## Design and characterization of single-mode holey fibers with low bending losses

Optics Express, Vol. 13, Issue 12, pp. 4770-4779 (2005)

http://dx.doi.org/10.1364/OPEX.13.004770

Acrobat PDF (477 KB)

### Abstract

As the fiber-to-the-home network construction increased, optical fiber cables are demanded to be easier to handle and require less space. Under this situation, a single mode fiber (SMF) permitting small bending radius is strongly requested. In this paper, we propose and demonstrate a novel type of bending-insensitive single-mode holey fiber that has a doped core and two layers of holes with different air-hole diameters. The fiber has a mode field diameter of 9.3 µm at 1.55 µm and a cutoff wavelength below 1.1 µm, and shows a bending loss of 0.011 dB/turn at 1.55 µm for a bending radius of 5 mm and a low splice loss of 0.08 dB per fusion-splicing to a conventional SMF.

© 2005 Optical Society of America

## 1. Introduction

1. P.St.J. Russell, “Photonic crystal fibers,” Science **299**, 358–362 (2003). [CrossRef] [PubMed]

3. T. Hasegawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, and M. Koshiba, “Hole-assisted lightguide fiber for large anomalous dispersion and low optical loss,” Opt. Express **9**, 681–686 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-681. [CrossRef] [PubMed]

## 2. Holey fiber design

*et al*. have investigated the hole-assisted fiber structure with one layer of air-holes in Fig. 1(a) for low bending and splice losses [4

4. K. Nakajima, K. Hogari, J. Zhou, K. Tajima, and I. Sankawa, “Hole-assisted fiber design for small bending and splice losses,” IEEE Photon. Technol. Lett. **15**, 1737–1739 (2003). [CrossRef]

*a*is the radius of the core,

*d*

_{1}and

*d*

_{2}are the diameters in the inner and the outer layers, respectively, and Λ is the hole pitch. Note that hole diameters

*d*

_{1}and

*d*

_{2}are not necessarily equal, whereas the hole pitch Λ is uniform in the cross section. This HF structure can be fabricated by a stack-and-draw fabrication process [6

6. A. Bjarklev, J. Broeng, and A.S. Bjarklev, *Photonic Crystal Fibres*, Kluwer Academic Publishers, 2003. [CrossRef]

*L*less than 0.3 dB at 1.55-µm operating wavelength, we employ the well-known formula [7]:

_{s}*w*and

_{SMF}*w*are the MFDs of the SMF and the HF, respectively. Figure 2 shows the MFD dependence of splice loss between the HF and the SMF, where the MFD of the SMF is assumed to be 11.4 µm. We can determine that the minimum value of the MFD of the HF is 8.8 µm. We have investigated the optimum structural parameters of the HF in Fig. 1(b). Here, we develop a full vectorial modal solver based on the finite element method (FEM) with anisotropic perfectly matched layer for the calculations of the cutoff wavelength, the bending loss, and the MFD.

_{HF}## 3. Finite element method for bending loss evaluation

*x*direction) for suppressing spurious reflection, where

*R*is the curvature radius,

*d*is the PML thickness, and

_{PML}*x*is the

_{PML}*x*coordinate of the PML surface. In the present analysis, we replace the curved HF by a straight fiber with equivalent refractive index as [8

8. D. Marcuse, “Influence of curvature on the losses of doubly clad fibers,” Appl. Opt. **21**, 4208–4213 (1982). [CrossRef] [PubMed]

*n*(

*x, y*) is the original refractive index profile of the HF. We should notice that the equivalent refractive index

*n*(

_{eq}*x, y*) in the PML region is no longer homogeneous along the

*x*-direction. Here, we apply the anisotropic PML [9

9. F.L. Teixeira and W.C. Chew, “General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media,” IEEE Microwave Guided Wave Lett. **8**, 223–225 (1998). [CrossRef]

10. K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers,” IEEE J. Quantum Electron. **38**, 927–933 (2002). [CrossRef]

*r*=[

*x, y, z*]

^{T}is converted by [9]

*̃ is the coordinate converted position vector,*

**r***S*(

*x*) is the complex stretching variable [9

9. F.L. Teixeira and W.C. Chew, “General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media,” IEEE Microwave Guided Wave Lett. **8**, 223–225 (1998). [CrossRef]

*denotes a transpose.*

^{T}*S*(

*x*) as [10

10. K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers,” IEEE J. Quantum Electron. **38**, 927–933 (2002). [CrossRef]

*̿, defined as [9*

**E**9. F.L. Teixeira and W.C. Chew, “General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media,” IEEE Microwave Guided Wave Lett. **8**, 223–225 (1998). [CrossRef]

