## Design and tolerance analysis of a low bending loss hole-assisted fiber using statistical design methodology

Optics Express, Vol. 16, Issue 7, pp. 5061-5074 (2008)

http://dx.doi.org/10.1364/OE.16.005061

Acrobat PDF (391 KB)

### Abstract

We present the design of a low bending loss hole-assisted fiber for a 180°-bend fiber socket application, including a tolerance analysis for manufacturability. To this aim, we make use of statistical design methodology, combined with a fully vectorial mode solver. Two resulting designs are presented and their performance in terms of bending loss, coupling loss to Corning SMF-28 standard telecom fiber, and cut-off wavelength is calculated.

© 2008 Optical Society of America

## 1. Introduction

1. D. B. Payne and R. P. Davey, “The future of fibre access systems?,” B T Technol. J. **20**, 104–114 (2002). [CrossRef]

2. K. Himeno, S. Matsuo, N. Guan, and A. Wada, “Low-bending-loss single-mode fibers for fiber-to-the-home,” J. Lightwave Technol. **23**, 3494–3499 (2005). [CrossRef]

2. K. Himeno, S. Matsuo, N. Guan, and A. Wada, “Low-bending-loss single-mode fibers for fiber-to-the-home,” J. Lightwave Technol. **23**, 3494–3499 (2005). [CrossRef]

2. K. Himeno, S. Matsuo, N. Guan, and A. Wada, “Low-bending-loss single-mode fibers for fiber-to-the-home,” J. Lightwave Technol. **23**, 3494–3499 (2005). [CrossRef]

9. J. Van Erps, et al., “Mass manufacturable 180°-bend single mode fiber socket using hole-assisted low bending loss fiber,” IEEE Photon. Technol. Lett. **20**, 187–189 (2008). [CrossRef]

*mm*, as shown in Fig. 1. Compared to other hole-assisted low bending loss fiber designs, an efficient coupling to SMF-28 is of utmost importance in this application.

10. Lumerical MODE Solutions™, http://www.lumerical.com/mode.php.

## 2. Modeling and analyzing conventional single-mode fiber SMF-28

*nm*and at 1550

*nm*. The implementation in MODE Solutions is done with the following parameters. The radius of the GeO2-doped core is 4.15

*µm*and its index of refraction as a function of wavelength is calculated using [11

11. H. R. D. Sunak and S. P. Bastien, “Refractive index and material dispersion of doped silica in the 0.6–1.8*µm* wavelength region,” IEEE Photon. Technol. Lett. **1**, 142–145 (1989). [CrossRef]

*A*

_{1}=0.2045154578;

*A*

_{2}=0.06451676258;

*A*

_{3}=0.1311583151;

*B*

_{1}=-0.1011783769;

*B*

_{2}=0.1778934999;

*B*

_{3}=-0.1064179581;

*z*

_{1}=0.06130807320×10

^{-6}

*µm*;

*z*

_{2}=0.1108859848×10

^{-6}

*µm*;

*z*

_{3}=8.964441861×10

^{-6}

*µm*and

*f*=0.033, the molar fraction of the dopant. The cladding, having a diameter of 125

*µm*, is modeled as Corning fused silica with the Sellmeier dispersion equation coefficients found in [13

13. Corning HPFS® Standard Grade, http://www.corning.com/docs/specialtymaterials/pisheets/H0607_hpfs_Standard_ProductSheet.pdf.

