40 04 909 and Swedish patent application 9002725-1, filed Aug. 24, 1990. The small difference between emissivity of the fiber cladding and the core at high temperatures, such as those of about 2000° C. existing in an electric arc used in the fusion process, make it possible to produce a bright image of the core, conventionally located in the middle of the fiber. The visible and near infrared part of the emitted waves from the heated fibers are collected and detected by the camera system. Hot images can be used for real time processing of the fibers during fusion and for making an accurate splice loss estimation after the splice is completed. 
     It is well known that core/cladding eccentricity, cleave angle, curl, fiber-end contamination and mode field diameter (MFD) mismatch are the main reasons of fusion splicing loss. An MFD mismatch can significantly influence the splice loss in particular in the case where different types of fibers are spliced to each other. To produce splices having a low loss made between fibers having different MFD it is necessary to characterize the types of fibers to be splice and based on the fiber types, select appropriate splice parameters like overlap, fusion heat and fusion time to be used in the splicing procedure, see e.g. W. Zheng, “Real time control of arc fusion for optical fiber splicing”, J. Ligthwave Technology, Vol. 11, pp. 548-553, March 1994, and W. Zheng, O. Hultén and Robert Rylander, “Erbium doped fiber splicing and splice loss estimation”, J. Ligthwave Technology, Vol. 12, pp. 430-435, March 1994. The appropriate choice of these parameters is highly dependent on the core sizes and the refractive index profiles of the fibers and the refractive index differences between the core and cladding. A method for identifying fibers before fusion for automatic selection of the splice parameters is therefore of great importance for making low loss splices of different types of fibers. 
     In Swedish patent application 9100979-5 for Telefonaktiebolaget L M Ericsson, inventors Ola Hultén and Wenxin Zheng, a method of determining characteristics of optical fibers is disclosed, the method including analyzing images of heated fibers and in particular light intensity profiles along lines perpendicular to the fibers. The general shape of the central peak and especially its width and height are evaluated. A mathematical method using the same basic analyzing process is disclosed in Swedish patent application 9201817-5 for Telefonaktiebolaget L M Ericsson, inventor Wenxin Zheng. 
     In an automatic fiber splicer the optical system for imaging an optical fiber on some light sensitive area cannot be easily set for different imaging conditions such a for producing a sharp picture of a cold fiber in which the core is visible or in particular the position and the width of the core are detectable or for producing a sharp picture of a heated optical fiber emitting light so that also in this picture the core region is detectable. Such focusing for different imaging conditions is generally made manually by observing the captured images for different focusing conditions, i.e. for different distances between the object, the optical fiber, and the imaging system, primarily the lens system. 
     SUMMARY 
     It is an object of the invention to provide a reliable method of deciding the type of an optical fiber. 
     It is another object of the invention to provide a robust, automatic method of setting an optical system for providing images of an optical fiber in which the core of the optical fiber is visible. 
     In determining the kind or type to which an unknown optical fiber belongs an automatic fiber splicer using fusion-welding is used having movable clamps or retainers for positioning aligning two fibers, electrodes for producing when energized an electric arc, camera devices such as CCD-matrices and light sources producing a background illumination. These devices are all coupled to electronic circuits containing control means ( 33 ) and the necessary driver and interface circuits. A portion of the fiber held one of the clamps is imaged on the light sensitive areas of the cameras through high-resolving lens systems, allowing the core of the fiber to be distinguished in the captured image, both when the fiber is cold and when it is heated such as to about or somewhat lower temperatures used in fusion-splicing and then issue sufficient light for capturing images without using any background illumination. From a first picture taken of the fiber in a heated state a first light intensity profile along a line substantially perpendicular to the longitudinal direction of the fiber is determined in an image processing and analysis module. This profile is further analyzed by calculating the derivative of the profile and comparing the derivative to derivatives of light intensity profiles previously determined for a optical fibers of known different kinds or types. A second picture is taken of the cold fiber for which a second light intensity profile can be similarly determined. This profile is then compared to corresponding profiles previously determined for the known optical fibers. The results of the comparing operations are finally evaluated to decide the kind of the tested fiber. 
