Abstract

The present paper describes a novel systematic solution to the problem of controlling the chromatic dispersion and dispersion slope in photonic crystal fibers (PCFs), using a structurally-simple PCF with a defected-core. By adjusting the size of the central air-hole defect we can successfully design an ultra-flattened PCF with low confinement losses, as well as small effective mode area. The design strategy is based on the mutual cancellation between the waveguide and the material dispersions of the PCF, by varying the size of the central defected region in the core. The verification of the ultra-flattened chromatic dispersion property of the proposed PCF is ensured with an accurate full-vector finite element method with anisotropic perfectly matched layers. The ultra-flattened dispersion feature, as well as the low confinement losses and the small effective mode area are the main advantages of the proposed PCF structure, making it suitable as a chromatic dispersion controller, dispersion compensator, or as candidate for nonlinear optical applications.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. J. A. Buck, Fundamentals of Optical Fibers, Wiley-Interscience (2004).
  2. J. C. Knight, �??Photonic crystal fibers,�?? Photonic crystal fibers Nature 424, 847-851 (2003).
    [CrossRef] [PubMed]
  3. 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]
  4. 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 <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]
  5. 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</a>
    [CrossRef] [PubMed]
  6. V. Finazzi, T. M. Monro, and D. J. Richardson, �??Small core silica holey fibers: Nonlinearity and confinement loss trade-offs,�?? J. Opt. Soc. Am. B 20, 1427-1436 (2003).
    [CrossRef]
  7. A. Ferrando, E. Silvestre, J. J. Miret, and P. Andres, �??Nearly zero ultraflattened dispersion in photonic crystal fibers,�?? Opt. Lett. 25, 790-792 (2000).
    [CrossRef]
  8. 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]
  9. W. H. Reeves, J. C. Knight, P. St. J. Russell, and P. J. Roberts, �??Demonstration of ultra-flattened dispersion in photonic crystal fibers,�?? Opt. Express 10, 609-613 (2002), <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>
    [PubMed]
  10. T. L. Wu and C. H. Chao, �??A novel ultraflattened dispersion photonic crystal fiber,�?? IEEE. Photon. Technol. Lett. 17, 67-69 (2005).
    [CrossRef]
  11. 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]
  12. 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 Elencron. 38, 927-933 (2002).
    [CrossRef]
  13. D. Davidson, Optical-Fiber Transmission (E. E. Bert Basch , ed., Howard W. Sams & Co, 1987).
  14. H. C. Nguyen, B. Kuhlmey, M. J. Steel, C. Smith, E. Magi, R. C. McPhedran, and B. Eggleton, �??Leakage of the fundamental mode in photonic crystal fiber tapers,�?? Opt. Lett. 30, 1123-1125 (2005).
    [CrossRef] [PubMed]

IEEE J. Quantum Elencron (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 Elencron. 38, 927-933 (2002).
[CrossRef]

IEEE. Photon. Technol. Lett. (1)

T. L. Wu and C. H. Chao, �??A novel ultraflattened dispersion photonic crystal fiber,�?? IEEE. Photon. Technol. Lett. 17, 67-69 (2005).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nature (1)

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

Opt. Express (5)

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 <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</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]

W. H. Reeves, J. C. Knight, P. St. J. Russell, and P. J. Roberts, �??Demonstration of ultra-flattened dispersion in photonic crystal fibers,�?? Opt. Express 10, 609-613 (2002), <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>
[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. Lett. (3)

Other (2)

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

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Schematic cross section 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 an extra air-hole with diameter dc . By a judicious choice of the geometrical parameters, this PCF structure can exhibit ultra-flattened dispersion characteristics with low confinement losses and small effective area.

Fig. 2.
Fig. 2.

Waveguide dispersion curves as a function of the normalized wavelength λ/Λ, for various incremental values of the design parameter dc /Λ, specifically dc /Λ=0 (red line), dc /Λ = 0.1 (green line), dc /Λ = 0.2 (blue line), dc /Λ = 0.3 (cyan line), dc /Λ = 0.35 (purple line), dc /Λ = 0.4 (brown line), at (a) d/Λ = 0.65, (b) d/Λ = 0.7, (c) d/Λ = 0.75 and (d) d/Λ = 0.8. Dashed curves in (c) represent the material dispersion while the inset picture shows the anti-symmetric curves of waveguide and material dispersions, which lead to nearly-zero total dispersion.

Fig. 3.
Fig. 3.

Impact of the micro-adjustment of the design parameters in the total dispersion curve of the PCF for (a) lattice constant, Λ=2.0 μm (blue line), Λ=2.05 μm (red line), Λ=2.1 μm (green line), (b) diameter of cladding air-holes, d/Λ=0.72 (blue line), d/Λ=0.73 (red line), d/Λ=0.74 (green line), and (c) diameter of the defected air-holes, dc /Λ=0.276 (blue line), dc /Λ=0.279 (red line), dc /Λ=0.282 (green line). The optimized design parameters corresponding to the total dispersion indicated with red lines, are Λ=2.05 μm, d/Λ=0.73, and dc /Λ=0.279.

Fig. 4.
Fig. 4.

Effective mode area (blue line) and leakage loss (red line) as a function of the wavelength λ, for the optimized design parameters, Λ = 2.05 μm, d/Λ = 0.73, and dc /Λ = 0.279. Observe the remarkable low leakage loss (0.013 dB/km at λ = 1.55 μm) we could obtain, by using only four air-hole rings in the cladding of the PCF.

Fig. 5.
Fig. 5.

Normalized electric field distribution of the x-polarized mode in (dB) at a wavelength of λ = 1.55 μm.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

D ( λ ) D w ( λ ) + D m ( λ ) ,
D ( λ ) = λ c d 2 n eff d λ 2

Metrics