*µm*×50

*µm*with a grid spacing of

*d*=

_{x}*d*=0.25

_{y}*µm*for this and all subsequent simulations, unless specified otherwise. We use Perfectly Matched Layer (PML) boundary conditions for the horizontal boundaries of the simulation area [14

14. J. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Computational Phys. **114**, 185–200 (1994). [CrossRef]

*nm*and 1550

*nm*are stored as reference modes for later coupling loss calculations. Notice that only the waveguide confinement loss is calculated, whereas no material or scattering loss has been taken into account in the simulations. For comparison purposes later on, we simulate the bending characteristics of the SMF-28 by sweeping the bending radius from 17

*mm*down to 4

*mm*, for a bend in the horizontal plane (see Fig. 2), at 1310

*nm*and at 1550

*nm*wavelength. MODE Solutions calculates the modes in a bent waveguide by solving Maxwell’s equations in a cylindrical coordinate system and measures the radiative losses caused by the bend by using PML boundary conditions to absorb the radiation from the bent waveguide. The results are shown in Fig. 3 (and Fig. 9), where the bending loss is calculated for the fundamental mode of the fiber. This Fig. shows that the bending loss of SMF-28 increases rapidly for decreasing bend radii. To prove the validity of our simulations, we have added to this graph the bend loss for SMF-28 single-mode fiber using the analytical method proposed by Faustini [12

12. L. Faustini and G. Martini, “Bend loss in single-mode fibers,” J. Lightwave Technol. **15**, 671–679 (1997). [CrossRef]

## 3. Design of low bending loss hole-assisted fibers

_{2}-doped core with an air gap to confine the light to the core region. To work towards the manufacturability of such a fiber, we investigate various ways to connect the inner cladding to the outer cladding, in a similar way as for the suspended core fiber presented in [15

15. A. S. Webb, F. Poletti, D. J. Richardson, and J. K. Sahu, “Suspended-core holey fiber for evanescent-field sensing,” Opt. Eng. **46**, 010503 (2007). [CrossRef]

### 3.1. Hole-assisted fiber Type A

*c*, the inner cladding radius

*r*, the bridge thickness

*t*and the hole width

*w*. Using MODE Solutions, we calculate the modes of the straight fiber and of the bent fiber for a bending radius of 5mm, both at 1310

*nm*and at 1550

*nm*wavelength. The bending radius of 5mmwas chosen in view of the special 180 °-bend fiber socket for which the low bending loss hole-assisted fiber was originally designed [9

9. J. Van Erps, et al., “Mass manufacturable 180°-bend single mode fiber socket using hole-assisted low bending loss fiber,” IEEE Photon. Technol. Lett. **20**, 187–189 (2008). [CrossRef]

*η*between the fundamental mode of the straight hole-assisted fiber (

*E⃗*,

*H⃗*) and the fundamental mode of the SMF-28 (

*E⃗*,

_{SMF}*H⃗*), found in section 2 [16]:

_{SMF}*BL*becomes:

*n*is the number of modes

*ϕ*(

_{i}*E⃗*,

*H⃗*) found by MODE Solutions for the bent hole-assisted fiber and

*L*is the waveguide loss of each mode

_{i}*ϕ*.

_{i}*η*is the overlap of each mode

_{i}*ϕ*of the bent fiber with the fundamental mode

_{i}*ζ*(

*E⃗*,

*H⃗*) of the straight hole-assisted fiber. This second method will result in an overestimation of the bending loss, since it assumes an abrupt transition between a straight and a bent fiber. However, if the transition occurs smoothly, i.e. if we ensure that the rate of change of the bend radius is small enough, the propagation along the waveguide will be approximately adiabatic [17

17. J. D. Love and C. Durniak, “Bend loss, tapering, and cladding-mode coupling in single-mode fibers,” *IEEE Photon. Technol. Lett.* . **19**1257–1259 (2007). [CrossRef]

9. J. Van Erps, et al., “Mass manufacturable 180°-bend single mode fiber socket using hole-assisted low bending loss fiber,” IEEE Photon. Technol. Lett. **20**, 187–189 (2008). [CrossRef]

*mm*radius (see Fig. 1). The extra turn is added in view of providing some fiber overlength for cleaving purposes. In the statistical design that follows, we target a minimization of this total link loss at 1310

*nm*and at 1550

*nm*.