     In an automatic fiber splicer a correct automatic focusing for different imaging conditions can be obtained by executing the following steps in a successive order. The distance between the optical fiber and the optical system of the splicer is varied and pictures are taken for different distances. In the pictures taken light intensity profiles are determined as above which are analyzed to find a measure of the apparent diameter of the optical fiber and a measure of the apparent width of the central peak which is normally obtained in such profiles and corresponds to the high intensity region in the center of the fiber and which at least for a high-resolving optical system corresponds to the core of the fiber. The ratio or quotient of these two measures is calculated and compared to a predetermined value. The distance giving a picture in which the ratio of the measure values agrees with the predetermined value or at least deviates as little as possible from that value is taken as the distance giving a correct imaging. It turns out that by measuring on fibers of different types a predetermined value can be determined which produces good pictures of cold pictures from which valuable information of the core such as its diameter can be obtained and a different predetermined value can be determined producing correspondingly good pictures of heated fibers. 
     Additional objects and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objects and advantages of the invention may be realized and obtained by means of the methods, processes, instrumentalities and combinations particularly pointed out in the appended claims. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     While the novel features of the invention are set forth with particularly in the appended claims, a complete understanding of the invention, both as to organization and content, and of the above and other features thereof may be gained from and the invention will be better appreciated from a consideration of the following detailed description of non-limiting embodiments presented hereinbelow with reference to the accompanying drawings, in which: 
     FIG. 1 a  is a schematic picture of a setup for fusion-splicing two optical fibers to each other, 
     FIG. 1 b  is a schematic picture similar to that of FIG. 1 a  also showing some components of electronic control circuits, 
     FIG. 2 a  is a cold image of an optical fiber, when the fiber is laterally illuminated by a light source, 
     FIG. 2 b  is a hot image of an optical fiber, captured in a fusion process when the fiber glows and radiates light, 
     FIG. 3 is a diagram showing the radiation spectrum of an optical fiber in fusion, the spectral response of a CCD-camera and the product of the radiation spectrum and the spectral response, 
     FIG. 4 is a diagram of the refractive index profile of a dispersion shifted fiber measured by a fiber geometry scanner, 
     FIG. 5 is a schematic view illustrating refraction of collimated lateral rays from a light source by an optical fiber, 
     FIG. 6 is schematic sectional view showing the design of a high-resolving lens system, 
     FIG. 7 a  is a plot of the modulation transfer function of the lens system of FIG. 6 for three wavelengths in the range of 610-690 nm, also showing the ideal MTF (diffraction limited), 
     FIG. 7 b  is a plot similar to that of FIG. 7 a  for wavelengths in the range of 500-700 nm, 
     FIGS. 8 a  and  8   b  are cold and hot images of a typical dispersion shifted fiber imaged by the lens system of FIG. 6 as captured by a CCD-camera, the cold image taken when the fiber is laterally illuminated by a red LED (λ c =660 nm) and the hot image taken during fusion, when temperature of the fiber is approximately 1900° C., 
     FIG. 9 is a plot of hot and cold image profiles of the dispersion shifted fiber of FIGS. 10 a ,  10   b  in grey scale values, 
     FIG. 10 is a plot of the hot image profile F(x) and its first order derivative G(x) for the dispersion shifted fiber of FIGS. 8 a ,  8   b,    
     FIG. 11 is flow diagram illustrating a procedure for fiber identification, 
     FIG. 12 a  is a diagram of the refractive index profile of a region at the core of a depressed cladding, highly doped dispersion shifted fiber, 
     FIG. 12 b  is a diagram showing measured pixel grey scale values Q m (x) and S h (x) for cold and hot fibers respectively and the derivative array G h (X) of the hot profile of the fiber of FIG. 12 a,    
     FIGS. 12 c ,  12   d  are cold and hot images of the fiber of FIG. 12 a,    
     FIGS. 13 a ,  13   b ,  13   c , and  13   d  are diagrams and pictures corresponding to those in FIGS. 12 a ,  12   b ,  12   c , and  12   d  but for a matched cladding, erbium doped fiber, 
     FIGS. 14 a ,  14   b ,  14   c , and  14   d  are diagrams and pictures corresponding to those in FIGS. 12 a ,  12   b ,  12   c , and  12   d  but for a standard single mode fiber, SMF 28, 
     FIGS. 15 a ,  15   b ,  15   c , and  15   d  are diagrams and pictures corresponding to those in FIGS. 12 a ,  12   b ,  12   c , and  12   d  but for a large effective area none zero dispersion shifted fiber, 
     FIGS. 16 a ,  16   b ,  16   c , and  16   d  are diagrams and pictures corresponding to those in FIGS. 12 a ,  12   b ,  12   c , and  12   d  but for a multi mode fiber, and 
     FIGS. 17 a ,  17   b ,  17   c , and  17   d  are diagrams and pictures corresponding to those in FIGS. 12 a ,  12   b ,  12   c , and  12   d  but for a pure silica core single mode fiber. 
    
