Abstract

Optically controlled one-dimensional photonic crystal structures for the THz range are studied both theoretically and experimentally. A GaAs:Cr layer constitutes a defect in the photonic crystals studied; its photoexcitation by 800 nm optical femtosecond pulses leads to the modulation of the THz beam. Since the THz field can be localized in the photoexcited layer of the photonic crystal, the interaction between photocarriers and THz light is strengthened and yields an appreciable modulation of the THz output beam even for low optical pump fluences. Optimum resonant structures are found, constructed and experimentally studied. The dynamical response of these elements is shown to be controlled by the lifetime of THz photons in the resonator and by the free carrier lifetime. The time response of the structures studied is shorter than 330 ps.

© 2007 Optical Society of America

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References

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  1. B. Ferguson and X.-C. Zhang, "Materials for terahertz science and technology," Nature materials 1, 26 (2002).
    [CrossRef]
  2. M. Koch, "Terahertz Technology: A land to be discovered," Opt. Photonics News 18, (2007).
    [CrossRef]
  3. A. Hirata, T. Kosugi, H. Takahashi, R. Yamaguchi, F. Nakajima, T. Furuta and H. Ito, "120-GHz-band millimeterwave photonic wireless link for 10-Gb/s data transmission," IEEE Transactions Microwave Theory Tech. 54, 1937 (2006)
    [CrossRef]
  4. P. Kužel and F. Kadlec, "Tunable structures and modulators for the THz light," Comptes Rendus de l’Académie des Sciences - Physique, (2007), in press.
  5. J. Bae, H. Mazaki, T. Fujii, and K. Mizuno, "An optically controlled modulator using a metal strip grating on a silicon plate for millimeter and sub-millimeter wavelengths," IEEE Microwave Theory and Techniques Symposium 3, 1239 (1996).
  6. T. Nozokido, H. Minamide, and K. Mizuno, "Modulation of sub-millimeter wave radiation by laser-produced free carriers in semiconductors," Electron. Commun. Jpn. II 80, 1 (1997).
    [CrossRef]
  7. S. Lee, Y. Kuga, and R. A. Mullen, "Optically tunable millimeter-wave attenuator based on layered structures," Microwave Opt. Technol. Lett. 27, 9 (2000).
    [CrossRef]
  8. S. Biber, D. Schneiderbanger, and L.-P. Schmidt, "Design of a controllable attenuator with high dynamic range for THz-frequencies based on optically stimulated free carriers in high-resistivity silicon," Frequenz 59, 141 (2005).
  9. L. Fekete, J. Y. Hlinka, F. Kadlec, P. Kužel, and P. Mounaix, "Active optical control of the terahertz reflectivity," Opt. Lett. 30, 1992 (2005).
    [CrossRef] [PubMed]
  10. L. Fekete, F. Kadlec, P. Kužel, and H. Němec, "Ultrafast opto-terahertz photonic crystal modulator," Opt. Lett. 32, 680 (2007).
    [CrossRef]
  11. H.-T. Chen, W. J. Padilla, J. M. O. Zide, S. R. Bank, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Ultrafast optical switching of terahertz metamaterials fabricated on ErAs/GaAs nanoisland superlattices," Opt. Lett. 32,1620 (2007).
    [CrossRef] [PubMed]
  12. C. Kadow, S. B. Fleischer, J. P. Ibbetwon, J. E. Bowers, A. C. G. J. Dong, and C. J. Palmstrom, "Self-assembled ErAs islands in GaAs: Growth and subpicosecond carrier dynamics," Appl. Phys. Lett. 75, 3548 (1999).
    [CrossRef]
  13. H. Nemec, L. Duvillaret, F. Quemeneur, and P. Kuzel, "Defect modes due to twinning in one-dimensional photonic crystals," J. Opt. Soc. Am. B 21, 548 (2004).
    [CrossRef]
  14. F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics, 2nd ed. (Prentice Hall, Englewood Cliffs, 1993).
  15. M. Born and E. Wolf, Principles of Optics, 7th ed., (University Press, Cambridge, 2003).
  16. H. Němec, F. Kadlec, and P. Kužel, "Methodology of an optical pump-terahertz probe experiment: An analytical frequency-domain approach," J. Chem. Phys. 117, 8454 (2002).
    [CrossRef]
  17. P. Kužel, F. Kadlec, and H. Němec, "Propagation of terahertz pulses in photoexcited media: analytical theory for layered systems," J. Chem. Phys. 127, (2007), in press.
    [PubMed]
  18. H. Němec, F. Kadlec, S. Surendran, P. Kužel, and P. Jungwirth, "Ultrafast far-infrared dynamics probed by terahertz pulses: a frequency domain approach. I. Model systems," J. Chem. Phys. 122, 104503 (2005).
    [CrossRef] [PubMed]
  19. H. Němec, F. Kadlec, C. Kadlec, P. Kužel, and P. Jungwirth, "Ultrafast far-infrared dynamics probed by terahertz pulses: a frequency domain approach. II. Applications," J. Chem. Phys. 122, 104504 (2005).
    [CrossRef] [PubMed]

