We propose a novel method of graded index plastic optical fiber (GI POF) to enhance bandwidth. Recently, it has been reported that perfluorinated GI POF with a double cladding structure had much higher bandwidth than theoretical value. The result of analysis of this fiber indicates that the high-bandwidth property is obtained because higher order modes are attenuated at a core and cladding polymer boundary. In addition, it does not induce large increment of attenuation of lower order modes and bending loss. Then, by adopting the rod-in-tube method, we control differential mode attenuation of PMMA based GI POF, and it is proved that bandwidth of GI POF can be enhanced by utilizing scattering of the core and cladding polymer boundary.
©2010 Optical Society of America
Recently, the required transmission capacity has been grown dramatically with the widespread of the internet. Silica-based single mode fiber (SMF) has been widely used as long-distance and high-speed optical network medium because of its great transparency and high-bandwidth property. However, due to small core size of SMF (less than 10 μm), extreme accuracy of connecting fibers is required. Therefore, it is necessary to lay fibers using expensive connectors. It makes total system cost too high at homes, offices and buildings which require many points of connecting. Plastic optical fiber (POF)  is regarded as a promising candidate for LANs, because it has large core (100-1000 μm), and it is more flexible and easier to handle than SMF. Therefore, it is possible to use inexpensive injection molding connectors which dramatically decrease the total cost of the system. However, step index (SI) POF does not have enough bandwidth due to its large intermodal dispersion, then it is proposed that graded index (GI) POF [2–4] is able to be an adequate medium for high-speed shout-haul data communication at homes, offices and buildings because it has not only the advantages of POF but also high-bandwidth property due to its parabolic refractive index profile. The intermodal dispersion of GI POF is much less than that of SI POF in principle. However the intermodal dispersion increases when refractive index profile is deviated from the optimal one. Diffusion of high refractive index dopant is utilized to form the GI profile within a fiber. Fabrication condition of GI POF with the optimum refractive index profile depends on the material of POF, dopant and fabrication method [5,6]. Therefore it is not easy to fabricate high bandwidth GI POF with the optimum refractive index profile and reduction of the intermodal dispersion is still an important assignment of GI POF.
On the other hand, it has been reported in 2008 that perfluorinated (PF) GI POF with double cladding structure, which was newly designed to improve bending property of GI POF, had much higher bandwidth than expected. In this study, we investigate the influence of this novel double cladding structure to bandwidth [7,8]. As a result, it is indicated that the high bandwidth property is obtained not because of the double cladding structure, but because the fabrication process influences to differential mode attenuation (DMA). The PF GI POF is fabricated by the co-extrusion process which utilizing diffusion of high refractive index dopant to form the GI profile. In this process, core and cladding polymer boundary locates inside the core region which formed after dopant diffusion. We consider the high bandwidth property is obtained because higher order modes, which increase intermodal dispersion, are scattered by irregularity of the boundary. On the basis of these results, we propose a novel structure and its fabrication method to control DMA as a novel technique to improve bandwidth of GI POF. It is confirmed that GI POF with such structure has high enough bandwidth despite the fact that it does not have an optimal refractive index profile.
2.1 Sample preparation
In this study, following 2 kinds of samples are investigated: 1. A PF GIPOF with double cladding structure, 2. Poly (methyl methacrylate) (PMMA) based GI POF.
PMMA based GI POF is fabricated by rod-in-tube method  and interfacial gel polymerization method . Schematic of the rod-in-tube method is shown in Fig. 1 . A core rod is prepared by polymerizing methyl methacrylate (MMA) with diphenyl sulfide as high refractive index dopant. A cladding tube is prepared by polymerizing MMA, where the outside diameter of core rod and the inside diameter of cladding tube are designed preliminarily so that the core rod can be easily inserted into the cladding tube. After the fabrication of both materials, the cladding tube with the core rod set inside is sandwiched between two Teflon rods within a heat shrinkable tube. This is heated at 160-180 °C for 24-48 hours, and thus become a preform. GI POF is obtained by heat drawing the GI preform.