    
     DETAILED DESCRIPTION 
     In FIG. 1 a  the basic setup in an automatic optical fiber splicer is shown which is similar to that used in a prior art ribbon fiber splicer, see U.S. Pat. No. 5,961,865. The optical fibers  1 ,  1 ′ to be or being spliced have their end regions located between points of electrodes  3 , between which an electrical discharge  5  is generated for heating the fiber ends, the intensity of the electrical discharge being controlled by the intensity of the electrical current between the electrodes  3 . Optical lens systems  7  depicts, in two perpendicular directions, the fiber end regions on light sensitive areas  9 , typically plates carrying a matrix of CCD elements. The splice position can be illuminated by suitably placed light sources such as LEDs  11  providing a background illumination when required. A digital imaging processing system  15  processes the electric signals from the light sensitive areas  9  to monitor the fibers used and the splicing procedure by controlling fiber positioning devices and the intensity of the electrode current. The image processing system is connected to a monitor or display element  17  for showing the captured images. 
     In the schematic picture of FIG. 1 b  some more electrical details of a fiber splicing device of the automatic type are shown. Thus, the splicing device has fixtures or retainers  21 , in which the end portions of the fibers  1 ,  1 ′ are placed and firmly held during the positioning and the splicing. The retainers are movable in three orthogonal coordinate directions both in parallel to the longitudinal direction of the fibers and in two directions perpendicular to this direction. The retainers  21  are thus displaced along suitable mechanical guides, not shown, by control motors  23 . Electric lines to the electrodes  3 , the light sources  11  and the motors  23  extend from an electronic circuit module  25 , from driver circuits  27 ,  28  and  29  respectively of the circuit module. From the light sensitive areas  9  electric lines are arranged to a video interface  31  in the electronic circuit module  25 , from which a suitable image signal is delivered to the image processing and image analysis unit  15 . The various procedural steps are controlled by a control circuit  33  of the circuit module, e.g. a suitable micro processor. The control circuit  33  performs the procedural steps mentioned above and thus controls the displacement of the fiber ends in relation to each other by energizing the motors  23  in suitable displacement directions, provides electrical current to the light sources  11  when pictures e.g. for the alignment procedure have to be captured, and provides a signal to the image processing and image analysis unit  15  for starting an analysis of an obtained image. Further, the control circuit  33  controls the time, when a fusion current is to be started to be provided to the electrodes  5  and the time period during which this current is to be delivered and the intensity of the fusion current. 
     In order to obtain images of cold fibers in which the fiber cores are visible and which are suited for digital processing, the lens systems  7  used must have special performance characteristics and features. Thus, the lens systems  7  must be capable of imaging the cores of the optical fibers both when the fibers are not heated and are laterally or from behind illuminated by a separate light source to get a “cold image” and such a picture is seen in FIG. 2 a  of a typical single-mode fiber. The lens systems  7  must also be capable of imaging the fibers during the fusion process when the fibers are hot and emit thermal radiation to get a “hot image”, see the picture of FIG. 2 b  of the same fiber as in FIG. 2 a.    
     The imaging system of a fiber splicer also contains the CCD matrices or CCD-cameras  9  which must be capable of capturing ordinary pictures and also detecting the radiation emitted by the hot fibers. FIG. 3 is a diagram showing the measured radiation spectrum from a hot fiber having a temperature of approximately 1900° C. The spectral response of the CCD-camera and its product by the hot-fiber radiation are also plotted in the diagram, the latter plotted curve demonstrating that the CCD-camera is sufficiently sensitive to the light emitted by hot fibers. Thus, achromatic lens systems  7  can create sharp “hot images” as captured by the CCD-devices  9 . 
     FIG. 4 is diagram showing a plot of the refractive index profile of a dispersion-shifted optical fiber as measured by a near-field fiber geometry scanner. The diameter of the fiber was 125 μm and the core diameter was approximately 4 μm. The index difference between core and cladding can in the diagram be read to comprise almost 0.01. This slightly higher index of the core is large enough to make the core behave as a thin cylindrical lens placed inside the fiber, the core refracting the lateral light rays from a light source placed at some distance behind the fiber as seen in FIG. 5. A camera system including a high numerical aperture objective, focused approximately at the focal point or more correctly at a point on the focal line of the fiber core, will thus be capable of producing a picture of the core, see the articles cited above. 
     A summary of the data for a lens system suited to produce good cold images and good hot images is given in Table 1. 
     