2007 (4)

2006 (1)

A. Hirata, T. Kosugi, H. Takahashi, R. Yamaguchi, F. Nakajima, T. Furuta and H. Ito, "120-GHz-band millimeterwave photonic wireless link for 10-Gb/s data transmission," IEEE Transactions Microwave Theory Tech. 54, 1937 (2006)
[CrossRef]

2005 (4)

H. Němec, F. Kadlec, S. Surendran, P. Kužel, and P. Jungwirth, "Ultrafast far-infrared dynamics probed by terahertz pulses: a frequency domain approach. I. Model systems," J. Chem. Phys. 122, 104503 (2005).
[CrossRef] [PubMed]

H. Němec, F. Kadlec, C. Kadlec, P. Kužel, and P. Jungwirth, "Ultrafast far-infrared dynamics probed by terahertz pulses: a frequency domain approach. II. Applications," J. Chem. Phys. 122, 104504 (2005).
[CrossRef] [PubMed]

S. Biber, D. Schneiderbanger, and L.-P. Schmidt, "Design of a controllable attenuator with high dynamic range for THz-frequencies based on optically stimulated free carriers in high-resistivity silicon," Frequenz 59, 141 (2005).

L. Fekete, J. Y. Hlinka, F. Kadlec, P. Kužel, and P. Mounaix, "Active optical control of the terahertz reflectivity," Opt. Lett. 30, 1992 (2005).
[CrossRef] [PubMed]

2004 (1)

2002 (2)

H. Němec, F. Kadlec, and P. Kužel, "Methodology of an optical pump-terahertz probe experiment: An analytical frequency-domain approach," J. Chem. Phys. 117, 8454 (2002).
[CrossRef]

B. Ferguson and X.-C. Zhang, "Materials for terahertz science and technology," Nature materials 1, 26 (2002).
[CrossRef]

2000 (1)

S. Lee, Y. Kuga, and R. A. Mullen, "Optically tunable millimeter-wave attenuator based on layered structures," Microwave Opt. Technol. Lett. 27, 9 (2000).
[CrossRef]

1999 (1)

C. Kadow, S. B. Fleischer, J. P. Ibbetwon, J. E. Bowers, A. C. G. J. Dong, and C. J. Palmstrom, "Self-assembled ErAs islands in GaAs: Growth and subpicosecond carrier dynamics," Appl. Phys. Lett. 75, 3548 (1999).
[CrossRef]

1997 (1)

T. Nozokido, H. Minamide, and K. Mizuno, "Modulation of sub-millimeter wave radiation by laser-produced free carriers in semiconductors," Electron. Commun. Jpn. II 80, 1 (1997).
[CrossRef]

Averitt, R. D.

Bank, S. R.

Biber, S.

S. Biber, D. Schneiderbanger, and L.-P. Schmidt, "Design of a controllable attenuator with high dynamic range for THz-frequencies based on optically stimulated free carriers in high-resistivity silicon," Frequenz 59, 141 (2005).

