## A simple and reliable method to determine LP_{11} cutoff wavelength of bend insensitive fiber

Optics Express, Vol. 18, Issue 13, pp. 13761-13771 (2010)

http://dx.doi.org/10.1364/OE.18.013761

Acrobat PDF (3048 KB)

### Abstract

We present a simple and reliable method based on the spectral splice loss measurement to determine the cutoff wavelength of bend insensitive fiber.

© 2010 OSA

## 1. Introduction

1. J. Van Erps, C. Debaes, T. Nasilowski, J. Watté, J. Wojcik, and H. Thienpont, “Design and tolerance analysis of a low bending loss hole-assisted fiber using statistical design methodology,” Opt. Express **16**(7), 5061–5074 (2008). [CrossRef] [PubMed]

10. P. R. Watekar, S. Ju, and W.-T. Han, “Design and development of a trenched optical fiber with ultra-low bending loss,” Opt. Express **17**(12), 10350–10363 (2009). [CrossRef] [PubMed]

1. J. Van Erps, C. Debaes, T. Nasilowski, J. Watté, J. Wojcik, and H. Thienpont, “Design and tolerance analysis of a low bending loss hole-assisted fiber using statistical design methodology,” Opt. Express **16**(7), 5061–5074 (2008). [CrossRef] [PubMed]

2. P. R. Watekar, S. Ju, and W.-T. Han, “Single-mode optical fiber design with wide-band ultra low bending-loss for FTTH application,” Opt. Express **16**(2), 1180–1185 (2008). [CrossRef] [PubMed]

7. Stokeryale bend insensitive fiber (2007), http://www.stockeryale.com/o/fiber/products/bif-1550-l2.htm

5. K. Himeno, S. Matsuo, Ning Guan, and A. Wada, “Low bending loss single mode fibers for Fiber-to-the-Home,” J. Lightwave Technol. **23**(11), 3494–3499 (2005). [CrossRef]

8. P. R. Watekar, S. Ju, and W.-T. Han, “Bend insensitive optical fiber with ultralow bending loss in the visible wavelength band,” Opt. Lett. **34**(24), 3830–3832 (2009). [CrossRef] [PubMed]

10. P. R. Watekar, S. Ju, and W.-T. Han, “Design and development of a trenched optical fiber with ultra-low bending loss,” Opt. Express **17**(12), 10350–10363 (2009). [CrossRef] [PubMed]

11. Draka BendBright Fiber data-sheets (2010). (http://communications.draka.com/sites/eu/Datasheets/SMF%20-%20BendBright-XS%20Single-Mode%20Optical%20Fiber.pdf)

_{11}mode is considered to be the effective cutoff wavelength [13]. For this, the spectral attenuation for the SMF with a loop of 6 cm diameter is measured in comparison with the straight fiber and the wavelength where the long wavelength edge of the bend induced loss is greater than the long wavelength baseline by 0.1 dB is considered as the effective cutoff wavelength [13,14

14. D. Pagnoux, J.-M. Blondy, P. Roy, and P. Facq, “Cutoff wavelength and mode field radius determinations in monomode fibers by means of a new single measurement device,” Pure Appl. Opt. **6**(5), 551–556 (1997). [CrossRef]

_{11}) has a very low bending loss in the BIF, which is a real hindrance in the determination of the cutoff wavelength using the existing instrument. Because of this difficulty, several methods have been reported to determine the cutoff wavelength of the BIF. A multimode reference technique, where transmission powers are measured with the SMF and the multimode fiber are compared to estimate the cutoff wavelength [15], however this measurement method is affected by ripples due to leaky modes. A far field MFD method has also been reported to determine the cutoff wavelength of optical fibers with improved bending insensitivity in [16

16. K. Nakajima, J. Zhou, K. Tajima, C. Fukai, K. Kurokawa, and I. Sankawa, “Cutoff wavelength measurement in a fiber with improved bending loss,” IEEE Photon. Technol. Lett. **16**(8), 1918–1920 (2004). [CrossRef]

