We numerically investigate by the finite-difference time-domain method the effects of surface termination on directional emission exiting a photonic crystal waveguide. The directed power and far-field beam profile for the original proposal [E. Moreno et al., Phys. Rev. B 69, 121402 (2004)] and its enhancement [S. K. Morrison et al., Appl. Phys. Lett. 86, 081110 (2005)] are computed for different values of some important parameters. We find another surface termination condition with a positive surface displacement in the structure of the original proposal which has a negative surface displacement. Our surface termination is more effective than the original structure, and nearly as effective as the termination for the enhancement, for directional emission. Besides, our termination is simpler than that for the enhancement. We confirm the effectiveness of directional emission from our termination in its far-field beam profile, radiation intensity distribution, and additionally the wave-vector space representation by the Fourier analysis.

© 2008 Optical Society of Korea

1. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,”Science, vol. 297, no. 5582, pp. 820-822, 2002 [CrossRef]
2. L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett., vol. 90, no. 16, pp. 167401-1167401-4, 2003 [CrossRef]
3. E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B, vol. 69, no. 12, pp. 121402-1-121402-4, 2004 [CrossRef]
4. P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muler, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett., vol. 92, no. 11, pp. 113903-1-113903-4, 2004 [CrossRef]
5. E. Moreno, L. Martin-Moreno, and F. J. Garcia-Vidal, “Efficient coupling of light into and out of a photonic crystal waveguide via surface modes,” Photonics Nanostruc. - Fundamen. Appl., vol. 2, no. 2, pp. 97-102, 2004 [CrossRef]
6. I. Bulu, H. Caglayan, and E. Ozbay, “Beaming of light and enhanced transmission via surface modes of photonic crystals,” Opt. Lett., vol. 30, no. 22, pp. 3078-3080, 2005 [CrossRef]
7. S. K. Morrison and Y. S. Kivshar, “Engineering of directional emission form photonic-crystal waveguides,” Appl. Phys. Lett., vol. 86, no. 8, pp. 081110-1-081110-3, 2005
8. S. K. Morrison and Y. S. Kivshar, “Beaming effect and directional emission from photonic-crystal waveguides,” Proc. SPIE, vol. 5733, pp. 104-113, 2005 [CrossRef]
9. W. Smigaj, “Model of light collimation by photonic crystal surface modes,” Phys. Rev. B, vol. 75, no. 20, pp. 205430-1-205430-8, 2007 [CrossRef]
10. K. B. Chung, “Properties of surface modes used for directional emission from photonic crystal waveguides,” J. Opt. Soc. Korea, in press, 2008 [CrossRef]
11. C.-C. Chen, T. Pertcsh, R. Iliew, F. Lederer, and A. Tunnermann, “Directional emission from photonic crystal waveguides,” Opt. Express, vol. 14, no. 6, pp. 2423- 2428, 2006 [CrossRef]
12. K. Guven and E. Ozbay, “Directivity enhancement and deflection of the beam emitted from a photonic crystal waveguide via defect coupling,” Opt. Express, vol. 15, no. 23, pp. 14973-14978, 2007 [CrossRef]
13. D. Tang, L. Chen, and W. Ding, “Efficient beaming from photonic crystal waveguides via self-collimation effect,” Appl. Phys. Lett., vol. 89, no. 13, pp. 131120-1-131120-3, 2006 [CrossRef]
14. W. Y. Liang, J. W. Dong, and H. Z. Wang, “Directional emitter and beam splitter based on self-collimation effect,” Opt. Express, vol. 15, no. 3, pp. 1234-1239, 2007 [CrossRef]
15. Z.-H. Zhu, W.-M. Ye, J.-R. Ji, X.-D. Yuan, and C. Zen, “Enhanced transmission and directional emission via coupled-resonator optical waveguides,” Appl. Phys. B, vol. 86, pp. 327-331, 2007 [CrossRef]
16. Z. Li, K. Aydin, and E. Ozbay, “Highly directional emission from photonic crystals with a wide bandwidth,” Appl. Phys. Lett., vol. 91, no. 12, pp. 121105-1-121105-3, 2007
17. Y. Zhang, Y. Zhang, and B. Li, “Highly-efficient directional emission from photonic crystal waveguides for coupling of freely propagated terahertz waves into Si slab waveguides,” Opt. Express, vol. 15, no. 15, pp. 9281-9286, 2007 [CrossRef]
18. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell"s equations in isotropic media,” IEEE Trans. Antennas Propag., vol. AP-14, no. 3, pp. 32-307, 1966
19. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys., vol. 114, no. 2, pp. 185-200, 1994 [CrossRef]
20. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Third Edition, Artech House, Boston, U.S.A., 2005)
21. I. D. Leon and F. S. Roux, “Fourier analysis of reflection and refraction in two-dimensional photonic crystals,” Phys. Rev. B., vol. 71, no. 23, pp. 235105-1-235105-10, 2005 [CrossRef]
22. F. S. Roux and I. D. Leon, “Planar photonic crystal gradient index lens, simulated with a finite difference time domain method,” Phys. Rev. B., vol. 74, no. 11, pp. 113103-1-113103-4, 2006 [CrossRef]
23. A. Kim, K. B. Chung, and J.W.Wu, “Control of selfcollimated Bloch waves by partially flat equifrequency contours in photonic crystals,” Appl. Phys. Lett., vol. 89, no. 25, pp. 251120-1-251120-3, 2006 [CrossRef]

Appl. Phys. Lett.