Bowers, J. E.

C. Kadow, S. B. Fleischer, J. P. Ibbetwon, J. E. Bowers, A. C. G. J. Dong, and C. J. Palmstrom, "Self-assembled ErAs islands in GaAs: Growth and subpicosecond carrier dynamics," Appl. Phys. Lett. 75, 3548 (1999).
[CrossRef]

Chen, H.-T.

Dong, A. C. G. J.

C. Kadow, S. B. Fleischer, J. P. Ibbetwon, J. E. Bowers, A. C. G. J. Dong, and C. J. Palmstrom, "Self-assembled ErAs islands in GaAs: Growth and subpicosecond carrier dynamics," Appl. Phys. Lett. 75, 3548 (1999).
[CrossRef]

Duvillaret, L.

Fekete, L.

Ferguson, B.

B. Ferguson and X.-C. Zhang, "Materials for terahertz science and technology," Nature materials 1, 26 (2002).
[CrossRef]

Fleischer, S. B.

C. Kadow, S. B. Fleischer, J. P. Ibbetwon, J. E. Bowers, A. C. G. J. Dong, and C. J. Palmstrom, "Self-assembled ErAs islands in GaAs: Growth and subpicosecond carrier dynamics," Appl. Phys. Lett. 75, 3548 (1999).
[CrossRef]

Furuta, T.

A. Hirata, T. Kosugi, H. Takahashi, R. Yamaguchi, F. Nakajima, T. Furuta and H. Ito, "120-GHz-band millimeterwave photonic wireless link for 10-Gb/s data transmission," IEEE Transactions Microwave Theory Tech. 54, 1937 (2006)
[CrossRef]

Gossard, A. C.

Hirata, A.

A. Hirata, T. Kosugi, H. Takahashi, R. Yamaguchi, F. Nakajima, T. Furuta and H. Ito, "120-GHz-band millimeterwave photonic wireless link for 10-Gb/s data transmission," IEEE Transactions Microwave Theory Tech. 54, 1937 (2006)
[CrossRef]

Hlinka, J. Y.

Ibbetwon, J. P.

C. Kadow, S. B. Fleischer, J. P. Ibbetwon, J. E. Bowers, A. C. G. J. Dong, and C. J. Palmstrom, "Self-assembled ErAs islands in GaAs: Growth and subpicosecond carrier dynamics," Appl. Phys. Lett. 75, 3548 (1999).
[CrossRef]

Ito, H.

A. Hirata, T. Kosugi, H. Takahashi, R. Yamaguchi, F. Nakajima, T. Furuta and H. Ito, "120-GHz-band millimeterwave photonic wireless link for 10-Gb/s data transmission," IEEE Transactions Microwave Theory Tech. 54, 1937 (2006)
[CrossRef]

Jungwirth, P.

H. Němec, F. Kadlec, S. Surendran, P. Kužel, and P. Jungwirth, "Ultrafast far-infrared dynamics probed by terahertz pulses: a frequency domain approach. I. Model systems," J. Chem. Phys. 122, 104503 (2005).
[CrossRef] [PubMed]

H. Němec, F. Kadlec, C. Kadlec, P. Kužel, and P. Jungwirth, "Ultrafast far-infrared dynamics probed by terahertz pulses: a frequency domain approach. II. Applications," J. Chem. Phys. 122, 104504 (2005).
[CrossRef] [PubMed]

Kadlec, C.

H. Němec, F. Kadlec, C. Kadlec, P. Kužel, and P. Jungwirth, "Ultrafast far-infrared dynamics probed by terahertz pulses: a frequency domain approach. II. Applications," J. Chem. Phys. 122, 104504 (2005).
[CrossRef] [PubMed]

Kadlec, F.

