Abstract

We investigate the physical origin of energy transfer from an incident light with frequency ω to a resonant mode via a linear photonic crystal microcavity. By delicate design of the resonant structure, it is found that the energy conversion efficiency can be greatly improved near the frequency of the incident light. In this way, we can precisely control the frequency of the output light, which is very important for frequency conversion in laser emitting devices and other fields. We also study the dynamic evolvement process in the time domain, and the simulation results show good agreement with the theoretical predictions.

© 2010 Optical Society of America

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  1. H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
    [CrossRef] [PubMed]
  2. X. S. Lin, J. H. Yan, L. J. Wu, and S. Lan, “High transmission contrast for single resonator based all-optical diodes with pump-assisting,” Opt. Express 16, 20949–20954 (2008).
    [CrossRef] [PubMed]
  3. E. Weidner, S. Combrie, A. de Rossi, N. V. Q. Tran, and S. Cassette, “Nonlinear and bistable behavior of an ultrahigh-Q GaAs photonic crystal nanocavity,” Appl. Phys. Lett. 90, 101118(2007).
    [CrossRef]
  4. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
    [CrossRef] [PubMed]
  5. S. Lan, X. W. Chen, J. D. Chen, and X. S. Lin, “Dynamics of nonlinear photonic crystal atoms characterized by numerical simulations in a pump-probe scheme,” Appl. Phys. Lett. 86, 131112 (2005).
    [CrossRef]
  6. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13, 2678–2687(2005).
    [CrossRef] [PubMed]
  7. P. E. Barclay, K. Srinivasan, and O. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13, 801–820 (2005).
    [CrossRef] [PubMed]
  8. H. Oda, K. Inoue, A. Yamanaka, N. Ikeda, Y. Sugimoto, and K. Asakawa, “Light amplification by stimulated Raman scattering in AlGaAs-based photonic-crystal line-defect waveguides,” Appl. Phys. Lett. 93, 051114 (2008).
    [CrossRef]
  9. J. F. McMillan, M. Yu, D. L. Kwong, and C. W. Wong, “Observation of spontaneous Raman scattering in silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 93, 251105 (2008).
    [CrossRef]
  10. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
  11. A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech, 2000).
  12. S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, “Analysis of defect coupling in one- and two-dimensional photonic crystals,” Phys. Rev. B 65, 165208 (2002).
    [CrossRef]

2008 (3)

X. S. Lin, J. H. Yan, L. J. Wu, and S. Lan, “High transmission contrast for single resonator based all-optical diodes with pump-assisting,” Opt. Express 16, 20949–20954 (2008).
[CrossRef] [PubMed]

H. Oda, K. Inoue, A. Yamanaka, N. Ikeda, Y. Sugimoto, and K. Asakawa, “Light amplification by stimulated Raman scattering in AlGaAs-based photonic-crystal line-defect waveguides,” Appl. Phys. Lett. 93, 051114 (2008).
[CrossRef]

J. F. McMillan, M. Yu, D. L. Kwong, and C. W. Wong, “Observation of spontaneous Raman scattering in silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 93, 251105 (2008).
[CrossRef]

2007 (1)

E. Weidner, S. Combrie, A. de Rossi, N. V. Q. Tran, and S. Cassette, “Nonlinear and bistable behavior of an ultrahigh-Q GaAs photonic crystal nanocavity,” Appl. Phys. Lett. 90, 101118(2007).
[CrossRef]

2005 (3)

2004 (1)

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

2003 (1)

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[CrossRef] [PubMed]

2002 (1)

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, “Analysis of defect coupling in one- and two-dimensional photonic crystals,” Phys. Rev. B 65, 165208 (2002).
[CrossRef]

2000 (1)

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech, 2000).

1984 (1)

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

Akahane, Y.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[CrossRef] [PubMed]

Asakawa, K.

H. Oda, K. Inoue, A. Yamanaka, N. Ikeda, Y. Sugimoto, and K. Asakawa, “Light amplification by stimulated Raman scattering in AlGaAs-based photonic-crystal line-defect waveguides,” Appl. Phys. Lett. 93, 051114 (2008).
[CrossRef]

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, “Analysis of defect coupling in one- and two-dimensional photonic crystals,” Phys. Rev. B 65, 165208 (2002).
[CrossRef]

Asano, T.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[CrossRef] [PubMed]

Baek, J. H.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Barclay, P. E.

Cassette, S.

E. Weidner, S. Combrie, A. de Rossi, N. V. Q. Tran, and S. Cassette, “Nonlinear and bistable behavior of an ultrahigh-Q GaAs photonic crystal nanocavity,” Appl. Phys. Lett. 90, 101118(2007).
[CrossRef]

Chen, J. D.

S. Lan, X. W. Chen, J. D. Chen, and X. S. Lin, “Dynamics of nonlinear photonic crystal atoms characterized by numerical simulations in a pump-probe scheme,” Appl. Phys. Lett. 86, 131112 (2005).
[CrossRef]

Chen, X. W.

