Abstract

We report particle swarm optimization (PSO) of photonic crystal (PC) structures through an example of a PC waveguide termination to achieve directional emission. PC waveguide termination is optimized by using the PSO algorithm by evaluating a fitness function by the scattering matrix method. We consider two different structures, reported earlier and designed through intuition and trial and error, for our optimization and compare the results obtained. Our results show that optimizing with PSO can provide more directed and intense beams compared with designs based purely on intuition and trial and error. Compared with the two earlier reported directional emission PC structures, increases in intensity by factors of 1.25 and 2 and decreases in beam divergence by factors of 1.25 and 2.4, respectively, were achieved.

© 2010 Optical Society of America

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  1. S. K. Morrison and Y. S. Kivshar, “Engineering of directional emission from photonic crystal waveguides,” Appl. Phys. Lett. 86, 081110 (2005).
    [CrossRef]
  2. H. Kurt, “Theoretical study of directional emission enhancement from photonic crystal waveguides with tapered exits,” IEEE Photon. Technol. Lett. 20, 1682-1684 (2008).
    [CrossRef]
  3. D. Tang, L. Chen, and W. Ding, “Efficient beaming from photonic crystal waveguides via self-collimation effect,” Appl. Phys. Lett. 89, 131120 (2006).
    [CrossRef]
  4. C.-C. Chen, T. Pertsch, R. Iliew, F. Lederer, and A. Tünnermann, “Directional emission from photonic crystal waveguides,” Opt. Express 14, 2423-2428 (2006).
    [CrossRef] [PubMed]
  5. W. R. Frei, D. A. Tortorelli, and H. T. Johnson, “Geometry projection method for optimizing photonic nanostructures,” Opt. Lett. 32, 77-79 (2007).
    [CrossRef]
  6. W. R. Frei, D. A. Tortorelli, and H. T. Johnson, “Topology optimization of a photonic crystal waveguide termination to maximize directional emission,” Appl. Phys. Lett. 86, 111114 (2005).
    [CrossRef]
  7. J. Kennedy and R. C. Eberhart, “Particle swarm optimization,” in Proceedings of IEEE International Conference on Neural Networks, 1995 (IEEE, 1995), Vol. 4, pp. 1942-1948.
    [CrossRef]
  8. J. Kennedy and W. M. Spears, “Matching algorithms to problems: an experimental test of the particle swarm and some genetic algorithms on multi modal problem generator,” in The 1998 IEEE International Conference on Evolutionary Computation Proceedings, 1998. IEEE World Congress on Computational Intelligence (IEEE, 1998), pp. 28-83.
  9. J. Kennedy and R. C. Eberhart, “A discrete binary version of particle swarm optimization,” in 1997 IEEE International Conference on Systems, Man, and Cybernetics, 1997, 'Computational Cybernetics and Simulation' (IEEE, 1997) Vol. x, pp. xx-xx.
  10. A. Marandi, F. Afshinmanesh, M. Shahabadi, and F. Bahrami, “Boolean particle swarm optimization and its application to the design of a dual-band dual-polarized planar antenna,” in IEEE Congress on Evolutionary Computation, 2006. CEC 2006 (IEEE, 2006), pp. 3212-3218.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
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    [CrossRef]

2009 (2)

2008 (2)

F. Afshinmanesh, A. Marandi, P. P. M. So, and R. Gordon, “Proposal for compact optical filters using large index step binary supergratings,” IEEE Photon. Technol. Lett. 20, 676-678 (2008).
[CrossRef]

H. Kurt, “Theoretical study of directional emission enhancement from photonic crystal waveguides with tapered exits,” IEEE Photon. Technol. Lett. 20, 1682-1684 (2008).
[CrossRef]

2007 (2)

2006 (2)

D. Tang, L. Chen, and W. Ding, “Efficient beaming from photonic crystal waveguides via self-collimation effect,” Appl. Phys. Lett. 89, 131120 (2006).
[CrossRef]

C.-C. Chen, T. Pertsch, R. Iliew, F. Lederer, and A. Tünnermann, “Directional emission from photonic crystal waveguides,” Opt. Express 14, 2423-2428 (2006).
[CrossRef] [PubMed]

2005 (2)

W. R. Frei, D. A. Tortorelli, and H. T. Johnson, “Topology optimization of a photonic crystal waveguide termination to maximize directional emission,” Appl. Phys. Lett. 86, 111114 (2005).
[CrossRef]

S. K. Morrison and Y. S. Kivshar, “Engineering of directional emission from photonic crystal waveguides,” Appl. Phys. Lett. 86, 081110 (2005).
[CrossRef]

2004 (2)

J. Robinson and Y. R-Samii, “Particle swarm optimization in electromagnetics,” IEEE Trans. Antennas Propag. 52, 397-407 (2004).
[CrossRef]

E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
[CrossRef]

1996 (1)

Abrishamian, M. S.

