Abstract

Particle swarm optimization (PSO) is an evolutionary, easy-to-implement technique to design optical diffraction gratings. Design of reflection and transmission guided-mode resonance (GMR) grating filters using PSO is reported. The spectra of the designed filters are in good agreement with the design targets in a reasonable computation time. Also, filters are designed with a genetic algorithm (GA) and the results obtained by the GA and PSO are compared.

© 2007 Optical Society of America

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  1. E. Johnson and M. A. G. Abushagur, J. Opt. Soc. Am. A 12, 1152 (1995).
    [CrossRef]
  2. S. Tibuleac and R. Magnusson, Opt. Lett. 26, 584 (2001).
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  3. B. Wang, J. Jiang, and G. P. Nordin, Opt. Express 12, 3313 (2004).
    [CrossRef] [PubMed]
  4. S. Manos and L. Poladian, Opt. Express 13, 7350 (2005).
    [CrossRef] [PubMed]
  5. R. L. Haupt and S. E. Haupt, Practical Genetic Algorithms (Wiley, 1998).
  6. J. Robinson and Y. Rahmat-Samii, IEEE Trans. Antennas Propag. 52, 397 (2004).
    [CrossRef]
  7. S. Genovesi, R. Mitra, A. Monorchio, and G. Manara, IEEE Antennas Wireless Propag. Lett. 5, 277 (2006).
    [CrossRef]
  8. R. Eberhart and J. Kennedy, in Proceedings of the Conference for Neural Networks (IEEE, 1995), p. 1942.
  9. M.-P. Song and G.-C. Gu, in Proceedings of the 3rd International Conference on Machine Learning and Cybernetics (IEEE, 2004), p. 2236.
  10. J. Kennedy and R. Eberhart, in Proceedings of the International Conference on System, Man and Cybernetics (IEEE, 1997), p. 4104.
  11. S. S. Wang and R. Magnusson, Appl. Opt. 32, 2606 (1993).
    [CrossRef] [PubMed]
  12. T. K. Gaylord and M. G. Moharam, Proc. IEEE 73, 894 (1985).
    [CrossRef]
  13. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, J. Opt. Soc. Am. A 12, 345 (1995).
  14. A personal computer with a 2.4GHz processor and 256Mbytes of RAM has been used for computations in this Letter.

2006 (1)

S. Genovesi, R. Mitra, A. Monorchio, and G. Manara, IEEE Antennas Wireless Propag. Lett. 5, 277 (2006).
[CrossRef]

2005 (1)

2004 (2)

B. Wang, J. Jiang, and G. P. Nordin, Opt. Express 12, 3313 (2004).
[CrossRef] [PubMed]

J. Robinson and Y. Rahmat-Samii, IEEE Trans. Antennas Propag. 52, 397 (2004).
[CrossRef]

2001 (1)

1995 (2)

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, J. Opt. Soc. Am. A 12, 345 (1995).

E. Johnson and M. A. G. Abushagur, J. Opt. Soc. Am. A 12, 1152 (1995).
[CrossRef]

1993 (1)

1985 (1)

T. K. Gaylord and M. G. Moharam, Proc. IEEE 73, 894 (1985).
[CrossRef]

Abushagur, M. A. G.

Eberhart, R.

R. Eberhart and J. Kennedy, in Proceedings of the Conference for Neural Networks (IEEE, 1995), p. 1942.

J. Kennedy and R. Eberhart, in Proceedings of the International Conference on System, Man and Cybernetics (IEEE, 1997), p. 4104.

Gaylord, T. K.

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, J. Opt. Soc. Am. A 12, 345 (1995).

T. K. Gaylord and M. G. Moharam, Proc. IEEE 73, 894 (1985).
[CrossRef]

Genovesi, S.

S. Genovesi, R. Mitra, A. Monorchio, and G. Manara, IEEE Antennas Wireless Propag. Lett. 5, 277 (2006).
[CrossRef]

Grann, E. B.

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, J. Opt. Soc. Am. A 12, 345 (1995).

Gu, G.-C.

M.-P. Song and G.-C. Gu, in Proceedings of the 3rd International Conference on Machine Learning and Cybernetics (IEEE, 2004), p. 2236.

Haupt, R. L.

R. L. Haupt and S. E. Haupt, Practical Genetic Algorithms (Wiley, 1998).

Haupt, S. E.

R. L. Haupt and S. E. Haupt, Practical Genetic Algorithms (Wiley, 1998).

Jiang, J.

Johnson, E.

Kennedy, J.

R. Eberhart and J. Kennedy, in Proceedings of the Conference for Neural Networks (IEEE, 1995), p. 1942.

J. Kennedy and R. Eberhart, in Proceedings of the International Conference on System, Man and Cybernetics (IEEE, 1997), p. 4104.