*k*≤

*N*-1 factors in

*N*runs, where

*N*is a multiple of 4 [18

18. R. L. Plackett and J. P. Burman, “The design of multifactorial experiments,” Biometrika **33**, 305–325 (1946). [CrossRef]

*y*(in our case the total link loss), and the independent variables

*x*to a second-order model [7]:

19. G. E. P. Box and D.W. Behnken, “Some new three level designs for the study of quantitative variables,” Technometrics **2**, 455–476 (1960). [CrossRef]

*runs for*

^{k}*k*factors) with incomplete block designs and are very efficient in terms of the number of required runs.

#### 3.1.1. Plackett-Burman screening analysis

*c*,

*r*,

*w*and

*t*, as defined above). The factor levels were chosen from expected technological fabrication constraints and initial parameter sweeps. No blocking or randomization of run order was used here, since it does not make any sense when using the statistical design tools for optimization via simulations, as opposed to the case of physical realizations in real design of experiments [7]. The total link loss values at 1310

*nm*and at 1550

*nm*result from simulations with MODE Solutions, and are used separately as the response in the statistical analysis. The latter was carried out with the help of Minitab 14 Statistical Software (by Minitab Inc., [20

20. Minitab Statistical Software, http://www.minitab.com/products/minitab/.

*α*=0.05 [21]. Any effect that extends past this reference line is potentially important with 95%(=1-

*α*) confidence. From these charts, we can see that the important factors in our design are the inner cladding radius

*r*, the hole width

*w*and the bridge thickness

*t*at 1310

*nm*and that, at 1550

*nm*, the core radius

*c*also turns out to be a significant factor. Therefore we select all 4 factors for the subsequent Box-Behnken design to fit the total link loss response surface.

#### 3.1.2. Refined Box-Behnken analysis

*t*is varied between 1.0

*µm*(the expected lower limit for practical fabrication of the fiber) and 3.0

*µm*. The boundary values for the inner cladding radius

*r*are 12.0

*µm*and 18.0

*µm*. The core radius

*c*ranges from 4.0

*µm*and 4.3

*µm*and finally, the hole width

*w*is varied between 2.5

*µm*and 5.0

*µm*. Notice that the last two runs in table 2 are replications of the center point, for which we changed the simulation grid spacing by ±8%. Including these extra runs allows the Box-Behnken analysis to take an estimate of the simulation error into account [7].

*R*

^{2}is 98.7% for 1310

*nm*and 99.7% for 1550

*nm*, indicating that the model fits the data very well. The minimum of this response surface gives us the optimal system parameters for both wavelengths:

*c*=4.15

*µm*,

*r*=16.9

*µm*,

*w*=5.0

*µm*and

*t*=2.0

*µm*. However, as the response surface is only quadratically fitted, we end up with total link loss values at this optimum that are negative, which is not physically possible. Because we want to use the response surface for a Monte-Carlo tolerance analysis, we decide to perform a second Box-Behnken analysis, in which the ranges for the factor levels are tightened around the found optimum, such that the resulting response surface would better fit the physical system (and thus avoid negative total link loss values). The new factor ranges for this second Box-Benhken analysis are: 4.05

*µm*<

*c*<4.25

*µm*, 16.5

*µm*<

*r*<17.3

*µm*, 4.6

*µm*<

*w*<5.4

*µm*and 1.8

*µm*<

*t*<2.2

*µm*. The quadratic fit parameters resulting from the Box-Behnken analysis by Minitab are given in Table 3. The coefficient of determination

*R*

^{2}has now increased to 100.0% for both the 1310

*nm*and the 1550

*nm*total link loss response.

