## Design of air-guiding modified honeycomb photonic band-gap fibers for effectively single-mode operation

Optics Express, Vol. 14, Issue 6, pp. 2404-2412 (2006)

http://dx.doi.org/10.1364/OE.14.002404

Acrobat PDF (539 KB)

### Abstract

We investigate photonic band-gap (PBG) profiles of a modified honeycomb lattice structure and we identify the structural parameters that possess the largest band-gap. By incorporating the identified profile into the cladding, the wavelength dependence of the dispersion properties and confinement losses of air-guiding modified honeycomb PBG fibers (PBGFs) is investigated through a full-vector modal solver based on finite element method. In particular, we find that broadband effectively single-mode operation from 1450 nm to 1850 nm can be achieved using a modified honeycomb PBGF with a defected core realized by removing 7 air holes.

© 2006 Optical Society of America

## 1. Introduction

*d*/Λ = 0.98 (where

*d*is the diameter of air holes and Λ is the distance between adjacent air holes). By incorporating the identified structural parameters into the fiber cladding, dispersion properties and confinement losses of air-guiding modified honeycomb PBGFs with a defected core realized by removing 7 and 13 air holes as a function of wavelength are investigated through a full-vector modal solver based on finite-element method (FEM) [16

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

## 2. PBG profiles of a modified honeycomb lattice

13. M. Chen and R. Yu, “Analysis of photonic bandgaps in modified honeycomb structures,” IEEE Photon. Technol. Lett. **16**, 819–821 (2004). [CrossRef]

*d*is the diameter of air holes in the basic honeycomb lattice,

*d*is the diameter of additional air holes in the center of unit cell, Λ is the distance between adjacent air holes, and

_{c}*n*

_{1}= 1.0 and

*n*

_{2}= 1.45 are the refractive indices of air and silica, respectively. To design a realistic cladding structure, both

*d*+

*d*< 2Λ and

_{c}*d*< √3Λ are necessary conditions. If the first condition is not satisfied, the air holes with diameters

_{c}*d*and adjacent air holes with diameters

_{c}*d*intersect between each other. If the second condition is not satisfied, the air holes with diameters

*d*intersect with the adjacent air holes of the same diameters.

_{c}*d*/Λ = 0.60 and

*d*/Λ = 1.30. The dispersion curves are calculated through FEM for an infinite periodic lattice of the cladding air-holes. The shaded regions represent the complete PBGs. For βΛ = 6.0, we can see that the region between band-6 and band-7 is large in Fig. 2(a), while for βΛ = 11.0, the regions between band-15 and band-16 as well as between band-6 and band-7 is large in Fig. 2(b). Figure 2(c) shows the βΛ-dependence of the band-gaps for the modified honeycomb lattice with

_{c}*d*/AΛ = 0.60 and

*d*/Λ = 1.30. In general, for air-guiding PBGFs, dispersion curve of the fundamental core mode appear near the air line in the PBG. To estimate the available transmission band, it is very useful to consider the spans of the air line over the PBG regions.

_{c}*d*/Λ = 0.30 to 0.98 and

*d*/Λ =

_{c}*d*/Λ to 1.96 -

*d*/Λ, because it has been reported that when

*d*<

_{c}*d*, the cladding structure does not exhibit wide PBGs [13

13. M. Chen and R. Yu, “Analysis of photonic bandgaps in modified honeycomb structures,” IEEE Photon. Technol. Lett. **16**, 819–821 (2004). [CrossRef]

*d*/Λ =

_{c}*d*/Λ) and the solid cyan line represents the maximum possible size of

*d*/Λ (

_{c}*d*/Λ = 1.96 -

_{c}*d*/Λ). When

*d*is increased, several band-gaps can be enlarged. When

_{c}*d*/Λ is small, band 12–13 is dominant, whereas when

*d*/Λ is between 0.5 and 0.7, band 6–7 is dominant. In addition, when

*d*/Λ becomes larger than 0.9, band 12–13 becomes dominant again. In order to compare each band-gap size quantitatively in the same wavelength range, we can use the following simple equation:

*k*

_{1}Λ and

*k*

_{2}Λ are the normalized wavenumbers at the band-gap edges obtained from Fig. 3 for the target structure. The value of

*w*× 2λ

_{0}represents the PBG wavelength range crossing the air-line, where λ

_{0}stands for the central wavelength in the PBG. Using Eq. (1), we can find which structural parameters result in the largest band-gap, and by done so, we have derived the optimized structural parameters as:

*d*/Λ = 0.60 and

*d*/Λ = 1.36, thus optimizing the 6–7 band-gap. When the cladding structure is realized based on these parameters,

_{c}*W*×2λ

_{0}≈ 400 nm is obtained (provided λ

_{0}= 1.55 μm), and this value is equivalent to that of a triangular lattice, with structural parameter of

*d*/Λ = 0.98.