*(*

**E***̃) is the coordinate converted electric field vector,*

**r***k*

_{0}is the free-space wavenumber, and

*n*(

_{eq}*̃) is the coordinate converted equivalent refractive index.*

**r**11. M. Koshiba and K. Saitoh, “Numerical verification of degeneracy in hexagonal photonic crystal fibers,” IEEE Photon. Technol. Lett. **13**, 1313–1315 (2001). [CrossRef]

*E*} is the discretized electric field vector, β is the complex propagation constant, and the finite element matrices [

*K*] and [

*M*] are given in Ref. [10

10. K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers,” IEEE J. Quantum Electron. **38**, 927–933 (2002). [CrossRef]

*L*, is defined as

_{B}## 4. The impact of the design parameters to the bending loss and cutoff wavelength characteristics

*d*

_{1}increases, while the cutoff wavelength increases. By keeping parameters

*d*

_{1}and Λ constant and varying only the value of

*d*

_{2}, we can control the cutoff wavelength and bending loss without changing the size of the MFD. We perform numerical simulation to obtain the optimum structural parameters, such as the core radius, the hole pitch, and the hole diameters through the vector FEM, where the material dispersion given by a Sellmeier formula is included directly in the calculation.

*d*

_{1},

*d*

_{2}, and

*a*. We found that the cutoff wavelength is strongly dependent on core radius

*a*, where the MFD of the fundamental mode is evaluated at 1.55-µm wavelength. When the hole pitch Λ is smaller than 8 µm, the MFD takes undesirable small value, resulting in the large splice losses. We can see that, to achieve the desired MFD (

*w*

_{HF}≥ 8.8 µm) and the desired cutoff wavelength (

*λ*≤ 1.25 µm), we should choose the values of Λ≅9.0 µm,

_{c}*d*

_{1}/Λ=0.38, and

*a*=3 µm. The value of Λ≅9.0 µm is the optimum, in the sense that when increases (e.g. Λ=10 µm), the MFD takes undesirable large values, resulting in the large bending losses. Figure 5 shows the impact of the pitch parameter Λ on the allowable bending radius, and we can deduce further optimum values such as

*d*

_{1}/Λ=0.38 and

*a*=3.0 µm, where the bending loss of the fundamental mode is evaluated at 1.65-µm wavelength. Notice that, for the previous parameters, the allowable bending radius is always less than 7 mm. In Fig. 6 we investigate the dependence of the cutoff wavelength on the allowable bending radius, by varying the parameter

*d*

_{2}. We found that by increasing the value of

*d*

_{2}, we can reduce further the allowable bending radius, which results in more compact applications.

*a*=3.0 µm, Λ=9.0 µm,

*d*

_{1}/Λ=0.38, and

*d*

_{2}/Λ=0.40. The MFD is 8.8 µm at 1.55-µm wavelength. The allowable bending radius and the cutoff wavelength for this HF are 5.9 mm and 1.28 µm, respectively. In Fig. 7 we plot the optical field distribution in the curved HF, where the operating wavelength is 1.55 µm and the bending radius is 6.0 mm. As we can see, there is a strong confinement of the light in the core and the radiation into the cladding region is minimized, showing the usefulness of the proposed hole-assisted HF and design procedure.

## 5. Experimental results and discussion

*a*=2.95 µm, hole pitch Λ=8.98 µm, and the hole diameters are

*d*

_{1}=3.51 µm (

*d*

_{1}/Λ=0.39) and

*d*

_{2}=3.71 µm (

*d*

_{2}/Λ=0.41), respectively. The structural parameters of the fabricated fiber are almost the same as those of the designed fiber. The characteristics of the fiber are summarized in Table 1. Even though this fiber has a relatively high transmission loss of 2.3 dB/km at 1.55-µm wavelength, this attenuation can be reduced by careful optimization of the fabrication process. The chromatic dispersion is 21.8 ps/(km·nm) at 1.55 µm. We measured the cutoff wavelength of the fiber using multimode excitation method recommended by ITU-T G.650 with a fiber of 2 m length and a 140 mm bending radius. The cutoff wavelength of the higher-order mode is 1.1 µm. Figure 9 shows the numerically evaluated wavelength dependence of the effective indices of the fundamental and higher-order modes of the fabricated HF, where the pure silica index is shown as a dotted curve. The effective index of the fundamental mode is higher than the pure silica index, on the other hand, the effective index of the higher-order mode becomes equal to the silica index at ~0.92-µm wavelength. It is noteworthy that the measured cutoff wavelength is longer than the wavelength of the intersection between the effective index of the higher-order mode and the pure silica index in Fig. 9, because the higher-order mode exists in the HF as a leaky mode when the effective index of the higher-order mode becomes lower than the silica index. Figure 10 shows the wavelength dependence of the leakage loss of the higher-order mode for this fiber. The leakage loss becomes 13 dB/m at 1.25 µm. Figure 11 shows the optical field distributions of the fundamental and higher-order modes at 0.92-µm wavelength, where the contours are spaced by 3 dB. As we can see, the fundamental mode is strongly confined to the core region, whereas the higher-order mode penetrates more deeply into the cladding region.

