Abstract

We have studied the propagation of half-cycle (i.e., unipolar) electromagnetic pulses centered at terahertz frequencies, in free space, through apertures, and through focusing optics. The temporal pulse shape of an apertured half-cycle pulse is significantly altered during propagation, but retains much of its unipolar character after traveling more than 20 times the aperture dimension. When focused by an achromatic lens, a half-cycle pulse evolves into a single-cycle pulse at the focal waist and an inverted half-cycle pulse in the far field.

© 1997 Optical Society of America

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  1. C. Fattinger and D. Grischkowsky, Appl. Phys. Lett. 53, 1480 (1988).
    [CrossRef]
  2. D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, Phys. Rev. Lett. 53, 1555 (1984); C. Fattinger and D. R. Grischkowsky, IEEE J. Quantum Electron. 25, 2608 (1989).
    [CrossRef]
  3. D. H. Auston, K. P. Cheung, and P. R. Smith, Appl. Phys. Lett. 45, 284 (1984); B. B. Hu, J. T. Darrow, X.-C. Zhang, and D. H. Auston, Appl. Phys. Lett. 56, 886 (1990).
    [CrossRef]
  4. C. Fattinger and D. Grischkowsky, Appl. Phys. Lett. 54, 490 (1989).
    [CrossRef]
  5. D. You, R. R. Jones, P. H. Bucksbaum, and D. R. Dykaar, Opt. Lett. 18, 290 (1993).
    [CrossRef]
  6. A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, Appl. Phys. Lett. 64, 137 (1994).
    [CrossRef]
  7. D. You, R. R. Jones, P. H. Bucksbaum, and D. R. Dykaar, J. Opt. Soc. Am. B 11, 486 (1994).
    [CrossRef]
  8. R. R. Jones, D. You, and P. H. Bucksbaum, Phys. Rev. Lett. 70, 1236 (1993).
    [CrossRef] [PubMed]
  9. C. Raman, C. W. S. Conover, C. I. Sukenik, and P. H. Bucksbaum, Phys. Rev. Lett. 76, 2436 (1996).
    [CrossRef] [PubMed]
  10. R. R. Jones, N. E. Tielking, D. You, C. Raman, and P. H. Bucksbaum, Phys. Rev. A 51, R2687 (1995).
    [CrossRef]
  11. G. M. Lankhuijzen and L. D. Noordam, Phys. Rev. Lett. 74, 355 (1995).
    [CrossRef] [PubMed]
  12. M. van Exter, Ch. Fattinger, and D. Grischkowsky, Opt. Lett. 14, 1128 (1989); B. I. Greene, J. F. Federici, D. R. Dykaar, A. F. J. Levi, and L. Pfeiffer, Opt. Lett. 16, 48 (1991).
    [CrossRef] [PubMed]
  13. D. H. Auston and K. P. Cheung, J. Opt. Soc. Am. B 2, 606 (1985); M. van Exter, D. R. Grischkowsky, IEEE Trans. Microwave Theory Tech. 38, 1684 (1990).
    [CrossRef]
  14. Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 67, 3523 (1995).
    [CrossRef]
  15. B. I. Greene, J. F. Federici, D. R. Dykaar, R. R. Jones, and P. H. Bucksbaum, Appl. Phys. Lett. 59, 893 (1991).
    [CrossRef]
  16. J. T. Darrow, X.-C. Zhang, and D. J. Auston, IEEE J. Quantum Electron. 28, 1067 (1992); A. J. Taylor, P. K. Benicewicz, and S. M. Young, Opt. Lett. 18, 1340 (1993).
    [CrossRef]
  17. X.-C. Zhang, Y. Jin, K. Yang, and L. J. Schowalter, Phys. Rev. Lett. 69, 2303 (1992).
    [CrossRef] [PubMed]
  18. S. L. Chuang, S. Schmitt-Rink, B. I. Greene, P. N. Saeta, and A. F. J. Levi, Phys. Rev. Lett. 68, 102 (1992).
    [CrossRef] [PubMed]
  19. A. Yariv, Optical Electronics (CBS College, New York, 1985).
  20. H. Kogelnik and T. Li, Appl. Opt. 5, 1550 (1966).
    [CrossRef] [PubMed]
  21. M. van Exter, C. Fattinger, and D. Grischkowsky, Appl. Phys. Lett. 55, 337 (1989); B. B. Hu, X.-C. Zhang, D. H. Auston, and P. R. Smith, Appl. Phys. Lett. 56, 506 (1990).
    [CrossRef]

1996 (1)

C. Raman, C. W. S. Conover, C. I. Sukenik, and P. H. Bucksbaum, Phys. Rev. Lett. 76, 2436 (1996).
[CrossRef] [PubMed]

1995 (3)