P. Kužel, F. Kadlec, and H. Němec, "Propagation of terahertz pulses in photoexcited media: analytical theory for layered systems," J. Chem. Phys. 127, (2007), in press.
[PubMed]

L. Fekete, F. Kadlec, P. Kužel, and H. Němec, "Ultrafast opto-terahertz photonic crystal modulator," Opt. Lett. 32, 680 (2007).
[CrossRef]

H. Němec, F. Kadlec, S. Surendran, P. Kužel, and P. Jungwirth, "Ultrafast far-infrared dynamics probed by terahertz pulses: a frequency domain approach. I. Model systems," J. Chem. Phys. 122, 104503 (2005).
[CrossRef] [PubMed]

H. Němec, F. Kadlec, C. Kadlec, P. Kužel, and P. Jungwirth, "Ultrafast far-infrared dynamics probed by terahertz pulses: a frequency domain approach. II. Applications," J. Chem. Phys. 122, 104504 (2005).
[CrossRef] [PubMed]

L. Fekete, J. Y. Hlinka, F. Kadlec, P. Kužel, and P. Mounaix, "Active optical control of the terahertz reflectivity," Opt. Lett. 30, 1992 (2005).
[CrossRef] [PubMed]

H. Němec, F. Kadlec, and P. Kužel, "Methodology of an optical pump-terahertz probe experiment: An analytical frequency-domain approach," J. Chem. Phys. 117, 8454 (2002).
[CrossRef]

Kadow, C.

C. Kadow, S. B. Fleischer, J. P. Ibbetwon, J. E. Bowers, A. C. G. J. Dong, and C. J. Palmstrom, "Self-assembled ErAs islands in GaAs: Growth and subpicosecond carrier dynamics," Appl. Phys. Lett. 75, 3548 (1999).
[CrossRef]

Koch, M.

M. Koch, "Terahertz Technology: A land to be discovered," Opt. Photonics News 18, (2007).
[CrossRef]

Kosugi, T.

A. Hirata, T. Kosugi, H. Takahashi, R. Yamaguchi, F. Nakajima, T. Furuta and H. Ito, "120-GHz-band millimeterwave photonic wireless link for 10-Gb/s data transmission," IEEE Transactions Microwave Theory Tech. 54, 1937 (2006)
[CrossRef]

Kuga, Y.

S. Lee, Y. Kuga, and R. A. Mullen, "Optically tunable millimeter-wave attenuator based on layered structures," Microwave Opt. Technol. Lett. 27, 9 (2000).
[CrossRef]

Kuzel, P.

Kužel, P.

P. Kužel, F. Kadlec, and H. Němec, "Propagation of terahertz pulses in photoexcited media: analytical theory for layered systems," J. Chem. Phys. 127, (2007), in press.
[PubMed]

L. Fekete, F. Kadlec, P. Kužel, and H. Němec, "Ultrafast opto-terahertz photonic crystal modulator," Opt. Lett. 32, 680 (2007).
[CrossRef]

H. Němec, F. Kadlec, S. Surendran, P. Kužel, and P. Jungwirth, "Ultrafast far-infrared dynamics probed by terahertz pulses: a frequency domain approach. I. Model systems," J. Chem. Phys. 122, 104503 (2005).
[CrossRef] [PubMed]

L. Fekete, J. Y. Hlinka, F. Kadlec, P. Kužel, and P. Mounaix, "Active optical control of the terahertz reflectivity," Opt. Lett. 30, 1992 (2005).
[CrossRef] [PubMed]

H. Němec, F. Kadlec, C. Kadlec, P. Kužel, and P. Jungwirth, "Ultrafast far-infrared dynamics probed by terahertz pulses: a frequency domain approach. II. Applications," J. Chem. Phys. 122, 104504 (2005).
[CrossRef] [PubMed]

H. Němec, F. Kadlec, and P. Kužel, "Methodology of an optical pump-terahertz probe experiment: An analytical frequency-domain approach," J. Chem. Phys. 117, 8454 (2002).
[CrossRef]

Lee, S.

S. Lee, Y. Kuga, and R. A. Mullen, "Optically tunable millimeter-wave attenuator based on layered structures," Microwave Opt. Technol. Lett. 27, 9 (2000).
[CrossRef]

Minamide, H.