## 2. Splice loss and cutoff wavelength

*ε*

_{0}is the permittivity of free space,

*μ*

_{0}is the permeability of free space,

*n*is the refractive index and

*t*represents time. By adopting the method of separation of variables and by considering

*n*

^{2}dependence only on transverse coordinates (

*ω*is the angular frequency,

*β*is the propagation constant, and

*z*is a coordinate along the fiber length. Further assuming

*n*

^{2}dependency only on

*r*and substituting Eq. (2) in Eq. (1) gives:where

*l*is the constant (an azimuthal mode number) expressed as

*φ*dependency is of the form

*l*> = 1 are four fold degenerate, while with

*l*= 0 are

*φ*independent and have two fold degeneracy (two independent states of polarization). It is known that intensity profiles of transverse electric fields belonging to the same LP mode have same distribution.

*R*is the mode field in the

_{i}*i*

^{th}region along the radius

*r*,

*J*is the Bessel function of first kind,

*I*and

*K*are modified Bessel functions,

*A*are constants and

_{i}*p*and

_{i}*q*are defined as follows:where

_{i}*k*

_{0}is a propagation constant in the free space ( = 2π/

*λ,*in which

*λ*is the operating wavelength),

*n*is the refractive index of optical fiber in the

_{i}*i*

^{th}region, and

*β*is the propagation constant of

_{l}*l*

^{th}mode in the optical fiber.

*β*/

_{l}*k*

_{0}>

*n*

_{4}, which is the case of the BIF of Fig. 1 that is operating without any bend. To solve Eq. (5) to Eq. (8), we use boundary conditions at

*i*

^{th}and (

*i*+ 1)

^{th}interfaces, i.e.,

*R*(

_{i}*r*) =

*R*

_{i}_{+1}(

*r*), and

*dR*(

_{i}*r*)/

*dr*=

*dR*

_{i}_{+1}(

*r*)/

*dr*and use

*r*= radial distance at the interface under consideration. A characteristic equation in the form of a determinant to find mode field values can be expressed as:where

*l.*After that, the mode field variation along the radius can be calculated by using Eq. (5) to Eq. (8) with

*A*

_{0}= 1. Field propagating at any time and at any distance in the optical fiber can be expressed from Eq. (2) as: where suffixes

*y*and

*x*are for y-polarization and x-polarization, respectively and

*R*’s are defined in Eq. (5) to Eq. (8). Normalization of Eq. (12) to Eq. (14) can also be carried out to get unity power for each mode [19].

20. K. Petermann and R. Kuhne, “Upper and lower limits for the microbending loss in arbitrary single-mode fibers,” J. Lightwave Technol. **4**(1), 2–7 (1986). [CrossRef]

*a*= 4 μm,

*b*= 8 μm,

*c*= 12 μm, ∆

*n*

_{1}= 0.006, and ∆

*n*

_{T}_{1}= −0.003, theoretical cutoff wavelength of LP

_{11}mode (with

*l*= 1) is about 1.3 μm. The LP

_{01}mode field and the LP

_{11}mode field at wavelengths below, above and at the cutoff wavelength are shown in Fig. 2 .

_{01}modal power and the LP

_{11}modal power can be written as [from Eq. (15)]: where

*C*

_{1}and

*C*

_{2}are constants, which can be determined from known power. It is noted that, if we launch equal power (

*p*(

*λ*)) in all degenerate modes then the fiber supporting two modes (LP

_{01}, LP

_{11}) will have 6

*p*(

*λ*) power and the fiber supporting only one mode (LP

_{01}) will have 2

*p*(

*λ*) power. Thus, moving from the two-mode propagation to the fundamental mode propagation in the optical fiber will cause the loss of around 4.77 dB.

