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Photonic crystal fiber design by means of a genetic algorithm

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Abstract

A Genetic Algorithm (GA) is used to design photonic crystal fiber structures with user-defined chromatic dispersion properties. This GA is combined with a full vectorial finite element method in order to determine the effective index of propagation of the modes and then, the chromatic dispersion of structures generated by GA. This method proves to be a powerful tool for solving this inverse problem.

©2004 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2004 (1)

2003 (1)

F. Zeng, J. Yao, and S.J. Mihailov, “Fiber Bragg-grating-based all optical microwave filter synthesis using genetic algorithm,” Opt. Eng. 42, 2250 (2003)
[Crossref]

2002 (2)

2001 (2)

A. Ferrando, E. Silvestre, P. Andrés, J.J. Miret, and M.V. Andrés, “Designing the properties of dispersion-flattened photonic crystal fibers,” Opt. Express 9, 687 (2001), ttp://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-14-609
[Crossref] [PubMed]

D. Correia, V. F. Rodriguez-Esquerre, and H. E. Hernandez-Figueroa, “Genetic-algorithm and finite-element approach to the synthesis of dispersion-flattened fiber,” Microw. Opt. Techn. Lett.,  31, 245 (2001)
[Crossref]

2000 (4)

1998 (2)

D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, “Group-velocity dispersion in photonic crystal fibers,” Opt. Lett 23 (21), 1662 (1998)
[Crossref]

J. Skaar and K. M. Risvik, “A genetic algorithm for the inverse problem in synthesis of fiber gratings,” J. Lightwave. Technol. 16, 1928 (1998)
[Crossref]

Andrés, M.V.

Andrés, P.

Arriaga, J.

Birks, T. A.

A. O. Blanch, J. C. Knight, W. J. Wadsworth, J. Arriaga, B. J. Mangan, T. A. Birks, and P. St. J. Russell, “Highly birefringent photonic crystal fibers,” Opt. Lett. 25, 1325 (2000)
[Crossref]

D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, “Group-velocity dispersion in photonic crystal fibers,” Opt. Lett 23 (21), 1662 (1998)
[Crossref]

Blanch, A. O.

Correia, D.

D. Correia, V. F. Rodriguez-Esquerre, and H. E. Hernandez-Figueroa, “Genetic-algorithm and finite-element approach to the synthesis of dispersion-flattened fiber,” Microw. Opt. Techn. Lett.,  31, 245 (2001)
[Crossref]

Ferrando, A.

He, S.

Hernandez-Figueroa, H. E.

D. Correia, V. F. Rodriguez-Esquerre, and H. E. Hernandez-Figueroa, “Genetic-algorithm and finite-element approach to the synthesis of dispersion-flattened fiber,” Microw. Opt. Techn. Lett.,  31, 245 (2001)
[Crossref]

Holland, J. H.

J. H. Holland, “Adaptation in Natural and Artificial Systems”, Cambridge, MA : The M.I.T. Press, (1975)

Jian, S.

Jiang, J.

Knight, J. C.

Knight, J.C.

Lu, J.

Mangan, B. J.

Mihailov, S.J.

F. Zeng, J. Yao, and S.J. Mihailov, “Fiber Bragg-grating-based all optical microwave filter synthesis using genetic algorithm,” Opt. Eng. 42, 2250 (2003)
[Crossref]

Miret, J.J.

Mogilevtsev, D.

D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, “Group-velocity dispersion in photonic crystal fibers,” Opt. Lett 23 (21), 1662 (1998)
[Crossref]

Nordin, G.P.

Ranka, J. K.

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett 25, 25 (2000)
[Crossref]

Reeves, W.H.

Risvik, K. M.

J. Skaar and K. M. Risvik, “A genetic algorithm for the inverse problem in synthesis of fiber gratings,” J. Lightwave. Technol. 16, 1928 (1998)
[Crossref]

Rodriguez-Esquerre, V. F.

D. Correia, V. F. Rodriguez-Esquerre, and H. E. Hernandez-Figueroa, “Genetic-algorithm and finite-element approach to the synthesis of dispersion-flattened fiber,” Microw. Opt. Techn. Lett.,  31, 245 (2001)
[Crossref]

Russell, P. St. J.

