Abstract

We report on investigations of the angular distribution of the radiation emitted from a terahertz antenna system equipped with a truncated spherical silicon lens. The pattern is calculated by wide-angle interference principles and Huygens–Fresnel diffraction theory. Experimental determination of the radiation pattern is performed by spatially resolved terahertz time-domain spectroscopy. Good agreement between theory and experiment is obtained, and we find that the terahertz beam can be represented by a Gaussian beam emitted from a circular aperture equal to the diameter of the lens.

© 1995 Optical Society of America

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  1. P. R. Smith, D. H. Auston, M. C. Nuss, IEEE J. Quantum Electron. 24, 255 (1988).
    [CrossRef]
  2. M. van Exter, Ch. Fattinger, D. Grischkowsky, Opt. Lett. 14, 1128 (1989).
    [CrossRef]
  3. D. Grischkowsky, Opt. Photon. News 3(5), 21 (1992).
    [CrossRef]
  4. Ch. Fattinger, D. Grischkowsky, Appl. Phys. Lett. 54, 490 (1989).
    [CrossRef]
  5. M. van Exter, D. Grischkowsky, IEEE Trans. Microwave Theory Technol. 38, 1684 (1990).
    [CrossRef]
  6. J. T. Darrow, B. B. Hu, X.-C. Zhang, D. H. Auston, Opt. Lett. 15, 323 (1990).
    [CrossRef] [PubMed]
  7. Y. Pastol, G. Arjavalingam, J.-M. Halbout, F. V. Kopcsay, Electron. Lett. 24, 1318 (1988).
    [CrossRef]
  8. C. R. Lutz, A. P. DeFonzo, Appl. Phys. Lett. 54, 2186 (1989).
    [CrossRef]
  9. Y. Pastol, G. Arjavalingam, J.-M. Halbout, Electron. Lett. 26, 133 (1990).
    [CrossRef]
  10. W. Lukosz, R. E. Kunz, J. Opt. Soc. Am. 67, 1607 (1977).
    [CrossRef]
  11. J. E. Pedersen, I. Balslev, J. M. Hvam, S. R. Keiding, Appl. Phys. Lett. 61, 1372 (1992).
    [CrossRef]
  12. Ch. Fattinger, D. Grischkowsky, presented at Picosecond Electronics and Optoelectronics Topical Meeting, Salt Lake City, Utah, March 8–10, 1989, paper FB-4.
  13. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Chap. 8, p. 375.
  14. F. E. Doany, D. Grischkowsky, C.-C. Chi, Appl. Phys. Lett. 50, 460 (1987).
    [CrossRef]
  15. D. Grischkowsky, S. Keiding, M. van Exter, Ch. Fattinger, J. Opt. Soc. Am. B 7, 2006 (1990).
    [CrossRef]

1992 (2)

D. Grischkowsky, Opt. Photon. News 3(5), 21 (1992).
[CrossRef]

J. E. Pedersen, I. Balslev, J. M. Hvam, S. R. Keiding, Appl. Phys. Lett. 61, 1372 (1992).
[CrossRef]

1990 (4)

Y. Pastol, G. Arjavalingam, J.-M. Halbout, Electron. Lett. 26, 133 (1990).
[CrossRef]

M. van Exter, D. Grischkowsky, IEEE Trans. Microwave Theory Technol. 38, 1684 (1990).
[CrossRef]

J. T. Darrow, B. B. Hu, X.-C. Zhang, D. H. Auston, Opt. Lett. 15, 323 (1990).
[CrossRef] [PubMed]

D. Grischkowsky, S. Keiding, M. van Exter, Ch. Fattinger, J. Opt. Soc. Am. B 7, 2006 (1990).
[CrossRef]

1989 (3)

C. R. Lutz, A. P. DeFonzo, Appl. Phys. Lett. 54, 2186 (1989).
[CrossRef]

M. van Exter, Ch. Fattinger, D. Grischkowsky, Opt. Lett. 14, 1128 (1989).
[CrossRef]

Ch. Fattinger, D. Grischkowsky, Appl. Phys. Lett. 54, 490 (1989).
[CrossRef]

1988 (2)

Y. Pastol, G. Arjavalingam, J.-M. Halbout, F. V. Kopcsay, Electron. Lett. 24, 1318 (1988).
[CrossRef]

P. R. Smith, D. H. Auston, M. C. Nuss, IEEE J. Quantum Electron. 24, 255 (1988).
[CrossRef]

1987 (1)

F. E. Doany, D. Grischkowsky, C.-C. Chi, Appl. Phys. Lett. 50, 460 (1987).
[CrossRef]

1977 (1)

Arjavalingam, G.