A SMF is used to launch some restricted mode groups of PMMA based and PF GI POF. The SMF is scanned across the fiber core under test in 1 or 5 μm increments. Output light intensity at each launch position is detected by using an optical power meter (ANDO AQ2140) and differential mode attenuation (DMA)  is obtained by the cut-back method. Scattered light intensity from GI POF at each launch position is measured by passing GI POF through an integrating sphere after stripping cladding modes by matching oil. Then scattered light is detected by using an optical power meter (ANDO AQ2140) connected to the integrating sphere. Transmitted light intensity is also measured by putting the end face of GI POF in the integrating sphere [11,12]. Far-field pattern (FFP) of PF GI POF under over-filled launch (OFL) condition via a SI POF is measured at 2 m and 100 m (Hamamatsu A-3267-12). Numerical aperture (NA) is calculated from output light angle at 5% of peak light intensity of FFP. Near-field pattern (NFP) of PMMA based GI POF under OFL condition is measured at 50-m end face (Hamamatsu A-6501). Bandwidth of PMMA based and PF GI POF are measured by the time domain method  by using an optical oscilloscope (Hamamatsu C8188-03) under OFL condition. Refractive index profile of PMMA based GI POF is measured by using an interferometric microscope. Bending loss of 50-m PMMA based GI POF under OFL condition is measured by the difference of the output light intensity before and after a quarter bend of various radii from 5 mm to 50 mm at 48 m from the launch position.
3. Result and discussion
3.1 Analysis of PF GI POF with double cladding structure
Figure 2 shows the refractive index profile of PF GI POF with double cladding structure. The horizontal axis is normalized by the radius of the inner cladding. It can be seen that the PF GI POF has outer cladding layer (Normalized radius: about 1.0-1.1) which refractive index is much lower than that of inner cladding (Normalized radius: about 0.9-1.0). Therefore, decrement of bandwidth is concerned because it is expected that the outer cladding layer induces large intermodal dispersion. However, it has been reported that the PF GI POF has very high bandwidth property [7,8]. We presume that this high bandwidth property is caused by DMA.
Figure 3 shows a measurement result of DMA of PF GI POF with double cladding structure. Although the attenuation around center of the core is about 30 dB/km, that of closer region to cladding layer increases to about 300 dB/km. This result indicates that the PF GI POF has high attenuation in higher order modes. Figure 4 shows a measurement result of FFP at 2-m and 100-m end faces of the PF GI POF. NA is 0.28 and 0.19 at 2-m and 100-m end faces, respectively. These results indicate that the high bandwidth property of PF GI POF is caused by attenuation of higher order modes which increase large intermodal dispersion.
We measured scattered light intensity and transmitted light intensity as shown in Fig. 5 . The scattered light intensity reaches maximum at about 0.8 in normalized radius. There is a high scattering layer in the core region and the result indicates that this high scattering layer causes high attenuation of higher order modes.
We think that the high scattering layer is caused by fabrication process of GI POF. The PF GI POF is fabricated by the co-extrusion process  which is regarded as a promising practical fabrication method of GI POF because co-extrusion process is continuous production method and suitable for mass-production. Figure 6 shows the formation process of refractive index profile in the co-extrusion process. In this process, core polymer with high refractive index dopant and cladding homopolymer are melted and to be bonded. Dopant diffuses to cladding polymer and GI profile is formed. As shown in Fig. 6, the core and cladding polymer boundary locates inside the core region (defined by refractive index profile) which formed by dopant diffusion. We assume that this boundary between core and cladding polymer is irregular enough to cause light scattering and the high bandwidth property of the GI POF is obtained because the boundary attenuates higher order modes. It indicates a possibility that high-bandwidth GI POF can be fabricated without forming optimal refractive index profile by complex control of fabrication conditions.
3.2 Fabrication and analysis of PMMA based GI POF with novel structure
In order to prove the hypothesis that higher order modes reduction is effective to enhance the bandwidth of GI POF, and to fabricate PMMA based GI POF which has high bandwidth property without optimizing refractive index profile, we adopt the rod-in-tube method. The rod-in-tube method is not suitable for mass production because it is a batch process. However, formation process of refractive index profile in the rod-in-tube method is similar to the co-extrusion process, and the core and cladding polymer boundary locates inside the core region.