T. Nozokido, H. Minamide, and K. Mizuno, "Modulation of sub-millimeter wave radiation by laser-produced free carriers in semiconductors," Electron. Commun. Jpn. II 80, 1 (1997).
[CrossRef]

Mizuno, K.

T. Nozokido, H. Minamide, and K. Mizuno, "Modulation of sub-millimeter wave radiation by laser-produced free carriers in semiconductors," Electron. Commun. Jpn. II 80, 1 (1997).
[CrossRef]

Mounaix, P.

Mullen, R. A.

S. Lee, Y. Kuga, and R. A. Mullen, "Optically tunable millimeter-wave attenuator based on layered structures," Microwave Opt. Technol. Lett. 27, 9 (2000).
[CrossRef]

N?emec, H.

Nakajima, F.

A. Hirata, T. Kosugi, H. Takahashi, R. Yamaguchi, F. Nakajima, T. Furuta and H. Ito, "120-GHz-band millimeterwave photonic wireless link for 10-Gb/s data transmission," IEEE Transactions Microwave Theory Tech. 54, 1937 (2006)
[CrossRef]

Nemec, H.

P. Kužel, F. Kadlec, and H. Němec, "Propagation of terahertz pulses in photoexcited media: analytical theory for layered systems," J. Chem. Phys. 127, (2007), in press.
[PubMed]

L. Fekete, F. Kadlec, P. Kužel, and H. Němec, "Ultrafast opto-terahertz photonic crystal modulator," Opt. Lett. 32, 680 (2007).
[CrossRef]

H. Němec, F. Kadlec, S. Surendran, P. Kužel, and P. Jungwirth, "Ultrafast far-infrared dynamics probed by terahertz pulses: a frequency domain approach. I. Model systems," J. Chem. Phys. 122, 104503 (2005).
[CrossRef] [PubMed]

H. Němec, F. Kadlec, C. Kadlec, P. Kužel, and P. Jungwirth, "Ultrafast far-infrared dynamics probed by terahertz pulses: a frequency domain approach. II. Applications," J. Chem. Phys. 122, 104504 (2005).
[CrossRef] [PubMed]

H. Němec, F. Kadlec, and P. Kužel, "Methodology of an optical pump-terahertz probe experiment: An analytical frequency-domain approach," J. Chem. Phys. 117, 8454 (2002).
[CrossRef]

Nozokido, T.

T. Nozokido, H. Minamide, and K. Mizuno, "Modulation of sub-millimeter wave radiation by laser-produced free carriers in semiconductors," Electron. Commun. Jpn. II 80, 1 (1997).
[CrossRef]

Padilla, W. J.

Palmstrom, C. J.

C. Kadow, S. B. Fleischer, J. P. Ibbetwon, J. E. Bowers, A. C. G. J. Dong, and C. J. Palmstrom, "Self-assembled ErAs islands in GaAs: Growth and subpicosecond carrier dynamics," Appl. Phys. Lett. 75, 3548 (1999).
[CrossRef]

Quemeneur, F.

Schmidt, L.-P.

S. Biber, D. Schneiderbanger, and L.-P. Schmidt, "Design of a controllable attenuator with high dynamic range for THz-frequencies based on optically stimulated free carriers in high-resistivity silicon," Frequenz 59, 141 (2005).

Schneiderbanger, D.

S. Biber, D. Schneiderbanger, and L.-P. Schmidt, "Design of a controllable attenuator with high dynamic range for THz-frequencies based on optically stimulated free carriers in high-resistivity silicon," Frequenz 59, 141 (2005).

Surendran, S.

H. Němec, F. Kadlec, S. Surendran, P. Kužel, and P. Jungwirth, "Ultrafast far-infrared dynamics probed by terahertz pulses: a frequency domain approach. I. Model systems," J. Chem. Phys. 122, 104503 (2005).
[CrossRef] [PubMed]

Takahashi, H.

