## The role of artificial defects for engineering large effective mode area, flat chromatic dispersion, and low leakage losses in photonic crystal fibers: Towards high speed reconfigurable transmission platforms

Optics Express, Vol. 14, Issue 2, pp. 901-913 (2006)

http://dx.doi.org/10.1364/OPEX.14.000901

Acrobat PDF (650 KB)

### Abstract

The present paper describes a novel systematic solution to the challenging task of realizing photonic crystal fibers (PCFs) with flat chromatic dispersion, low leakage losses, and large mode area, mainly for applications as information carriers in wide-band high speed optical transmission systems. The proposed design strategy is based on the existence of an artificially-defected air-hole ring in the cladding and on the modulation of the refractive index of the core by assembling additional defected air-holes in the central core region of the fiber. The validation of the proposed design is carried out by adopting an efficient full-vectorial finite element method with perfectly matched layers for accurate characterization of PCFs. The remarkable flat chromatic dispersion as well as the large mode area and the low leakage losses are the main advantages of the proposed PCF structure, making it an ideal candidate for performing wavelength division multiplexing operation in reconfigurable optical transmission systems or as an information delivering platform in high speed optical communication systems. Typical characteristics of the newly proposed PCF are: flattened chromatic dispersion of 6.3±0.5 ps/km/nm in the S+C+L telecommunication band, and effective mode area as large as 100 μm^{2} in the same wavelength range. We additionally provide numerical data about the performance of the proposed PCF in splicing mode as well as during macrobending operation and we give qualitative information regarding the sensitivity of the proposed transmission platform to structural disorders of the design parameters.

© 2006 Optical Society of America

## 1. Introduction

02. J. C. Knight, “Photonic crystal fibers,” Nature **424**, 847–851 (2003). [CrossRef] [PubMed]

03. J. C. Knight, T. A. Birks, P. St. J. Russel, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. **21**, 484–485 (1996). [CrossRef]

04. M. D. Nielsen, C. Jacobsen, N. A. Mortensen, J. R. Folkenberg, and H. R. Simonsen, “Low-loss photonic crystal fibers for transmission system and their dispersion properties,” Opt. Express **12**, 1372–1376 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-24-1372. [CrossRef] [PubMed]

05. K. Saitoh, M. Koshiba, T. Hasegawa, and E. Sasaoka, “Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion,” Opt. Express **11**, 843–852 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-08-843. [CrossRef] [PubMed]

06. J. Zhou, K. Tajima, K. Nakajima, K. Kurokawa, C. Fukai, T. Matsui, and I. Sankawa, “Progress on low loss photonic crystal fibers,” Opt. Fiber Technol. **11**, 101–106 (2005). [CrossRef]

04. M. D. Nielsen, C. Jacobsen, N. A. Mortensen, J. R. Folkenberg, and H. R. Simonsen, “Low-loss photonic crystal fibers for transmission system and their dispersion properties,” Opt. Express **12**, 1372–1376 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-24-1372. [CrossRef] [PubMed]

07. K. Tajima, J. Zhou, K. Nakajima, and K. Sato, “Ultralow loss and long length photonic crystal fiber,” J. Lightwave Technol. **22**, 7–10 (2004). [CrossRef]

08. K. Nakajima, J. Zhou, K. Tajima, K. Kurokawa, C. Fukai, and I. Sankawa, “Ultrawide-band single-mode transmission performance in a low-loss photonic crystal fiber,” J. Lightwave Technol. **23**, 7–12 (2005). [CrossRef]

09. A. Ferrando, E. Silvestre, P. Andres, J. J. Miret, and M. V. Andres, “Designing the properties of dispersion-flattened photonic crystal fibers,” Opt. Express **9**, 687–697 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-687. [CrossRef] [PubMed]

13. A. Belahlou, S. Bickham, D. Chowdhury, P. D. A. Evans, J. M. Grochocinski, P. Han, A. Kobyakov, S. Kumar, G. Lutter, J. C. Mauro, Y. Mauro, M. Mlejnek, M. S. K. Muktoyuk, M. T. Murtagh, S. Raghavan, V. R. A. Sevian, N. Taylor, S. Tsuda, M. Vasilyev, and L. Wang, “Fiber design considerations for 40 Gb/s systems,” J. Lightwave Technol. **20**, 2290–2305 (2002). [CrossRef]

14. 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]

15. K. Mukasa, F. Poletti, K. Imamura, N. Kumano, T. Yagi, and D. J. Richardson, “A high performance GeO_{2}/SiO_{2} NZ-DSF and the prospects for future improvements using Holey Fiber technology,” in proceedings of European Conference on Optical Communications (ECOC2005), paper Tu1.4.6, Glasgow, Scotland, (2005).

