Abstract

In this paper, we report an inverse strategy to design a directional emitter and power splitter based on two-dimensional photonic crystal waveguides (PCWs). Our approach is illustrated by employing a genetic algorithm in conjunction with the finite-difference time domain (FDTD) method to design a corrugated surface added behind the termination of PCWs. By arranging symmetrical or asymmetrical surface corrugations along the axis of a waveguide, we have successfully realized both a highly efficient directional emitter and an open-type Y-shaped power splitter from planar PCWs. Moreover, the angle of directional emission and split beams can be easily controlled by changing the location of the detector in the output area.

© 2009 Optical Society of America

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References

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  1. E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B 69, 121402 (2004).
    [CrossRef]
  2. P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
    [CrossRef] [PubMed]
  3. W. Smigaj, “Model of light collimation by photonic crystal surface modes,” Phys. Rev. B 75, 205430 (2007).
    [CrossRef]
  4. S. K. Morrison, and Y. S. Kivshar, “Engineering of directional emission from photonic-crystal waveguides,” Appl. Phys. Lett. 86, 081110 (2005).
    [CrossRef]
  5. R. Moussa, B. Wang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Effect of beaming and enhanced transmission in photonic crystals,” Phys. Rev. B 76, 235417 (2007).
    [CrossRef]
  6. K. B. Chung, “Analysis of directional emission via surface modes on photonic crystals,” Opt. Commun. 281, 5349-5354 (2008).
    [CrossRef]
  7. D. Gan, Y. Qi, X. Yang, J. Ma, J. Cui, C. Wang, and X. Luo, “Improved directional emission by resonant defect cavity modes in photonic crystal waveguide with corrugated surface,” Appl. Phys. B: Photophys. Laser Chem. 93, 849-852 (2008).
    [CrossRef]
  8. H. Caglayan, I. Bulu, and E. Ozbay, “Off-axis directional beaming via photonic crystal surface modes,” Appl. Phys. Lett. 92, 092114 (2008).
    [CrossRef]
  9. L. Y. Jiang, H. P. Li, W. Jia, X. Y. Li, and Z. X. Shen, “Genetic optimization of photonic crystal waveguide termination for both on-axis and off-axis highly efficient directional emission,” Opt. Express 17, 10126 (2009).
    [CrossRef] [PubMed]
  10. M. Bayindir, B. Temelkuran, and E. Ozbay, “Photonic-crystal-based beam splitters,” Appl. Phys. Lett. 77, 3902-3904 (2000).
    [CrossRef]
  11. T. Sondergaard and K. H. Dridi, “Energy flow in photonic crystal waveguides,” Phys. Rev. B 61, 15688 (2000).
    [CrossRef]
  12. Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K. Inoue, “Light-propagation characteristics of Y-branch defect waveguides in AlGaAs-based air-bridge-type two-dimensional photonic crystal slabs,” Opt. Lett. 27, 388-390 (2002).
    [CrossRef]
  13. W. Y. Liang, J. W. Dong, and H. Z. Wang, “Directional emitter and beam splitter based on self-collimation effect,” Opt. Express 15, 1234-1239 (2007).
    [CrossRef]
  14. J. Holland, Adaptation in Natural and Artificial Systems (Univ. Michigan Press, 1975).
  15. L. F. Shen, S. L. He, and S. S. Xiao, “Large absolute band gaps in two-dimensional photonic crystals formed by large dielectric pixels,” Phys. Rev. B 66, 165315 (2002).
    [CrossRef]
  16. E. Kerrinckx, L. Bigot, M. Douay, and Y. Quiquempois, “Photonic crystal fiber design by means of a genetic algorithm,” Opt. Express 12, 1990-1995 (2004).
    [CrossRef] [PubMed]
  17. L. Sanchis, A. Hakansson, D. Lopez-Zanon, J. Bravo-Abad, and J. Sanchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84, 4460-4462 (2004).
    [CrossRef]
  18. R. P. Drupp, J. A. Bossard, D. H. Werner, and T. S. Mayer, “Single-layer multiband infrared metallodielectric photonic crystals designed by genetic algorithm optimization,” Appl. Phys. Lett. 86, 081102 (2005).
    [CrossRef]
  19. A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, “Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures,” Phys. Rev. Lett. 96, 143904 (2006).
    [CrossRef] [PubMed]
  20. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time Domain Method (Artech House, 2000).