A. Hirata, T. Kosugi, H. Takahashi, R. Yamaguchi, F. Nakajima, T. Furuta and H. Ito, "120-GHz-band millimeterwave photonic wireless link for 10-Gb/s data transmission," IEEE Transactions Microwave Theory Tech. 54, 1937 (2006)
[CrossRef]

Taylor, A. J.

Yamaguchi, R.

A. Hirata, T. Kosugi, H. Takahashi, R. Yamaguchi, F. Nakajima, T. Furuta and H. Ito, "120-GHz-band millimeterwave photonic wireless link for 10-Gb/s data transmission," IEEE Transactions Microwave Theory Tech. 54, 1937 (2006)
[CrossRef]

Zhang, X.-C.

B. Ferguson and X.-C. Zhang, "Materials for terahertz science and technology," Nature materials 1, 26 (2002).
[CrossRef]

Zide, J. M. O.

Appl. Phys. Lett. (1)

C. Kadow, S. B. Fleischer, J. P. Ibbetwon, J. E. Bowers, A. C. G. J. Dong, and C. J. Palmstrom, "Self-assembled ErAs islands in GaAs: Growth and subpicosecond carrier dynamics," Appl. Phys. Lett. 75, 3548 (1999).
[CrossRef]

Electron. Commun. Jpn. II (1)

T. Nozokido, H. Minamide, and K. Mizuno, "Modulation of sub-millimeter wave radiation by laser-produced free carriers in semiconductors," Electron. Commun. Jpn. II 80, 1 (1997).
[CrossRef]

Frequenz (1)

S. Biber, D. Schneiderbanger, and L.-P. Schmidt, "Design of a controllable attenuator with high dynamic range for THz-frequencies based on optically stimulated free carriers in high-resistivity silicon," Frequenz 59, 141 (2005).

IEEE Transactions Microwave Theory Tech. (1)

A. Hirata, T. Kosugi, H. Takahashi, R. Yamaguchi, F. Nakajima, T. Furuta and H. Ito, "120-GHz-band millimeterwave photonic wireless link for 10-Gb/s data transmission," IEEE Transactions Microwave Theory Tech. 54, 1937 (2006)
[CrossRef]

J. Chem. Phys. (4)

H. Němec, F. Kadlec, and P. Kužel, "Methodology of an optical pump-terahertz probe experiment: An analytical frequency-domain approach," J. Chem. Phys. 117, 8454 (2002).
[CrossRef]

P. Kužel, F. Kadlec, and H. Němec, "Propagation of terahertz pulses in photoexcited media: analytical theory for layered systems," J. Chem. Phys. 127, (2007), in press.
[PubMed]

H. Němec, F. Kadlec, S. Surendran, P. Kužel, and P. Jungwirth, "Ultrafast far-infrared dynamics probed by terahertz pulses: a frequency domain approach. I. Model systems," J. Chem. Phys. 122, 104503 (2005).
[CrossRef] [PubMed]

H. Němec, F. Kadlec, C. Kadlec, P. Kužel, and P. Jungwirth, "Ultrafast far-infrared dynamics probed by terahertz pulses: a frequency domain approach. II. Applications," J. Chem. Phys. 122, 104504 (2005).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (1)

Microwave Opt. Technol. Lett. (1)

S. Lee, Y. Kuga, and R. A. Mullen, "Optically tunable millimeter-wave attenuator based on layered structures," Microwave Opt. Technol. Lett. 27, 9 (2000).
[CrossRef]

Nature materials (1)

B. Ferguson and X.-C. Zhang, "Materials for terahertz science and technology," Nature materials 1, 26 (2002).
[CrossRef]

Opt. Lett. (3)

Opt. Photonics News (1)

M. Koch, "Terahertz Technology: A land to be discovered," Opt. Photonics News 18, (2007).
[CrossRef]

Other (4)

P. Kužel and F. Kadlec, "Tunable structures and modulators for the THz light," Comptes Rendus de l’Académie des Sciences - Physique, (2007), in press.

J. Bae, H. Mazaki, T. Fujii, and K. Mizuno, "An optically controlled modulator using a metal strip grating on a silicon plate for millimeter and sub-millimeter wavelengths," IEEE Microwave Theory and Techniques Symposium 3, 1239 (1996).