## 2. Schematic cross section and design guidelines of the proposed PCF

*d*. The host material is pure silica. The central core area of the fiber has been perturbed to have nearly triangular shape, while it has also been modulated by embedding three extra air-holes with reduced in size diameters-

*d*

_{1}whose function is the controllability of the chromatic dispersion as it will be demonstrated later on. The core region therefore has an area as large as that of three unit cells, where the unit cell is defined the same way as in regular photonic crystal structures. The inclusion of an artificially-defected air-hole ring in the cladding of the fiber with reduced in size diameters-

*d*

_{2}has the function to enlarge the mode area without destroying the flattened chromatic dispersion. To accurately predict the propagation properties of this PCF structure we have adopted an efficient FEM modal solver [14

14. 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]

*d*

_{1}, while the incorporation of a defected air-hole ring at the cladding will enlarge the effective mode area with a result of improving the quality of the signal transmittivity through this PCF structure.

## 3. Numerical results and performance verification of the proposed PCF topology

*D*(λ) nearly opposite to that of the material dispersion

_{w}*D*(λ), namely

_{m}*D*(λ)≅-

_{w}*D*(λ) over a continuous spectral range [9

_{m}09. A. Ferrando, E. Silvestre, P. Andres, J. J. Miret, and M. V. Andres, “Designing the properties of dispersion-flattened photonic crystal fibers,” Opt. Express **9**, 687–697 (2001), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-687. [CrossRef] [PubMed]

*d*

_{1}to the chromatic dispersion curve, in Fig. 2 we plot the normalized waveguide dispersion (colored curves) of the proposed PCF as a function of the normalized wavelength λ/Λ, for various incremental values of the normalized design parameter

*d*

_{1}/Λ, for (a) uniformly fixed parameters

*d*/Λ=

*d*

_{2}/Λ=0.35, (b) uniformly fixed parameters

*d*/Λ=

*d*

_{2}/Λ=0.4, and (c) uniformly fixed parameters

*d*/Λ=

*d*

_{2}/Λ=0.45, while the silica index is assumed equal to 1.45 for calculating the waveguide dispersion. The black curve represents the material dispersion in all graphs, which has been calculated using the Sellmeier’s equation, assuming the lattice constant fixed to the value of Λ= 2.8 μm. From the results in Fig. 2 we can observe that by increasing the value of the design parameter-

*d*

_{1}the waveguide dispersion decreases. Eventually there will be a value of

*d*

_{1}such that the waveguide dispersion curve in all cases will become nearly anti-symmetric to that of the material dispersion, namely

*D*(λ)≅-

_{w}*D*(λ) and thus we can fulfill the requirement for flat dispersion. The approximate value in such a case is

_{m}*d*

_{1}/Λ=0.28 at fixed lattice constant of Λ= 2.8 μm and

*d*/Λ=0.35, while for

*d*/Λ=0.4 the approximate value has been determined to be

*d*

_{1}/Λ=0.29 and for

*d*/Λ=0.45 it has been determined to be

*d*

_{1}/Λ=0.30.

*d*

_{2}we can successfully enlarge the effective mode area to a desired value. In order to show the impact of the design parameter-

*d*

_{2}of the defected ring to the chromatic dispersion and to the effective mode area, in Fig. 3 we plot the total chromatic dispersion (i.e. including the material dispersion in the calculations) and its corresponding effective mode areas. Particularly Fig. 3(a) shows the tendency of the chromatic dispersion curves as a function of the wavelength λ for different values of the design parameter

*d*

_{2}/Λ, with the other design parameters fixed at values of

*d*/Λ=0.35,

*d*

_{1}/Λ=0.28, Λ=2.8 μm, considering in total 11 air-hole rings in the PCF, while in Fig. 3(b) we plot the corresponding effective mode areas. The same is repeated in Fig. 3(c) for the chromatic dispersion but for different fixed set of design parameters, that is

*d*/Λ=0.4,

*d*

_{1}/Λ=0.29, and Λ=2.8 μm, while Fig. 3(d) shows the corresponding effective mode areas for the same set of design parameters as in Fig. 3(c). In Fig. 3(e) we show the calculated dispersion curves for a different set of design parameters, that is for

