Abstract

We report on the efficient coupling of terahertz (THz) waves into a dielectric waveguide by means of a diffraction grating engraved at the top of the waveguide. The waveguide is made of a 201-µm-thick high-resistivity silicon wafer. The transmission of the device, measured versus frequency by terahertz time-domain spectroscopy, shows usual m lines when a frequency component of the THz pulse spectrum satisfies the phase-matching condition and is coupled into the waveguide. The experimental data are well modeled with the differential electromagnetic method to compute the diffraction pattern of the grating device. The dispersion curve of the first four modes of propagation is determined from the frequency position of the m lines recorded for different angles of incidence of the THz beam. The waveguide exhibits a weak group velocity dispersion at high frequencies.

© 2002 Optical Society of America

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  1. See, for example, Terahertz Sources and Systems, R. E. Miles, P. Harrison, D. Lippens, eds. Vol. 27 of the North Atlantic Treaty Organization Science Series II (Kluwer Academic, Dordrecht, The Netherlands, 2001).
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    [CrossRef]
  3. H. Kobayashi, R. Takahashi, Y. Matsuoka, H. Iwamura, “1 Tbit/s demultiplexing using low-temperature grown InGaAs/InA1As multiple quantum wells,” Electron. Lett. 34, 908–910 (1998).
    [CrossRef]
  4. G. Mouret, W. Chen, D. Boucher, R. Bocquet, P. Mounaix, D. Lippens, “Gas filter correlation instrument for air monitoring at submillimeter wavelengths,” Opt. Lett. 24, 351–353 (1999).
    [CrossRef]
  5. M. Brucherseifer, M. Nagel, P. Haring Bolivar, H. Kurz, A. Bosserhoff, R. Büttner, “Label free probing of the binding state of DNA by time-domain terahertz sensing,” Appl. Phys. Lett. 77, 4049–4051 (2000).
    [CrossRef]
  6. G. Gallot, S. P. Jamison, R. W. McGowan, D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17, 851–863 (2000).
    [CrossRef]
  7. D. Grischkowsky, “Optoelectronic characterization of transmission lines and waveguides by THz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 6, 1122–1135 (2000), LEOS Millenium issue.
    [CrossRef]
  8. R. Mendis, D. Grischkowsky, “Undistorted guided wave propagation of subpsec THz pulses,” Opt. Lett. 26, 846–848 (2001).
    [CrossRef]
  9. R. Mendis, D. Grischkowsky. “THz interconnect with low loss and low group velocity dispersion,” IEEE Microwaves Wireless Comp. Lett. 11, 444–446 (2001).
    [CrossRef]
  10. R. Mendis, D. Grischkowsky, “Plastic ribbon THz waveguides,” J. Appl. Phys. 88, 4449–4451 (2000).
    [CrossRef]
  11. R. E. Miles, D. P. Steenson, J. M. Chamberlain. “Micromachining for terahertz circuits and systems,” in Terahertz Sources and Systems, R. E. Miles, P. Harrison, D. Lippens eds., Vol. 27 of the North Atlantic Treaty Organization Science Series, (Kluwer Academic, Dordrecht, The Netherlands, 2001), pp. 285–297.
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    [CrossRef]
  14. S. Kono, M. Tani, K. Sakai, “Ultrabroadband photoconductive detection: comparison with free-space electro-optic sampling,” Appl. Phys. Lett. 79, 898–900 (2001).
    [CrossRef]
  15. J. O. White, Ch. Ludwig, J. Kuhl, “Response of grating pairs to single-cycle electromagnetic pulses,” J. Opt. Soc. Am. B 12, 1687–1694 (1995).
    [CrossRef]
  16. A. Filin, M. Stowe, R. Kersting, “Terahertz time-domain differentiators,” presented at the 26th International Conference on Infrared and Millimeter Waves, Toulouse France, 10–14 September 2001.
  17. J.-F. Roux, F. Aquistapace, F. Garet, L. Duvillaret, J.-L. Coutaz, “High efficiency grating coupling of THz pulse radiation into dielectric waveguide,” Electron. Lett. 37, 1390–1392 (2001).
    [CrossRef]
  18. P. Vincent in Electromagnetic Theory of Grating, R. Petit, ed. (Springer Verlag, Berlin, 1980).
  19. M. Nevière, E. Popov, R. Reinisch, G. Vitrant, Electromagnetic Resonances in Nonlinear Optics (Gordon and Breach Science Publishers, Amsterdam, 2000).
  20. L. Duvillaret, F. Garet, J.-L. Coutaz, “Reliable method for extraction of material parameters in time domain THz spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2, 739–746 (1996).
    [CrossRef]
  21. D. Grischkowsky, S. Keiding, M. van Exter, C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semi-conductors,” J. Opt. Soc. Am. B 7, 2006–2015 (1990).
    [CrossRef]
  22. T.-I. Jeon, D. Grischkowsky, “Nature of conduction in doped silicon,” Phys. Rev. Lett. 78, 1106–1109 (1997).
    [CrossRef]
  23. J.-L. Coutaz, L. Duvillaret, F. Garet, S. Rowson, A. Chelnokov, J.-M. Lourtioz, “Photoinduced change of dielectric constant of silicon in the far infrared: applications to light-controllable photonic band-gap crystals in the terahertz frequency range,” in Terahertz and Gigahertz Photonics, R. J. Hwu, K. Wu, eds., Proc. SPIE3795, 457–467 (1999).
  24. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, Mass., 1999).
  25. R. Reinisch, J. Fick, P. Coupier, J.-L. Coutaz, G. Vitrant, “Grating and prism couplers: radiation pattern and m-line,” Optics Commun 120, 121–128 (1995).
    [CrossRef]
  26. See, for example, P. K. Tien, “Integrated optics and new wave phenomena in optical waveguides,” Rev. Mod. Phys. 49, 361–420 (1977).
    [CrossRef]
  27. M. C. Hutley, Diffraction Gratings (Academic, New York, 1982).
  28. A. Tchelnokov, S. Rowson, J.-M. Lourtioz, L. Duvillaret, J.-L. Coutaz, “Light commendable defect modes in a three dimensional photonic crystal,” Electron. Lett. 34, 1965–1967 (1998).
    [CrossRef]