S. Lan, X. W. Chen, J. D. Chen, and X. S. Lin, “Dynamics of nonlinear photonic crystal atoms characterized by numerical simulations in a pump-probe scheme,” Appl. Phys. Lett. 86, 131112 (2005).
[CrossRef]

Combrie, S.

E. Weidner, S. Combrie, A. de Rossi, N. V. Q. Tran, and S. Cassette, “Nonlinear and bistable behavior of an ultrahigh-Q GaAs photonic crystal nanocavity,” Appl. Phys. Lett. 90, 101118(2007).
[CrossRef]

de Rossi, A.

E. Weidner, S. Combrie, A. de Rossi, N. V. Q. Tran, and S. Cassette, “Nonlinear and bistable behavior of an ultrahigh-Q GaAs photonic crystal nanocavity,” Appl. Phys. Lett. 90, 101118(2007).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech, 2000).

Haus, H. A.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

Ikeda, N.

H. Oda, K. Inoue, A. Yamanaka, N. Ikeda, Y. Sugimoto, and K. Asakawa, “Light amplification by stimulated Raman scattering in AlGaAs-based photonic-crystal line-defect waveguides,” Appl. Phys. Lett. 93, 051114 (2008).
[CrossRef]

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, “Analysis of defect coupling in one- and two-dimensional photonic crystals,” Phys. Rev. B 65, 165208 (2002).
[CrossRef]

Inoue, K.

H. Oda, K. Inoue, A. Yamanaka, N. Ikeda, Y. Sugimoto, and K. Asakawa, “Light amplification by stimulated Raman scattering in AlGaAs-based photonic-crystal line-defect waveguides,” Appl. Phys. Lett. 93, 051114 (2008).
[CrossRef]

Ishikawa, H.

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, “Analysis of defect coupling in one- and two-dimensional photonic crystals,” Phys. Rev. B 65, 165208 (2002).
[CrossRef]

Ju, Y. G.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Kim, S. B.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Kim, S. H.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Kira, G.

Kuramochi, E.

Kwon, S. H.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Kwong, D. L.

J. F. McMillan, M. Yu, D. L. Kwong, and C. W. Wong, “Observation of spontaneous Raman scattering in silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 93, 251105 (2008).
[CrossRef]

Lan, S.

X. S. Lin, J. H. Yan, L. J. Wu, and S. Lan, “High transmission contrast for single resonator based all-optical diodes with pump-assisting,” Opt. Express 16, 20949–20954 (2008).
[CrossRef] [PubMed]

S. Lan, X. W. Chen, J. D. Chen, and X. S. Lin, “Dynamics of nonlinear photonic crystal atoms characterized by numerical simulations in a pump-probe scheme,” Appl. Phys. Lett. 86, 131112 (2005).
[CrossRef]

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, “Analysis of defect coupling in one- and two-dimensional photonic crystals,” Phys. Rev. B 65, 165208 (2002).
[CrossRef]

Lee, Y. H.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Lin, X. S.

X. S. Lin, J. H. Yan, L. J. Wu, and S. Lan, “High transmission contrast for single resonator based all-optical diodes with pump-assisting,” Opt. Express 16, 20949–20954 (2008).
[CrossRef] [PubMed]

S. Lan, X. W. Chen, J. D. Chen, and X. S. Lin, “Dynamics of nonlinear photonic crystal atoms characterized by numerical simulations in a pump-probe scheme,” Appl. Phys. Lett. 86, 131112 (2005).
[CrossRef]

McMillan, J. F.

J. F. McMillan, M. Yu, D. L. Kwong, and C. W. Wong, “Observation of spontaneous Raman scattering in silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 93, 251105 (2008).
[CrossRef]

Mitsugi, S.

Nishikawa, S.

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, “Analysis of defect coupling in one- and two-dimensional photonic crystals,” Phys. Rev. B 65, 165208 (2002).
[CrossRef]

Noda, S.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[CrossRef] [PubMed]

Notomi, M.

Oda, H.

H. Oda, K. Inoue, A. Yamanaka, N. Ikeda, Y. Sugimoto, and K. Asakawa, “Light amplification by stimulated Raman scattering in AlGaAs-based photonic-crystal line-defect waveguides,” Appl. Phys. Lett. 93, 051114 (2008).
[CrossRef]

Painter, O.

Park, H. G.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Shinya, A.

Song, B. S.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[CrossRef] [PubMed]

Srinivasan, K.

Sugimoto, Y.

H. Oda, K. Inoue, A. Yamanaka, N. Ikeda, Y. Sugimoto, and K. Asakawa, “Light amplification by stimulated Raman scattering in AlGaAs-based photonic-crystal line-defect waveguides,” Appl. Phys. Lett. 93, 051114 (2008).
[CrossRef]

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, “Analysis of defect coupling in one- and two-dimensional photonic crystals,” Phys. Rev. B 65, 165208 (2002).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech, 2000).