F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics, 2nd ed. (Prentice Hall, Englewood Cliffs, 1993).

M. Born and E. Wolf, Principles of Optics, 7th ed., (University Press, Cambridge, 2003).

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Figures (11)

Fig. 1.
Fig. 1.

Top: scheme of experimentally studied PC structures (the thicknesses of layers are out of scale); the sample consists of three blocks: P, S and Q, where S is the GaAs layer and the sequence of layers in the blocks P and Q differs for the two samples shown (nL -layer is white; nH -layer is dark). Bottom: notation introduced for the electric field in the photo-excited PC.

Fig. 2.
Fig. 2.

(a) Spectral dependence of the enhancement factor Ũ P for the structures discussed in the text. The yellow blocks approximately delimit the edges of the band gap (which is slightly different for the four structures). (b) Spatial profile of the THz electric field amplitude in the vicinity of GaAs defect (yellow block) at the defect mode frequency f 0.

Fig. 3.
Fig. 3.

Power transmittance of the structures HLH (a) and LHL (b) versus frequency and relative optical thickness of the defect. The transmittance level is represented by colors (T = 1 for black color and T = 0 for white color). Odd and even defect modes of the structure are identified.

Fig. 4.
Fig. 4.

Calculated THz spectra of four PCs. Lines: ground state; symbols: photoexcited state with a surface carrier density of 1016 cm-3.

Fig. 5.
Fig. 5.

Spectral functions X̃ P defining the structural part of the dynamical response of the PCs for HL and LHL structures. The symbols were calculated by using the transfer matrix formalism and the structural and optical data of the PCs; the lines correspond to the best approximation using Eq. (11). Very similar plots are found also for XSQ with the same values of parameters τ PC, τ 0 and ω 0.

Fig. 6.
Fig. 6.

Dynamical response of the LHL structure expressed by the function ΔEt (ω, ωp )/E inc(ω - ωp ) in the (ω,ωp ) space. The function is normalized to unity and its amplitude is plotted in the logarithmic scale. (a) Δσ (ω, ωp ) = const in the plotted range; this is obtained for an ultrafast semiconductor with a response faster than 1 ps. The sharp maxima correspond to defect modes in several forbidden bands. (b) Δσ (ω, ωp ) is given by Eq. (7) with time constants corresponding to our GaAs wafer. The response coming from higher-order forbidden bands is strongly suppressed and the only appreciable signal comes from the close vicinity of ωp = 0.

Fig. 7.
Fig. 7.

Power transmission I(τ) of the PCs at ω 0 after a photoexcitation event occurring at time τ = 0. (a) Carrier lifetime: τc = 170 ps, momentum scattering time: τs = 160 fs; initial concentration of photocarriers Ne and structure parameters are varied. (b) Ne = 1× 1016 cm-3; τc is varied.

Fig. 8.
Fig. 8.

Transient THz spectra of a GaAs:Cr wafer (used later as a defect in photonic structures) obtained at several pump-probe delays indicated in the legend. Symbols: experimental data; lines: fits by a Drude model using Ne = 1.5 × 1016 cm-3, τs = 160 fs and τc = 170 ps.

Fig. 9.
Fig. 9.

Examples of amplitude (circles) and phase (crosses) transmittance of samples in LHL (a–d) and HL (aa–dd) configuration as a function of the pump pulse fluence: LHL:(a) 0μJ/cm2 (ground state), (b) 0.4μJ/cm2, (c) 2.4μJ/cm2. (d) 8.0μJ/cm2; HL: (aa) 0μJ/cm2 (ground state), (bb) 0.24μJ/cm2, (cc) 0.9μJ/cm2, (dd) 2.0μJ/cm2. The pump-probe delay is 5 ps. Lines correspond to the data calculated by using the transfer matrix formalism.

Fig. 10.
Fig. 10.