_{1}(

*x*,

*y*) in Fiber-1 and ψ

_{2}(

*x*,

*y*) in Fiber-2) after the transverse misalignment of

*u*(a movement with respect to aligned axes and which is parallel to end faces) can be expressed in Cartesian co-ordinates as:where

*α*(in dB) between two fibers with the transverse offset of

*u*is expressed by

*u*) between two fibers in

*x*-direction, the fundamental LP

_{01}mode (

*x*,

*y*LP

_{11}modes (

*u*[21

21. K. Thyagarajan, A. Gupta, B. P. Pal, and A. K. Ghatak, “An analytical model for studying two-mode fibers: splice loss prediction,” Opt. Commun. **42**(2), 92–996 (1982). [CrossRef]

*T*is the overlap integration between

_{ij}*w*is the fundamental mode spot size ( =

*MFD*/2). The transverse splice loss is then expressed by:where

*A*,

*B*and

*C*are constants; for equal power in all modes,

*A*=

*B*=

*C*= 1/3. It is noted that in Eq. (22), LP

_{01}and LP

_{11}modes have been approximated by a Gaussian function and a Hermite-Gauss function, respectively, which are accurate within a few percent of exact field profiles [21

21. K. Thyagarajan, A. Gupta, B. P. Pal, and A. K. Ghatak, “An analytical model for studying two-mode fibers: splice loss prediction,” Opt. Commun. **42**(2), 92–996 (1982). [CrossRef]

*MFD*and the splice loss determined for the above fiber are shown in Fig. 3 for equal power distributed in all modes. It can be observed that at the vicinity of the cutoff wavelength, the transverse splice loss is the lowest and jumps to the high value when only LP

_{01}mode propagates in the fiber. Thus, it can be stated that the wavelength where we get the lowest splice loss is the cutoff wavelength. Now, we use this idea to determine the cutoff wavelength of experimental BIFs.

## 3. Experiments

11. Draka BendBright Fiber data-sheets (2010). (http://communications.draka.com/sites/eu/Datasheets/SMF%20-%20BendBright-XS%20Single-Mode%20Optical%20Fiber.pdf)

11. Draka BendBright Fiber data-sheets (2010). (http://communications.draka.com/sites/eu/Datasheets/SMF%20-%20BendBright-XS%20Single-Mode%20Optical%20Fiber.pdf)

*u*= 0). Typical measurements of splice loss for the SMF (Fiber-1) are shown in Fig. 4 and a linear curve fit at the central points of the transition curve (indicating a transition from the multimode to the single mode regime) was used to obtain transition values of the splice loss as shown in Fig. 5 . Subsequent splice loss measurements for bend insensitive fibers, Fiber-2, Fiber-3 and Fiber-4 are shown in Fig. 6 , Fig. 7 and Fig. 8 , respectively.

_{11}mode attenuation peak. Bending loss measurements for Fiber-1, Fiber-2, Fiber-3 and Fiber-4 are shown in Fig. 4, Fig. 6, Fig. 7 and Fig. 8, respectively.

## 4. Results and discussion

_{11}mode field starts to suffer attenuation much before the cutoff wavelength due to spreading and leakage of the mode field and the pure single mode operation starts earlier than the cutoff wavelength; the wavelength where single mode starts before the theoretical cutoff is known as an effective cutoff wavelength. In contrast to this, increase in the spreading of the LP

_{11}mode decreases the splice loss as the operating wavelength approaches the LP

_{11}mode field cutoff wavelength. Because no bending is applied to leak the LP

_{11}mode field, the splice loss where it again reaches a high value nearly represents a pure single mode operation that is predicted by theory. We obtained the pure single mode regime for the SMF at about 1226.3 nm as illustrated in Fig. 5.

_{11}cutoff wavelength.

## 5. Summary

## Acknowledgments

## References and links

1. | J. Van Erps, C. Debaes, T. Nasilowski, J. Watté, J. Wojcik, and H. Thienpont, “Design and tolerance analysis of a low bending loss hole-assisted fiber using statistical design methodology,” Opt. Express |

2. | P. R. Watekar, S. Ju, and W.-T. Han, “Single-mode optical fiber design with wide-band ultra low bending-loss for FTTH application,” Opt. Express |

3. | S. Matsuo, M. Ikeda, and K. Himeno, “Bend insensitive and low splice loss optical fiber for indoor wiring in FTTH,” Proceedings of Optical Fiber Communication Conference (OFC), Anaheim, USA, Feb. 23–27, 2004, ThI3 (2004). |