2001 (4)

R. Mendis, D. Grischkowsky. “THz interconnect with low loss and low group velocity dispersion,” IEEE Microwaves Wireless Comp. Lett. 11, 444–446 (2001).
[CrossRef]

S. Kono, M. Tani, K. Sakai, “Ultrabroadband photoconductive detection: comparison with free-space electro-optic sampling,” Appl. Phys. Lett. 79, 898–900 (2001).
[CrossRef]

J.-F. Roux, F. Aquistapace, F. Garet, L. Duvillaret, J.-L. Coutaz, “High efficiency grating coupling of THz pulse radiation into dielectric waveguide,” Electron. Lett. 37, 1390–1392 (2001).
[CrossRef]

R. Mendis, D. Grischkowsky, “Undistorted guided wave propagation of subpsec THz pulses,” Opt. Lett. 26, 846–848 (2001).
[CrossRef]

2000 (5)

G. Gallot, S. P. Jamison, R. W. McGowan, D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17, 851–863 (2000).
[CrossRef]

P. Y. Han, G. C. Cho, X.-C. Zhang, “Time-domain transillumination of biological tissues with terahertz pulses,” Opt. Lett. 25, 242–244 (2000).
[CrossRef]

D. Grischkowsky, “Optoelectronic characterization of transmission lines and waveguides by THz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 6, 1122–1135 (2000), LEOS Millenium issue.
[CrossRef]

R. Mendis, D. Grischkowsky, “Plastic ribbon THz waveguides,” J. Appl. Phys. 88, 4449–4451 (2000).
[CrossRef]

M. Brucherseifer, M. Nagel, P. Haring Bolivar, H. Kurz, A. Bosserhoff, R. Büttner, “Label free probing of the binding state of DNA by time-domain terahertz sensing,” Appl. Phys. Lett. 77, 4049–4051 (2000).
[CrossRef]

1999 (1)

1998 (2)

A. Tchelnokov, S. Rowson, J.-M. Lourtioz, L. Duvillaret, J.-L. Coutaz, “Light commendable defect modes in a three dimensional photonic crystal,” Electron. Lett. 34, 1965–1967 (1998).
[CrossRef]

H. Kobayashi, R. Takahashi, Y. Matsuoka, H. Iwamura, “1 Tbit/s demultiplexing using low-temperature grown InGaAs/InA1As multiple quantum wells,” Electron. Lett. 34, 908–910 (1998).
[CrossRef]

