Abstract

With the method of adding two point defects on modulated surface, novel photonic crystal (PC) waveguide-based beam splitters were presented. The modulated surface layer supports surface states, and introduced discrete point defects can serve as discrete light emitters. The finite-difference time-domain (FDTD) simulations show that the number of beams is sensitive to the distance of two point defects. By adjusting the positions of the point defects, 1-to-N beam splitters can be realized. These simple, easy-to-fabricate and controllable structures have important potential applications in integrated optical circuits.

© 2010 OSA

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    [CrossRef]
  4. M. Q. Xin, L. Zhang, C. Eng Png, J. H. Teng, and J. Aaron Danner, “Asymmetric open cavities for beam steering and switching from line-defect photonic crystals,” J. Opt. Soc. Am. B 27(6), 1153–1157 (2010).
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2010 (2)

W. Jia, L. Y. Jiang, K. Chen, and X. Y. Li, “Design of photonic crystal power beam splitters via corrugated and gratinglike surfaces,” Opt. Commun. 283(20), 4078–4084 (2010).
[CrossRef]

M. Q. Xin, L. Zhang, C. Eng Png, J. H. Teng, and J. Aaron Danner, “Asymmetric open cavities for beam steering and switching from line-defect photonic crystals,” J. Opt. Soc. Am. B 27(6), 1153–1157 (2010).
[CrossRef]

2009 (2)

2008 (2)

Z. F. Li, K. Aydin, and E. Ozbay, “Wide band width directional beaming via waveguide ports in photonic crystals,” J. Phys. D Appl. Phys. 41(15), 155115 (2008).
[CrossRef]

H. Caglayan, I. Bulu, and E. Ozbay, “Off-axis directional beaming via photonic crystal surface modes,” Appl. Phys. Lett. 92(9), 092114 (2008).
[CrossRef]

2007 (3)

2006 (3)

R. Mousse, Th. Koschny, and C. M. Soukoulis, “Excitation of surface waves in a photonic crystal with negative refraction: The role of surface termination,” Phys. Rev. B 74(11), 115111 (2006).
[CrossRef]

B. Wang, W. Dai, A. Fang, L. Zhang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Surface waves in photonic crystal slabs,” Phys. Rev. B 74(19), 195104 (2006).
[CrossRef]

D. Z. Lin, C. K. Chang, Y. C. Chen, D. L. Yang, M. W. Lin, J. T. Yeh, J. M. Liu, C. H. Kuan, C. S. Yeh, and C. K. Lee, “Beaming light from a subwavelength metal slit surrounded by dielectric surface gratings,” Opt. Express 14(8), 3503–3511 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-8-3503 .
[CrossRef] [PubMed]

2005 (1)

S. K. Morrison and Y. S. Kivshar, “Engineering of directional emission from photonic-crystal waveguide,” Appl. Phys. Lett. 86(8), 081110 (2005).
[CrossRef]

2004 (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(12), 121402 (2004).
[CrossRef]

2003 (1)

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4502 (2003).
[CrossRef]

2002 (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 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

1994 (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

1991 (1)

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B Condens. Matter 44(19), 10961–10964 (1991).
[CrossRef] [PubMed]

Aaron Danner, J.

Aydin, K.

Z. F. Li, K. Aydin, and E. Ozbay, “Wide band width directional beaming via waveguide ports in photonic crystals,” J. Phys. D Appl. Phys. 41(15), 155115 (2008).
[CrossRef]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

Brommer, K. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B Condens. Matter 44(19), 10961–10964 (1991).
[CrossRef] [PubMed]

Bulu, I.

H. Caglayan, I. Bulu, and E. Ozbay, “Off-axis directional beaming via photonic crystal surface modes,” Appl. Phys. Lett. 92(9), 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(9), 092114 (2008).
[CrossRef]

Chang, C. K.

Chen, K.

W. Jia, L. Y. Jiang, K. Chen, and X. Y. Li, “Design of photonic crystal power beam splitters via corrugated and gratinglike surfaces,” Opt. Commun. 283(20), 4078–4084 (2010).
[CrossRef]

Chen, Y. C.

