## A mechanical criterion for the design of readily cleavable microstructured optical fibers

Optics Express, Vol. 14, Issue 16, pp. 7312-7318 (2006)

http://dx.doi.org/10.1364/OE.14.007312

Acrobat PDF (1795 KB)

### Abstract

Some complex microstructured fibers (MSFs) are well known to produce poor-quality cleaves or even to break at cleavage. But to find widespread use in photonics technology, MSFs will have to be easily cleavable using mechanical cleavers, since more sophisticated techniques add complexity. In this paper, the very different, yet reproducible cleavage patterns of three high air-fraction, double-clad microstructured fibers are analyzed. Fracture faces reveal the fracture propagation paths and provide measurements of the fracture lengths in the intercapillary bridges. These lengths prove to be always shorter than the critical fracture length predicted by fracture mechanics. A criterion based on critical fracture length is thus proposed to design cleavage-robust MSFs.

© 2006 Optical Society of America

## 1. Introduction

1. S. Huntington, K. Lyytikainen, and J. Canning “Analysis and removal of fracture damage during and subsequent to holey fiber cleaving,” Opt. Express **11**, 535–540 (2003). [CrossRef] [PubMed]

1. S. Huntington, K. Lyytikainen, and J. Canning “Analysis and removal of fracture damage during and subsequent to holey fiber cleaving,” Opt. Express **11**, 535–540 (2003). [CrossRef] [PubMed]

4. R. O. Ritchie, “Mechanics of fatigue-crack propagation in ductile and brittle solids,” Int. J. Fract. **100**, 55–83 (1999). [CrossRef]

## 2. Experiments

8. T. Haibara, M. Matsumoto, and M. Miyauchi, “Design and developpement of an automatic cutting tool for optical fibers,” J. Lightwave Technol. **LT-4**, 1434–1439 (1986). [CrossRef]

1. S. Huntington, K. Lyytikainen, and J. Canning “Analysis and removal of fracture damage during and subsequent to holey fiber cleaving,” Opt. Express **11**, 535–540 (2003). [CrossRef] [PubMed]

*stop*propagating somewhere on the bridges, preventing high-quality cleavage of the inner cladding.

## 3. Analysis

*critical fracture length*that can induce rupture of the material under the given applied stress

*σ*

_{app},

*Y*is a geometrical configuration factor and

*K*is the material toughness.

_{IC}*K*is an experimentally measurable material constant, which is a simple function of the Young’s modulus and the surface tension used in the general theory [9].

_{IC}*a*or the applied tensile stress

*σ*

_{app}increase, more and more strain energy is converted into kinetic energy, until the fracture reaches a limiting velocity. At this point, the excess energy begins to be taken up by the creation of additional surfaces in the mist zone. This condition is generally written as [7]:

*D*is the distance from the crack initiation site to the mist boundary and

_{mist}*K*is another material constant, which is a function of the material toughness

_{frac}*K*, the material density and the fracture limiting velocity [9].

_{IC}*a*subject to a locally applied tensile stress

*σ*produces a mirror like fracture face. There, we can write:

_{app}*K*of pure silicate optical fibers is 0.73 MPa.m

_{IC}^{1/2}[10

10. NIST, “SiO2 Base Glasses: S100a”, retrieved May 31, 2006, http://www.ceramics.nist.gov/srd/summary/glss100a.htm.

*K*was experimentally measured to be 2.18 MPa.m

_{frac}^{1/2}using SMF-28 fracture faces cleaved under various tensile strengths [11]. This value is in reasonable agreement with the value of ~1.8 MPa.m

^{1/2}extracted from a plot in [7] and the value of 2.32 MPa.m

^{1/2}reported in [9] for fused silica glass. Both

*K*and

_{IC}*K*are expected to be the same for our MSF samples as they are made of usual fiber glass.

_{frac}*Y*is a dimensionless geometrical factor equal to √π·

*f*(

*a*/

*W*), where

*f*(

*a*/

*W*) accounts for the finite with

*W*of the material compared to the fracture length

*a*, which intensifies the local stress at the fracture tip as compared to the remote applied stress

*σ*. In the case of a fracture propagating from the material boundary in a plane perpendicular to the stress direction [12

_{app}12. H. Tada, P. C. Paris, and G. R. Irwin, *The Stress Analysis of Cracks Handbook*, 3^{rd} ed. (American Society of Mechanical Engineers Press, New York,2000). [CrossRef]

*W*is the outer cladding diameter and, when the fracture reaches the intercapillary bridges, the fracture length is already equal to the outer cladding thickness, which can be computed from the data of Table 1 as

*a*= (

*W*-

*D*) /2, where

_{c}*D*is the diameter of the ring of capillaries. The corresponding values of

_{c}*f*(

*a*/

*W*) are tabulated in Table 2. For any given applied stress, the critical length

*a*required to cleave a bridge can then be computed using Eq. (1) and could be made as short as necessary by increasing the applied stress. However, Eq. (2) provides a maximum value for the applied stress, as the minimum mist diameter should be equal to the fiber outer diameter to ensure that the entire cross sectional area of the fiber falls within the mirror zone.