Magnusson, R.

Manara, G.

S. Genovesi, R. Mitra, A. Monorchio, and G. Manara, IEEE Antennas Wireless Propag. Lett. 5, 277 (2006).
[CrossRef]

Manos, S.

Mitra, R.

S. Genovesi, R. Mitra, A. Monorchio, and G. Manara, IEEE Antennas Wireless Propag. Lett. 5, 277 (2006).
[CrossRef]

Moharam, M. G.

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, J. Opt. Soc. Am. A 12, 345 (1995).

T. K. Gaylord and M. G. Moharam, Proc. IEEE 73, 894 (1985).
[CrossRef]

Monorchio, A.

S. Genovesi, R. Mitra, A. Monorchio, and G. Manara, IEEE Antennas Wireless Propag. Lett. 5, 277 (2006).
[CrossRef]

Nordin, G. P.

Poladian, L.

Pommet, D. A.

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, J. Opt. Soc. Am. A 12, 345 (1995).

Rahmat-Samii, Y.

J. Robinson and Y. Rahmat-Samii, IEEE Trans. Antennas Propag. 52, 397 (2004).
[CrossRef]

Robinson, J.

J. Robinson and Y. Rahmat-Samii, IEEE Trans. Antennas Propag. 52, 397 (2004).
[CrossRef]

Song, M.-P.

M.-P. Song and G.-C. Gu, in Proceedings of the 3rd International Conference on Machine Learning and Cybernetics (IEEE, 2004), p. 2236.

Tibuleac, S.

Wang, B.

Wang, S. S.

Appl. Opt. (1)

IEEE Antennas Wireless Propag. Lett. (1)

S. Genovesi, R. Mitra, A. Monorchio, and G. Manara, IEEE Antennas Wireless Propag. Lett. 5, 277 (2006).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

J. Robinson and Y. Rahmat-Samii, IEEE Trans. Antennas Propag. 52, 397 (2004).
[CrossRef]

J. Opt. Soc. Am. A (2)

M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, J. Opt. Soc. Am. A 12, 345 (1995).

E. Johnson and M. A. G. Abushagur, J. Opt. Soc. Am. A 12, 1152 (1995).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Proc. IEEE (1)

T. K. Gaylord and M. G. Moharam, Proc. IEEE 73, 894 (1985).
[CrossRef]

Other (5)

A personal computer with a 2.4GHz processor and 256Mbytes of RAM has been used for computations in this Letter.

R. L. Haupt and S. E. Haupt, Practical Genetic Algorithms (Wiley, 1998).

R. Eberhart and J. Kennedy, in Proceedings of the Conference for Neural Networks (IEEE, 1995), p. 1942.

M.-P. Song and G.-C. Gu, in Proceedings of the 3rd International Conference on Machine Learning and Cybernetics (IEEE, 2004), p. 2236.

J. Kennedy and R. Eberhart, in Proceedings of the International Conference on System, Man and Cybernetics (IEEE, 1997), p. 4104.

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Figures (4)

Fig. 1
Fig. 1

Schematic of a GMR grating structure. Λ and d are grating period and thickness, respectively. F is the fraction of period with n H refractive index. I, R, and T denote incidence, reflectance, and transmittance, respectively. The incident light is assumed to be TE polarized (electric field vector normal to the plane of incidence).

Fig. 2
Fig. 2

(a) FF of the best particle (Gbest) versus number of iterations for the reflection filter. (b) Reflectance spectrum of the designed filter by PSO coplotted with the target spectrum. The parameters of the grating are: n H = 2.1 , n L = 1.0 , n inc = 1.0 , and n sub = 1.5 . Λ = 0.3359 μ m , d = 0.2791 μ m , and F = 0.7830 .

Fig. 3
Fig. 3

Reflectance spectra of the filter designed by GA with the same structure and target as the filter designed by PSO. Λ = 0.3654 μ m , d = 0.2785 μ m , and F = 0.9074 .

Fig. 4
Fig. 4

Spectrum of the narrow-line transmission filter in the visible region. The inset shows the grating structure used for the design problem. Λ = 0.3638 μ m , d = 0.8531 μ m , F 1 = 0.4195 , F 2 = 0.2156 , F 3 = 0.1192 , and F 4 = 0.2457 .

Equations (4)

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X m = { x 1 m , x 2 m , , x N m } , 1 m N P O P ,
V m k + 1 = w V m k + c 1 rand 1 ( ) ( P m X m k ) + c 2 rand 2 ( ) ( G X m k ) ,
X m k + 1 = X m k + V m k + 1 Δ t ,
FF = { 1 M λ i [ R desired ( λ ) R design ( λ ) ] 2 } 1 2 ,

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