Afshinmanesh, F.

F. Afshinmanesh, A. Marandi, P. P. M. So, and R. Gordon, “Proposal for compact optical filters using large index step binary supergratings,” IEEE Photon. Technol. Lett. 20, 676-678 (2008).
[CrossRef]

A. Marandi, F. Afshinmanesh, M. Shahabadi, and F. Bahrami, “Boolean particle swarm optimization and its application to the design of a dual-band dual-polarized planar antenna,” in IEEE Congress on Evolutionary Computation, 2006. CEC 2006 (IEEE, 2006), pp. 3212-3218.

A. Marandi, F. Afshinmanesh, and P. P. M. So, “Design of a highly focused photonic crystal lens using boolean particle swarm optimization,” in The 20th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2007 LEOS 2007 (IEEE, 2007), pp. 931-932.

Bahrami, F.

A. Marandi, F. Afshinmanesh, M. Shahabadi, and F. Bahrami, “Boolean particle swarm optimization and its application to the design of a dual-band dual-polarized planar antenna,” in IEEE Congress on Evolutionary Computation, 2006. CEC 2006 (IEEE, 2006), pp. 3212-3218.

Chen, C.-C.

Chen, L.

D. Tang, L. Chen, and W. Ding, “Efficient beaming from photonic crystal waveguides via self-collimation effect,” Appl. Phys. Lett. 89, 131120 (2006).
[CrossRef]

Ding, W.

D. Tang, L. Chen, and W. Ding, “Efficient beaming from photonic crystal waveguides via self-collimation effect,” Appl. Phys. Lett. 89, 131120 (2006).
[CrossRef]

Djavid, M.

Eberhart, R. C.

J. Kennedy and R. C. Eberhart, “Particle swarm optimization,” in Proceedings of IEEE International Conference on Neural Networks, 1995 (IEEE, 1995), Vol. 4, pp. 1942-1948.
[CrossRef]

J. Kennedy and R. C. Eberhart, “A discrete binary version of particle swarm optimization,” in 1997 IEEE International Conference on Systems, Man, and Cybernetics, 1997, 'Computational Cybernetics and Simulation' (IEEE, 1997) Vol. x, pp. xx-xx.

Frei, W. R.

W. R. Frei, D. A. Tortorelli, and H. T. Johnson, “Geometry projection method for optimizing photonic nanostructures,” Opt. Lett. 32, 77-79 (2007).
[CrossRef]

W. R. Frei, D. A. Tortorelli, and H. T. Johnson, “Topology optimization of a photonic crystal waveguide termination to maximize directional emission,” Appl. Phys. Lett. 86, 111114 (2005).
[CrossRef]

Garcia-Vidal, F. J.

E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
[CrossRef]

Gordon, R.

F. Afshinmanesh, A. Marandi, P. P. M. So, and R. Gordon, “Proposal for compact optical filters using large index step binary supergratings,” IEEE Photon. Technol. Lett. 20, 676-678 (2008).
[CrossRef]

Iliew, R.

Johnson, H. T.

W. R. Frei, D. A. Tortorelli, and H. T. Johnson, “Geometry projection method for optimizing photonic nanostructures,” Opt. Lett. 32, 77-79 (2007).
[CrossRef]

W. R. Frei, D. A. Tortorelli, and H. T. Johnson, “Topology optimization of a photonic crystal waveguide termination to maximize directional emission,” Appl. Phys. Lett. 86, 111114 (2005).
[CrossRef]

Kennedy, J.

J. Kennedy and R. C. Eberhart, “Particle swarm optimization,” in Proceedings of IEEE International Conference on Neural Networks, 1995 (IEEE, 1995), Vol. 4, pp. 1942-1948.
[CrossRef]

J. Kennedy and W. M. Spears, “Matching algorithms to problems: an experimental test of the particle swarm and some genetic algorithms on multi modal problem generator,” in The 1998 IEEE International Conference on Evolutionary Computation Proceedings, 1998. IEEE World Congress on Computational Intelligence (IEEE, 1998), pp. 28-83.