1997 (1)

T.-I. Jeon, D. Grischkowsky, “Nature of conduction in doped silicon,” Phys. Rev. Lett. 78, 1106–1109 (1997).
[CrossRef]

1996 (1)

L. Duvillaret, F. Garet, J.-L. Coutaz, “Reliable method for extraction of material parameters in time domain THz spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2, 739–746 (1996).
[CrossRef]

1995 (2)

R. Reinisch, J. Fick, P. Coupier, J.-L. Coutaz, G. Vitrant, “Grating and prism couplers: radiation pattern and m-line,” Optics Commun 120, 121–128 (1995).
[CrossRef]

J. O. White, Ch. Ludwig, J. Kuhl, “Response of grating pairs to single-cycle electromagnetic pulses,” J. Opt. Soc. Am. B 12, 1687–1694 (1995).
[CrossRef]

1990 (1)

1977 (1)

See, for example, P. K. Tien, “Integrated optics and new wave phenomena in optical waveguides,” Rev. Mod. Phys. 49, 361–420 (1977).
[CrossRef]

1976 (1)

M. C. Hutley, D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
[CrossRef]

Aquistapace, F.

J.-F. Roux, F. Aquistapace, F. Garet, L. Duvillaret, J.-L. Coutaz, “High efficiency grating coupling of THz pulse radiation into dielectric waveguide,” Electron. Lett. 37, 1390–1392 (2001).
[CrossRef]

Bocquet, R.

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, Mass., 1999).

Bosserhoff, A.

M. Brucherseifer, M. Nagel, P. Haring Bolivar, H. Kurz, A. Bosserhoff, R. Büttner, “Label free probing of the binding state of DNA by time-domain terahertz sensing,” Appl. Phys. Lett. 77, 4049–4051 (2000).
[CrossRef]

Boucher, D.

Brucherseifer, M.

M. Brucherseifer, M. Nagel, P. Haring Bolivar, H. Kurz, A. Bosserhoff, R. Büttner, “Label free probing of the binding state of DNA by time-domain terahertz sensing,” Appl. Phys. Lett. 77, 4049–4051 (2000).
[CrossRef]

Büttner, R.

M. Brucherseifer, M. Nagel, P. Haring Bolivar, H. Kurz, A. Bosserhoff, R. Büttner, “Label free probing of the binding state of DNA by time-domain terahertz sensing,” Appl. Phys. Lett. 77, 4049–4051 (2000).
[CrossRef]

Chamberlain, J. M.

R. E. Miles, D. P. Steenson, J. M. Chamberlain. “Micromachining for terahertz circuits and systems,” in Terahertz Sources and Systems, R. E. Miles, P. Harrison, D. Lippens eds., Vol. 27 of the North Atlantic Treaty Organization Science Series, (Kluwer Academic, Dordrecht, The Netherlands, 2001), pp. 285–297.

Chelnokov, A.

J.-L. Coutaz, L. Duvillaret, F. Garet, S. Rowson, A. Chelnokov, J.-M. Lourtioz, “Photoinduced change of dielectric constant of silicon in the far infrared: applications to light-controllable photonic band-gap crystals in the terahertz frequency range,” in Terahertz and Gigahertz Photonics, R. J. Hwu, K. Wu, eds., Proc. SPIE3795, 457–467 (1999).

Chen, W.

Cho, G. C.

Coupier, P.

R. Reinisch, J. Fick, P. Coupier, J.-L. Coutaz, G. Vitrant, “Grating and prism couplers: radiation pattern and m-line,” Optics Commun 120, 121–128 (1995).
[CrossRef]

Coutaz, J.-L.