       
         
               
               
               
             
               
               
               
               
               
             
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 Item 
                 Target Cold Image 
                 Target Hot Image 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Optical Magnifica- 
                 &gt;8x 
                   
                 &gt;8x 
                   
               
               
                 tion 
                   
                   
                   
                   
               
               
                 Conjugate Length 
                 &lt;125 
                 mm 
                 &lt;125 
                 mm 
               
               
                 Object distance 
                 &gt;11.0 
                 mm 
                 &gt;11.0 
                 mm 
               
               
                 Field of view 
                 0.25 
                 mm 
                 0.25 
                 mm 
               
             
          
           
               
                 Numerical Aperture 
                 &gt;0.38 
                   
                 — 
               
             
          
           
               
                 Resolution Power 
                 &gt;40% 
                 at 400 c/mm 
                 &gt;50% 
                 at 100 c/mm 
               
               
                 (MTF) on axis 
                   
                   
                   
                   
               
               
                 Spectral Bandwidth 
                 610-690 
                 nm 
                 500-700 
                 nm 
               
               
                 Distortion 
                 &lt;0.01% 
                   
                 &lt;0.01% 
                   
               
               
                   
               
             
          
         
       
     
     A lens according to Table 1 having a low number of lens elements, in which the effect produced by production variation of dimensions was minimized, was chosen to have a basic configuration analogous of a retrofocus camera lens, see FIG.  6 . The objective was made of two positive components and a negative doublet placed in the long conjugate. The conjugate length was 121 mm for an object distance of 11.1 mm. 
     FIGS. 7 a  and  7   b  show plots of the Modulation Transfer Function for the selected lens system for two spectral intervals. Thus, FIG. 7 a  illustrates the resolution power of the objective for “cold images” using a background illumination from a 610-690 nm light source and FIG. 7 b  for “hot images”, i.e. for thermal radiation from glowing fibers detected by the CCD-camera, in the wavelength range of 500-700 nm. 
     An automatic fusion splicer having an imaging system capable of capturing both cold and hot images can be used for making a reliable determination of the kind of optical fibers to be spliced as will be demonstrated hereinafter. Thereby, correct parameters to be used in the splicing process can be selected to give splices having improved properties such as low insertion losses. A process for such identification will now be described. 
     Thus, FIGS. 8 a ,  8   b  show cold and hot images respectively of a typical dispersion shifted fiber taken by the lens system as described above. The core is sharply visible in the hot image due to the higher emissivity of the doped core glass. The intensity (gray level) profiles of the cold and hot images are given in FIG. 9 as functions of the pixel position in the captured images, the pixel positions corresponding to a physical position in fiber taken along the solid lines, drawn on the pictures, extending perpendicularly to the longitudinal direction of the fiber. The center of the fiber core is visible as a central peak and the thin ring around the core can be seen as two lower peaks at each side of the core in the cold image profile. The fiber core can also be seen as the central peak of the hot image profile. The image of the ring is partly superimposed on the picture of the core and can be observed as increased gray-level values around the core in the hot image profile. 
     The cold image profile and the hot image profile contain information on the geometry and the shape of the fiber core. This information can be further processed to identify the kind of optical fiber used. Such a process will now be described with reference to the flow diagram in FIG.  12 . 
     In a first block  81  the focus position of the camera is set to a first value t 1  given by                t   1     =         d   c     D     =   0.24             (   1   )                                
     where D is the diameter of the fiber as seen in the cold image and d c  is width of the refracted illumination rays at half the maximum in the cold image as shown in FIGS. 5 and 9. This means that in the focusing step pictures are taken when varying the focus position of the lens system  7  and then analyzed to determine the values d c  and D, until, in a captured image, the relation (1) is valid, i.e. so that the ratio of the half-width value d c  to the apparent diameter D is equal to a predetermined value. This digital cold-image having the desired ratio is then stored in a memory of the process circuits  33 . Then in a block  83  the focus position of the camera is changed to t 2                  t   2     =         d   h     D     =   0.48             (   2   )                                
     where d h  in the corresponding manner is the width of the refracted illumination rays at half the maximum in the hot image. Thus, in this case the same procedure is executed but now there is no background illumination, i.e. the light sources  11  are not energized, but the arc between the electrodes  9  is lit by providing a suitable current to flow through the electrodes. The electrode current should be lower than that used for actually fusing the ends of the fibers to each other. The focus position is varied, pictures are captured and analyzed to find the half-width value d h  and the apparent diameter D, until the focus position gives a picture in which the condition (2) is fulfilled, i.e. in which the ratio of said quantities is equal to a predetermined value larger than that used for setting the focus position for cold images, e.g. equal to about twice that value Then this digital hot-image is stored in the processor memory. 
