Abstract

We study the forward-dominant output of second-harmonic generation (SHG) in single-defect and dual-localized photonic crystals within the saturation limit. We propose that an asymmetric structure can be used to improve the performance of the enhanced SHG. We get two empirical expressions for the total saturation SHG efficiency and the forward factor and provide a reasonable explanation. The theoretical results predict a nearly 100% conversion efficiency and a nearly 100% forward output. Our work is very valuable for designing nonlinear photonic devices. As a test, a practical asymmetrical structure is presented.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2004

M. Soljacic and J. D. Joannopoulos, Nat. Mater. 3, 211 (2004).
[CrossRef] [PubMed]

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. R. Qiu, J. H. Si, and K. Hirao, Phys. Rev. B 70, 245109 (2004).
[CrossRef]

2001

2000

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, Science 289, 604 (2000).
[CrossRef] [PubMed]

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, Nature 407, 983 (2000).
[CrossRef] [PubMed]

1998

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, Nature 391, 463 (1998).
[CrossRef]

1997

1987

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Alleman, A.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, Nature 407, 983 (2000).
[CrossRef] [PubMed]

Berger, V.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, Nature 391, 463 (1998).
[CrossRef]

V. Berger, J. Opt. Soc. Am. B 14, 1351 (1997).
[CrossRef]

Bravetti, P.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, Nature 391, 463 (1998).
[CrossRef]

Cheng, C.

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. R. Qiu, J. H. Si, and K. Hirao, Phys. Rev. B 70, 245109 (2004).
[CrossRef]

Chow, E.

E. Chow, S. Y. Lin, J. R. Wendt, S. G. Johnson, and J. D. Joannopoulos, Opt. Lett. 26, 286 (2001).
[CrossRef]

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, Nature 407, 983 (2000).
[CrossRef] [PubMed]

Chutinan, A.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, Science 289, 604 (2000).
[CrossRef] [PubMed]

Fiore, A.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, Nature 391, 463 (1998).
[CrossRef]

Hirao, K.

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. R. Qiu, J. H. Si, and K. Hirao, Phys. Rev. B 70, 245109 (2004).
[CrossRef]

Hou, H.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, Nature 407, 983 (2000).
[CrossRef] [PubMed]

Jiang, Z. M.

Joannopoulos, J. D.

M. Soljacic and J. D. Joannopoulos, Nat. Mater. 3, 211 (2004).
[CrossRef] [PubMed]

E. Chow, S. Y. Lin, J. R. Wendt, S. G. Johnson, and J. D. Joannopoulos, Opt. Lett. 26, 286 (2001).
[CrossRef]

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, Nature 407, 983 (2000).
[CrossRef] [PubMed]

John, S.

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Johnson, S. G.

E. Chow, S. Y. Lin, J. R. Wendt, S. G. Johnson, and J. D. Joannopoulos, Opt. Lett. 26, 286 (2001).
[CrossRef]

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, Nature 407, 983 (2000).
[CrossRef] [PubMed]

Li, R.

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. R. Qiu, J. H. Si, and K. Hirao, Phys. Rev. B 70, 245109 (2004).
[CrossRef]

Lin, S. Y.

E. Chow, S. Y. Lin, J. R. Wendt, S. G. Johnson, and J. D. Joannopoulos, Opt. Lett. 26, 286 (2001).
[CrossRef]

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, Nature 407, 983 (2000).
[CrossRef] [PubMed]

Nagle, J.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, Nature 391, 463 (1998).
[CrossRef]

Noda, S.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, Science 289, 604 (2000).
[CrossRef] [PubMed]

Qiu, J. R.

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. R. Qiu, J. H. Si, and K. Hirao, Phys. Rev. B 70, 245109 (2004).
[CrossRef]

Ren, F. F.

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. R. Qiu, J. H. Si, and K. Hirao, Phys. Rev. B 70, 245109 (2004).
[CrossRef]

Rosencher, E.

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, Nature 391, 463 (1998).
[CrossRef]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

Shi, B.

Si, J. H.

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. R. Qiu, J. H. Si, and K. Hirao, Phys. Rev. B 70, 245109 (2004).
[CrossRef]

Soljacic, M.

M. Soljacic and J. D. Joannopoulos, Nat. Mater. 3, 211 (2004).
[CrossRef] [PubMed]

Tomoda, K.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, Science 289, 604 (2000).
[CrossRef] [PubMed]

Vawter, G. A.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, Nature 407, 983 (2000).
[CrossRef] [PubMed]

Villeneuve, P. R.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, Nature 407, 983 (2000).
[CrossRef] [PubMed]

Wang, H. T.

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. R. Qiu, J. H. Si, and K. Hirao, Phys. Rev. B 70, 245109 (2004).
[CrossRef]

Wang, X.

Wendt, J. R.

E. Chow, S. Y. Lin, J. R. Wendt, S. G. Johnson, and J. D. Joannopoulos, Opt. Lett. 26, 286 (2001).
[CrossRef]

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, Nature 407, 983 (2000).
[CrossRef] [PubMed]

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Yamamoto, N.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, Science 289, 604 (2000).
[CrossRef] [PubMed]

Zubrzycki, W.

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, Nature 407, 983 (2000).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B

Nat. Mater.

M. Soljacic and J. D. Joannopoulos, Nat. Mater. 3, 211 (2004).
[CrossRef] [PubMed]

Nature

A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, Nature 391, 463 (1998).
[CrossRef]

E. Chow, S. Y. Lin, S. G. Johnson, P. R. Villeneuve, J. D. Joannopoulos, J. R. Wendt, G. A. Vawter, W. Zubrzycki, H. Hou, and A. Alleman, Nature 407, 983 (2000).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. B

F. F. Ren, R. Li, C. Cheng, H. T. Wang, J. R. Qiu, J. H. Si, and K. Hirao, Phys. Rev. B 70, 245109 (2004).
[CrossRef]

Phys. Rev. Lett.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

S. John, Phys. Rev. Lett. 58, 2486 (1987).
[CrossRef] [PubMed]

Science

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, Science 289, 604 (2000).
[CrossRef] [PubMed]

Other

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

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Figures (3)

Fig. 1
Fig. 1

Dependence of η on r L , R ω : (a) η versus r L ω for r R ω = 0.90 , 0.94, 0.98; (b) η versus r R ω for r L ω = 0.90 , 0.94, 0.98. Symbols indicate the simulated results. Curves are the results given by Eq. (1). The dashed-dotted line is a visual guide.

Fig. 2
Fig. 2

Dependence of Q on r L , R 2 ω : (a) Q versus r L 2 ω , r R 2 ω = 0.90 , 0.94, 0.98; (b) Q versus r R 2 ω at different values of r L ω = 0.90 , 0.94, 0.98. Symbols indicate the simulated results. Curves are the results given by Eq. (2). The dashed-dotted line is a visual guide.

Fig. 3
Fig. 3

Spatial distributions of normalized amplitudes of (a) FW and (b) SH inside a PhC operating at the saturation limit.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

η = 1 ( r L ω ) 2 [ 1 ( r L ω ) 2 ] + [ 1 ( r R ω ) 2 ] = T L ω T L ω + T R ω ,
Q = 1 ( r R 2 ω ) 2 [ 1 ( r L 2 ω ) 2 ] + [ 1 ( r R 2 ω ) 2 ] = T R 2 ω T L 2 ω + T R 2 ω .

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