DMA and bandwidth of the GI POF is compared to those of PMMA based GI POF fabricated by the interfacial gel polymerization method which does not form the core and cladding polymer boundary inside the core region. Also, the interfacial gel polymerization method is not suitable for mass production. In the method, refractive index profile is formed by the selective diffusion which caused by the difference of molecular size between monomer and high-refractive index dopant. GI preform is prepared by polymerizing core monomer mixture inside the cladding tube polymerized preliminarily. Therefore, the irregular boundary between core and cladding polymer is not formed in the method. Figure 7 shows a measurement result of DMA of PMMA based GI POF fabricated by the rod-in-tube method and the interfacial gel polymerization method. It is confirmed that DMA of the GI POF fabricated by the interfacial gel polymerization method is almost constant in the core region. The GI POF fabricated by the rod-in-tube method has attenuation as small as the GI POF fabricated by the interfacial gel polymerization method in lower order modes, but high attenuation in higher order modes. Figure 8 shows a measured result of scattered light intensity of the GI POF fabricated by the rod-in-tube method. Scattered light intensity reaches maximum at about 0.9 normalized core radius, and it is indicated that light is scattered at the core and cladding polymer boundary as same as a case of the PF GI POF.
Comparison between refractive index profile and NFP of GI POF fabricated by the rod-in-tube method is shown in Fig. 9 . It is well known that there is a similarity between NFP and refractive index profile of GI POF when all modes propagate equally. However, NFP is narrower than refractive index profile in Fig. 9. This result indicates higher order modes of GI POF fabricated by the rod-in-tube method are attenuated. Figure 10 shows comparison of transmitted pulse width between GI POF fabricated by the rod-in-tube method and fabricated by the interfacial gel polymerization method. As shown in Fig. 10, transmitted pulse of GI POF fabricated by the rod-in-tube method is much narrower than that of GI POF fabricated by the interfacial gel polymerization method.
In order to analyze the bandwidth of GI POF theoretically, refractive index profile is approximated by a power law form shown by Eq. (1).
In Fig. 11 , bandwidth of GI POF fabricated by the rod-in-tube method and the interfacial gel polymerization method are plotted against the index exponent g which is approximated by using a least-square technique for Eq. (1). The theoretical bandwidth with refractive index profile written by Eq. (1) is estimated by using WKB method with consideration of material dispersion [15,16]. The Bandwidth of GI POF fabricated by the interfacial gel polymerization method shows good agreement with the theoretical values. However, the bandwidth of GI POF fabricated by the rod-in-tube method is much higher than theoretical values. Especially, with increase of refractive index exponent, a difference between measured and calculated bandwidth increases. The PMMA based GI POF fabricated by the rod-in-tube method shows very high bandwidth of approximately 5 GHz, although its refractive index exponent (g=6.0) is apart from optimal one (g=2.4).
From these results, it is proved that bandwidth of GI POF can be enhanced by utilizing scattering of the core and cladding polymer boundary without optimizing refractive index profile. We consider that it is possible to fabricate high bandwidth GI POF easily, on the basis of this novel knowledge.
In these GI POF, conventional bandwidth prediction which based on the refractive index profile is broken. Therefore, to analyze GI POF fabricated by the co-extrusion process, it is important to measure effective NA and DMA rather than refractive index profile.
On the other hand, it is concerned that bending loss is increased by high attenuation in higher order modes. However, it has been reported that bending loss of the PF GI POF with double cladding structure was very small . Bending loss with several bending radius of GI POF fabricated by the rod-in-tube method is shown in Fig. 12 . NA and core diameter of GI POF fabricated by the rod-in-tube method are 0.22 and 260 mm, those of GI POF fabricated by the interfacial gel polymerization method are 0.22 and 300 mm, respectively. The bending loss of GI POF fabricated by the rod-in-tube method is as small as that of GI POF fabricated by the interfacial gel polymerization method. We consider that attenuation of higher order modes has little effect on bending loss property. It is because bending loss occurs at short distance (several centimeters) but DMA is measured at long distance (several tens meters).
From measurements of PF GI POF with double cladding structure, we indicated a possibility that a GI POF fabricated by the co-extrusion process had high attenuation in higher order modes. From DMA and FFP analysis of PF GI POF, we assumed that the irregular boundary between core and cladding polymer formed during fabrication of GI POF by the co-extrusion process caused light scattering and enhancement of the bandwidth of GI POF. To investigate this assumption, we fabricated GI POF by the rod-in-tube method and analyzed its DMA, bandwidth and light scattering property. These results indicated that high-bandwidth GI POF in which refractive index profile was deviated from the optimal one could be fabricated without large increment of attenuation of lower order modes and bending loss.
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