J.-F. Roux, F. Aquistapace, F. Garet, L. Duvillaret, J.-L. Coutaz, “High efficiency grating coupling of THz pulse radiation into dielectric waveguide,” Electron. Lett. 37, 1390–1392 (2001).
[CrossRef]

A. Tchelnokov, S. Rowson, J.-M. Lourtioz, L. Duvillaret, J.-L. Coutaz, “Light commendable defect modes in a three dimensional photonic crystal,” Electron. Lett. 34, 1965–1967 (1998).
[CrossRef]

L. Duvillaret, F. Garet, J.-L. Coutaz, “Reliable method for extraction of material parameters in time domain THz spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2, 739–746 (1996).
[CrossRef]

R. Reinisch, J. Fick, P. Coupier, J.-L. Coutaz, G. Vitrant, “Grating and prism couplers: radiation pattern and m-line,” Optics Commun 120, 121–128 (1995).
[CrossRef]

J.-L. Coutaz, L. Duvillaret, F. Garet, S. Rowson, A. Chelnokov, J.-M. Lourtioz, “Photoinduced change of dielectric constant of silicon in the far infrared: applications to light-controllable photonic band-gap crystals in the terahertz frequency range,” in Terahertz and Gigahertz Photonics, R. J. Hwu, K. Wu, eds., Proc. SPIE3795, 457–467 (1999).

Duvillaret, L.

J.-F. Roux, F. Aquistapace, F. Garet, L. Duvillaret, J.-L. Coutaz, “High efficiency grating coupling of THz pulse radiation into dielectric waveguide,” Electron. Lett. 37, 1390–1392 (2001).
[CrossRef]

A. Tchelnokov, S. Rowson, J.-M. Lourtioz, L. Duvillaret, J.-L. Coutaz, “Light commendable defect modes in a three dimensional photonic crystal,” Electron. Lett. 34, 1965–1967 (1998).
[CrossRef]

L. Duvillaret, F. Garet, J.-L. Coutaz, “Reliable method for extraction of material parameters in time domain THz spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2, 739–746 (1996).
[CrossRef]

J.-L. Coutaz, L. Duvillaret, F. Garet, S. Rowson, A. Chelnokov, J.-M. Lourtioz, “Photoinduced change of dielectric constant of silicon in the far infrared: applications to light-controllable photonic band-gap crystals in the terahertz frequency range,” in Terahertz and Gigahertz Photonics, R. J. Hwu, K. Wu, eds., Proc. SPIE3795, 457–467 (1999).

Fattinger, C.

Fick, J.

R. Reinisch, J. Fick, P. Coupier, J.-L. Coutaz, G. Vitrant, “Grating and prism couplers: radiation pattern and m-line,” Optics Commun 120, 121–128 (1995).
[CrossRef]

Filin, A.

A. Filin, M. Stowe, R. Kersting, “Terahertz time-domain differentiators,” presented at the 26th International Conference on Infrared and Millimeter Waves, Toulouse France, 10–14 September 2001.

Gallot, G.

Garet, F.

J.-F. Roux, F. Aquistapace, F. Garet, L. Duvillaret, J.-L. Coutaz, “High efficiency grating coupling of THz pulse radiation into dielectric waveguide,” Electron. Lett. 37, 1390–1392 (2001).
[CrossRef]

L. Duvillaret, F. Garet, J.-L. Coutaz, “Reliable method for extraction of material parameters in time domain THz spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 2, 739–746 (1996).
[CrossRef]

J.-L. Coutaz, L. Duvillaret, F. Garet, S. Rowson, A. Chelnokov, J.-M. Lourtioz, “Photoinduced change of dielectric constant of silicon in the far infrared: applications to light-controllable photonic band-gap crystals in the terahertz frequency range,” in Terahertz and Gigahertz Photonics, R. J. Hwu, K. Wu, eds., Proc. SPIE3795, 457–467 (1999).

Grischkowsky, D.

R. Mendis, D. Grischkowsky. “THz interconnect with low loss and low group velocity dispersion,” IEEE Microwaves Wireless Comp. Lett. 11, 444–446 (2001).
[CrossRef]

R. Mendis, D. Grischkowsky, “Undistorted guided wave propagation of subpsec THz pulses,” Opt. Lett. 26, 846–848 (2001).
[CrossRef]

G. Gallot, S. P. Jamison, R. W. McGowan, D. Grischkowsky, “Terahertz waveguides,” J. Opt. Soc. Am. B 17, 851–863 (2000).
[CrossRef]

R. Mendis, D. Grischkowsky, “Plastic ribbon THz waveguides,” J. Appl. Phys. 88, 4449–4451 (2000).
[CrossRef]

D. Grischkowsky, “Optoelectronic characterization of transmission lines and waveguides by THz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 6, 1122–1135 (2000), LEOS Millenium issue.
[CrossRef]

T.-I. Jeon, D. Grischkowsky, “Nature of conduction in doped silicon,” Phys. Rev. Lett. 78, 1106–1109 (1997).
[CrossRef]

D. Grischkowsky, S. Keiding, M. van Exter, C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semi-conductors,” J. Opt. Soc. Am. B 7, 2006–2015 (1990).
[CrossRef]

Han, P. Y.

