Abstract

Using a three-dimensional fully vectorial nonlinear time-domain analysis, we numerically investigate generation of terahertz radiation by pumping a photonic crystal microcavity out of resonance. High quality factors and a quadratic susceptibility lead to few-cycle terahertz pulses via optical rectification. Material dispersion as well as linear and nonlinear anisotropy is fully accounted for.

© 2005 Optical Society of America

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  1. J. Darmo, R. Bratschitsch, T. Müller, R. Kersting, G. Strasser, and K. Unterrainer, Phys. Med. Biol. 47, 3691 (2002).
    [CrossRef] [PubMed]
  2. A. G. Davies, E. H. Linfield, and M. B. Johnston, Phys. Med. Biol. 47, 3679 (2002).
    [CrossRef] [PubMed]
  3. Y. J. Ding and J. B. Khurgin, Opt. Commun. 148, 105 (1998).
    [CrossRef]
  4. Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, Appl. Phys. Lett. 76, 2505 (2000).
    [CrossRef]
  5. W. Shi, Y. J. Ding, and P. G. Schunemann, Opt. Commun. 233, 183 (2004).
    [CrossRef]
  6. J. Darmo, T. Müller, G. Strasser, K. Unterrainer, and G. Tempea, Electron. Lett. 39, 460 (2003).
    [CrossRef]
  7. K. Othaka, Phys. Rev. B 19, 5057 (1979).
    [CrossRef]
  8. S. John, Phys. Rev. Lett. 58, 2486 (1987).
    [CrossRef] [PubMed]
  9. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
    [CrossRef] [PubMed]
  10. H. Y. Ryu, M. Notomi, and Y. H. Lee, Appl. Phys. Lett. 83, 4294 (2003).
    [CrossRef]
  11. Z. Zhang and M. Qiu, Opt. Express 12, 3988 (2004), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
  12. R. M. De La Rue, M. R. S. Taylor, K. Li, M. Sasaki, and M. Izutsu, in Terahertz Electronics Proceedings (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), pp. 106–109.
  13. Y. Lu, M. Xiao, and G. J. Salamo, J. Photochem. 38, 481 (2002).
  14. M. Tani, P. Gu, K. Sakai, M. Suenaga, H. Kondo, H. Kitahara, and M. W. Takeda, in the 4th Pacific Rim Conference on Lasers and Electro-Optics, 2001, CLEO/Pacific Rim 2001 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2001), Vol. 1, pp. 196–198.
    [CrossRef]
  15. M. A. Zudov, J. Kono, A. P. Mitchell, and A. H. Chin, Phys. Rev. B 64, R121204 (2001).
    [CrossRef]
  16. A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, Oxford, 1997).
  17. A. Di Falco, C. Conti, and G. Assanto, Appl. Phys. B 79, 9 (2004).
    [CrossRef]
  18. R. W. Ziolkowski and E. Heyman, Phys. Rev. E 64, 56625 (2001).
    [CrossRef]
  19. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).
  20. C. M. Mann, in Terahertz Electronics Proceedings (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), pp. 46–49.

2004

W. Shi, Y. J. Ding, and P. G. Schunemann, Opt. Commun. 233, 183 (2004).
[CrossRef]

Z. Zhang and M. Qiu, Opt. Express 12, 3988 (2004), http://www.opticsexpress.org.
[CrossRef] [PubMed]

A. Di Falco, C. Conti, and G. Assanto, Appl. Phys. B 79, 9 (2004).
[CrossRef]

2003

J. Darmo, T. Müller, G. Strasser, K. Unterrainer, and G. Tempea, Electron. Lett. 39, 460 (2003).
[CrossRef]

H. Y. Ryu, M. Notomi, and Y. H. Lee, Appl. Phys. Lett. 83, 4294 (2003).
[CrossRef]

2002

J. Darmo, R. Bratschitsch, T. Müller, R. Kersting, G. Strasser, and K. Unterrainer, Phys. Med. Biol. 47, 3691 (2002).
[CrossRef] [PubMed]

A. G. Davies, E. H. Linfield, and M. B. Johnston, Phys. Med. Biol. 47, 3679 (2002).
[CrossRef] [PubMed]

Y. Lu, M. Xiao, and G. J. Salamo, J. Photochem. 38, 481 (2002).

2001

M. A. Zudov, J. Kono, A. P. Mitchell, and A. H. Chin, Phys. Rev. B 64, R121204 (2001).
[CrossRef]

R. W. Ziolkowski and E. Heyman, Phys. Rev. E 64, 56625 (2001).
[CrossRef]

2000

Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, Appl. Phys. Lett. 76, 2505 (2000).
[CrossRef]

1998

Y. J. Ding and J. B. Khurgin, Opt. Commun. 148, 105 (1998).
[CrossRef]

1987

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

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

1979

K. Othaka, Phys. Rev. B 19, 5057 (1979).
[CrossRef]

Assanto, G.