#### 3.1.3. Monte-Carlo tolerance for manufacturability analysis

23. Crystal ball predictive modeling software, http://www.crystalball.com/cbpro/index.html.

*µm*with

*σ*=0.1

*µm*, hole width

*w*target of 5

*µm*with

*σ*=0.1

*µm*, bridge thickness

*t*target of 2

*µm*with

*σ*=0.15

*µm*and finally the core radius

*c*target of 4.15

*µm*with

*σ*=0.05

*µm*. These parameters are independent and were chosen in accordance with the expected fabrication errors. The total link loss probability charts resulting from these Monte-Carlo simulations for 500000 runs are shown in Fig. 6. The mean loss value is 2.8×10

^{-4}

*dB*, with a standard deviation of 3.2×10

^{-4}

*dB*for 1310

*nm*and 1.0×10

^{-3}

*dB*±2.0×10

^{-4}

*dB*for 1550

*nm*. From these charts, it is clear that the designed hole-assisted fiber design Type A conforms with the fabrication method. However, the sensitivity values (

*σ*) assigned to the parameters might have to be adjusted once the fabrication process for the hole-assisted fiber is established.

### 3.2. Hole-assisted fiber Type B

*c*, the inner cladding radius

*r*and the hole width

*w*remain parameters of the system. However, two extra parameters are introduced here: the capillary width

*d*and the capillary overlap

*o*. The latter can be considered as being more or less the equivalent of the bridge thickness

*t*used in fiber design Type A for the mode calculation simulations.

*c*,

*r*and

*w*are chosen the same as for the Plackett-Burman design of hole-assisted fiber Type A. The range for

*d*was set from 1

*µm*to 2

*µm*and for

*o*from 1

*µm*to 3

*µm*. From the Plackett-Burman screening analysis of this system, the only significant parameter turns out to be the inner cladding radius

*r*at a significance level

*α*=0.05, as can be seen from the Pareto charts shown in Fig. 7. However, we chose to include the capillary overlap

*o*and the hole width

*w*in our Box-Behnken analysis, in view of their relatively large importance over the factors

*c*and

*d*. The latter factors are kept at their baseline level (

*c*=4.15

*µm*and

*d*=1.5

*µm*) for the Box-Behnken analysis. The response surface defined in Eq. (4) resulting from this three-factor three-level Box-Behnken analysis allows us again to determine the optimal system parameters. The coefficient of determination

*R*

^{2}is 96.4% for 1310

*nm*and 99.2% for 1550

*nm*. The minimum of the response surface is achieved for

*r*=16.9

*µm*,

*o*=1.0

*µm*and

*w*=5.0

*µm*. The response surface gives again negative total link loss values around this optimum, hence we perform a second analysis with refined ranges for the factors around the found optimum, in analogy to the approach followed for hole-assisted fiber Type A. The ranges for the second Box-Behnken analysis are: 16.5

*µm*<

*r*<17.3

*µm*, 0.8

*µm*<

*o*<1.2

*µm*and 4.6

*µm*<

*w*<5.4

*µm*. The coefficient of determination

*R*

^{2}has increased to 100.0% for both the 1310

*nm*and the 1550

*nm*total link loss response.

*r*target of 16.9

*µm*with

*σ*=0.1

*µm*, capillary overlap

*o*target of 1.0

*µm*with

*σ*=0.05

*µm*, hole width

*w*target of 5

*µm*with

*σ*=0.1

*µm*, core radius

*c*target of 4.15

*µm*with

*σ*=0.1

*µm*and finally capillary width

*d*target of 1.5

*µm*with

*σ*=0.1

*µm*. The total link loss probability charts resulting from these Monte-Carlo simulations for 500000 runs are shown in Fig. 8. The tolerance window for the manufacturability of the hole-assited fiber design Type B is again excellent, with a mean loss value of 5.2×10

^{-5}

*dB*, and a standard deviation of 4.5×10

^{-6}

*dB*for 1310

*nm*and 9.0×10

^{-4}

*dB*±6.0×10

^{-5}

*dB*for 1550

*nm*.