## 3. Dispersion and confinement loss properties

*d*/Λ = 0.60 and

*d*/Λ = 1.36 as were obtained in Section 2 for the cladding structure, we evaluate the dispersion characteristics and confinement losses for these air-guiding modified honeycomb PBGFs. Because the defected core surface does not intersect the silica material where bulk mode has a high intensity, no surface modes exist in such core types [7

_{c}7. H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, “Designing air-core photonic bandgap fibers free of surface modes,” IEEE J. Quantum Electron. **40**, 551–556 (2004). [CrossRef]

*x*-component of the electric field distribution |

*E*|, for (a) the

_{x}*x*-polarized HE

_{11}mode and (b) the TE

_{01}mode of type-A PBGF with six cell rings at a wavelength of 1.55 μm, where Λ = 1.747 μm,

*d*/Λ = 0.60, and

*d*/Λ = 1.36. The second-order mode is well confined in the air-core region as well as the fundamental mode. For actual PBGFs, due to the finite number of cladding rings, the power of guided modes attenuates in some degree. The confinement losses of the modes can be evaluated from the following equation [5

_{c}5. K. Saitoh and M. Koshiba, “Leakage loss and group velocity dispersion in air-core photonic bandgap fibers,” Opt. Express **11**, 3100–3109 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-23-3100. [CrossRef] [PubMed]

3. J. Broeng, S. E. Barkou, T. Sϕndergaard, and A. Bjarklev, “Analysis of air-guiding photonic bandgap fibers,” Opt. Lett. **25**, 96–98 (2000). [CrossRef]

7. H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, “Designing air-core photonic bandgap fibers free of surface modes,” IEEE J. Quantum Electron. **40**, 551–556 (2004). [CrossRef]

*x*-component of the electric field distribution |

*E*|, for (a) the

_{x}*x*-polarized HE

_{11}mode and (b) the TE

_{01}mode with six cell rings at a wavelength of 1.55 μm, where Λ = 1.747 μm,

*d*/Λ = 0.60, and

*d*/Λ = 1.36. The fundamental mode is well confined to the air-core region, while the confinement of the second-order mode is weak and the confinement loss is very large. Figure 10 shows the wavelength dependence of the confinement losses of the type-B PBGF with six and ten cell rings. The confinement loss of the second-order mode is about 2-orders of magnitude larger than that of the fundamental mode for a six-rings fiber, and 4-orders of magnitude larger for a ten-rings fiber. So, as a conclusion type-B PBGF with ten cell rings and structural parameters of Λ = 1.747 μm,

_{c}*d*/Λ = 0.60, and

*d*/Λ = 1.36 has low-losses and can operate as an effectively single-mode air-guiding PBGF from 1450 nm to 1850 nm.

_{c}## 4. Conclusions

*d*/Λ and

*d*/Λ, in order to identify the optimum parameters that possess the largest band-gap. Using the obtained optimized structural parameters, an air-guiding PBGF based on a modified honeycomb lattice has been demonstrated. We have analyzed the dispersion characteristics and confinement losses in two types of defected air-cores. The fundamental mode is well confined to the air-core region in both core types. In particular we showed that an air-guiding modified honeycomb PBGF with a defected core realized by removing 7 air holes can operate as an effectively single-mode fiber with low confinement losses, over a wide wavelength range. According to our calculation based on full-vector FEM, no surface modes exist in the proposed PBGFs.

_{c}## Acknowledgments

## References and links

1. | T. A. Birks, P. J. Roberts, P. S. J. Russell, D. M. Atkin, and T. J. Shepherd, “Full 2-D photonic bandgaps in silica/air structures,” Electron. Lett. |

2. | R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science |

3. | J. Broeng, S. E. Barkou, T. Sϕndergaard, and A. Bjarklev, “Analysis of air-guiding photonic bandgap fibers,” Opt. Lett. |

4. | C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature |

5. | K. Saitoh and M. Koshiba, “Leakage loss and group velocity dispersion in air-core photonic bandgap fibers,” Opt. Express |

6. | K. Saitoh, N. A. Mortensen, and M. Koshiba, “Air-core photonic band-gap fibers: the impact of surface modes,” Opt. Express |

7. | H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, “Designing air-core photonic bandgap fibers free of surface modes,” IEEE J. Quantum Electron. |

8. | M. Yan and P. Shum, “Air guiding with honeycomb photonic bandgap fiber,” IEEE Photon. Technol. Lett. |

9. | M. Yan, P. Shum, and J. Hu, “Design of air-guiding honeycomb photonic bandgap fiber,” Opt. Lett. |

10. | J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. S. J. Russell, “Highly increased photonic band gaps in silica/air structures,” Opt. Commun. |