2009 (1)

2008 (3)

K. B. Chung, “Analysis of directional emission via surface modes on photonic crystals,” Opt. Commun. 281, 5349-5354 (2008).
[CrossRef]

D. Gan, Y. Qi, X. Yang, J. Ma, J. Cui, C. Wang, and X. Luo, “Improved directional emission by resonant defect cavity modes in photonic crystal waveguide with corrugated surface,” Appl. Phys. B: Photophys. Laser Chem. 93, 849-852 (2008).
[CrossRef]

H. Caglayan, I. Bulu, and E. Ozbay, “Off-axis directional beaming via photonic crystal surface modes,” Appl. Phys. Lett. 92, 092114 (2008).
[CrossRef]

2007 (3)

W. Smigaj, “Model of light collimation by photonic crystal surface modes,” Phys. Rev. B 75, 205430 (2007).
[CrossRef]

R. Moussa, B. Wang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Effect of beaming and enhanced transmission in photonic crystals,” Phys. Rev. B 76, 235417 (2007).
[CrossRef]

W. Y. Liang, J. W. Dong, and H. Z. Wang, “Directional emitter and beam splitter based on self-collimation effect,” Opt. Express 15, 1234-1239 (2007).
[CrossRef]

2006 (1)

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, “Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures,” Phys. Rev. Lett. 96, 143904 (2006).
[CrossRef] [PubMed]

2005 (2)

R. P. Drupp, J. A. Bossard, D. H. Werner, and T. S. Mayer, “Single-layer multiband infrared metallodielectric photonic crystals designed by genetic algorithm optimization,” Appl. Phys. Lett. 86, 081102 (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 (4)

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

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

E. Kerrinckx, L. Bigot, M. Douay, and Y. Quiquempois, “Photonic crystal fiber design by means of a genetic algorithm,” Opt. Express 12, 1990-1995 (2004).
[CrossRef] [PubMed]

L. Sanchis, A. Hakansson, D. Lopez-Zanon, J. Bravo-Abad, and J. Sanchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84, 4460-4462 (2004).
[CrossRef]

2002 (2)

2000 (2)

M. Bayindir, B. Temelkuran, and E. Ozbay, “Photonic-crystal-based beam splitters,” Appl. Phys. Lett. 77, 3902-3904 (2000).
[CrossRef]

T. Sondergaard and K. H. Dridi, “Energy flow in photonic crystal waveguides,” Phys. Rev. B 61, 15688 (2000).
[CrossRef]

Agio, M.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Asakawa, K.

Bayindir, M.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Photonic-crystal-based beam splitters,” Appl. Phys. Lett. 77, 3902-3904 (2000).
[CrossRef]

Bigot, L.

Birner, A.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Bossard, J. A.

R. P. Drupp, J. A. Bossard, D. H. Werner, and T. S. Mayer, “Single-layer multiband infrared metallodielectric photonic crystals designed by genetic algorithm optimization,” Appl. Phys. Lett. 86, 081102 (2005).
[CrossRef]

Bravo-Abad, J.

L. Sanchis, A. Hakansson, D. Lopez-Zanon, J. Bravo-Abad, and J. Sanchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84, 4460-4462 (2004).
[CrossRef]

Bulu, I.

H. Caglayan, I. Bulu, and E. Ozbay, “Off-axis directional beaming via photonic crystal surface modes,” Appl. Phys. Lett. 92, 092114 (2008).
[CrossRef]

Caglayan, H.

H. Caglayan, I. Bulu, and E. Ozbay, “Off-axis directional beaming via photonic crystal surface modes,” Appl. Phys. Lett. 92, 092114 (2008).
[CrossRef]

Carlsson, N.

Chen, L.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, “Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures,” Phys. Rev. Lett. 96, 143904 (2006).
[CrossRef] [PubMed]

Chung, K. B.

K. B. Chung, “Analysis of directional emission via surface modes on photonic crystals,” Opt. Commun. 281, 5349-5354 (2008).
[CrossRef]

Cui, J.