## 4. Detailed optical simulation of the resulting hole-assisted fiber designs

*c*=4.15

*µm*,

*r*=16.9

*µm*,

*w*=5.0

*µm*and

*t*=2.0

*µm*) and Type B (

*c*=4.15

*µm*,

*r*=16.9

*µm*,

*w*=5.0

*µm*,

*o*=1.0

*µm*and

*d*=1.5

*µm*) are shown in respectively Table 4 and Table 5. These tables show the coupling loss to SMF-28 and the bending loss (at 5

*mm*radius) at 1310

*nm*and 1550

*nm*respectively. The bending loss of the fundamental mode is mentioned in the third column, whereas the bending loss

*BL*in the fourth column is calculated using Eq. (3). Notice that the loss for a fiber exposed to a macro-bend of 5

*mm*is calculated for the worst case, i.e. when the fiber is bent in the direction of a bridge. It is clear that the bending loss at 5

*mm*radius is negligible in comparison to the coupling loss to SMF-28. As mentioned in section 3.1, the bending loss calculated using Eq. (3) is higher than when taking bending loss of only the fundamental mode into account. The difference is smaller than one order of magnitude. The total link loss, comprising twice the coupling loss to SMF-28 and the loss for one and a half turn of 5

*mm*radius, results in 5.2×10

^{-5}

*dB*at 1310

*nm*and 9.0×10

^{-4}

*dB*at 1550

^{nm}for design Type A and 5.1×10

^{-5}

*dB*at 1310

*nm*and 9.0×10

^{-4}

*dB*at 1550

*nm*for design Type B. The total link loss is thus virtually the same for both hole-assisted fiber designs. Notice that the simulation for a single system takes about 20 minutes to complete on a dual-core Pentium D system running at 3.0 Ghz with 2GB of memory. This clearly illustrates the advantage of a statistical approach over a traditional sensitivity analysis by sweeping all parameters of the hole-assisted fiber one by one to come to an optimal design.

### 4.1. Increasing the number of bridges in design Type A

*c*=4.15

*µm*, inner cladding radius

*r*=16.9

*µm*, hole width

*w*=5

*µm*and bridge thickness

*t*=2

*µm*), the simulation results are shown in Table 6. The total link loss becomes 6.4×10

^{-5}

*dB*at 1310

*nm*and 8.8×10

*dB*at 1550

*nm*.

### 4.2. Bending performance compared to conventional single-mode fiber SMF-28

12. L. Faustini and G. Martini, “Bend loss in single-mode fibers,” J. Lightwave Technol. **15**, 671–679 (1997). [CrossRef]

24. T. Martynkien, J. Olszewski, M. Szpulak, G. Golojuch, W. Urbanczyk, T. Nasilowski, F. Berghmans, and H. Thienpont, “Experimental investigations of bending loss oscillations in large mode area photonic crystal fibers,” Opt. Express **15**, 13547–13556 (2007). [CrossRef] [PubMed]

### 4.3. Cut-off wavelength calculation

*nm*(for a straight fiber) to ensure that the cut-off frequency is far enough below 1310

*nm*as required. We define the fibers as being single mode when the waveguide loss of the fundamental mode is at least three orders of magnitude smaller than the waveguide loss of the higher-order modes. Notice that we use this approach because it is difficult to determine the exact cut-off wavelength of hole-assisted fibers since higher-order modes may exist as leaky modes. In a strict sense, these low bending-loss fibers are multimode fibers as there will exist many modes with a reasonably low loss in the inner cladding. These modes have as a consequence only a small leakage to radiative modes through the bridges (or capillaries) connecting the inner cladding to the outer cladding. However, there is only one mode with significant energy in the core region of the fibers. This mode has furthermore an extremely high overlap (more than 99%) with the fundamental mode of standard single mode fiber (SMF-28). In practice, experimental measurement of the cut-off wavelength of the fabricated hole-assisted fibers will have to prove the validity of our approach to ensure single-mode operation. However, the experimental measurement of the cut-off wavelength of hole-assisted fibers is very tedious because the conventional bending method for cut-off wavelength measurement can not be used in a fiber with superior bending loss performance [25

25. K. Nakajima, et al., “Cutoff wavelength measurement in a fiber with improved bending loss,” IEEE Photon. Technol. Lett. **16**, 1918–1920 (2004). [CrossRef]

## 5. Conclusion

**20**, 187–189 (2008). [CrossRef]

*mm*.