11. | Y. Li, C. Wang, M. Hu, B. Liu, X. Sun, and L. Chai, “Honeycomb photonic bandgap fibers with and without interstitial air holes,” Opt. Express |

12. | T. Haas, S. Belau, and T. Doll, “Realistic monomode air-core honeycomb photonic bandgap fiber with pockets,” J. Lightwave Technol. |

13. | M. Chen and R. Yu, “Analysis of photonic bandgaps in modified honeycomb structures,” IEEE Photon. Technol. Lett. |

14. | S. Selleri, L. Vincetti, F. Poli, A. Cucinotta, and M. Foroni, “Air-guiding photonic crystal fibers with modified honeycomb lattice,” in |

15. | L. Vincetti, F. Poli, and S. Selleri, “Confinement loss and nonlinearity analysis of air-guiding modified honeycomb photonic bandgap fibers,” IEEE Photon. Technol. Lett. |

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

**OCIS Codes**

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

(060.2400) Fiber optics and optical communications : Fiber properties

(060.2430) Fiber optics and optical communications : Fibers, single-mode

**ToC Category:**

Photonic Crystal Fibers

**History**

Original Manuscript: January 23, 2006

Revised Manuscript: March 2, 2006

Manuscript Accepted: March 9, 2006

Published: March 20, 2006

**Citation**

Tadashi Murao, Kunimasa Saitoh, and Masanori Koshiba, "Design of air-guiding modified honeycomb photonic band-gap fibers for effectively singlemode operation," Opt. Express **14**, 2404-2412 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-6-2404

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### References

- T. A. Birks, P. J. Roberts, P. S. J. Russell, D. M. Atkin, and T. J. Shepherd, "Full 2-D photonic bandgaps in silica/air structures," Electron. Lett. 31, 1941-1943 (1995). [CrossRef]
- R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999). [CrossRef] [PubMed]
- J. Broeng, S. E. Barkou, T. Sφndergaard, and A. Bjarklev, "Analysis of air-guiding photonic bandgap fibers," Opt. Lett. 25, 96-98 (2000). [CrossRef]
- C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003). [CrossRef] [PubMed]
- K. Saitoh and M. Koshiba, "Leakage loss and group velocity dispersion in air-core photonic bandgap fibers," Opt. Express 11,3100-3109 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-23-3100. [CrossRef] [PubMed]
- K. Saitoh, N. A. Mortensen, and M. Koshiba, "Air-core photonic band-gap fibers: the impact of surface modes," Opt. Express 12,394-400 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-394. [CrossRef] [PubMed]
- H. K. Kim, J. Shin, S. Fan, M. J. F. Digonnet, and G. S. Kino, "Designing air-core photonic bandgap fibers free of surface modes," IEEE J. Quantum Electron. 40, 551-556 (2004). [CrossRef]
- M. Yan and P. Shum, "Air guiding with honeycomb photonic bandgap fiber," IEEE Photon. Technol. Lett. 17, 64-66 (2005). [CrossRef]
- M. Yan, P. Shum, and J. Hu, "Design of air-guiding honeycomb photonic bandgap fiber," Opt. Lett. 30, 465-467 (2005). [CrossRef] [PubMed]
- J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. S. J. Russell, "Highly increased photonic band gaps in silica/air structures," Opt. Commun. 156, 240-244 (1998). [CrossRef]
- Y. Li, C. Wang, M. Hu, B. Liu, X. Sun, and L. Chai, "Honeycomb photonic bandgap fibers with and without interstitial air holes," Opt. Express 13,6856-6863 (2005). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-6856. [CrossRef] [PubMed]
- T. Haas, S. Belau, and T. Doll, "Realistic monomode air-core honeycomb photonic bandgap fiber with pockets," J. Lightwave Technol. 23, 2702-2706 (2005). [CrossRef]
- M. Chen and R. Yu, "Analysis of photonic bandgaps in modified honeycomb structures," IEEE Photon. Technol. Lett. 16, 819-821 (2004). [CrossRef]
- S. Selleri, L. Vincetti, F. Poli, A. Cucinotta, and M. Foroni, "Air-guiding photonic crystal fibers with modified honeycomb lattice," in Proceedings of 2005 IEEE/LEOS Workshop on Fibers and Optical Passive Components (WFOPC), 20-25 (2005).
- L. Vincetti, F. Poli, and S. Selleri, "Confinement loss and nonlinearity analysis of air-guiding modified honeycomb photonic bandgap fibers," IEEE Photon. Technol. Lett. 18, 508-510 (2006). [CrossRef]
- K. Saitoh and M. Koshiba, "Full-vectorial imaginary-distance beam propagation method based on finite element scheme: Application to photonic crystal fibers," IEEE J. Quantum Electron. 38, 927-933 (2002). [CrossRef]

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