D. Gan, Y. Qi, X. Yang, J. Ma, J. Cui, C. Wang, and X. Luo, “Improved directional emission by resonant defect cavity modes in photonic crystal waveguide with corrugated surface,” Appl. Phys. B: Photophys. Laser Chem. 93, 849-852 (2008).
[CrossRef]

Dong, J. W.

Douay, M.

Dridi, K. H.

T. Sondergaard and K. H. Dridi, “Energy flow in photonic crystal waveguides,” Phys. Rev. B 61, 15688 (2000).
[CrossRef]

Drupp, R. P.

R. P. Drupp, J. A. Bossard, D. H. Werner, and T. S. Mayer, “Single-layer multiband infrared metallodielectric photonic crystals designed by genetic algorithm optimization,” Appl. Phys. Lett. 86, 081102 (2005).
[CrossRef]

Gan, D.

D. Gan, Y. Qi, X. Yang, J. Ma, J. Cui, C. Wang, and X. Luo, “Improved directional emission by resonant defect cavity modes in photonic crystal waveguide with corrugated surface,” Appl. Phys. B: Photophys. Laser Chem. 93, 849-852 (2008).
[CrossRef]

García-Vidal, F. J.

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

Gondarenko, A.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, “Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures,” Phys. Rev. Lett. 96, 143904 (2006).
[CrossRef] [PubMed]

Gösele, U.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time Domain Method (Artech House, 2000).

Hakansson, A.

L. Sanchis, A. Hakansson, D. Lopez-Zanon, J. Bravo-Abad, and J. Sanchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84, 4460-4462 (2004).
[CrossRef]

He, S. L.

L. F. Shen, S. L. He, and S. S. Xiao, “Large absolute band gaps in two-dimensional photonic crystals formed by large dielectric pixels,” Phys. Rev. B 66, 165315 (2002).
[CrossRef]

Holland, J.

J. Holland, Adaptation in Natural and Artificial Systems (Univ. Michigan Press, 1975).

Ikeda, N.

Inoue, K.

Jia, W.

Jiang, L. Y.

Kawai, N.

Kerrinckx, E.

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]

Koschny, T.

R. Moussa, B. Wang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Effect of beaming and enhanced transmission in photonic crystals,” Phys. Rev. B 76, 235417 (2007).
[CrossRef]

Kramper, P.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Li, H. P.

Li, X. Y.

Liang, W. Y.

Lipson, H.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, “Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures,” Phys. Rev. Lett. 96, 143904 (2006).
[CrossRef] [PubMed]

Lipson, M.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, “Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures,” Phys. Rev. Lett. 96, 143904 (2006).
[CrossRef] [PubMed]

Lopez-Zanon, D.

L. Sanchis, A. Hakansson, D. Lopez-Zanon, J. Bravo-Abad, and J. Sanchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84, 4460-4462 (2004).
[CrossRef]

Luo, X.

D. Gan, Y. Qi, X. Yang, J. Ma, J. Cui, C. Wang, and X. Luo, “Improved directional emission by resonant defect cavity modes in photonic crystal waveguide with corrugated surface,” Appl. Phys. B: Photophys. Laser Chem. 93, 849-852 (2008).
[CrossRef]

Ma, J.

D. Gan, Y. Qi, X. Yang, J. Ma, J. Cui, C. Wang, and X. Luo, “Improved directional emission by resonant defect cavity modes in photonic crystal waveguide with corrugated surface,” Appl. Phys. B: Photophys. Laser Chem. 93, 849-852 (2008).
[CrossRef]

Martín-Moreno, L.

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

Mayer, T. S.

R. P. Drupp, J. A. Bossard, D. H. Werner, and T. S. Mayer, “Single-layer multiband infrared metallodielectric photonic crystals designed by genetic algorithm optimization,” Appl. Phys. Lett. 86, 081102 (2005).
[CrossRef]

Moreno, E.

E. Moreno, F. J. García-Vidal, and L. Martín-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]

Moussa, R.

R. Moussa, B. Wang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Effect of beaming and enhanced transmission in photonic crystals,” Phys. Rev. B 76, 235417 (2007).
[CrossRef]

Müller, F.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Ozbay, E.