R. R. Jones, N. E. Tielking, D. You, C. Raman, and P. H. Bucksbaum, Phys. Rev. A 51, R2687 (1995).
[CrossRef]

G. M. Lankhuijzen and L. D. Noordam, Phys. Rev. Lett. 74, 355 (1995).
[CrossRef] [PubMed]

Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 67, 3523 (1995).
[CrossRef]

1994 (2)

A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, Appl. Phys. Lett. 64, 137 (1994).
[CrossRef]

D. You, R. R. Jones, P. H. Bucksbaum, and D. R. Dykaar, J. Opt. Soc. Am. B 11, 486 (1994).
[CrossRef]

1993 (2)

1992 (2)

X.-C. Zhang, Y. Jin, K. Yang, and L. J. Schowalter, Phys. Rev. Lett. 69, 2303 (1992).
[CrossRef] [PubMed]

S. L. Chuang, S. Schmitt-Rink, B. I. Greene, P. N. Saeta, and A. F. J. Levi, Phys. Rev. Lett. 68, 102 (1992).
[CrossRef] [PubMed]

1991 (1)

B. I. Greene, J. F. Federici, D. R. Dykaar, R. R. Jones, and P. H. Bucksbaum, Appl. Phys. Lett. 59, 893 (1991).
[CrossRef]

1989 (1)

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

1988 (1)

C. Fattinger and D. Grischkowsky, Appl. Phys. Lett. 53, 1480 (1988).
[CrossRef]

1966 (1)

Auston, D. H.

A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, Appl. Phys. Lett. 64, 137 (1994).
[CrossRef]

Bucksbaum, P. H.

C. Raman, C. W. S. Conover, C. I. Sukenik, and P. H. Bucksbaum, Phys. Rev. Lett. 76, 2436 (1996).
[CrossRef] [PubMed]

R. R. Jones, N. E. Tielking, D. You, C. Raman, and P. H. Bucksbaum, Phys. Rev. A 51, R2687 (1995).
[CrossRef]

D. You, R. R. Jones, P. H. Bucksbaum, and D. R. Dykaar, J. Opt. Soc. Am. B 11, 486 (1994).
[CrossRef]

D. You, R. R. Jones, P. H. Bucksbaum, and D. R. Dykaar, Opt. Lett. 18, 290 (1993).
[CrossRef]

R. R. Jones, D. You, and P. H. Bucksbaum, Phys. Rev. Lett. 70, 1236 (1993).
[CrossRef] [PubMed]

B. I. Greene, J. F. Federici, D. R. Dykaar, R. R. Jones, and P. H. Bucksbaum, Appl. Phys. Lett. 59, 893 (1991).
[CrossRef]

Chuang, S. L.

S. L. Chuang, S. Schmitt-Rink, B. I. Greene, P. N. Saeta, and A. F. J. Levi, Phys. Rev. Lett. 68, 102 (1992).
[CrossRef] [PubMed]

Conover, C. W. S.

C. Raman, C. W. S. Conover, C. I. Sukenik, and P. H. Bucksbaum, Phys. Rev. Lett. 76, 2436 (1996).
[CrossRef] [PubMed]

Dykaar, D. R.

Fattinger, C.

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

C. Fattinger and D. Grischkowsky, Appl. Phys. Lett. 53, 1480 (1988).
[CrossRef]

Federici, J. F.

B. I. Greene, J. F. Federici, D. R. Dykaar, R. R. Jones, and P. H. Bucksbaum, Appl. Phys. Lett. 59, 893 (1991).
[CrossRef]

Froberg, N. M.

A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, Appl. Phys. Lett. 64, 137 (1994).
[CrossRef]

Greene, B. I.

S. L. Chuang, S. Schmitt-Rink, B. I. Greene, P. N. Saeta, and A. F. J. Levi, Phys. Rev. Lett. 68, 102 (1992).
[CrossRef] [PubMed]

B. I. Greene, J. F. Federici, D. R. Dykaar, R. R. Jones, and P. H. Bucksbaum, Appl. Phys. Lett. 59, 893 (1991).
[CrossRef]

Grischkowsky, D.

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

C. Fattinger and D. Grischkowsky, Appl. Phys. Lett. 53, 1480 (1988).
[CrossRef]

Hu, B. B.

A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, Appl. Phys. Lett. 64, 137 (1994).
[CrossRef]

Jin, Y.

X.-C. Zhang, Y. Jin, K. Yang, and L. J. Schowalter, Phys. Rev. Lett. 69, 2303 (1992).
[CrossRef] [PubMed]

Jones, R. R.