J. Kennedy and R. C. Eberhart, “A discrete binary version of particle swarm optimization,” in 1997 IEEE International Conference on Systems, Man, and Cybernetics, 1997, 'Computational Cybernetics and Simulation' (IEEE, 1997) Vol. x, pp. xx-xx.

Kim, H.

Kivshar, Y. S.

S. K. Morrison and Y. S. Kivshar, “Engineering of directional emission from photonic crystal waveguides,” Appl. Phys. Lett. 86, 081110 (2005).
[CrossRef]

Kurt, H.

H. Kurt, “Theoretical study of directional emission enhancement from photonic crystal waveguides with tapered exits,” IEEE Photon. Technol. Lett. 20, 1682-1684 (2008).
[CrossRef]

Lederer, F.

Lee, B.

Lee, I.-M.

Li, L.

Li, Y.

Y. Li, “Hybrid intelligent approach for modeling and optimization of semiconductor devices and nanostructures,” Comput. Mater. Sci. 45, 41-51 (2009).
[CrossRef]

Marandi, A.

F. Afshinmanesh, A. Marandi, P. P. M. So, and R. Gordon, “Proposal for compact optical filters using large index step binary supergratings,” IEEE Photon. Technol. Lett. 20, 676-678 (2008).
[CrossRef]

A. Marandi, F. Afshinmanesh, M. Shahabadi, and F. Bahrami, “Boolean particle swarm optimization and its application to the design of a dual-band dual-polarized planar antenna,” in IEEE Congress on Evolutionary Computation, 2006. CEC 2006 (IEEE, 2006), pp. 3212-3218.

A. Marandi, F. Afshinmanesh, and P. P. M. So, “Design of a highly focused photonic crystal lens using boolean particle swarm optimization,” in The 20th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2007 LEOS 2007 (IEEE, 2007), pp. 931-932.

Martin-Moreno, L.

E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
[CrossRef]

Mirtaheri, S. A.

Moreno, E.

E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
[CrossRef]

Morrison, S. K.

S. K. Morrison and Y. S. Kivshar, “Engineering of directional emission from photonic crystal waveguides,” Appl. Phys. Lett. 86, 081110 (2005).
[CrossRef]

Pertsch, T.

Robinson, J.

J. Robinson and Y. R-Samii, “Particle swarm optimization in electromagnetics,” IEEE Trans. Antennas Propag. 52, 397-407 (2004).
[CrossRef]

R-Samii, Y.

J. Robinson and Y. R-Samii, “Particle swarm optimization in electromagnetics,” IEEE Trans. Antennas Propag. 52, 397-407 (2004).
[CrossRef]

Shahabadi, M.

A. Marandi, F. Afshinmanesh, M. Shahabadi, and F. Bahrami, “Boolean particle swarm optimization and its application to the design of a dual-band dual-polarized planar antenna,” in IEEE Congress on Evolutionary Computation, 2006. CEC 2006 (IEEE, 2006), pp. 3212-3218.

So, P. P. M.

F. Afshinmanesh, A. Marandi, P. P. M. So, and R. Gordon, “Proposal for compact optical filters using large index step binary supergratings,” IEEE Photon. Technol. Lett. 20, 676-678 (2008).
[CrossRef]

A. Marandi, F. Afshinmanesh, and P. P. M. So, “Design of a highly focused photonic crystal lens using boolean particle swarm optimization,” in The 20th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2007 LEOS 2007 (IEEE, 2007), pp. 931-932.

Spears, W. M.

J. Kennedy and W. M. Spears, “Matching algorithms to problems: an experimental test of the particle swarm and some genetic algorithms on multi modal problem generator,” in The 1998 IEEE International Conference on Evolutionary Computation Proceedings, 1998. IEEE World Congress on Computational Intelligence (IEEE, 1998), pp. 28-83.

Tang, D.

D. Tang, L. Chen, and W. Ding, “Efficient beaming from photonic crystal waveguides via self-collimation effect,” Appl. Phys. Lett. 89, 131120 (2006).
[CrossRef]

Tortorelli, D. A.

W. R. Frei, D. A. Tortorelli, and H. T. Johnson, “Geometry projection method for optimizing photonic nanostructures,” Opt. Lett. 32, 77-79 (2007).
[CrossRef]

W. R. Frei, D. A. Tortorelli, and H. T. Johnson, “Topology optimization of a photonic crystal waveguide termination to maximize directional emission,” Appl. Phys. Lett. 86, 111114 (2005).
[CrossRef]

Tünnermann, A.