H. Caglayan, I. Bulu, and E. Ozbay, “Off-axis directional beaming via photonic crystal surface modes,” Appl. Phys. Lett. 92, 092114 (2008).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, “Photonic-crystal-based beam splitters,” Appl. Phys. Lett. 77, 3902-3904 (2000).
[CrossRef]

Preble, S.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, “Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures,” Phys. Rev. Lett. 96, 143904 (2006).
[CrossRef] [PubMed]

Qi, Y.

D. Gan, Y. Qi, X. Yang, J. Ma, J. Cui, C. Wang, and X. Luo, “Improved directional emission by resonant defect cavity modes in photonic crystal waveguide with corrugated surface,” Appl. Phys. B: Photophys. Laser Chem. 93, 849-852 (2008).
[CrossRef]

Quiquempois, Y.

Robinson, J.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, “Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures,” Phys. Rev. Lett. 96, 143904 (2006).
[CrossRef] [PubMed]

Sanchez-Dehesa, J.

L. Sanchis, A. Hakansson, D. Lopez-Zanon, J. Bravo-Abad, and J. Sanchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84, 4460-4462 (2004).
[CrossRef]

Sanchis, L.

L. Sanchis, A. Hakansson, D. Lopez-Zanon, J. Bravo-Abad, and J. Sanchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84, 4460-4462 (2004).
[CrossRef]

Sandoghdar, V.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Shen, L. F.

L. F. Shen, S. L. He, and S. S. Xiao, “Large absolute band gaps in two-dimensional photonic crystals formed by large dielectric pixels,” Phys. Rev. B 66, 165315 (2002).
[CrossRef]

Shen, Z. X.

Smigaj, W.

W. Smigaj, “Model of light collimation by photonic crystal surface modes,” Phys. Rev. B 75, 205430 (2007).
[CrossRef]

Sondergaard, T.

T. Sondergaard and K. H. Dridi, “Energy flow in photonic crystal waveguides,” Phys. Rev. B 61, 15688 (2000).
[CrossRef]

Soukoulis, C. M.

R. Moussa, B. Wang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Effect of beaming and enhanced transmission in photonic crystals,” Phys. Rev. B 76, 235417 (2007).
[CrossRef]

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Sugimoto, Y.

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time Domain Method (Artech House, 2000).

Temelkuran, B.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Photonic-crystal-based beam splitters,” Appl. Phys. Lett. 77, 3902-3904 (2000).
[CrossRef]

Tuttle, G.

R. Moussa, B. Wang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Effect of beaming and enhanced transmission in photonic crystals,” Phys. Rev. B 76, 235417 (2007).
[CrossRef]

Wang, B.

R. Moussa, B. Wang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Effect of beaming and enhanced transmission in photonic crystals,” Phys. Rev. B 76, 235417 (2007).
[CrossRef]

Wang, C.

D. Gan, Y. Qi, X. Yang, J. Ma, J. Cui, C. Wang, and X. Luo, “Improved directional emission by resonant defect cavity modes in photonic crystal waveguide with corrugated surface,” Appl. Phys. B: Photophys. Laser Chem. 93, 849-852 (2008).
[CrossRef]

Wang, H. Z.

Wehrspohn, R. B.

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

Werner, D. H.

R. P. Drupp, J. A. Bossard, D. H. Werner, and T. S. Mayer, “Single-layer multiband infrared metallodielectric photonic crystals designed by genetic algorithm optimization,” Appl. Phys. Lett. 86, 081102 (2005).
[CrossRef]

Xiao, S. S.

L. F. Shen, S. L. He, and S. S. Xiao, “Large absolute band gaps in two-dimensional photonic crystals formed by large dielectric pixels,” Phys. Rev. B 66, 165315 (2002).
[CrossRef]

Yang, X.

D. Gan, Y. Qi, X. Yang, J. Ma, J. Cui, C. Wang, and X. Luo, “Improved directional emission by resonant defect cavity modes in photonic crystal waveguide with corrugated surface,” Appl. Phys. B: Photophys. Laser Chem. 93, 849-852 (2008).
[CrossRef]

Appl. Phys. B: Photophys. Laser Chem. (1)

D. Gan, Y. Qi, X. Yang, J. Ma, J. Cui, C. Wang, and X. Luo, “Improved directional emission by resonant defect cavity modes in photonic crystal waveguide with corrugated surface,” Appl. Phys. B: Photophys. Laser Chem. 93, 849-852 (2008).
[CrossRef]