Cong, C. X.

Dai, W.

B. Wang, W. Dai, A. Fang, L. Zhang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Surface waves in photonic crystal slabs,” Phys. Rev. B 74(19), 195104 (2006).
[CrossRef]

Degiron, A.

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 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Devaux, E.

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 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Dong, J. W.

Ebbesen, T. W.

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4502 (2003).
[CrossRef]

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 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Eng Png, C.

Fang, A.

B. Wang, W. Dai, A. Fang, L. Zhang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Surface waves in photonic crystal slabs,” Phys. Rev. B 74(19), 195104 (2006).
[CrossRef]

Garcia-Vidal, F. J.

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 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

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(12), 121402 (2004).
[CrossRef]

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4502 (2003).
[CrossRef]

Jia, W.

W. Jia, L. Y. Jiang, K. Chen, and X. Y. Li, “Design of photonic crystal power beam splitters via corrugated and gratinglike surfaces,” Opt. Commun. 283(20), 4078–4084 (2010).
[CrossRef]

L. Y. Jiang, W. Jia, H. P. Li, X. Y. Li, C. X. Cong, and Z. X. Shen, “Inverse design for directional emitter and power splitter based on photonic crystal waveguide with surface corrugations,” J. Opt. Soc. Am. B 26(11), 2157–2160 (2009).
[CrossRef]

Jiang, L. Y.

W. Jia, L. Y. Jiang, K. Chen, and X. Y. Li, “Design of photonic crystal power beam splitters via corrugated and gratinglike surfaces,” Opt. Commun. 283(20), 4078–4084 (2010).
[CrossRef]

L. Y. Jiang, W. Jia, H. P. Li, X. Y. Li, C. X. Cong, and Z. X. Shen, “Inverse design for directional emitter and power splitter based on photonic crystal waveguide with surface corrugations,” J. Opt. Soc. Am. B 26(11), 2157–2160 (2009).
[CrossRef]

Jiang, X. Y.

Y. L. Zhang, D. Y. Zhao, C. H. Zhou, and X. Y. Jiang, “Directional light emission through a metallic nanostructure,” J. Appl. Phys. 105(11), 113124 (2009).
[CrossRef]

Joannopoulos, J. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B Condens. Matter 44(19), 10961–10964 (1991).
[CrossRef] [PubMed]

Kivshar, Y. S.

S. K. Morrison and Y. S. Kivshar, “Engineering of directional emission from photonic-crystal waveguide,” Appl. Phys. Lett. 86(8), 081110 (2005).
[CrossRef]

Koschny, Th.

R. Moussa, B. Wang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Effect of beaming and enhanced transmission in photonic crystals,” Phys. Rev. B 76(23), 235417 (2007).
[CrossRef]

R. Mousse, Th. Koschny, and C. M. Soukoulis, “Excitation of surface waves in a photonic crystal with negative refraction: The role of surface termination,” Phys. Rev. B 74(11), 115111 (2006).
[CrossRef]

B. Wang, W. Dai, A. Fang, L. Zhang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Surface waves in photonic crystal slabs,” Phys. Rev. B 74(19), 195104 (2006).
[CrossRef]

Kuan, C. H.

Lee, C. K.

Lezec, H. J.

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4502 (2003).
[CrossRef]

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 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Li, H. P.

Li, X. Y.

W. Jia, L. Y. Jiang, K. Chen, and X. Y. Li, “Design of photonic crystal power beam splitters via corrugated and gratinglike surfaces,” Opt. Commun. 283(20), 4078–4084 (2010).
[CrossRef]

L. Y. Jiang, W. Jia, H. P. Li, X. Y. Li, C. X. Cong, and Z. X. Shen, “Inverse design for directional emitter and power splitter based on photonic crystal waveguide with surface corrugations,” J. Opt. Soc. Am. B 26(11), 2157–2160 (2009).
[CrossRef]

Li, Z. F.