*d*/Λ=0.45,

*d*

_{1}/Λ=0.3, and Λ=2.8 μm, and for different values of the design parameter

*d*

_{2}/Λ, while in Fig. 3(f) we plot the corresponding effective mode areas for this set of design parameters. Notice that the results concerning the chromatic dispersion in all cases have been obtained using the knowledge of the effective index of the fundamental mode including the wavelength-dependence of pure silica in the FEM modal solver. From the results in Figs. 3(a), 3(c) and 3(e) we may observe that by decreasing the size of the air-holes in the artificially-defected air-hole ring, the chromatic dispersion decreases, but without destroying the flatness. The thick orange curves in Figs. 3(c) and 3(d) correspond to the optimum selection of the design parameters as it will be explained later on. In Figs. 3(b), 3(d), and 3(f) we can examine what happens to the effective mode area. From these results we can clearly see that the continuous decrement of the design parameter-

*d*

_{2}results in the continuous increment of the effective mode area in all cases. Thus by an additional micro-adjustment of this design parameter-

*d*

_{2}we can obtain remarkable flat dispersion with low value, while at the same time we can engineer the effective mode area to have a large value. It is worth to notice that for all these groups of design parameters the effect to the modal area is almost the same. Further increment of the effective mode area will result in the multi-mode operation of the proposed fiber. A direct way to increase further the effective mode area, while keeping the single mode operation, is by decreasing the air-hole diameters in the cladding-d, on the expense of increasing the required number of air-hole rings, for compensating the higher leakage losses. Keeping this limitation in mind, the finalized optimum values of the proposed PCF have been derived as follows: Λ=2.8 μm,

*d*/Λ=0.4,

*d*

_{1}/Λ=0.29, and

*d*

_{2}/Λ=0.3l. With this set of design parameters the newly proposed HF structure has the following performance; flattened chromatic dispersion of 6.3±0.5 ps/km/nm between 1.45 μm to 1.65 μm, and effective mode area as large as 100 μm

^{2}in the same wavelength. The choice of this set of design parameters is not random, since it will additionally have an optimum influence to the leakage loss property of the proposed PCF structure in conjunction to all the other sets of design parameters, as will be demonstrated in the next section. In addition we would like to comment on the obtained chromatic dispersion of about 6.3 ps/km/nm, which may seem somewhat large. A direct way to reduce the value of the group velocity dispersion is by decreasing a little bit the pitch constant Λ, on the expense of decreasing a little bit the obtained effective mode area. Even in such case however, the flatness of the chromatic dispersion remains remarkably flat and in addition the effective mode area has higher value than usual optical fibers.

## 5. Feasibility and compatibility of the proposed PCF with conventional fibers

17. 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), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4770. [CrossRef] [PubMed]

18. M. Koshiba, H. Saitoh, M. Eguchi, and K. Hirayama, “A simple scalar finite element approach to optical rib waveguide,” IEE Proc. Part J: Optoelectron. **139**, 166–171 (1992). [CrossRef]

## 6. Sensitivity analysis of structural disorders to the PCF performance

*d*

_{1}/Λ and

*d*

_{2}/Λ in Fig. 8(a), we plot the effective mode area fluctuation at a wavelength of 1.55 μm as a function of the design parameters,

*d*

_{1}/Λ and

*d*

_{2}/Λ, while Fig. 8(b) shows the map of constant effective mode area curves. From the resulting behavior we can clearly see that the effective mode area changes almost linearly as a function of the design parameters. In this case however we observe that as soon as the structural variations of the design parameter-

*d*

_{2}significantly increase from its nominal value, the dynamic behavior of the effective mode area will deviate from its linear behavior in a quadratic fashion. The quadratic behavior of the effective mode area for larger values of the tolerance was confirmed by fitting quadratic functions to the calculated by the FEM solver effective mode curves. On the other hand the effect of the structural disorders of the design parameter-

*d*

_{1}can be considered negligible. As a conclusion we can say that regarding the dynamic rate of change of the effective mode area the design parameter-

*d*

_{2}has to be kept at low tolerances if we want our design to be robust in terms of information transmission. This result is actually something that we expected to observe, since the results in Figs. 5(a)–5(c) suggest that the optical field enhancement into the cladding of the proposed PCF associated with the possibility of the effective mode area enlargement is indeed sensitive to the size of the air-holes in the defected ring.