Tanabe, T.

Tran, N. V. Q.

E. Weidner, S. Combrie, A. de Rossi, N. V. Q. Tran, and S. Cassette, “Nonlinear and bistable behavior of an ultrahigh-Q GaAs photonic crystal nanocavity,” Appl. Phys. Lett. 90, 101118(2007).
[CrossRef]

Weidner, E.

E. Weidner, S. Combrie, A. de Rossi, N. V. Q. Tran, and S. Cassette, “Nonlinear and bistable behavior of an ultrahigh-Q GaAs photonic crystal nanocavity,” Appl. Phys. Lett. 90, 101118(2007).
[CrossRef]

Wong, C. W.

J. F. McMillan, M. Yu, D. L. Kwong, and C. W. Wong, “Observation of spontaneous Raman scattering in silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 93, 251105 (2008).
[CrossRef]

Wu, L. J.

Yamanaka, A.

H. Oda, K. Inoue, A. Yamanaka, N. Ikeda, Y. Sugimoto, and K. Asakawa, “Light amplification by stimulated Raman scattering in AlGaAs-based photonic-crystal line-defect waveguides,” Appl. Phys. Lett. 93, 051114 (2008).
[CrossRef]

Yan, J. H.

Yang, J. K.

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Yu, M.

J. F. McMillan, M. Yu, D. L. Kwong, and C. W. Wong, “Observation of spontaneous Raman scattering in silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 93, 251105 (2008).
[CrossRef]

Appl. Phys. Lett. (4)

E. Weidner, S. Combrie, A. de Rossi, N. V. Q. Tran, and S. Cassette, “Nonlinear and bistable behavior of an ultrahigh-Q GaAs photonic crystal nanocavity,” Appl. Phys. Lett. 90, 101118(2007).
[CrossRef]

H. Oda, K. Inoue, A. Yamanaka, N. Ikeda, Y. Sugimoto, and K. Asakawa, “Light amplification by stimulated Raman scattering in AlGaAs-based photonic-crystal line-defect waveguides,” Appl. Phys. Lett. 93, 051114 (2008).
[CrossRef]

J. F. McMillan, M. Yu, D. L. Kwong, and C. W. Wong, “Observation of spontaneous Raman scattering in silicon slow-light photonic crystal waveguides,” Appl. Phys. Lett. 93, 251105 (2008).
[CrossRef]

S. Lan, X. W. Chen, J. D. Chen, and X. S. Lin, “Dynamics of nonlinear photonic crystal atoms characterized by numerical simulations in a pump-probe scheme,” Appl. Phys. Lett. 86, 131112 (2005).
[CrossRef]

Nature (1)

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[CrossRef] [PubMed]

Opt. Express (3)

Phys. Rev. B (1)

S. Lan, S. Nishikawa, Y. Sugimoto, N. Ikeda, K. Asakawa, and H. Ishikawa, “Analysis of defect coupling in one- and two-dimensional photonic crystals,” Phys. Rev. B 65, 165208 (2002).
[CrossRef]

Science (1)

H. G. Park, S. H. Kim, S. H. Kwon, Y. G. Ju, J. K. Yang, J. H. Baek, S. B. Kim, and Y. H. Lee, “Electrically driven single-cell photonic crystal laser,” Science 305, 1444–1447 (2004).
[CrossRef] [PubMed]

Other (2)

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech, 2000).

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Figures (2)

Fig. 1
Fig. 1

(a) Schematic PC structure with a linear microcavity coupled to two symmetric W3 defect WGs. (b) Frequency spectra of the transmitted light. One peak is located at ω = 0.3381 ( 2 π c / a ) , and another little peak is located at ω 0 = 0.3281 ( 2 π c / a ) , where a is the lattice constant.

Fig. 2
Fig. 2

(a) Schematic PC structure with two “caps” added to each side of the resonant cavity, respectively. The resonant mode is excited by a current source within the cavity. (b) Frequency spectra of the transmitted light. The peak intensity of ω 0 = 0.3281 ( 2 π c / a ) is greatly strengthened. (c) Corresponding dynamic evolvement process in time domain. The long oscillation period is Δ T 1 = 2778 ( a / c ) , and the tiny oscillation period is Δ T 2 = 100 ( a / c ) .

Equations (4)

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{ d A d t = ( i ω 0 γ ) A + 2 γ 1 s in s out = 2 γ 2 A ,
A = 2 γ 1 | s in | i ( ω ω 0 ) + γ ( e i ω t e γ t · e i ω 0 t ) ,
S out = 4 γ 1 γ 2 | s in | i ( ω ω 0 ) + γ ( e i ω t e γ t · e i ω 0 t ) .
T = | s out | 2 | s in | 2 = 4 γ 1 γ 2 ( ω ω 0 ) 2 + γ 2 [ e 2 γ t 2 e γ t cos ( ω ω 0 ) t + 1 ] .

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