## Acknowledgments

## References and links

1. | D. B. Payne and R. P. Davey, “The future of fibre access systems?,” B T Technol. J. |

2. | K. Himeno, S. Matsuo, N. Guan, and A. Wada, “Low-bending-loss single-mode fibers for fiber-to-the-home,” J. Lightwave Technol. |

3. | K. Nakajima, K. Hogari, J. Zhou, K. Tajima, and I. Sankawa, “Hole-assisted fiber for small bending and splice losses,” IEEE Photon. Technol. Lett. |

4. | Y. Tsuchida, K. Saitoh, and M. Koshiba, “Design and characterization of single-mode holey fibers with low bending losses,” Opt. Express |

5. | N. Guan, et al., “Holey fibers for low bending loss,” IEICE Trans. Electron. |

6. | Y. Bing, K. Oshono, Y. Kurosawa, T. Kumagai, and M. Tachikura, “Low-loss holey fiber,” Hitachi Cable Review |

7. | D. C. Montgomery, |

8. | T. J. Santner, B. J Williams, and W. I. Notz, |

9. | J. Van Erps, et al., “Mass manufacturable 180°-bend single mode fiber socket using hole-assisted low bending loss fiber,” IEEE Photon. Technol. Lett. |

10. | Lumerical MODE Solutions™, http://www.lumerical.com/mode.php. |

11. | H. R. D. Sunak and S. P. Bastien, “Refractive index and material dispersion of doped silica in the 0.6–1.8 |

12. | L. Faustini and G. Martini, “Bend loss in single-mode fibers,” J. Lightwave Technol. |

13. | Corning HPFS® Standard Grade, http://www.corning.com/docs/specialtymaterials/pisheets/H0607_hpfs_Standard_ProductSheet.pdf. |

14. | J. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Computational Phys. |

15. | A. S. Webb, F. Poletti, D. J. Richardson, and J. K. Sahu, “Suspended-core holey fiber for evanescent-field sensing,” Opt. Eng. |

16. | A. W. Snyder and J. D. Love, |

17. | J. D. Love and C. Durniak, “Bend loss, tapering, and cladding-mode coupling in single-mode fibers,” |

18. | R. L. Plackett and J. P. Burman, “The design of multifactorial experiments,” Biometrika |

19. | G. E. P. Box and D.W. Behnken, “Some new three level designs for the study of quantitative variables,” Technometrics |

20. | Minitab Statistical Software, http://www.minitab.com/products/minitab/. |

21. | G. E. P. Box, W. G. Hunter, and J. S. Hunter, |

22. | I. M. Sobol, |

23. | Crystal ball predictive modeling software, http://www.crystalball.com/cbpro/index.html. |

24. | T. Martynkien, J. Olszewski, M. Szpulak, G. Golojuch, W. Urbanczyk, T. Nasilowski, F. Berghmans, and H. Thienpont, “Experimental investigations of bending loss oscillations in large mode area photonic crystal fibers,” Opt. Express |

25. | K. Nakajima, et al., “Cutoff wavelength measurement in a fiber with improved bending loss,” IEEE Photon. Technol. Lett. |

**OCIS Codes**

(060.2280) Fiber optics and optical communications : Fiber design and fabrication

(060.4005) Fiber optics and optical communications : Microstructured fibers

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: January 18, 2008

Revised Manuscript: March 22, 2008

Manuscript Accepted: March 24, 2008

Published: March 28, 2008

**Citation**

Jurgen Van Erps, Christof Debaes, Tomasz Nasilowski, Jan Watté, Jan Wojcik, and Hugo Thienpont, "Design and tolerance analysis of a low bending loss hole-assisted fiber using statistical design methodology," Opt. Express **16**, 5061-5074 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-7-5061