A. Di Falco, C. Conti, and G. Assanto, Appl. Phys. B 79, 9 (2004).
[CrossRef]

Bratschitsch, R.

J. Darmo, R. Bratschitsch, T. Müller, R. Kersting, G. Strasser, and K. Unterrainer, Phys. Med. Biol. 47, 3691 (2002).
[CrossRef] [PubMed]

Chin, A. H.

M. A. Zudov, J. Kono, A. P. Mitchell, and A. H. Chin, Phys. Rev. B 64, R121204 (2001).
[CrossRef]

Conti, C.

A. Di Falco, C. Conti, and G. Assanto, Appl. Phys. B 79, 9 (2004).
[CrossRef]

Darmo, J.

J. Darmo, T. Müller, G. Strasser, K. Unterrainer, and G. Tempea, Electron. Lett. 39, 460 (2003).
[CrossRef]

J. Darmo, R. Bratschitsch, T. Müller, R. Kersting, G. Strasser, and K. Unterrainer, Phys. Med. Biol. 47, 3691 (2002).
[CrossRef] [PubMed]

Davies, A. G.

A. G. Davies, E. H. Linfield, and M. B. Johnston, Phys. Med. Biol. 47, 3679 (2002).
[CrossRef] [PubMed]

De La Rue, R. M.

R. M. De La Rue, M. R. S. Taylor, K. Li, M. Sasaki, and M. Izutsu, in Terahertz Electronics Proceedings (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), pp. 106–109.

Di Falco, A.

A. Di Falco, C. Conti, and G. Assanto, Appl. Phys. B 79, 9 (2004).
[CrossRef]

Ding, Y. J.

W. Shi, Y. J. Ding, and P. G. Schunemann, Opt. Commun. 233, 183 (2004).
[CrossRef]

Y. J. Ding and J. B. Khurgin, Opt. Commun. 148, 105 (1998).
[CrossRef]

Galvanauskas, A.

Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, Appl. Phys. Lett. 76, 2505 (2000).
[CrossRef]

Gu, P.

M. Tani, P. Gu, K. Sakai, M. Suenaga, H. Kondo, H. Kitahara, and M. W. Takeda, in the 4th Pacific Rim Conference on Lasers and Electro-Optics, 2001, CLEO/Pacific Rim 2001 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2001), Vol. 1, pp. 196–198.
[CrossRef]

Haus, H. A.

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

Heyman, E.

R. W. Ziolkowski and E. Heyman, Phys. Rev. E 64, 56625 (2001).
[CrossRef]

Izutsu, M.

R. M. De La Rue, M. R. S. Taylor, K. Li, M. Sasaki, and M. Izutsu, in Terahertz Electronics Proceedings (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), pp. 106–109.

John, S.

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

Johnston, M. B.

A. G. Davies, E. H. Linfield, and M. B. Johnston, Phys. Med. Biol. 47, 3679 (2002).
[CrossRef] [PubMed]

Kersting, R.

J. Darmo, R. Bratschitsch, T. Müller, R. Kersting, G. Strasser, and K. Unterrainer, Phys. Med. Biol. 47, 3691 (2002).
[CrossRef] [PubMed]

Khurgin, J. B.

Y. J. Ding and J. B. Khurgin, Opt. Commun. 148, 105 (1998).
[CrossRef]

Kitahara, H.

M. Tani, P. Gu, K. Sakai, M. Suenaga, H. Kondo, H. Kitahara, and M. W. Takeda, in the 4th Pacific Rim Conference on Lasers and Electro-Optics, 2001, CLEO/Pacific Rim 2001 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2001), Vol. 1, pp. 196–198.
[CrossRef]

Kondo, H.

M. Tani, P. Gu, K. Sakai, M. Suenaga, H. Kondo, H. Kitahara, and M. W. Takeda, in the 4th Pacific Rim Conference on Lasers and Electro-Optics, 2001, CLEO/Pacific Rim 2001 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2001), Vol. 1, pp. 196–198.
[CrossRef]

Kono, J.

M. A. Zudov, J. Kono, A. P. Mitchell, and A. H. Chin, Phys. Rev. B 64, R121204 (2001).
[CrossRef]

Lee, Y. H.

H. Y. Ryu, M. Notomi, and Y. H. Lee, Appl. Phys. Lett. 83, 4294 (2003).
[CrossRef]

Lee, Y. S.

Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, Appl. Phys. Lett. 76, 2505 (2000).
[CrossRef]

Li, K.

R. M. De La Rue, M. R. S. Taylor, K. Li, M. Sasaki, and M. Izutsu, in Terahertz Electronics Proceedings (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), pp. 106–109.

Linfield, E. H.