R. R. Jones, N. E. Tielking, D. You, C. Raman, and P. H. Bucksbaum, Phys. Rev. A 51, R2687 (1995).
[CrossRef]

D. You, R. R. Jones, P. H. Bucksbaum, and D. R. Dykaar, J. Opt. Soc. Am. B 11, 486 (1994).
[CrossRef]

D. You, R. R. Jones, P. H. Bucksbaum, and D. R. Dykaar, Opt. Lett. 18, 290 (1993).
[CrossRef]

R. R. Jones, D. You, and P. H. Bucksbaum, Phys. Rev. Lett. 70, 1236 (1993).
[CrossRef] [PubMed]

B. I. Greene, J. F. Federici, D. R. Dykaar, R. R. Jones, and P. H. Bucksbaum, Appl. Phys. Lett. 59, 893 (1991).
[CrossRef]

Kogelnik, H.

Lankhuijzen, G. M.

G. M. Lankhuijzen and L. D. Noordam, Phys. Rev. Lett. 74, 355 (1995).
[CrossRef] [PubMed]

Levi, A. F. J.

S. L. Chuang, S. Schmitt-Rink, B. I. Greene, P. N. Saeta, and A. F. J. Levi, Phys. Rev. Lett. 68, 102 (1992).
[CrossRef] [PubMed]

Li, T.

Noordam, L. D.

G. M. Lankhuijzen and L. D. Noordam, Phys. Rev. Lett. 74, 355 (1995).
[CrossRef] [PubMed]

Raman, C.

C. Raman, C. W. S. Conover, C. I. Sukenik, and P. H. Bucksbaum, Phys. Rev. Lett. 76, 2436 (1996).
[CrossRef] [PubMed]

R. R. Jones, N. E. Tielking, D. You, C. Raman, and P. H. Bucksbaum, Phys. Rev. A 51, R2687 (1995).
[CrossRef]

Saeta, P. N.

S. L. Chuang, S. Schmitt-Rink, B. I. Greene, P. N. Saeta, and A. F. J. Levi, Phys. Rev. Lett. 68, 102 (1992).
[CrossRef] [PubMed]

Schmitt-Rink, S.

S. L. Chuang, S. Schmitt-Rink, B. I. Greene, P. N. Saeta, and A. F. J. Levi, Phys. Rev. Lett. 68, 102 (1992).
[CrossRef] [PubMed]

Schowalter, L. J.

X.-C. Zhang, Y. Jin, K. Yang, and L. J. Schowalter, Phys. Rev. Lett. 69, 2303 (1992).
[CrossRef] [PubMed]

Sukenik, C. I.

C. Raman, C. W. S. Conover, C. I. Sukenik, and P. H. Bucksbaum, Phys. Rev. Lett. 76, 2436 (1996).
[CrossRef] [PubMed]

Tielking, N. E.

R. R. Jones, N. E. Tielking, D. You, C. Raman, and P. H. Bucksbaum, Phys. Rev. A 51, R2687 (1995).
[CrossRef]

Weling, A. S.

A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, Appl. Phys. Lett. 64, 137 (1994).
[CrossRef]

Wu, Q.

Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 67, 3523 (1995).
[CrossRef]

Yang, K.

X.-C. Zhang, Y. Jin, K. Yang, and L. J. Schowalter, Phys. Rev. Lett. 69, 2303 (1992).
[CrossRef] [PubMed]

You, D.

R. R. Jones, N. E. Tielking, D. You, C. Raman, and P. H. Bucksbaum, Phys. Rev. A 51, R2687 (1995).
[CrossRef]

D. You, R. R. Jones, P. H. Bucksbaum, and D. R. Dykaar, J. Opt. Soc. Am. B 11, 486 (1994).
[CrossRef]

D. You, R. R. Jones, P. H. Bucksbaum, and D. R. Dykaar, Opt. Lett. 18, 290 (1993).
[CrossRef]

R. R. Jones, D. You, and P. H. Bucksbaum, Phys. Rev. Lett. 70, 1236 (1993).
[CrossRef] [PubMed]

Zhang, X.-C.

Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 67, 3523 (1995).
[CrossRef]

X.-C. Zhang, Y. Jin, K. Yang, and L. J. Schowalter, Phys. Rev. Lett. 69, 2303 (1992).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (5)

Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 67, 3523 (1995).
[CrossRef]

B. I. Greene, J. F. Federici, D. R. Dykaar, R. R. Jones, and P. H. Bucksbaum, Appl. Phys. Lett. 59, 893 (1991).
[CrossRef]

C. Fattinger and D. Grischkowsky, Appl. Phys. Lett. 53, 1480 (1988).
[CrossRef]

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

A. S. Weling, B. B. Hu, N. M. Froberg, and D. H. Auston, Appl. Phys. Lett. 64, 137 (1994).
[CrossRef]

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

Opt. Lett. (1)