Haring Bolivar, P.

M. Brucherseifer, M. Nagel, P. Haring Bolivar, H. Kurz, A. Bosserhoff, R. Büttner, “Label free probing of the binding state of DNA by time-domain terahertz sensing,” Appl. Phys. Lett. 77, 4049–4051 (2000).
[CrossRef]

Hutley, M. C.

M. C. Hutley, D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
[CrossRef]

M. C. Hutley, Diffraction Gratings (Academic, New York, 1982).

Iwamura, H.

H. Kobayashi, R. Takahashi, Y. Matsuoka, H. Iwamura, “1 Tbit/s demultiplexing using low-temperature grown InGaAs/InA1As multiple quantum wells,” Electron. Lett. 34, 908–910 (1998).
[CrossRef]

Jamison, S. P.

Jeon, T.-I.

T.-I. Jeon, D. Grischkowsky, “Nature of conduction in doped silicon,” Phys. Rev. Lett. 78, 1106–1109 (1997).
[CrossRef]

Keiding, S.

Kersting, R.

A. Filin, M. Stowe, R. Kersting, “Terahertz time-domain differentiators,” presented at the 26th International Conference on Infrared and Millimeter Waves, Toulouse France, 10–14 September 2001.

Kobayashi, H.

H. Kobayashi, R. Takahashi, Y. Matsuoka, H. Iwamura, “1 Tbit/s demultiplexing using low-temperature grown InGaAs/InA1As multiple quantum wells,” Electron. Lett. 34, 908–910 (1998).
[CrossRef]

Kono, S.

S. Kono, M. Tani, K. Sakai, “Ultrabroadband photoconductive detection: comparison with free-space electro-optic sampling,” Appl. Phys. Lett. 79, 898–900 (2001).
[CrossRef]

Kuhl, J.

Kurz, H.

M. Brucherseifer, M. Nagel, P. Haring Bolivar, H. Kurz, A. Bosserhoff, R. Büttner, “Label free probing of the binding state of DNA by time-domain terahertz sensing,” Appl. Phys. Lett. 77, 4049–4051 (2000).
[CrossRef]

Lippens, D.

Lourtioz, J.-M.

A. Tchelnokov, S. Rowson, J.-M. Lourtioz, L. Duvillaret, J.-L. Coutaz, “Light commendable defect modes in a three dimensional photonic crystal,” Electron. Lett. 34, 1965–1967 (1998).
[CrossRef]

J.-L. Coutaz, L. Duvillaret, F. Garet, S. Rowson, A. Chelnokov, J.-M. Lourtioz, “Photoinduced change of dielectric constant of silicon in the far infrared: applications to light-controllable photonic band-gap crystals in the terahertz frequency range,” in Terahertz and Gigahertz Photonics, R. J. Hwu, K. Wu, eds., Proc. SPIE3795, 457–467 (1999).

Ludwig, Ch.

Matsuoka, Y.

H. Kobayashi, R. Takahashi, Y. Matsuoka, H. Iwamura, “1 Tbit/s demultiplexing using low-temperature grown InGaAs/InA1As multiple quantum wells,” Electron. Lett. 34, 908–910 (1998).
[CrossRef]

Maystre, D.

M. C. Hutley, D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
[CrossRef]

McGowan, R. W.

Mendis, R.

R. Mendis, D. Grischkowsky, “Undistorted guided wave propagation of subpsec THz pulses,” Opt. Lett. 26, 846–848 (2001).
[CrossRef]

R. Mendis, D. Grischkowsky. “THz interconnect with low loss and low group velocity dispersion,” IEEE Microwaves Wireless Comp. Lett. 11, 444–446 (2001).
[CrossRef]

R. Mendis, D. Grischkowsky, “Plastic ribbon THz waveguides,” J. Appl. Phys. 88, 4449–4451 (2000).
[CrossRef]

Miles, R. E.