4. | I. Sakabe, H. Ishikawa, H. Tanji, Y. Terasawa, M. Ito, and T. Ueda, “Enhanced bending loss insensitive fiber and new cables for CWDM access networks,” Proceeding of 53rd International Wire and Cable Symposium, Philadelphia, USA, November 14–17, 2004, 112–118, (2004). |

5. | K. Himeno, S. Matsuo, Ning Guan, and A. Wada, “Low bending loss single mode fibers for Fiber-to-the-Home,” J. Lightwave Technol. |

6. | M.-J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low bending loss single-mode fiber for FTTH,” Proceedings of OFC/NFOEC-2008, San Diego, USA, Feb. 24–28, 2008, PDP10 (2008). |

7. | Stokeryale bend insensitive fiber (2007), http://www.stockeryale.com/o/fiber/products/bif-1550-l2.htm |

8. | P. R. Watekar, S. Ju, and W.-T. Han, “Bend insensitive optical fiber with ultralow bending loss in the visible wavelength band,” Opt. Lett. |

9. | P. R. Watekar, S. Ju, and W.-T. Han, “Near zero bending loss in a double-trenched bend insensitive optical fiber at 1550 nm,” Opt. Express |

10. | P. R. Watekar, S. Ju, and W.-T. Han, “Design and development of a trenched optical fiber with ultra-low bending loss,” Opt. Express |

11. | Draka BendBright Fiber data-sheets (2010). (http://communications.draka.com/sites/eu/Datasheets/SMF%20-%20BendBright-XS%20Single-Mode%20Optical%20Fiber.pdf) |

12. | ITU-T recommendation G.652. |

13. | A. Ghatak, and K. Thyagarajan, |

14. | D. Pagnoux, J.-M. Blondy, P. Roy, and P. Facq, “Cutoff wavelength and mode field radius determinations in monomode fibers by means of a new single measurement device,” Pure Appl. Opt. |

15. | International Standard IEC 60793–1-42, 2007–04 (2007). |

16. | K. Nakajima, J. Zhou, K. Tajima, C. Fukai, K. Kurokawa, and I. Sankawa, “Cutoff wavelength measurement in a fiber with improved bending loss,” IEEE Photon. Technol. Lett. |

17. | T. Nakanishi, M. Hirano, and T. Sasaki, “Proposal of reliable cutoff wavelength measurement for bend insensitive fiber,” Proceedings of European Conference on Optical Communications (ECOC), Vienna, Austria, Sept. 20–24, 2009, P1.14 (2009). |

18. | A. W. Snyder, and J. D. Love, Optical waveguide theory, Chapman and Hall (1983). |

19. | L. B. Jeunhomme, |

20. | K. Petermann and R. Kuhne, “Upper and lower limits for the microbending loss in arbitrary single-mode fibers,” J. Lightwave Technol. |

21. | K. Thyagarajan, A. Gupta, B. P. Pal, and A. K. Ghatak, “An analytical model for studying two-mode fibers: splice loss prediction,” Opt. Commun. |

22. | Samsung single mode fiber data-sheets (2010). |

**OCIS Codes**

(060.2310) Fiber optics and optical communications : Fiber optics

(060.2330) Fiber optics and optical communications : Fiber optics communications

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: March 4, 2010

Revised Manuscript: May 18, 2010

Manuscript Accepted: May 26, 2010

Published: June 11, 2010

**Citation**

Pramod R. Watekar, Seongmin Ju, Lin Htein, and Won-Taek Han, "A simple and reliable method to determine LP_{11} cutoff wavelength of bend insensitive fiber," Opt. Express **18**, 13761-13771 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-13-13761

