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 μm2 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

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ECOC2005 (1)

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).

IEE Proc. Part J: Optoelectron. (1)

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]

IEEE J. Quantum Electron. (1)

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]

J. Lightwave Technol. (3)

Nature (1)

J. C. Knight, "Photonic crystal fibers," Nature 424, 847-851 (2003).
[CrossRef] [PubMed]

Opt. Express (8)

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]

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]

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]

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]

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]

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]

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 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]

Opt. Fiber Technol. (1)

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]

Opt. Lett. (2)

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]

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).

Other (2)

D. Davidson, Optical-Fiber Transmission E. E. Bert Basch, ed., (H. W. Sams & Co, Indianapolis, Ind. 1987).

J. A. Buck, Fundamentals of Optical Fibers, (Wiley-Interscience, New York, 2004).

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Figures (8)

Fig. 1.
Fig. 1.

Schematic representation of the proposed PCF structure. The air-holes in the cladding are arranged in a triangular configuration with lattice constant Λ and air-hole diameters-d. The central core is perturbed with three extra air-holes (red colored circles) with reduced in size diameters-d 1 positioned in the core-region. An artificially defected air-hole ring with reduced air-hole diameters-d 2 (blue colored circles) is assembled in the cladding. By a judicious choice of the geometrical parameters, this PCF structure can exhibit flat chromatic dispersion with large mode area and low confinement losses.

Fig. 2.
Fig. 2.

Normalized waveguide dispersion curves Dw Λ as a function of the normalized wavelength λ/Λ, for various incremental values of the design parameter d 1/Λ, specifically d 1/Λ=0 (red curve), d 1/Λ = 0.1 (green curve), d 1/Λ = 0.2 (blue curve), d 1/Λ = 0.25 (purple curve), and dc /Λ = 0.3 (orange curve), for (a) fixed air-hole diameters in the cladding d/Λ = d 2/Λ= 0.35, (b) fixed air-hole diameters in the cladding d/Λ = d 2/Λ= 0.4, and (c) fixed air-hole diameters in the cladding d/Λ = d 2/Λ= 0.45. The black curve in all cases represents the normalized material dispersion of silica Dm Λ at a fixed lattice constant of Λ = 2.8 μm.

Fig. 3.
Fig. 3.

(a). Total chromatic dispersion curves as a function of the wavelength-λ, for different values of the design parameter-d 2/Λ, for fixed air-hole diameters in the cladding d/Λ=0.35 and fixed defected air-holes in the core d 1/Λ=0.28, (b) the corresponding effective mode areas, (c) total chromatic dispersion curves as a function of the wavelength-λ, for different values of the design parameter-d 2/Λ, for fixed air-hole diameters in the cladding d/Λ=0.4 and fixed defected air-holes in the core d 1/Λ=0.29, (d) the corresponding effective mode areas, (e) total chromatic dispersion curves as a function of the wavelength-λ, for different values of the design parameter-d 2/Λ, for fixed air-hole diameters in the cladding d/Λ=0.45 and fixed defected airholes in the core d 1/Λ=0.3, (f) the corresponding effective mode areas. It is evident that for the three different groups of design parameters the continuous decrement of the design parameter-d 2 will result in the continuous increment of the effective mode area while the chromatic dispersion will continuously decrease, while keeping its flatness.

Fig. 4.
Fig. 4.

Calculated leakage loss of the fundamental (circles) as well as of the higher order mode (triangles) in the proposed PCF, at wavelengths of λ = 1.45 μm (red color), λ = 1.55 μm (blue color), and λ = 1.65 μm (green color), as a function of the total number of air-hole rings for (a) the following set of design parameters, Λ = 2.8 μm, d/Λ = 0.35, d 1/Λ = 0.28, and d 2/Λ = 0.32, (b) the optimized set of design parameters Λ = 2.8 μm, d/Λ = 0.4, d 1/Λ = 0.29, and d 2/Λ = 0.31, and (c) Λ = 2.8 μm, d/Λ = 0.45, d 1/Λ = 0.3, and d 2/Λ = 0.305. It is clear that the choice of the set of design parameters in (b) results in a leakage loss of the fundamental mode of three orders of magnitude lower than that of the higher order mode for a total number of eleven air-hole rings.

Fig. 5.
Fig. 5.

Normalized electric field distribution of the x-polarized mode in (dB) at a wavelength of λ = 1.55 μm, for (a) d 2/Λ = 0.4 (effective mode area of 35 μm2), (b) d 2/Λ = 0.34 (effective mode area of 55 μm2), (c) d 2/Λ = 0.31 (effective mode area of 100 μm2), while the other parameters were fixed at values of d/Λ = 0.4, and d 1/Λ = 0.29. Notice that once the effective mode area increases the light confinement is strongly enhanced into the cladding.

Fig. 6.
Fig. 6.

(a). Calculated bending loss of the proposed PCF with eleven air-hole rings, as a function of the bending radius at fixed operational wavelength of λ = 1.55 μm for the optimized design parameters, Λ = 2.8 μm, d/Λ = 0.4, d 1/Λ = 0.29, d 2/Λ = 0.31, (b) splice losses between the proposed PCF and a standard single mode fiber (SMF) with core radius 4.8 μm and index difference 0.3%. It is evident from these results that the bending losses remain in a lower level compared to standard SMFs, while the splice losses also remain in a relatively low level of about 0.6 dB.

Fig. 7.
Fig. 7.

Sensitivity performance of the chromatic dispersion at a wavelength of 1.55 μm as a function of the design parameter space formed by the variables d 1/Λ and d 2/Λ, (a) a three-dimensional plot and (b) a contour map of constant dispersion curves. It is evident from these graphs that the variation to both structural imperfections is linear. In addition we can see that the dynamic rate of change of the chromatic dispersion remains within a ±0.5 ps/km/nm of its nominal optimized value and therefore we can fairly say that the chromatic dispersion is insensitive to both structural fluctuations.

Fig. 8.
Fig. 8.

Sensitivity performance of the effective mode area at a wavelength of 1.55 μm as a function of the design parameter space formed by the variables d 1/Λ and d 2/Λ, for (a) a three-dimensional plot and (b) a contour map of constant effective mode area curves. It is evident from these graphs that the variation to both structural imperfections is linear. In addition we can see that the dynamic rate of change of the effective mode area is more sensitive to the variations of the structural parameter d 2/Λ and less sensitive to the fluctuations of the parameter d 1/Λ.

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