     A 3×3 mean filter is in the next block  85  applied to the gray-level values of the whole or some selected area of the stored hot image taken for the correct focus position. In the block  87  the hot fiber profile F h (x) which is a function or more exactly a one-dimensional array containing gray-level values of the picture of points on a line perpendicular to the longitudinal direction of the hot image of the fiber, is selected from the filtered area, this line thus extending in the x-coordinate direction and x representing the position in this direction. The values F h (x) are thus measured values representing the intensity of light emitted from the corresponding points of the fiber. A differential array, G h (x) with accentuated spatial amplitude changes is then generated in the same block and is given by Eq. (3). 
       G ( x )= F ( x +1)− F ( x −1)  (3) 
     In the same block  87  also the cold fiber profile F c (x) is selected which in the corresponding way is a one-dimensional array containing gray level values of the picture of points on a line perpendicular to the longitudinal direction of the cold image of the fiber. The values F h (x) are thus measured values representing the intensity of light coming from the cold fiber. 
     The hot grey-level array or hot fiber profile F h (x) for the dispersion shifted fiber for which the images in FIGS. 8 a ,  8   b  are taken is plotted in FIG.  10  and in the same figure its first order derivative G h (x) containing 225 pixels is also plotted. Boundaries of the core and the ring are clearly detected as four local maximum points at the middle of the curve of the derivative. They can be compared to the four local minimum points at the middle of the cold-image profile, see FIG.  9 . 
     A range of w=100 pixels surrounding the core in the derivative array G h (x), see FIG. 9, is then selected in a block  89 . The values of the derivative array are then compared to corresponding derivative arrays S n (x) for known fibers. Before the comparison the derivative array or arrays can be normalized and/or displaced so that the comparison can be made in an appropriate way. In the comparison the mean-square error E n  of the derivative array G h (x) considered as a deviation of the array S n (x) of each of the known fiber types is calculated according to                E   n     =       ∑     x   =   1     100            [         S   n          (   x   )       -     G        (   x   )         ]     2               (   4   )                                
     Thereafter the minimum value E m  of the calculated errors is determined in a block  91 , m thus defining the fiber type most resembling the tested fiber. This minimum value is in a next block  93  compared to a threshold value ε 1 . If the minimum value E m  is not below this threshold, the fiber is considered to be an unknown type and a signal thereof to some control device in order to e.g. showing some message on a display is sent in a block  95 . If the minimum value is below the threshold, also the intensity profile obtained from the cold image will be evaluated. 
     Thus, in a block  97  the cold intensity profile F c (x) is low-pass filtered by subjecting it to a 3×1 median filter. Thereupon, in the block  99  the filtered intensity profile is normalized and displaced to some predetermined x-position and in the corresponding way, as previously executed in the block  89 , the mean-square error E c  is calculated for the filtered and normalized intensity profile as compared to the cold image intensity profile Q m  of the m:th fiber type. The calculated mean-square error E c  is in a block  101  compared to a threshold value ε 2 . If the result of the comparison is that the mean-square error is smaller than the threshold value, the tested fiber is determined to be type m and a signal thereof is sent in a block  103  to some control device for e.g. appropriately setting welding parameters and/or displaying some message. If it is determined in the block  101  that the mean-square error is not smaller than the second threshold value the tested fiber is decided not to be any of the known types and then a signal thereof is sent in a block  105  to some control device. 
     FIG. 12 a  is a diagram of the refractive index profile of the core, FIG. 12 b  is a diagram showing measured pixel gray level values Q m (x) and S h (x) for cold and hot fibers respectively and the derivative array G h (X) of the hot profile and FIGS. 12 c - 12   d  show hot and cold images of a depressed cladding, highly doped dispersion shifted fiber. FIGS. 13 a - 13   d  are the corresponding diagrams and pictures for an erbium doped fiber, FIGS. 14 a - 14   d  for a standard single-mode fiber, SMF-28, FIGS. 15 a - 15   d  a for large effective area none-zero dispersion shifted fiber, FIGS. 16 a - 16   d  for a multi-mode fiber, and FIGS. 17 a - 17   d  for a pure silica core single-mode fiber. 
     While specific embodiments of the invention have been illustrated and described herein, it is realized that numerous additional advantages, modifications and changes will readily occur to those skilled in the art. Therefore, the invention in its broader aspects is not limited to the specific details, representative devices and illustrated examples shown and described herein. Accordingly, various modifications may be made without departing from the spirit or scope of the general inventive concept as defined by the appended claims and their equivalents. It is therefore to be understood that the appended claims are intended to cover all such modifications and changes as fall within a true spirit and scope of the invention.