• S. K. Morrison and Y. S. Kivshar, “Engineering of directional emission form photonic-crystal waveguides,” Appl. Phys. Lett., vol. 86, no. 8, pp. 081110-1-081110-3, 2005
• D. Tang, L. Chen, and W. Ding, “Efficient beaming from photonic crystal waveguides via self-collimation effect,” Appl. Phys. Lett., vol. 89, no. 13, pp. 131120-1-131120-3, 2006 [CrossRef]
• Z. Li, K. Aydin, and E. Ozbay, “Highly directional emission from photonic crystals with a wide bandwidth,” Appl. Phys. Lett., vol. 91, no. 12, pp. 121105-1-121105-3, 2007
• A. Kim, K. B. Chung, and J.W.Wu, “Control of selfcollimated Bloch waves by partially flat equifrequency contours in photonic crystals,” Appl. Phys. Lett., vol. 89, no. 25, pp. 251120-1-251120-3, 2006 [CrossRef]

Applied Physics B: Lasers and Optics

• Z.-H. Zhu, W.-M. Ye, J.-R. Ji, X.-D. Yuan, and C. Zen, “Enhanced transmission and directional emission via coupled-resonator optical waveguides,” Appl. Phys. B, vol. 86, pp. 327-331, 2007 [CrossRef]

IEEE Trans. Antennas Propag.

• K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell"s equations in isotropic media,” IEEE Trans. Antennas Propag., vol. AP-14, no. 3, pp. 32-307, 1966

J. Opt. Soc. Korea

• K. B. Chung, “Properties of surface modes used for directional emission from photonic crystal waveguides,” J. Opt. Soc. Korea, in press, 2008 [CrossRef]

Journal of Computational Physics

• J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys., vol. 114, no. 2, pp. 185-200, 1994 [CrossRef]

Opt. Lett.

• I. Bulu, H. Caglayan, and E. Ozbay, “Beaming of light and enhanced transmission via surface modes of photonic crystals,” Opt. Lett., vol. 30, no. 22, pp. 3078-3080, 2005 [CrossRef]

Optics Express

• C.-C. Chen, T. Pertcsh, R. Iliew, F. Lederer, and A. Tunnermann, “Directional emission from photonic crystal waveguides,” Opt. Express, vol. 14, no. 6, pp. 2423- 2428, 2006 [CrossRef]
• K. Guven and E. Ozbay, “Directivity enhancement and deflection of the beam emitted from a photonic crystal waveguide via defect coupling,” Opt. Express, vol. 15, no. 23, pp. 14973-14978, 2007 [CrossRef]
• W. Y. Liang, J. W. Dong, and H. Z. Wang, “Directional emitter and beam splitter based on self-collimation effect,” Opt. Express, vol. 15, no. 3, pp. 1234-1239, 2007 [CrossRef]
• Y. Zhang, Y. Zhang, and B. Li, “Highly-efficient directional emission from photonic crystal waveguides for coupling of freely propagated terahertz waves into Si slab waveguides,” Opt. Express, vol. 15, no. 15, pp. 9281-9286, 2007 [CrossRef]

Photonics and Nanostructures - Fundamentals and Applications

• E. Moreno, L. Martin-Moreno, and F. J. Garcia-Vidal, “Efficient coupling of light into and out of a photonic crystal waveguide via surface modes,” Photonics Nanostruc. - Fundamen. Appl., vol. 2, no. 2, pp. 97-102, 2004 [CrossRef]

Phys. Rev. B

• E. Moreno, F. J. Garcia-Vidal, and L. Martin-Moreno, “Enhanced transmission and beaming of light via photonic crystal surface modes,” Phys. Rev. B, vol. 69, no. 12, pp. 121402-1-121402-4, 2004 [CrossRef]
• W. Smigaj, “Model of light collimation by photonic crystal surface modes,” Phys. Rev. B, vol. 75, no. 20, pp. 205430-1-205430-8, 2007 [CrossRef]
• I. D. Leon and F. S. Roux, “Fourier analysis of reflection and refraction in two-dimensional photonic crystals,” Phys. Rev. B., vol. 71, no. 23, pp. 235105-1-235105-10, 2005 [CrossRef]

Phys. Rev. B.

• F. S. Roux and I. D. Leon, “Planar photonic crystal gradient index lens, simulated with a finite difference time domain method,” Phys. Rev. B., vol. 74, no. 11, pp. 113103-1-113103-4, 2006 [CrossRef]

Phys. Rev. Lett.

• P. Kramper, M. Agio, C. M. Soukoulis, A. Birner, F. Muler, R. B. Wehrspohn, U. Gosele, and V. Sandoghdar “Highly directional emission from photonic crystal waveguides of subwavelength width,” Phys. Rev. Lett., vol. 92, no. 11, pp. 113903-1-113903-4, 2004 [CrossRef]
• L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, “Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations,” Phys. Rev. Lett., vol. 90, no. 16, pp. 167401-1167401-4, 2003 [CrossRef]

Proceedings of SPIE

• S. K. Morrison and Y. S. Kivshar, “Beaming effect and directional emission from photonic-crystal waveguides,” Proc. SPIE, vol. 5733, pp. 104-113, 2005 [CrossRef]

Science

• H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,”Science, vol. 297, no. 5582, pp. 820-822, 2002 [CrossRef]

Other

• A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Third Edition, Artech House, Boston, U.S.A., 2005)

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