Y. Pastol, G. Arjavalingam, J.-M. Halbout, Electron. Lett. 26, 133 (1990).
[CrossRef]

Y. Pastol, G. Arjavalingam, J.-M. Halbout, F. V. Kopcsay, Electron. Lett. 24, 1318 (1988).
[CrossRef]

Auston, D. H.

J. T. Darrow, B. B. Hu, X.-C. Zhang, D. H. Auston, Opt. Lett. 15, 323 (1990).
[CrossRef] [PubMed]

P. R. Smith, D. H. Auston, M. C. Nuss, IEEE J. Quantum Electron. 24, 255 (1988).
[CrossRef]

Balslev, I.

J. E. Pedersen, I. Balslev, J. M. Hvam, S. R. Keiding, Appl. Phys. Lett. 61, 1372 (1992).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Chap. 8, p. 375.

Chi, C.-C.

F. E. Doany, D. Grischkowsky, C.-C. Chi, Appl. Phys. Lett. 50, 460 (1987).
[CrossRef]

Darrow, J. T.

DeFonzo, A. P.

C. R. Lutz, A. P. DeFonzo, Appl. Phys. Lett. 54, 2186 (1989).
[CrossRef]

Doany, F. E.

F. E. Doany, D. Grischkowsky, C.-C. Chi, Appl. Phys. Lett. 50, 460 (1987).
[CrossRef]

Fattinger, Ch.

D. Grischkowsky, S. Keiding, M. van Exter, Ch. Fattinger, J. Opt. Soc. Am. B 7, 2006 (1990).
[CrossRef]

Ch. Fattinger, D. Grischkowsky, Appl. Phys. Lett. 54, 490 (1989).
[CrossRef]

M. van Exter, Ch. Fattinger, D. Grischkowsky, Opt. Lett. 14, 1128 (1989).
[CrossRef]

Ch. Fattinger, D. Grischkowsky, presented at Picosecond Electronics and Optoelectronics Topical Meeting, Salt Lake City, Utah, March 8–10, 1989, paper FB-4.

Grischkowsky, D.

D. Grischkowsky, Opt. Photon. News 3(5), 21 (1992).
[CrossRef]

M. van Exter, D. Grischkowsky, IEEE Trans. Microwave Theory Technol. 38, 1684 (1990).
[CrossRef]

D. Grischkowsky, S. Keiding, M. van Exter, Ch. Fattinger, J. Opt. Soc. Am. B 7, 2006 (1990).
[CrossRef]

Ch. Fattinger, D. Grischkowsky, Appl. Phys. Lett. 54, 490 (1989).
[CrossRef]

M. van Exter, Ch. Fattinger, D. Grischkowsky, Opt. Lett. 14, 1128 (1989).
[CrossRef]

F. E. Doany, D. Grischkowsky, C.-C. Chi, Appl. Phys. Lett. 50, 460 (1987).
[CrossRef]

Ch. Fattinger, D. Grischkowsky, presented at Picosecond Electronics and Optoelectronics Topical Meeting, Salt Lake City, Utah, March 8–10, 1989, paper FB-4.

Halbout, J.-M.

Y. Pastol, G. Arjavalingam, J.-M. Halbout, Electron. Lett. 26, 133 (1990).
[CrossRef]

Y. Pastol, G. Arjavalingam, J.-M. Halbout, F. V. Kopcsay, Electron. Lett. 24, 1318 (1988).
[CrossRef]

Hu, B. B.

Hvam, J. M.

J. E. Pedersen, I. Balslev, J. M. Hvam, S. R. Keiding, Appl. Phys. Lett. 61, 1372 (1992).
[CrossRef]

Keiding, S.

Keiding, S. R.

J. E. Pedersen, I. Balslev, J. M. Hvam, S. R. Keiding, Appl. Phys. Lett. 61, 1372 (1992).
[CrossRef]

Kopcsay, F. V.

Y. Pastol, G. Arjavalingam, J.-M. Halbout, F. V. Kopcsay, Electron. Lett. 24, 1318 (1988).
[CrossRef]

Kunz, R. E.

Lukosz, W.