_{c}## 4. Design criterion

*a*. In general, a fracture will remain autonomous in a bridge if each line tangential to c1 from the points on the perimeter of c2 has a length at least equal to

_{c}*a*(i.e. ED >

_{c}*a*). This condition guarantees fracture propagation in those bridges that are not directly in line with the initial fracture point. The same condition should be satisfied when the fracture travels from the inner cladding to the outer cladding. The criterion to determine the suitability of capillary shape and position within the fiber cross-section can be summarized as follows: 1) For each point on a capillary perimeter, draw a tangential line to its neighbouring capillaries. 2) Place adjacent capillaries so that the length of those tangential lines is slightly longer than

_{c}*a*. This guarantees the existence of at least one autonomous fracture point and is verified for Fiber 1.

_{c}## 5. Conclusion

## Acknowledgments

## References and links

1. | S. Huntington, K. Lyytikainen, and J. Canning “Analysis and removal of fracture damage during and subsequent to holey fiber cleaving,” Opt. Express |

2. | C. Simonneau, P. Bousselet, G. Melin, L. Provost, C. Moreau, X. Rejeaunier, A.Le Sauze, L. Gassa, and D. Bayart, “High-power air-clad photonic crystal fiber cladding-pumped EDFA for WDM applications in the C-band,” presented at the Europeen Conference on Optical Communications (ECOC), PD57, (2003). |

3. | W. J. Wadsworth, M. R. Percival, G. Bouwmans, J. C. Knight, T. A. Birks, T. D. Hedley, and P. S. J. Russel, “Very high numerical aperture fibers,” IEEE Photon. Technol. Lett. |

4. | R. O. Ritchie, “Mechanics of fatigue-crack propagation in ductile and brittle solids,” Int. J. Fract. |

5. | D. G. Holloway, “The fracture of glass,” in |

6. | T. Kuwabara, Y. Mitsunaga, and H. Koga “Calculation method of failure probabilities of optical fibers,” J. Lightwave Technol. |

7. | A. D. Yablon, |

8. | T. Haibara, M. Matsumoto, and M. Miyauchi, “Design and developpement of an automatic cutting tool for optical fibers,” J. Lightwave Technol. |

9. | D. Glodge, P. W. Smith, D. L. Bisbee, and E. L. Chinnock, “Optical fiber end preparation for low-loss splices,” Bell Syst. Tech. J. |

10. | NIST, “SiO2 Base Glasses: S100a”, retrieved May 31, 2006, http://www.ceramics.nist.gov/srd/summary/glss100a.htm. |

11. | S. S. Aboutorabi, “Clivage mécanique des fibres microstructurées,” M. Eng. Thesis (École de Technologie supérieure, Montreal, QC, Canada,2006). |

12. | H. Tada, P. C. Paris, and G. R. Irwin, |

**OCIS Codes**

(060.0060) Fiber optics and optical communications : Fiber optics and optical communications

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

(160.2290) Materials : Fiber materials

**ToC Category:**

Photonic Crystal Fibers

**History**

Original Manuscript: June 13, 2006

Revised Manuscript: July 27, 2006

Manuscript Accepted: July 27, 2006

Published: August 7, 2006

**Citation**

Véronique François and Seyed Sadreddin Aboutorabi, "A mechanical criterion for the design of readily cleavable microstructured optical fibers," Opt. Express **14**, 7312-7318 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-16-7312

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### References

- S. Huntington, K. Lyytikainen and J. Canning "Analysis and removal of fracture damage during and subsequent to holey fiber cleaving," Opt. Express 11, 535-540 (2003). [CrossRef] [PubMed]
- C. Simonneau, P. Bousselet, G. Melin, L. Provost, C. Moreau, X. Rejeaunier, A. Le Sauze, L. Gassa and D. Bayart, "High-power air-clad photonic crystal fiber cladding-pumped EDFA for WDM applications in the C-band," presented at the Europeen Conference on Optical Communications (ECOC), PD57, (2003).
- W. J. Wadsworth, M. R. Percival, G. Bouwmans, J. C. Knight, T. A. Birks, T. D. Hedley and P. S. J. Russel, "Very high numerical aperture fibers," IEEE Photon. Technol. Lett. 16, 843-845 (2004). [CrossRef]
- R. O. Ritchie, "Mechanics of fatigue-crack propagation in ductile and brittle solids," Int. J. Fract. 100, 55-83 (1999). [CrossRef]
- D. G. Holloway, "The fracture of glass," inPhysics Education (1968), pp. 317-322. [CrossRef]
- T. Kuwabara, Y. Mitsunaga and H. Koga "Calculation method of failure probabilities of optical fibers," J. Lightwave Technol. 11, 1132-1138 (1993). [CrossRef]
- A. D. Yablon, Optical Fiber Fusion Splicing (Springer, Germany, 2005).
- T. Haibara, M. Matsumoto and M. Miyauchi, "Design and developpement of an automatic cutting tool for optical fibers," J. Lightwave Technol. LT-4, 1434-1439 (1986). [CrossRef]
- D. Glodge, P. W. Smith, D. L. Bisbee and E. L. Chinnock, "Optical fiber end preparation for low-loss splices," Bell Syst. Tech. J. 52, 1579-1587 (1973).
- NIST, "SiO2 Base Glasses: S100a," retrieved May 31, 2006, http://www.ceramics.nist.gov/srd/summary/glss100a.htm.
- S. S. Aboutorabi, "Clivage mécanique des fibres microstructurées," M. Eng. Thesis (École de Technologie supérieure, Montreal, QC, Canada, 2006).
- H. Tada, P. C. Paris and G. R. Irwin, The Stress Analysis of Cracks Handbook, 3rd ed. (American Society of Mechanical Engineers Press, New York, 2000). [CrossRef]

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