*d*

_{1}/Λ and

*d*

_{2}/Λ, while on the other hand the effective mode area of the proposed PCF seems to be sensitive only to the structural tolerances of the air-hole diameters in defected ring in the cladding.

## 7. Conclusions

## References and links

01. | J. A. Buck, |

02. | J. C. Knight, “Photonic crystal fibers,” Nature |

03. | J. C. Knight, T. A. Birks, P. St. J. Russel, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. |

04. | M. D. Nielsen, C. Jacobsen, N. A. Mortensen, J. R. Folkenberg, and H. R. Simonsen, “Low-loss photonic crystal fibers for transmission system and their dispersion properties,” Opt. Express |

05. | K. Saitoh, M. Koshiba, T. Hasegawa, and E. Sasaoka, “Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion,” Opt. Express |

06. | J. Zhou, K. Tajima, K. Nakajima, K. Kurokawa, C. Fukai, T. Matsui, and I. Sankawa, “Progress on low loss photonic crystal fibers,” Opt. Fiber Technol. |

07. | K. Tajima, J. Zhou, K. Nakajima, and K. Sato, “Ultralow loss and long length photonic crystal fiber,” J. Lightwave Technol. |

08. | K. Nakajima, J. Zhou, K. Tajima, K. Kurokawa, C. Fukai, and I. Sankawa, “Ultrawide-band single-mode transmission performance in a low-loss photonic crystal fiber,” J. Lightwave Technol. |

09. | A. Ferrando, E. Silvestre, P. Andres, J. J. Miret, and M. V. Andres, “Designing the properties of dispersion-flattened photonic crystal fibers,” Opt. Express |

10. | T. Yamamoto, H. Kubota, S. Kawanishi, M. Tanaka, and S. Yamaguchi, “Supercontinuum generation at 1.55 μm in a dispersion-flattened polarization-maintaining photonic crystal fiber,” Opt. Express |

11. | K. Saitoh and M. Koshiba, “Highly nonlinear dispersion-flattened photonic crystal fibers for supercontinuum generation in a telecommunication window,” Opt. Express |

12. | K. Saitoh, N. Florous, and M. Koshiba, “Ultra-flattened chromatic dispersion controllability using a defected-core photonic crystal fiber with low confinement losses,” Opt. Express |

13. | A. Belahlou, S. Bickham, D. Chowdhury, P. D. A. Evans, J. M. Grochocinski, P. Han, A. Kobyakov, S. Kumar, G. Lutter, J. C. Mauro, Y. Mauro, M. Mlejnek, M. S. K. Muktoyuk, M. T. Murtagh, S. Raghavan, V. R. A. Sevian, N. Taylor, S. Tsuda, M. Vasilyev, and L. Wang, “Fiber design considerations for 40 Gb/s systems,” J. Lightwave Technol. |

14. | 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. |

15. | K. Mukasa, F. Poletti, K. Imamura, N. Kumano, T. Yagi, and D. J. Richardson, “A high performance GeO |

16. | D. Davidson, |

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

18. | M. Koshiba, H. Saitoh, M. Eguchi, and K. Hirayama, “A simple scalar finite element approach to optical rib waveguide,” IEE Proc. Part J: Optoelectron. |

19. | J. C. Knight, T. A. Birks, P. St J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” Opt. Lett. |

20. | F. Poletti, V. Finazzi, T. M. Monro, N. G. R. Broderick, V. Tse, and D. J. Richardson, “Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers,” Opt. Express |

**OCIS Codes**

(060.2270) Fiber optics and optical communications : Fiber characterization

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

**ToC Category:**

Photonic Crystal Fibers

**Citation**

Nikolaos Florous, Kunimasa Saitoh, and Masanori Koshiba, "The role of artificial defects for engineering large effective mode area, flat chromatic dispersion, and low leakage losses in photonic crystal fibers: Towards high speed reconfigurable transmission platforms," Opt. Express **14**, 901-913 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-2-901