Lutz, C. R.

C. R. Lutz, A. P. DeFonzo, Appl. Phys. Lett. 54, 2186 (1989).
[CrossRef]

Nuss, M. C.

P. R. Smith, D. H. Auston, M. C. Nuss, IEEE J. Quantum Electron. 24, 255 (1988).
[CrossRef]

Pastol, Y.

Y. Pastol, G. Arjavalingam, J.-M. Halbout, Electron. Lett. 26, 133 (1990).
[CrossRef]

Y. Pastol, G. Arjavalingam, J.-M. Halbout, F. V. Kopcsay, Electron. Lett. 24, 1318 (1988).
[CrossRef]

Pedersen, J. E.

J. E. Pedersen, I. Balslev, J. M. Hvam, S. R. Keiding, Appl. Phys. Lett. 61, 1372 (1992).
[CrossRef]

Smith, P. R.

P. R. Smith, D. H. Auston, M. C. Nuss, IEEE J. Quantum Electron. 24, 255 (1988).
[CrossRef]

van Exter, M.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Chap. 8, p. 375.

Zhang, X.-C.

Appl. Phys. Lett. (4)

Ch. Fattinger, D. Grischkowsky, Appl. Phys. Lett. 54, 490 (1989).
[CrossRef]

C. R. Lutz, A. P. DeFonzo, Appl. Phys. Lett. 54, 2186 (1989).
[CrossRef]

J. E. Pedersen, I. Balslev, J. M. Hvam, S. R. Keiding, Appl. Phys. Lett. 61, 1372 (1992).
[CrossRef]

F. E. Doany, D. Grischkowsky, C.-C. Chi, Appl. Phys. Lett. 50, 460 (1987).
[CrossRef]

Electron. Lett. (2)

Y. Pastol, G. Arjavalingam, J.-M. Halbout, Electron. Lett. 26, 133 (1990).
[CrossRef]

Y. Pastol, G. Arjavalingam, J.-M. Halbout, F. V. Kopcsay, Electron. Lett. 24, 1318 (1988).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. R. Smith, D. H. Auston, M. C. Nuss, IEEE J. Quantum Electron. 24, 255 (1988).
[CrossRef]

IEEE Trans. Microwave Theory Technol. (1)

M. van Exter, D. Grischkowsky, IEEE Trans. Microwave Theory Technol. 38, 1684 (1990).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Lett. (2)

Opt. Photon. News (1)

D. Grischkowsky, Opt. Photon. News 3(5), 21 (1992).
[CrossRef]

Other (2)

Ch. Fattinger, D. Grischkowsky, presented at Picosecond Electronics and Optoelectronics Topical Meeting, Salt Lake City, Utah, March 8–10, 1989, paper FB-4.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Chap. 8, p. 375.

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Figures (4)

Fig. 1
Fig. 1

Radiation patterns from the terahertz emitter shown as density plots. Dark shading corresponds to large field amplitudes. The x axis is the horizontal position perpendicular to the lens tip, and the y axis is the distance from the lens tip. Examples are shown for 0.5 and 1.0 THz.

Fig. 2
Fig. 2

Experimental setup. BS, beam splitter; M’s, mirrors; VDL, variable delay line; RR’s, retroreflectors. The inset illustrates the electrical circuit connected to the emitter (E) and detector (D) chips. LIA, lock in amplifier. (x, y) is the position of the detector with respect to the emitter.

Fig. 3
Fig. 3

Left: the time dependence of the terahertz pulse. The x axis shows the time delay, spanning 9 ps. The y axis is the detected current, which is proportional to the instantaneous electric field at the detector. Right: the corresponding frequency spectrum. The x axis is the frequency, showing a −3-dB bandwidth of 600 GHz, and the y axis shows the strength of the individual Fourier components.

Fig. 4
Fig. 4

Experimentally determined radiation patterns obtained at a distance of 35 mm from the lens tip at six different frequencies. The radiation patterns found by calculation (solid curves) are shown together with the experimental data (symbols). The x axes show the horizontal position of the detector with respect to the emitter (illustrated in Fig. 2), and the y axes show the field strength.

Equations (2)

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E vac = μ 0 c 2 4 π k 2 exp ( ikr ) r ( n ^ × p ) × n ^ ,
Ψ Q = ik 4 π A Ψ out exp ( ikr ) r ( cos   θ out n si   cos   θ in ) d A .

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