Z. F. Li, K. Aydin, and E. Ozbay, “Wide band width directional beaming via waveguide ports in photonic crystals,” J. Phys. D Appl. Phys. 41(15), 155115 (2008).
[CrossRef]

Liang, W. Y.

Lin, D. Z.

Lin, M. W.

Linke, R. A.

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 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Liu, J. M.

Martin-Moreno, L.

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 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

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(12), 121402 (2004).
[CrossRef]

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4502 (2003).
[CrossRef]

Meade, R. D.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B Condens. Matter 44(19), 10961–10964 (1991).
[CrossRef] [PubMed]

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(12), 121402 (2004).
[CrossRef]

Morrison, S. K.

S. K. Morrison and Y. S. Kivshar, “Engineering of directional emission from photonic-crystal waveguide,” Appl. Phys. Lett. 86(8), 081110 (2005).
[CrossRef]

Moussa, R.

R. Moussa, B. Wang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Effect of beaming and enhanced transmission in photonic crystals,” Phys. Rev. B 76(23), 235417 (2007).
[CrossRef]

Mousse, R.

R. Mousse, Th. Koschny, and C. M. Soukoulis, “Excitation of surface waves in a photonic crystal with negative refraction: The role of surface termination,” Phys. Rev. B 74(11), 115111 (2006).
[CrossRef]

Ozbay, E.

H. Caglayan, I. Bulu, and E. Ozbay, “Off-axis directional beaming via photonic crystal surface modes,” Appl. Phys. Lett. 92(9), 092114 (2008).
[CrossRef]

Z. F. Li, K. Aydin, and E. Ozbay, “Wide band width directional beaming via waveguide ports in photonic crystals,” J. Phys. D Appl. Phys. 41(15), 155115 (2008).
[CrossRef]

Qiu, M.

Rappe, A. M.

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B Condens. Matter 44(19), 10961–10964 (1991).
[CrossRef] [PubMed]

Shen, Z. X.

Soukoulis, C. M.

R. Moussa, B. Wang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Effect of beaming and enhanced transmission in photonic crystals,” Phys. Rev. B 76(23), 235417 (2007).
[CrossRef]

R. Mousse, Th. Koschny, and C. M. Soukoulis, “Excitation of surface waves in a photonic crystal with negative refraction: The role of surface termination,” Phys. Rev. B 74(11), 115111 (2006).
[CrossRef]

B. Wang, W. Dai, A. Fang, L. Zhang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Surface waves in photonic crystal slabs,” Phys. Rev. B 74(19), 195104 (2006).
[CrossRef]

Teng, J. H.

Tuttle, G.

R. Moussa, B. Wang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Effect of beaming and enhanced transmission in photonic crystals,” Phys. Rev. B 76(23), 235417 (2007).
[CrossRef]

B. Wang, W. Dai, A. Fang, L. Zhang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Surface waves in photonic crystal slabs,” Phys. Rev. B 74(19), 195104 (2006).
[CrossRef]

Wang, B.

R. Moussa, B. Wang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Effect of beaming and enhanced transmission in photonic crystals,” Phys. Rev. B 76(23), 235417 (2007).
[CrossRef]

B. Wang, W. Dai, A. Fang, L. Zhang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Surface waves in photonic crystal slabs,” Phys. Rev. B 74(19), 195104 (2006).
[CrossRef]

Wang, H. Z.

Xiao, S. S.

Xin, M. Q.

Yang, D. L.

Yeh, C. S.

Yeh, J. T.

Zhang, L.

M. Q. Xin, L. Zhang, C. Eng Png, J. H. Teng, and J. Aaron Danner, “Asymmetric open cavities for beam steering and switching from line-defect photonic crystals,” J. Opt. Soc. Am. B 27(6), 1153–1157 (2010).
[CrossRef]

B. Wang, W. Dai, A. Fang, L. Zhang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Surface waves in photonic crystal slabs,” Phys. Rev. B 74(19), 195104 (2006).
[CrossRef]

Zhang, Y. L.