A. G. Davies, E. H. Linfield, and M. B. Johnston, Phys. Med. Biol. 47, 3679 (2002).
[CrossRef] [PubMed]

Lu, Y.

Y. Lu, M. Xiao, and G. J. Salamo, J. Photochem. 38, 481 (2002).

Mann, C. M.

C. M. Mann, in Terahertz Electronics Proceedings (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), pp. 46–49.

Meade, T.

Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, Appl. Phys. Lett. 76, 2505 (2000).
[CrossRef]

Mitchell, A. P.

M. A. Zudov, J. Kono, A. P. Mitchell, and A. H. Chin, Phys. Rev. B 64, R121204 (2001).
[CrossRef]

Müller, T.

J. Darmo, T. Müller, G. Strasser, K. Unterrainer, and G. Tempea, Electron. Lett. 39, 460 (2003).
[CrossRef]

J. Darmo, R. Bratschitsch, T. Müller, R. Kersting, G. Strasser, and K. Unterrainer, Phys. Med. Biol. 47, 3691 (2002).
[CrossRef] [PubMed]

Norris, T. B.

Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, Appl. Phys. Lett. 76, 2505 (2000).
[CrossRef]

Notomi, M.

H. Y. Ryu, M. Notomi, and Y. H. Lee, Appl. Phys. Lett. 83, 4294 (2003).
[CrossRef]

Othaka, K.

K. Othaka, Phys. Rev. B 19, 5057 (1979).
[CrossRef]

Perlin, V.

Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, Appl. Phys. Lett. 76, 2505 (2000).
[CrossRef]

Qiu, M.

Ryu, H. Y.

H. Y. Ryu, M. Notomi, and Y. H. Lee, Appl. Phys. Lett. 83, 4294 (2003).
[CrossRef]

Sakai, K.

M. Tani, P. Gu, K. Sakai, M. Suenaga, H. Kondo, H. Kitahara, and M. W. Takeda, in the 4th Pacific Rim Conference on Lasers and Electro-Optics, 2001, CLEO/Pacific Rim 2001 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2001), Vol. 1, pp. 196–198.
[CrossRef]

Salamo, G. J.

Y. Lu, M. Xiao, and G. J. Salamo, J. Photochem. 38, 481 (2002).

Sasaki, M.

R. M. De La Rue, M. R. S. Taylor, K. Li, M. Sasaki, and M. Izutsu, in Terahertz Electronics Proceedings (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), pp. 106–109.

Schunemann, P. G.

W. Shi, Y. J. Ding, and P. G. Schunemann, Opt. Commun. 233, 183 (2004).
[CrossRef]

Shi, W.

W. Shi, Y. J. Ding, and P. G. Schunemann, Opt. Commun. 233, 183 (2004).
[CrossRef]

Strasser, G.

J. Darmo, T. Müller, G. Strasser, K. Unterrainer, and G. Tempea, Electron. Lett. 39, 460 (2003).
[CrossRef]

J. Darmo, R. Bratschitsch, T. Müller, R. Kersting, G. Strasser, and K. Unterrainer, Phys. Med. Biol. 47, 3691 (2002).
[CrossRef] [PubMed]

Suenaga, M.

M. Tani, P. Gu, K. Sakai, M. Suenaga, H. Kondo, H. Kitahara, and M. W. Takeda, in the 4th Pacific Rim Conference on Lasers and Electro-Optics, 2001, CLEO/Pacific Rim 2001 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2001), Vol. 1, pp. 196–198.
[CrossRef]

Takeda, M. W.

M. Tani, P. Gu, K. Sakai, M. Suenaga, H. Kondo, H. Kitahara, and M. W. Takeda, in the 4th Pacific Rim Conference on Lasers and Electro-Optics, 2001, CLEO/Pacific Rim 2001 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2001), Vol. 1, pp. 196–198.
[CrossRef]

Tani, M.

M. Tani, P. Gu, K. Sakai, M. Suenaga, H. Kondo, H. Kitahara, and M. W. Takeda, in the 4th Pacific Rim Conference on Lasers and Electro-Optics, 2001, CLEO/Pacific Rim 2001 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2001), Vol. 1, pp. 196–198.
[CrossRef]

Taylor, M. R. S.

R. M. De La Rue, M. R. S. Taylor, K. Li, M. Sasaki, and M. Izutsu, in Terahertz Electronics Proceedings (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), pp. 106–109.

Tempea, G.

J. Darmo, T. Müller, G. Strasser, K. Unterrainer, and G. Tempea, Electron. Lett. 39, 460 (2003).
[CrossRef]

Unterrainer, K.

J. Darmo, T. Müller, G. Strasser, K. Unterrainer, and G. Tempea, Electron. Lett. 39, 460 (2003).
[CrossRef]

J. Darmo, R. Bratschitsch, T. Müller, R. Kersting, G. Strasser, and K. Unterrainer, Phys. Med. Biol. 47, 3691 (2002).
[CrossRef] [PubMed]

Winful, H.

Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, Appl. Phys. Lett. 76, 2505 (2000).
[CrossRef]

Xiao, M.

Y. Lu, M. Xiao, and G. J. Salamo, J. Photochem. 38, 481 (2002).

Yablonovitch, E.

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

Yariv, A.

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, Oxford, 1997).

Zhang, Z.

Ziolkowski, R. W.

R. W. Ziolkowski and E. Heyman, Phys. Rev. E 64, 56625 (2001).
[CrossRef]

Zudov, M. A.

M. A. Zudov, J. Kono, A. P. Mitchell, and A. H. Chin, Phys. Rev. B 64, R121204 (2001).
[CrossRef]

Appl. Phys. B

A. Di Falco, C. Conti, and G. Assanto, Appl. Phys. B 79, 9 (2004).
[CrossRef]

Appl. Phys. Lett.

H. Y. Ryu, M. Notomi, and Y. H. Lee, Appl. Phys. Lett. 83, 4294 (2003).
[CrossRef]

Y. S. Lee, T. Meade, V. Perlin, H. Winful, T. B. Norris, and A. Galvanauskas, Appl. Phys. Lett. 76, 2505 (2000).
[CrossRef]

Electron. Lett.

J. Darmo, T. Müller, G. Strasser, K. Unterrainer, and G. Tempea, Electron. Lett. 39, 460 (2003).
[CrossRef]

J. Photochem.

Y. Lu, M. Xiao, and G. J. Salamo, J. Photochem. 38, 481 (2002).

Opt. Commun.

W. Shi, Y. J. Ding, and P. G. Schunemann, Opt. Commun. 233, 183 (2004).
[CrossRef]

Y. J. Ding and J. B. Khurgin, Opt. Commun. 148, 105 (1998).
[CrossRef]

Opt. Express

Phys. Med. Biol.

J. Darmo, R. Bratschitsch, T. Müller, R. Kersting, G. Strasser, and K. Unterrainer, Phys. Med. Biol. 47, 3691 (2002).
[CrossRef] [PubMed]

A. G. Davies, E. H. Linfield, and M. B. Johnston, Phys. Med. Biol. 47, 3679 (2002).
[CrossRef] [PubMed]

Phys. Rev. B

K. Othaka, Phys. Rev. B 19, 5057 (1979).
[CrossRef]

M. A. Zudov, J. Kono, A. P. Mitchell, and A. H. Chin, Phys. Rev. B 64, R121204 (2001).
[CrossRef]

Phys. Rev. E

R. W. Ziolkowski and E. Heyman, Phys. Rev. E 64, 56625 (2001).
[CrossRef]

Phys. Rev. Lett.

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

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

Other

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

C. M. Mann, in Terahertz Electronics Proceedings (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), pp. 46–49.

R. M. De La Rue, M. R. S. Taylor, K. Li, M. Sasaki, and M. Izutsu, in Terahertz Electronics Proceedings (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1998), pp. 106–109.

M. Tani, P. Gu, K. Sakai, M. Suenaga, H. Kondo, H. Kitahara, and M. W. Takeda, in the 4th Pacific Rim Conference on Lasers and Electro-Optics, 2001, CLEO/Pacific Rim 2001 (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2001), Vol. 1, pp. 196–198.
[CrossRef]

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, Oxford, 1997).

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Figures (4)

Fig. 1
Fig. 1

Spectrum of the electric field (y component) probed inside the cavity. The arrow indicates the out-of-resonance input wavelength. Inset, device geometry.

Fig. 2
Fig. 2

Electric field evolution of the signal inside the cavity when pumped by a steplike excitation at λ = 1.462 μ m and λ = 1.467 μ m , corresponding to Δ λ = 15 nm and Δ λ = 20 nm , respectively.

Fig. 3
Fig. 3

THz generated power at λ = 1.462 μ m (squares) and λ = 1.467 μ m (diamonds) versus input power.

Fig. 4
Fig. 4

Two m n m pulses at λ = 1.462 μ m (top) giving rise to two THz pulses after filtering (bottom).

Equations (4)

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

× E = μ 0 H t , × H = ϵ 0 E t + P t ,
2 P t 2 + 2 γ 0 P t + ω R 2 P + D ͇ : P P = ϵ 0 ( ϵ s 1 ) ω ̂ R 2 E .
a ( t ) = 2 τ e s j ( ω ω 0 ) + 1 τ { exp ( j ω t ) exp [ ( j ω 0 1 ) τ t ] } .
P THz j = χ j k l f k f l * Q o ω 0 P input τ o τ e ( 1 + 2 τ o τ e ) 2 + δ 2 τ o 2 .

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