Appl. Phys. Lett. (3)

S. K. Morrison and Y. S. Kivshar, “Engineering of directional emission from photonic crystal waveguides,” Appl. Phys. Lett. 86, 081110 (2005).
[CrossRef]

D. Tang, L. Chen, and W. Ding, “Efficient beaming from photonic crystal waveguides via self-collimation effect,” Appl. Phys. Lett. 89, 131120 (2006).
[CrossRef]

W. R. Frei, D. A. Tortorelli, and H. T. Johnson, “Topology optimization of a photonic crystal waveguide termination to maximize directional emission,” Appl. Phys. Lett. 86, 111114 (2005).
[CrossRef]

Comput. Mater. Sci. (1)

Y. Li, “Hybrid intelligent approach for modeling and optimization of semiconductor devices and nanostructures,” Comput. Mater. Sci. 45, 41-51 (2009).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

F. Afshinmanesh, A. Marandi, P. P. M. So, and R. Gordon, “Proposal for compact optical filters using large index step binary supergratings,” IEEE Photon. Technol. Lett. 20, 676-678 (2008).
[CrossRef]

H. Kurt, “Theoretical study of directional emission enhancement from photonic crystal waveguides with tapered exits,” IEEE Photon. Technol. Lett. 20, 1682-1684 (2008).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

J. Robinson and Y. R-Samii, “Particle swarm optimization in electromagnetics,” IEEE Trans. Antennas Propag. 52, 397-407 (2004).
[CrossRef]

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

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

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
[CrossRef]

Other (5)

J. Kennedy and R. C. Eberhart, “Particle swarm optimization,” in Proceedings of IEEE International Conference on Neural Networks, 1995 (IEEE, 1995), Vol. 4, pp. 1942-1948.
[CrossRef]

J. Kennedy and W. M. Spears, “Matching algorithms to problems: an experimental test of the particle swarm and some genetic algorithms on multi modal problem generator,” in The 1998 IEEE International Conference on Evolutionary Computation Proceedings, 1998. IEEE World Congress on Computational Intelligence (IEEE, 1998), pp. 28-83.

J. Kennedy and R. C. Eberhart, “A discrete binary version of particle swarm optimization,” in 1997 IEEE International Conference on Systems, Man, and Cybernetics, 1997, 'Computational Cybernetics and Simulation' (IEEE, 1997) Vol. x, pp. xx-xx.

A. Marandi, F. Afshinmanesh, M. Shahabadi, and F. Bahrami, “Boolean particle swarm optimization and its application to the design of a dual-band dual-polarized planar antenna,” in IEEE Congress on Evolutionary Computation, 2006. CEC 2006 (IEEE, 2006), pp. 3212-3218.

A. Marandi, F. Afshinmanesh, and P. P. M. So, “Design of a highly focused photonic crystal lens using boolean particle swarm optimization,” in The 20th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2007 LEOS 2007 (IEEE, 2007), pp. 931-932.

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Figures (4)

Fig. 1
Fig. 1

Waveguide structure to be optimized; the power at the target plane is to be maximized.

Fig. 2
Fig. 2

Dispersion diagram for the waveguide under consideration.

Fig. 3
Fig. 3

Results of PSO optimization: (a) PSO optimized zigzag structure (b) zoomed in view of part of optimized surface layer region showing the definition of the parameters optimized (c) electric field within PSO optimized zigzag structure (d) & (e) normalized intensity along a radius of 35 a from the waveguide output; (d) also shows the frequency sensitivity of the PSO optimized structure. The values given in the highlighted box are the optimized values of the parameters discussed in the text.

Fig. 4
Fig. 4

Results of PSO and Boolean PSO optimization: (a) Tapered PSO-1 structure (b) electric field within Tapered PSO-1 structure (c) Tapered PSO-2 structure (d) electric field within Tapered PSO-2 structure (e) Boolean PSO optimized structure (f) electric field within Boolean PSO optimized structure (g) & (h) intensity along a radius of 10 a from the waveguide output.

Tables (1)

Tables Icon

Table 1 Diameter and Displacement of Rods within the Optimized Region Normalized with Respect to d and a, Respectively a

Equations (2)

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v d i ( n + 1 ) = w v d i ( n ) + c 1 r 1 d i ( n ) ( p d i ( n ) x d i ( n ) ) + c 2 r 2 d i ( n ) ( g d ( n ) x d i ( n ) ) ,
x d i ( n + 1 ) = x d i ( n ) + v d i ( n + 1 ) ,

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