R. E. Miles, D. P. Steenson, J. M. Chamberlain. “Micromachining for terahertz circuits and systems,” in Terahertz Sources and Systems, R. E. Miles, P. Harrison, D. Lippens eds., Vol. 27 of the North Atlantic Treaty Organization Science Series, (Kluwer Academic, Dordrecht, The Netherlands, 2001), pp. 285–297.

Mounaix, P.

Mouret, G.

Nagel, M.

M. Brucherseifer, M. Nagel, P. Haring Bolivar, H. Kurz, A. Bosserhoff, R. Büttner, “Label free probing of the binding state of DNA by time-domain terahertz sensing,” Appl. Phys. Lett. 77, 4049–4051 (2000).
[CrossRef]

Nevière, M.

M. Nevière, E. Popov, R. Reinisch, G. Vitrant, Electromagnetic Resonances in Nonlinear Optics (Gordon and Breach Science Publishers, Amsterdam, 2000).

Popov, E.

M. Nevière, E. Popov, R. Reinisch, G. Vitrant, Electromagnetic Resonances in Nonlinear Optics (Gordon and Breach Science Publishers, Amsterdam, 2000).

Reinisch, R.

R. Reinisch, J. Fick, P. Coupier, J.-L. Coutaz, G. Vitrant, “Grating and prism couplers: radiation pattern and m-line,” Optics Commun 120, 121–128 (1995).
[CrossRef]

M. Nevière, E. Popov, R. Reinisch, G. Vitrant, Electromagnetic Resonances in Nonlinear Optics (Gordon and Breach Science Publishers, Amsterdam, 2000).

Roux, J.-F.

J.-F. Roux, F. Aquistapace, F. Garet, L. Duvillaret, J.-L. Coutaz, “High efficiency grating coupling of THz pulse radiation into dielectric waveguide,” Electron. Lett. 37, 1390–1392 (2001).
[CrossRef]

Rowson, S.

A. Tchelnokov, S. Rowson, J.-M. Lourtioz, L. Duvillaret, J.-L. Coutaz, “Light commendable defect modes in a three dimensional photonic crystal,” Electron. Lett. 34, 1965–1967 (1998).
[CrossRef]

J.-L. Coutaz, L. Duvillaret, F. Garet, S. Rowson, A. Chelnokov, J.-M. Lourtioz, “Photoinduced change of dielectric constant of silicon in the far infrared: applications to light-controllable photonic band-gap crystals in the terahertz frequency range,” in Terahertz and Gigahertz Photonics, R. J. Hwu, K. Wu, eds., Proc. SPIE3795, 457–467 (1999).

Sakai, K.

S. Kono, M. Tani, K. Sakai, “Ultrabroadband photoconductive detection: comparison with free-space electro-optic sampling,” Appl. Phys. Lett. 79, 898–900 (2001).
[CrossRef]

Steenson, D. P.

R. E. Miles, D. P. Steenson, J. M. Chamberlain. “Micromachining for terahertz circuits and systems,” in Terahertz Sources and Systems, R. E. Miles, P. Harrison, D. Lippens eds., Vol. 27 of the North Atlantic Treaty Organization Science Series, (Kluwer Academic, Dordrecht, The Netherlands, 2001), pp. 285–297.

Stowe, M.

A. Filin, M. Stowe, R. Kersting, “Terahertz time-domain differentiators,” presented at the 26th International Conference on Infrared and Millimeter Waves, Toulouse France, 10–14 September 2001.

Takahashi, R.

H. Kobayashi, R. Takahashi, Y. Matsuoka, H. Iwamura, “1 Tbit/s demultiplexing using low-temperature grown InGaAs/InA1As multiple quantum wells,” Electron. Lett. 34, 908–910 (1998).
[CrossRef]

Tani, M.

S. Kono, M. Tani, K. Sakai, “Ultrabroadband photoconductive detection: comparison with free-space electro-optic sampling,” Appl. Phys. Lett. 79, 898–900 (2001).
[CrossRef]

Tchelnokov, A.

A. Tchelnokov, S. Rowson, J.-M. Lourtioz, L. Duvillaret, J.-L. Coutaz, “Light commendable defect modes in a three dimensional photonic crystal,” Electron. Lett. 34, 1965–1967 (1998).
[CrossRef]

Tien, P. K.