Sort: Year | Journal | Reset

### References

- D. B. Payne and R. P. Davey, "The future of fibre access systems?," B T Technol. J. 20, 104-114 (2002). [CrossRef]
- K. Himeno, S. Matsuo, N. Guan, and A. Wada, "Low-bending-loss single-mode fibers for fiber-to-the-home," J. Lightwave Technol. 23, 3494-3499 (2005). [CrossRef]
- K. Nakajima, K. Hogari, J. Zhou, K. Tajima, and I. Sankawa, "Hole-assisted fiber for small bending and splice losses," IEEE Photon. Technol. Lett. 15, 1737-1739 (2003). [CrossRef]
- Y. Tsuchida, K. Saitoh, and M. Koshiba, "Design and characterization of single-mode holey fibers with low bending losses," Opt. Express 13, 4770-4779 (2005). [CrossRef] [PubMed]
- N. Guan, et al., "Holey fibers for low bending loss," IEICE Trans. Electron. E89, 191-196 (2006). [CrossRef]
- Y. Bing, K. Oshono, Y. Kurosawa, T. Kumagai, and M. Tachikura, "Low-loss holey fiber," Hitachi Cable Review 24, 1-4 (2005).
- D. C. Montgomery, Design and Analysis of Experiments, 5th ed. (John Wiley & Sons, New York, 2001).
- T. J. Santner, B. J. Williams, and W. I. Notz, The Design and Analysis of Computer Experiment (Springer-Verlag, 2003).
- J. Van Erps, et al., "Mass manufacturable 180◦-bend single mode fiber socket using hole-assisted low bending loss fiber," IEEE Photon. Technol. Lett. 20, 187-189 (2008). [CrossRef]
- LumericalMODE Solutions™, http://www.lumerical.com/mode.php.
- H. R. D. Sunak and S. P. Bastien, "Refractive index and material dispersion of doped silica in the 0.6-1.8um wavelength region," IEEE Photon. Technol. Lett. 1, 142-145 (1989). [CrossRef]
- L. Faustini and G. Martini, "Bend loss in single-mode fibers," J. Lightwave Technol. 15, 671-679 (1997). [CrossRef]
- Corning HPFS® Standard Grade, http://www.corning.com/docs/specialtymaterials/pisheets/H0607 hpfs Standard ProductSheet.pdf.
- J. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Computational Phys. 114, 185-200 (1994). [CrossRef]
- A. S. Webb, F. Poletti, D. J. Richardson, and J. K. Sahu, "Suspended-core holey fiber for evanescent-field sensing," Opt. Eng. 46, 010503 (2007). [CrossRef]
- A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
- J. D. Love and C. Durniak, "Bend loss, tapering, and cladding-mode coupling in single-mode fibers," IEEE Photon. Technol. Lett. 191257-1259 (2007). [CrossRef]
- R. L. Plackett and J. P. Burman, "The design of multifactorial experiments," Biometrika 33, 305-325 (1946). [CrossRef]
- G. E. P. Box and D.W. Behnken, "Some new three level designs for the study of quantitative variables," Technometrics 2, 455-476 (1960). [CrossRef]
- Minitab Statistical Software, http://www.minitab.com/products/minitab/.
- G. E. P. Box, W. G. Hunter, and J. S. Hunter, Statistics for experimenters: An Introduction to Design, Data Analysis and Model Building (John Wiley & Sons, New York, 1978).
- I. M. Sobol, A Primer for the Monte Carlo Method (CRC Press, 1994).
- Crystal ball predictive modeling software, http://www.crystalball.com/cbpro/index.html.
- T. Martynkien, J. Olszewski, M. Szpulak, G. Golojuch, W. Urbanczyk, T. Nasilowski, F. Berghmans, and H. Thienpont, "Experimental investigations of bending loss oscillations in large mode area photonic crystal fibers," Opt. Express 15, 13547-13556 (2007). [CrossRef] [PubMed]
- K. Nakajima, et al., "Cutoff wavelength measurement in a fiber with improved bending loss," IEEE Photon. Technol. Lett. 16, 1918-1920 (2004). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.