Phys. Rev. A (1)

R. R. Jones, N. E. Tielking, D. You, C. Raman, and P. H. Bucksbaum, Phys. Rev. A 51, R2687 (1995).
[CrossRef]

Phys. Rev. Lett. (5)

G. M. Lankhuijzen and L. D. Noordam, Phys. Rev. Lett. 74, 355 (1995).
[CrossRef] [PubMed]

R. R. Jones, D. You, and P. H. Bucksbaum, Phys. Rev. Lett. 70, 1236 (1993).
[CrossRef] [PubMed]

C. Raman, C. W. S. Conover, C. I. Sukenik, and P. H. Bucksbaum, Phys. Rev. Lett. 76, 2436 (1996).
[CrossRef] [PubMed]

X.-C. Zhang, Y. Jin, K. Yang, and L. J. Schowalter, Phys. Rev. Lett. 69, 2303 (1992).
[CrossRef] [PubMed]

S. L. Chuang, S. Schmitt-Rink, B. I. Greene, P. N. Saeta, and A. F. J. Levi, Phys. Rev. Lett. 68, 102 (1992).
[CrossRef] [PubMed]

Other (7)

A. Yariv, Optical Electronics (CBS College, New York, 1985).

D. H. Auston, K. P. Cheung, J. A. Valdmanis, and D. A. Kleinman, Phys. Rev. Lett. 53, 1555 (1984); C. Fattinger and D. R. Grischkowsky, IEEE J. Quantum Electron. 25, 2608 (1989).
[CrossRef]

D. H. Auston, K. P. Cheung, and P. R. Smith, Appl. Phys. Lett. 45, 284 (1984); B. B. Hu, J. T. Darrow, X.-C. Zhang, and D. H. Auston, Appl. Phys. Lett. 56, 886 (1990).
[CrossRef]

M. van Exter, C. Fattinger, and D. Grischkowsky, Appl. Phys. Lett. 55, 337 (1989); B. B. Hu, X.-C. Zhang, D. H. Auston, and P. R. Smith, Appl. Phys. Lett. 56, 506 (1990).
[CrossRef]

J. T. Darrow, X.-C. Zhang, and D. J. Auston, IEEE J. Quantum Electron. 28, 1067 (1992); A. J. Taylor, P. K. Benicewicz, and S. M. Young, Opt. Lett. 18, 1340 (1993).
[CrossRef]

M. van Exter, Ch. Fattinger, and D. Grischkowsky, Opt. Lett. 14, 1128 (1989); B. I. Greene, J. F. Federici, D. R. Dykaar, A. F. J. Levi, and L. Pfeiffer, Opt. Lett. 16, 48 (1991).
[CrossRef] [PubMed]

D. H. Auston and K. P. Cheung, J. Opt. Soc. Am. B 2, 606 (1985); M. van Exter, D. R. Grischkowsky, IEEE Trans. Microwave Theory Tech. 38, 1684 (1990).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Amplitude of FIR pulse in free space as functions of time (picoseconds) at (A) 0 cm, (B) 20 cm, and (C) 40 cm.

Fig. 2
Fig. 2

Amplitude FIR radiation in free space as functions of frequency (THz) at (A) 0 cm, (B) 20 cm, and (C) 40 cm.

Fig. 3
Fig. 3

Configuration in which the calculation is performed. The FIR pulse is assumed to propagate through a converging lens.

Fig. 4
Fig. 4

Calculated amplitude as functions of time (picoseconds) at (A) 10 cm, (B) 25 cm, and (C) 40 cm after the FIR pulse propagates through a converging lens of 15 cm located at a distance of 10 cm from the transmitter.

Fig. 5
Fig. 5

Calculated amplitude as functions of frequency (terahertz) at (A) 10 cm, (B) 25 cm, and (C) 40 cm after the FIR pulse propagates through a converging lens.

Equations (11)

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

F(r, z, ϕ)=F0 w0w(z)exp-i[kz-η(z)]-r21w2(z)+ik2R(z).
w2(z)=w021+z2z02,
R(z)=z1+z02z2,
η(z)=arctanzz0,
z0=πw02nλ.
1q(z)=1R(z)-i λπnw2(z).
F(r, z=0, ϕ, t)=F0 exp-t2τ2-r2w02,
F(r, z=0, ϕ, ω)=πτF0 exp-ω2τ24-r2w02.
ω02=w02f2(l2+z02)(l2+z02-lf )2+f2z02,
d=f(l2+z02)(l2+z02-lf)(l2+z02-lf )2+f2z02.
F(r, z, ϕ, ω)=F0 w0w(z-l-d)exp-i[kz-η×(z-l-d)-η(l)-η(d)]-r21w2(z-l-d)+ik2R(z-l-d),

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