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### References

- J. A. Buck, Fundamentals of Optical Fibers, (Wiley-Interscience, New York, 2004).
- J. C. Knight, "Photonic crystal fibers," Nature 424, 847-851 (2003). [CrossRef] [PubMed]
- J. C. Knight, T. A. Birks, P. St. J. Russel, and D. M. Atkin, "All-silica single-mode optical fiber with photonic crystal cladding," Opt. Lett. 21, 484-485 (1996). [CrossRef]
- M. D. Nielsen, C. Jacobsen, N. A. Mortensen, J. R. Folkenberg, and H. R. Simonsen, "Low-loss photonic crystal fibers for transmission system and their dispersion properties," Opt. Express 12, 1372-1376 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-24-1372">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-24-1372</a>. [CrossRef] [PubMed]
- K. Saitoh, M. Koshiba, T. Hasegawa, and E. Sasaoka, "Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion," Opt. Express 11, 843-852 (2003), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-08-843">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-08-843. [CrossRef] [PubMed]
- J. Zhou, K. Tajima, K. Nakajima, K. Kurokawa, C. Fukai, T. Matsui, and I. Sankawa, "Progress on low loss photonic crystal fibers," Opt. Fiber Technol. 11, 101-106 (2005). [CrossRef]
- K. Tajima, J. Zhou, K. Nakajima, and K. Sato, "Ultralow loss and long length photonic crystal fiber," J. Lightwave Technol. 22, 7-10 (2004). [CrossRef]
- K. Nakajima, J. Zhou, K. Tajima, K. Kurokawa, C. Fukai, and I. Sankawa, "Ultrawide-band single-mode transmission performance in a low-loss photonic crystal fiber," J. Lightwave Technol. 23, 7-12 (2005). [CrossRef]
- A. Ferrando, E. Silvestre, P. Andres, J. J. Miret, and M. V. Andres, "Designing the properties of dispersion-flattened photonic crystal fibers," Opt. Express 9, 687-697 (2001) , <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-687">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-13-687</a>. [CrossRef] [PubMed]
- T. Yamamoto, H. Kubota, S. Kawanishi, M. Tanaka, and S. Yamaguchi, "Supercontinuum generation at 1.55 µm in a dispersion-flattened polarization-maintaining photonic crystal fiber," Opt. Express 11, 1537-1540 (2003), <a href= "http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-13-1537">http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-13-1537</a>. [CrossRef] [PubMed]
- K. Saitoh and M. Koshiba, "Highly nonlinear dispersion-flattened photonic crystal fibers for supercontinuum generation in a telecommunication window," Opt. Express 12, 2027-2032 (2004), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-10-2027">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-10-2027</a>. [CrossRef] [PubMed]
- K. Saitoh, N. Florous, and M. Koshiba, "Ultra-flattened chromatic dispersion controllability using a defected-core photonic crystal fiber with low confinement losses," Opt. Express 13, 8365-8371 (2005)<a href= "http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-21-8365">http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-21-8365</a>. [CrossRef] [PubMed]
- A. Belahlou, S. Bickham, D. Chowdhury, P. D. A. Evans, J. M. Grochocinski, P. Han, A. Kobyakov, S. Kumar, G. Lutter, J. C. Mauro, Y. Mauro, M. Mlejnek, M. S. K. Muktoyuk, M. T. Murtagh, S. Raghavan, V. R. A. Sevian, N. Taylor, S. Tsuda, M. Vasilyev, and L. Wang, "Fiber design considerations for 40 Gb/s systems," J. Lightwave Technol. 20, 2290-2305 (2002). [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]
- K. Mukasa, F. Poletti, K. Imamura, N. Kumano, T. Yagi, and D. J. Richardson, "A high performance GeO2/SiO2 NZ-DSF and the prospects for future improvements using Holey Fiber technology," in proceedings of European Conference on Optical Communications (ECOC2005), paper Tu1.4.6, Glasgow, Scotland, (2005).
- D. Davidson, Optical-Fiber Transmission E. E. Bert Basch, ed., (H. W. Sams & Co, Indianapolis, Ind. 1987).
- 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), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4770">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4770</a>. [CrossRef] [PubMed]
- M. Koshiba, H. Saitoh, M. Eguchi, and K. Hirayama, "A simple scalar finite element approach to optical rib waveguide," IEE Proc. Part J: Optoelectron. 139, 166-171 (1992). [CrossRef]
- J. C. Knight, T. A. Birks, P. St J. Russell, and J. P. de Sandro, "Properties of photonic crystal fiber and the effective index model," Opt. Lett. 15, 748-752 (1998).
- F. Poletti, V. Finazzi, T. M. Monro, N. G. R. Broderick, V. Tse, and D. J. Richardson, "Inverse design and fabrication tolerances of ultra-flattened dispersion holey fibers," Opt. Express 13, 3728-3736 (2005), <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-10-3728">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-10-3728</a>. [CrossRef] [PubMed]

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