Y. L. Zhang, D. Y. Zhao, C. H. Zhou, and X. Y. Jiang, “Directional light emission through a metallic nanostructure,” J. Appl. Phys. 105(11), 113124 (2009).
[CrossRef]

Zhao, D. Y.

Y. L. Zhang, D. Y. Zhao, C. H. Zhou, and X. Y. Jiang, “Directional light emission through a metallic nanostructure,” J. Appl. Phys. 105(11), 113124 (2009).
[CrossRef]

Zhou, C. H.

Y. L. Zhang, D. Y. Zhao, C. H. Zhou, and X. Y. Jiang, “Directional light emission through a metallic nanostructure,” J. Appl. Phys. 105(11), 113124 (2009).
[CrossRef]

Appl. Phys. Lett. (3)

S. K. Morrison and Y. S. Kivshar, “Engineering of directional emission from photonic-crystal waveguide,” Appl. Phys. Lett. 86(8), 081110 (2005).
[CrossRef]

H. Caglayan, I. Bulu, and E. Ozbay, “Off-axis directional beaming via photonic crystal surface modes,” Appl. Phys. Lett. 92(9), 092114 (2008).
[CrossRef]

F. J. García-Vidal, L. Martín-Moreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4502 (2003).
[CrossRef]

J. Appl. Phys. (1)

Y. L. Zhang, D. Y. Zhao, C. H. Zhou, and X. Y. Jiang, “Directional light emission through a metallic nanostructure,” J. Appl. Phys. 105(11), 113124 (2009).
[CrossRef]

J. Comput. Phys. (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994).
[CrossRef]

J. Opt. Soc. Am. B (3)

J. Phys. D Appl. Phys. (1)

Z. F. Li, K. Aydin, and E. Ozbay, “Wide band width directional beaming via waveguide ports in photonic crystals,” J. Phys. D Appl. Phys. 41(15), 155115 (2008).
[CrossRef]

Opt. Commun. (1)

W. Jia, L. Y. Jiang, K. Chen, and X. Y. Li, “Design of photonic crystal power beam splitters via corrugated and gratinglike surfaces,” Opt. Commun. 283(20), 4078–4084 (2010).
[CrossRef]

Opt. Express (2)

Phys. Rev. B (4)

R. Mousse, Th. Koschny, and C. M. Soukoulis, “Excitation of surface waves in a photonic crystal with negative refraction: The role of surface termination,” Phys. Rev. B 74(11), 115111 (2006).
[CrossRef]

B. Wang, W. Dai, A. Fang, L. Zhang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Surface waves in photonic crystal slabs,” Phys. Rev. B 74(19), 195104 (2006).
[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(12), 121402 (2004).
[CrossRef]

R. Moussa, B. Wang, G. Tuttle, Th. Koschny, and C. M. Soukoulis, “Effect of beaming and enhanced transmission in photonic crystals,” Phys. Rev. B 76(23), 235417 (2007).
[CrossRef]

Phys. Rev. B Condens. Matter (1)

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, “Electromagnetic Bloch waves at the surface of a photonic crystal,” Phys. Rev. B Condens. Matter 44(19), 10961–10964 (1991).
[CrossRef] [PubMed]

Science (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 297(5582), 820–822 (2002).
[CrossRef] [PubMed]

Other (4)

A. Degiron and T. W. Ebbesen, “Analysis of the transmission process through single apertures surrounded by periodic corrugations,” Opt. Express12, 3694–3700 (2004). http://www.opticsinfobase.org/oe/abstract. cfm?URI=oe-12-16-3694 .
[CrossRef] [PubMed]

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, Berlin, 1988)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic crystal: Molding the flow of light (Princeton University Press, Princeton, 1995).

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

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Figures (14)

Fig. 1
Fig. 1

Schematic diagram of the photonic crystal waveguide structures, output surface cylinders with rs = 0.09a (denoted by red dots).