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### References

- J. Van Erps, C. Debaes, T. Nasilowski, J. Watté, J. Wojcik, and H. Thienpont, “Design and tolerance analysis of a low bending loss hole-assisted fiber using statistical design methodology,” Opt. Express 16(7), 5061–5074 (2008). [CrossRef] [PubMed]
- P. R. Watekar, S. Ju, and W.-T. Han, “Single-mode optical fiber design with wide-band ultra low bending-loss for FTTH application,” Opt. Express 16(2), 1180–1185 (2008). [CrossRef] [PubMed]
- S. Matsuo, M. Ikeda, and K. Himeno, “Bend insensitive and low splice loss optical fiber for indoor wiring in FTTH,” Proceedings of Optical Fiber Communication Conference (OFC), Anaheim, USA, Feb. 23–27, 2004, ThI3 (2004).
- I. Sakabe, H. Ishikawa, H. Tanji, Y. Terasawa, M. Ito, and T. Ueda, “Enhanced bending loss insensitive fiber and new cables for CWDM access networks,” Proceeding of 53rd International Wire and Cable Symposium, Philadelphia, USA, November 14–17, 2004, 112–118, (2004).
- K. Himeno, S. Matsuo, Ning Guan, and A. Wada, “Low bending loss single mode fibers for Fiber-to-the-Home,” J. Lightwave Technol. 23(11), 3494–3499 (2005). [CrossRef]
- M.-J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low bending loss single-mode fiber for FTTH,” Proceedings of OFC/NFOEC-2008, San Diego, USA, Feb. 24–28, 2008, PDP10 (2008).
- Stokeryale bend insensitive fiber (2007), http://www.stockeryale.com/o/fiber/products/bif-1550-l2.htm
- P. R. Watekar, S. Ju, and W.-T. Han, “Bend insensitive optical fiber with ultralow bending loss in the visible wavelength band,” Opt. Lett. 34(24), 3830–3832 (2009). [CrossRef] [PubMed]
- P. R. Watekar, S. Ju, and W.-T. Han, “Near zero bending loss in a double-trenched bend insensitive optical fiber at 1550 nm,” Opt. Express 17(22), 20155–20166 (2009). [CrossRef] [PubMed]
- P. R. Watekar, S. Ju, and W.-T. Han, “Design and development of a trenched optical fiber with ultra-low bending loss,” Opt. Express 17(12), 10350–10363 (2009). [CrossRef] [PubMed]
- Draka BendBright Fiber data-sheets (2010). ( http://communications.draka.com/sites/eu/Datasheets/SMF%20-%20BendBright-XS%20Single-Mode%20Optical%20Fiber.pdf )
- ITU-T recommendation G.652.
- A. Ghatak, and K. Thyagarajan, Introduction to Fiber Optics, Cambridge University Press, USA (1998).
- D. Pagnoux, J.-M. Blondy, P. Roy, and P. Facq, “Cutoff wavelength and mode field radius determinations in monomode fibers by means of a new single measurement device,” Pure Appl. Opt. 6(5), 551–556 (1997). [CrossRef]
- International Standard IEC 60793–1-42, 2007–04 (2007).
- K. Nakajima, J. Zhou, K. Tajima, C. Fukai, K. Kurokawa, and I. Sankawa, “Cutoff wavelength measurement in a fiber with improved bending loss,” IEEE Photon. Technol. Lett. 16(8), 1918–1920 (2004). [CrossRef]
- T. Nakanishi, M. Hirano, and T. Sasaki, “Proposal of reliable cutoff wavelength measurement for bend insensitive fiber,” Proceedings of European Conference on Optical Communications (ECOC), Vienna, Austria, Sept. 20–24, 2009, P1.14 (2009).
- A. W. Snyder, and J. D. Love, Optical waveguide theory, Chapman and Hall (1983).
- L. B. Jeunhomme, Single Mode Fiber Optics, Marcel Dekker Inc., New York, USA (1990).
- K. Petermann and R. Kuhne, “Upper and lower limits for the microbending loss in arbitrary single-mode fibers,” J. Lightwave Technol. 4(1), 2–7 (1986). [CrossRef]
- K. Thyagarajan, A. Gupta, B. P. Pal, and A. K. Ghatak, “An analytical model for studying two-mode fibers: splice loss prediction,” Opt. Commun. 42(2), 92–996 (1982). [CrossRef]
- Samsung single mode fiber data-sheets (2010).

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