Examples of transient THz wave forms ΔE for a pump-probe delay τp = 5 ps. (a) LHL structure, pump fluence: 0.8μJ/cm2; (b) HL structure, pump fluence: 0.24μJ/cm2. Inset in (a): reference wave form; Inset in (b): 30-ps-long detail of the wave form. (c) Ratio T/T 0 between the power transmission of the PCs in photoexcited and ground state at the defect mode frequency versus the incident fluence and surface carrier density. The line is a guide for the eye.

Fig. 11.
Fig. 11.

The rise and decay of the photo-induced signal ΔT = ΔEt /E ref at the defect mode frequency for the two structures studied. Pump pulse fluence: 0.4μJ/cm2; points: measured data; solid lines fit by expression (18).

Equations (20)

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( E in η 0 H in ) = M ( E out η 0 H out ) ,
S = ( cos ( nk 0 d ) i n sin ( nk 0 d ) in sin ( nk 0 d ) cos ( nk 0 d ) ) ;
t = 2 m 11 + m 12 + m 21 + m 22 , r = m 11 + m 12 m 21 m 22 m 11 + m 12 + m 21 + m 22 .
E ( ω ; z ) = E in ( ω ) cos ( nk 0 z ) i η 0 H in ( ω ) n sin ( nk 0 z ) ,
d 2 Δ E dz 2 + n 2 k 0 2 Δ E = 0 k 0 Δ j ( ω , ω p ; z ) .
Δ j ( ω , ω p ; z ) = exp [ ( p v g + α ) z ] E ( ω ω p ; z ) Δσ ( ω , ω p ) ,
Δσ ( ω , ω p ) = e 2 N e m * 1 + 1 τ S + 1 τ C 1 p + 1 τ C .
Δ E t ω ω p = η 0 2 α U ˜ P ( ω ) t ( ω ) U SQ ( ω ω p ) t ( ω ω p ) Δσ ω ω p E inc ( ω ω p ) ,
U ˜ P ( ω ) = 1 + r ˜ P ( ω ) t P ( ω ) , U SQ ( ω ω p ) = 1 + r SQ ( ω ω p ) t SQ ( ω ω p ) .
X ˜ P ( ω ) = U ˜ P ( ω ) t ( ω ) , X SQ ( ω ω p ) = U SQ ( ω ω p ) t ( ω ω p )
X ˜ j ( Ω ) U ˜ j ( ω 0 ) t ( ω 0 ) exp [ i ( Ω ω 0 ) τ 0 ] 1 + i ( Ω ω 0 ) τ PC
E inc ( ω ω p ) = E inc δ ( ω ω p ω 0 ) ,
Δ E t ( ω ) = η 0 e 2 N e 2 α m * E inc t ( ω 0 ) U SQ ( ω 0 ) + 1 τ s X ˜ P ( ω ) i ( ω ω 0 ) + 1 τ c .
I ( τ ) = Δ E t ( τ ) + E inc t ( ω 0 ) exp ( 0 τ ) 2 .
I ( τ = τ ˜ + τ 0 ) t ( ω 0 ) 2 I inc Y ( τ ˜ ) B exp ( τ ˜ τ PC ) exp ( τ ˜ τ C ) 1 τ PC τ C + 1 2
B = η 0 e 2 N e 2 α m * t ( ω 0 ) U ˜ P ( ω 0 ) U SQ ( ω 0 ) 0 + 1 τ s .
Δ E t ω 0 ω p = η 0 e 2 N e 2 α * E inc ( ω 0 ω p ) t ( ω 0 ) U ˜ P ( ω 0 ) 0 + 1 τ s X ˜ SQ ( ω 0 ω p ) p + 1 τ c .
Δ E t ( ω 0 , τ p = τ ˜ p τ 0 ) = t ( ω 0 ) E inc B 1 + τ PC τ c [ Y ( τ ˜ p ) exp ( τ ˜ p τ c ) + Y ( τ ˜ p ) exp ( τ ˜ p τ PC ) ] .
N eff = N e 1 + τ PC τ c .
1 τ ˜ PC 1 τ PC + 1 τ L + 1 τ W ,

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