*et al*. [5] formed a taper region for gradual MFD transition to splice a HF with an SMF, however, the proposed HF can be spliced to an SMF only by arc fusion splicing with low loss. If we keep hole diameter

*d*

_{1}in the inner layer and hole pitch Λ constant and increase hole diameter

*d*

_{2}in the outer layer, we can further reduce the bending loss without changing the MFD.

## 6. Conclusions

## References and links

1. | P.St.J. Russell, “Photonic crystal fibers,” Science |

2. | T. Hasegawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, and M. Koshiba, “Novel hole-assisted lightguide fiber exhibiting large anomalous dispersion and low loss below 1 dB/km,” in proceedings of Optical Fiber Communication Conference (OFC2001), paper PD5, Anaheim, USA, (2001). |

3. | T. Hasegawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, and M. Koshiba, “Hole-assisted lightguide fiber for large anomalous dispersion and low optical loss,” Opt. Express |

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

5. | T. Hasegawa, T. Saitoh, D. Nishioka, E. Sasaoka, and T. Hosoya, “Bending-insensitive single-mode holey fiber with SMF-compatibility for optical wiring applications,” in proceedings of European Conference on Optical Communications (ECOC2003), paper We2.7.3, Rimini, Italy, (2003). |

6. | A. Bjarklev, J. Broeng, and A.S. Bjarklev, |

7. | D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. |

8. | D. Marcuse, “Influence of curvature on the losses of doubly clad fibers,” Appl. Opt. |

9. | F.L. Teixeira and W.C. Chew, “General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media,” IEEE Microwave Guided Wave Lett. |

10. | K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers,” IEEE J. Quantum Electron. |

11. | M. Koshiba and K. Saitoh, “Numerical verification of degeneracy in hexagonal photonic crystal fibers,” IEEE Photon. Technol. Lett. |

**OCIS Codes**

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

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

**ToC Category:**

Research Papers

**History**

Original Manuscript: April 19, 2005

Revised Manuscript: April 19, 2005

Published: June 13, 2005

**Citation**

Yukihiro Tsuchida, Kunimasa Saitoh, and Masanori Koshiba, "Design and characterization of single-mode holey fibers with low bending losses," Opt. Express **13**, 4770-4779 (2005)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-12-4770

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### References

- P.St.J. Russell, “Photonic crystal fibers,” Science 299, 358-362 (2003). [CrossRef] [PubMed]
- T. Hasegawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, and M. Koshiba, “Novel hole-assisted lightguide fiber exhibiting large anomalous dispersion and low loss below 1 dB/km,” in proceedings of Optical Fiber Communication Conference (OFC2001), paper PD5, Anaheim, USA, (2001).
- T. Hasegawa, E. Sasaoka, M. Onishi, M. Nishimura, Y. Tsuji, and M. Koshiba, “Hole-assisted lightguide fiber for large anomalous dispersion and low optical loss,” Opt. Express 9, 681-686 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-681.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-681.</a> [CrossRef] [PubMed]
- K. Nakajima, K. Hogari, J. Zhou, K. Tajima, and I. Sankawa, “Hole-assisted fiber design for small bending and splice losses,” IEEE Photon. Technol. Lett. 15, 1737-1739 (2003). [CrossRef]
- T. Hasegawa, T. Saitoh, D. Nishioka, E. Sasaoka, and T. Hosoya, “Bending-insensitive single-mode holey fiber with SMF-compatibility for optical wiring applications,” in proceedings of European Conference on Optical Communications (ECOC2003), paper We2.7.3, Rimini, Italy, (2003).
- A. Bjarklev, J. Broeng, and A.S. Bjarklev, Photonic Crystal Fibres, Kluwer Academic Publishers, 2003. [CrossRef]
- D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703-718 (1977).
- D. Marcuse, “Influence of curvature on the losses of doubly clad fibers,” Appl. Opt. 21, 4208-4213 (1982). [CrossRef] [PubMed]
- F.L. Teixeira and W.C. Chew, “General closed-form PML constitutive tensors to match arbitrary bianisotropic and dispersive linear media,” IEEE Microwave Guided Wave Lett. 8, 223-225 (1998). [CrossRef]
- K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers,” IEEE J. Quantum Electron. 38, 927-933 (2002). [CrossRef]
- M. Koshiba and K. Saitoh, “Numerical verification of degeneracy in hexagonal photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 1313-1315 (2001). [CrossRef]

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