Fig. 2
Fig. 2

Simulated spatial distributions of |Ey|2 for the structure illustrated in Fig. 1. The frequency and width of the incident beam are ω = 0.408 (2πc/a) and a, respectively. (a) Unchanged surface (no surface modes allowed), (b) surface cylinders with rs = 0.09a.

Fig. 3
Fig. 3

Schematic drawing of the photonic crystal waveguide structures under study. (a) Structure with Ns modified surface cylinders rs = 0.09a (denoted by red dots) but without point defect. A part of surface cylinders (denoted by blue dots) are not modified, (b) structure with Ns modified surface cylinders rs = 0.09a (denoted by red dots) and two point defect at position (xs , 24.5), (-xs , 24.5), L = 2xs .

Fig. 4
Fig. 4

Simulated spatial distributions of |Ey|2 for the structure illustrated in Fig. 3(a). (a) Ns = 2, (b) Ns = 3, (c) Ns = 4, (d) Ns = 5.

Fig. 5
Fig. 5

Simulated spatial distributions of |Ey|2 for the structure illustrated in Fig. 3(b), (a)L = 4a (b)L = 6a (c)L = 8a (d) L = 10a.

Fig. 6
Fig. 6

Calculated angular distribution of |Ey|2 for radiation pattern plotted in Fig. 5 (along a half circle of r = 20λ). All the above results are obtained at a frequency of ω = 0.408 (2πc/a).

Fig. 7
Fig. 7

Poynting field Sz(x, z = 24.5a) along the PC-air interface for the case of L = 4a, 6a, 8a, 10a.

Fig. 8
Fig. 8

Schematic drawing of the photonic crystal waveguide structure with Ns + Nb modified surface cylinders rs = 0.09a (denoted by red dots) and two point defects at position (xs , 24.5a), (-xs , 24.5a), L = 2xs .

Fig. 9
Fig. 9

Spatial distributions of |Ey|2 for the structure illustrated in Fig. 8, (a) L = 4a, Nb = 0. (b) L = 4a, Nb = 1. (c) L = 4a, Nb = 2. (d) L = 6a, Nb = 0. (e) L = 6a, Nb = 1. (f) L = 6a, Nb = 2. (g) L = 8a, Nb = 0 (h) L = 8a, Nb = 1. (i) L = 8a, Nb = 2. (j) L = 10a, Nb = 0. (k) L = 10a, Nb = 1. (l) L = 10a, Nb = 2.

Fig. 10
Fig. 10

Calculated angular distribution of |Ey|2 for radiation pattern plotted in Fig. 9 (along a half circle of r = 20λ), (a) L = 4a. (b) L = 6a. (c) L = 8a. (d) L = 10a.

Fig. 11
Fig. 11

Poynting field Sz(x, z = 24.5a) along the PC-air interface for Nb = 0, 1, 2, (a) L = 4a. (b) L = 6a. (c) L = 8a. (d) L = 10a.

Fig. 12
Fig. 12

Schematic drawing of the photonic crystal waveguide structure with two extra point defects are introduced to the adjacent layer of output surface. These two extra point defects at position (xs -1, zs -1), here zs -1 = 23.5a, xs -1 = xs + a.

Fig. 13
Fig. 13

Spatial distributions of |Ey|2 for the structure illustrated in Fig. 12, (a) L = 4a, without A. (b) L = 4a, with A. (c) L = 6a, without A. (d) L = 6a, with A. (e) L = 8a, without A. (f) L = 8a, with A. (g) L = 10a, without A. (h) L = 10a, with A.

Fig. 14
Fig. 14

Calculated angular distribution of |Ey|2 for radiation pattern plotted in Fig. 12 (along a half circle of r = 20λ). (a) L = 4a (b) L = 6a. (c) L = 8a. (d) L = 10a.

Equations (3)

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E y ( x , y ) = i = 1 3 E y , i ( x , y )
δ i j = k a i r ( r i r j ) + Δ ϕ i j i , j = 1 , 2 , 3
Δ ϕ 12 = Δ ϕ 32 k λ f f L / 2 , and Δ ϕ 13 = 0

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