A. O. Blanch, J. C. Knight, W. J. Wadsworth, J. Arriaga, B. J. Mangan, T. A. Birks, and P. St. J. Russell, “Highly birefringent photonic crystal fibers,” Opt. Lett. 25, 1325 (2000)
[Crossref]

D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, “Group-velocity dispersion in photonic crystal fibers,” Opt. Lett 23 (21), 1662 (1998)
[Crossref]

Russell, P.St.J.

Silvestre, E.

Skaar, J.

J. Skaar and K. M. Risvik, “A genetic algorithm for the inverse problem in synthesis of fiber gratings,” J. Lightwave. Technol. 16, 1928 (1998)
[Crossref]

Stentz, A. J.

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett 25, 25 (2000)
[Crossref]

Tong, Z.

Wadsworth, W. J.

Wang, Q.

Wei, H.

Windeler, R. S.

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett 25, 25 (2000)
[Crossref]

Yao, J.

F. Zeng, J. Yao, and S.J. Mihailov, “Fiber Bragg-grating-based all optical microwave filter synthesis using genetic algorithm,” Opt. Eng. 42, 2250 (2003)
[Crossref]

Zeng, F.

F. Zeng, J. Yao, and S.J. Mihailov, “Fiber Bragg-grating-based all optical microwave filter synthesis using genetic algorithm,” Opt. Eng. 42, 2250 (2003)
[Crossref]

Appl. Opt. (1)

J. Lightwave. Technol. (1)

J. Skaar and K. M. Risvik, “A genetic algorithm for the inverse problem in synthesis of fiber gratings,” J. Lightwave. Technol. 16, 1928 (1998)
[Crossref]

Microw. Opt. Techn. Lett. (1)

D. Correia, V. F. Rodriguez-Esquerre, and H. E. Hernandez-Figueroa, “Genetic-algorithm and finite-element approach to the synthesis of dispersion-flattened fiber,” Microw. Opt. Techn. Lett.,  31, 245 (2001)
[Crossref]

Opt. Eng. (1)

F. Zeng, J. Yao, and S.J. Mihailov, “Fiber Bragg-grating-based all optical microwave filter synthesis using genetic algorithm,” Opt. Eng. 42, 2250 (2003)
[Crossref]

Opt. Express (4)

Opt. Lett (2)

D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, “Group-velocity dispersion in photonic crystal fibers,” Opt. Lett 23 (21), 1662 (1998)
[Crossref]

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett 25, 25 (2000)
[Crossref]

Opt. Lett. (2)

Other (1)

J. H. Holland, “Adaptation in Natural and Artificial Systems”, Cambridge, MA : The M.I.T. Press, (1975)

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Figures (3)

Fig. 1.
Fig. 1. Schematic description of the different calculation steps of the genetic algorithm used in this work.
Fig. 2.
Fig. 2. (a) Chromatic dispersion curves calculated by GA routine for a three rings PCF. Red curves correspond to the chromatic dispersion for the best offspring at the first generation (empty circles) and at the thirteenth generation (empty squares) in the case of population B. Blue curves correspond to population A (filled circles for the first generation, and filled squares for the thirteenth). (b) Example of the three rings PCF used in the GA method (black is air and grey is silica).
Fig. 3.
Fig. 3. Blue curve: Chromatic dispersion as a function of wavelength calculated by GA routine for the 9 rings structure. The pitch Λ and the radius r are respectively equal to 2.35 μm and 0.33 μm. Black curve: chromatic dispersion obtained for a 9 ring structure with the following parameters: Λ = 2.59 μm and r = 0.29 μm, corresponding to ref. [4]. Inset: dashed green lines represent the dispersion curves for the minimum pitch and the maximum radius (upper curve) and for the minimum pitch and minimum radius (lower curve) authorized in the GA.

Equations (4)

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

J = ( D target ( λ ) D ( λ ) ) 2
× ( ε r 1 × H ) = k 0 2 n eff 2 H
k 0 = 2 π λ 0
D ( λ ) = λ c d n eff 2 d λ 2

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