See, for example, P. K. Tien, “Integrated optics and new wave phenomena in optical waveguides,” Rev. Mod. Phys. 49, 361–420 (1977).
[CrossRef]

van Exter, M.

Vincent, P.

P. Vincent in Electromagnetic Theory of Grating, R. Petit, ed. (Springer Verlag, Berlin, 1980).

Vitrant, G.

R. Reinisch, J. Fick, P. Coupier, J.-L. Coutaz, G. Vitrant, “Grating and prism couplers: radiation pattern and m-line,” Optics Commun 120, 121–128 (1995).
[CrossRef]

M. Nevière, E. Popov, R. Reinisch, G. Vitrant, Electromagnetic Resonances in Nonlinear Optics (Gordon and Breach Science Publishers, Amsterdam, 2000).

White, J. O.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, Mass., 1999).

Zhang, X.-C.

Appl. Phys. Lett. (2)

M. Brucherseifer, M. Nagel, P. Haring Bolivar, H. Kurz, A. Bosserhoff, R. Büttner, “Label free probing of the binding state of DNA by time-domain terahertz sensing,” Appl. Phys. Lett. 77, 4049–4051 (2000).
[CrossRef]

S. Kono, M. Tani, K. Sakai, “Ultrabroadband photoconductive detection: comparison with free-space electro-optic sampling,” Appl. Phys. Lett. 79, 898–900 (2001).
[CrossRef]

Electron. Lett. (3)

H. Kobayashi, R. Takahashi, Y. Matsuoka, H. Iwamura, “1 Tbit/s demultiplexing using low-temperature grown InGaAs/InA1As multiple quantum wells,” Electron. Lett. 34, 908–910 (1998).
[CrossRef]

J.-F. Roux, F. Aquistapace, F. Garet, L. Duvillaret, J.-L. Coutaz, “High efficiency grating coupling of THz pulse radiation into dielectric waveguide,” Electron. Lett. 37, 1390–1392 (2001).
[CrossRef]

A. Tchelnokov, S. Rowson, J.-M. Lourtioz, L. Duvillaret, J.-L. Coutaz, “Light commendable defect modes in a three dimensional photonic crystal,” Electron. Lett. 34, 1965–1967 (1998).
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D. Grischkowsky, “Optoelectronic characterization of transmission lines and waveguides by THz time-domain spectroscopy,” IEEE J. Sel. Top. Quantum Electron. 6, 1122–1135 (2000), LEOS Millenium issue.
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Figures (8)

Fig. 1
Fig. 1

Experimental THz time-domain spectroscopy setup.

Fig. 2
Fig. 2

Temporal THz signal transmitted by the grating device at normal incidence. The peak at 65 ps is a temporal echo from parasitic reflection in the emitting antenna.

Fig. 3
Fig. 3

Transmission spectrum of the grating device recorded at normal incidence (open circles). The frequency resolution of the experimental setup is 6 GHz at 300 GHz and 20 GHz at 1 THz. The continuous curve is calculated with the differential method.

Fig. 4
Fig. 4

Experimental effective optical thickness d phase (phase retardation divided by 2πv/ c) of the device versus frequency (circles). The continuous line is calculated with the differential method.

Fig. 5
Fig. 5

Angular position of the excited modes versus frequency. Open circles, experimental data deduced from Fig. 3 and similar records. Lines, dispersion curves of the modes of an uncorrugated waveguide excited by grating-type coupling and calculated with the approximate expression (2). Each line is labeled by (m, p), where m is the mode number and p is the order of diffraction that leads to coupling. A negative value of m indicates that the excited mode is contrapropagative.

Fig. 6
Fig. 6

Zoom of Fig. 5 centered at the crossing of two dispersion curves. The open squares, together with the error bars, are experimental data. The continuous lines are calculated with the differential method. The energy gap, centered at 425 GHz, is 7.1 GHz wide.

Fig. 7
Fig. 7

Frequency dispersion of the guided mode of the silicon grating (open circles). The continuous curves are calculated for an uncorrugated 201-µm-thick silicon waveguide with the measured refractive index of silicon.

Fig. 8
Fig. 8

Dispersion of the effective refractive index, related to the group velocity, calculated from Fig. 7, for the first four modes of the waveguide.

Equations (2)

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ki+p2πΛ=kp,
ki+p2πΛ=2πλneff,m  sin θi+pλΛ=neff,m,

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