Appl. Phys. Lett. (5)

H. Caglayan, I. Bulu, and E. Ozbay, “Off-axis directional beaming via photonic crystal surface modes,” Appl. Phys. Lett. 92, 092114 (2008).
[CrossRef]

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

M. Bayindir, B. Temelkuran, and E. Ozbay, “Photonic-crystal-based beam splitters,” Appl. Phys. Lett. 77, 3902-3904 (2000).
[CrossRef]

L. Sanchis, A. Hakansson, D. Lopez-Zanon, J. Bravo-Abad, and J. Sanchez-Dehesa, “Integrated optical devices design by genetic algorithm,” Appl. Phys. Lett. 84, 4460-4462 (2004).
[CrossRef]

R. P. Drupp, J. A. Bossard, D. H. Werner, and T. S. Mayer, “Single-layer multiband infrared metallodielectric photonic crystals designed by genetic algorithm optimization,” Appl. Phys. Lett. 86, 081102 (2005).
[CrossRef]

Opt. Commun. (1)

K. B. Chung, “Analysis of directional emission via surface modes on photonic crystals,” Opt. Commun. 281, 5349-5354 (2008).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (5)

L. F. Shen, S. L. He, and S. S. Xiao, “Large absolute band gaps in two-dimensional photonic crystals formed by large dielectric pixels,” Phys. Rev. B 66, 165315 (2002).
[CrossRef]

T. Sondergaard and K. H. Dridi, “Energy flow in photonic crystal waveguides,” Phys. Rev. B 61, 15688 (2000).
[CrossRef]

W. Smigaj, “Model of light collimation by photonic crystal surface modes,” Phys. Rev. B 75, 205430 (2007).
[CrossRef]

R. Moussa, B. Wang, G. Tuttle, T. Koschny, and C. M. Soukoulis, “Effect of beaming and enhanced transmission in photonic crystals,” Phys. Rev. B 76, 235417 (2007).
[CrossRef]

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

Phys. Rev. Lett. (2)

P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Müller, R. B. Wehrspohn, U. Gösele, and V. Sandoghdar, “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett. 92, 113903 (2004).
[CrossRef] [PubMed]

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, “Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures,” Phys. Rev. Lett. 96, 143904 (2006).
[CrossRef] [PubMed]

Other (2)

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time Domain Method (Artech House, 2000).

J. Holland, Adaptation in Natural and Artificial Systems (Univ. Michigan Press, 1975).

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic sketch of the structure to be designed. A corrugated surface is put behind the termination of a normal planar 2D PCW. There are 8 total variables to be optimized in the surface corrugations, and a detector with width l is used to characterize the quality of DEB in the output area. (b) Dispersion relation of the waveguide as shown in the inset.

Fig. 2
Fig. 2

(Left) Time average | E z | 2 distribution for three optimum structures: (a) on-axis directional emitter, (b) off-axis directional emitter, and (c) open-type Y-shaped power splitter. (Right) Time average | E z | 2 distribution detected along the y direction ( | y | = 30 a ) at the position of x = 50 a .

Fig. 3
Fig. 3

Time average angular intensity distribution of the electric field for three optimum structures as indicated in Fig. 2. The detector plane is a half-circle with center at ( 10 a , 0), ( 15 a , 0), and ( 10 a , 0), respectively, for three structures, and the radius of all circles is 40 a .

Fig. 4
Fig. 4

Normalized transmission coefficient versus detector location for three optimum structures. As indicated in Fig. 2, the detectors are placed along 0°, 11.5°, and 23.8°, respectively, for three optimum structures.

Fig. 5
Fig. 5

Time average power of detector, P D ( ω ) versus wavelength for three optimum structures.

Tables (1)

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Table 1 Optimum Parameters of Corrugated Surfaces for Three Examples

Equations (1)

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P D ( ω ) = | 2 t 2 t 1 t 1 t 2 | Re [ 0 8 a [ E D ( t ) × H D * ( t ) ] d l ] Re [ 0 λ [ E S ( t ) × H S * ( t ) ] d l ] | d t | , ( t 1 = N 1 Δ t , t 2 = N 2 Δ t , Δ t = 1 c 1 Δ x 2 + 1 Δ y 2 ) .

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