Abstract

We present spatially resolved measurements of the electric field of terahertz pulses undergoing optical tunneling that show strong pulse reshaping in both time and space. This reshaping is shown to be a result of frequency and incidence-angle filtering of the complex amplitude of the plane-wave basis set that makes up the pulse. This filtering leads to spreading of the pulse in the time and space dimensions, as expected from linear dispersion theory. Measurement of the pulse shape after transmission through an optical tunneling barrier permits direct determination of the complex system transfer function in two dimensions. The transfer function, measured over both thin and thick barrier limits, contains a complete description of the tunneling barrier system from which the phase and loss times can be directly determined.

© 2001 Optical Society of America

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References

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  1. L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960).
  2. R. Landauer and Th. Martin, “Barrier interaction time in tunneling,” Rev. Mod. Phys. 66, 217–221 (1994).
    [CrossRef]
  3. R. Y. Chiao and A. M. Steinberg, “Tunneling times and superluminality,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1997), Vol. 37 pp. 345–405.
    [CrossRef]
  4. J. J. Carey, J. Zawadzka, D. A. Jaroszynski, and K. Wynne, “Noncausal time response in frustrated total internal reflection,” Phys. Rev. Lett. 84, 1431–1434 (2000).
    [CrossRef] [PubMed]
  5. M. T. Reiten, D. Grischkowsky, and R. A. Cheville, Phys. Rev. E 64, 036604 (2001).
    [CrossRef]
  6. D. Grischkowsky, S. Keiding, M. van Exter, and Ch. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7, 2006–2015 (1990).
    [CrossRef]
  7. A. K. Ghatak, M. R. Shenoy, I. C. Goyal, and K. Thyagarajan, “Beam propagation under frustrated total internal reflection,” Opt. Commun. 56, 313–317 (1986).
    [CrossRef]
  8. Ph. Balcou and L. Dutriaux, “Dual optical tunneling times is frustrated total internal reflection,” Phys. Rev. Lett. 78, 851–854 (1997).
    [CrossRef]

2001 (1)

M. T. Reiten, D. Grischkowsky, and R. A. Cheville, Phys. Rev. E 64, 036604 (2001).
[CrossRef]

2000 (1)

J. J. Carey, J. Zawadzka, D. A. Jaroszynski, and K. Wynne, “Noncausal time response in frustrated total internal reflection,” Phys. Rev. Lett. 84, 1431–1434 (2000).
[CrossRef] [PubMed]

1997 (1)

Ph. Balcou and L. Dutriaux, “Dual optical tunneling times is frustrated total internal reflection,” Phys. Rev. Lett. 78, 851–854 (1997).
[CrossRef]

1994 (1)

R. Landauer and Th. Martin, “Barrier interaction time in tunneling,” Rev. Mod. Phys. 66, 217–221 (1994).
[CrossRef]

1990 (1)

1986 (1)

A. K. Ghatak, M. R. Shenoy, I. C. Goyal, and K. Thyagarajan, “Beam propagation under frustrated total internal reflection,” Opt. Commun. 56, 313–317 (1986).
[CrossRef]

Balcou, Ph.

Ph. Balcou and L. Dutriaux, “Dual optical tunneling times is frustrated total internal reflection,” Phys. Rev. Lett. 78, 851–854 (1997).
[CrossRef]

Brillouin, L.

L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960).

Carey, J. J.

J. J. Carey, J. Zawadzka, D. A. Jaroszynski, and K. Wynne, “Noncausal time response in frustrated total internal reflection,” Phys. Rev. Lett. 84, 1431–1434 (2000).
[CrossRef] [PubMed]

Cheville, R. A.

M. T. Reiten, D. Grischkowsky, and R. A. Cheville, Phys. Rev. E 64, 036604 (2001).
[CrossRef]

Chiao, R. Y.

R. Y. Chiao and A. M. Steinberg, “Tunneling times and superluminality,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1997), Vol. 37 pp. 345–405.
[CrossRef]

Dutriaux, L.

Ph. Balcou and L. Dutriaux, “Dual optical tunneling times is frustrated total internal reflection,” Phys. Rev. Lett. 78, 851–854 (1997).
[CrossRef]

Fattinger, Ch.

Ghatak, A. K.

A. K. Ghatak, M. R. Shenoy, I. C. Goyal, and K. Thyagarajan, “Beam propagation under frustrated total internal reflection,” Opt. Commun. 56, 313–317 (1986).
[CrossRef]

Goyal, I. C.

A. K. Ghatak, M. R. Shenoy, I. C. Goyal, and K. Thyagarajan, “Beam propagation under frustrated total internal reflection,” Opt. Commun. 56, 313–317 (1986).
[CrossRef]

Grischkowsky, D.

Jaroszynski, D. A.

J. J. Carey, J. Zawadzka, D. A. Jaroszynski, and K. Wynne, “Noncausal time response in frustrated total internal reflection,” Phys. Rev. Lett. 84, 1431–1434 (2000).
[CrossRef] [PubMed]

Keiding, S.

Landauer, R.

R. Landauer and Th. Martin, “Barrier interaction time in tunneling,” Rev. Mod. Phys. 66, 217–221 (1994).
[CrossRef]

Martin, Th.

R. Landauer and Th. Martin, “Barrier interaction time in tunneling,” Rev. Mod. Phys. 66, 217–221 (1994).
[CrossRef]

Reiten, M. T.

M. T. Reiten, D. Grischkowsky, and R. A. Cheville, Phys. Rev. E 64, 036604 (2001).
[CrossRef]

Shenoy, M. R.

A. K. Ghatak, M. R. Shenoy, I. C. Goyal, and K. Thyagarajan, “Beam propagation under frustrated total internal reflection,” Opt. Commun. 56, 313–317 (1986).
[CrossRef]

Steinberg, A. M.

R. Y. Chiao and A. M. Steinberg, “Tunneling times and superluminality,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1997), Vol. 37 pp. 345–405.
[CrossRef]

Thyagarajan, K.

A. K. Ghatak, M. R. Shenoy, I. C. Goyal, and K. Thyagarajan, “Beam propagation under frustrated total internal reflection,” Opt. Commun. 56, 313–317 (1986).
[CrossRef]

van Exter, M.

Wynne, K.

J. J. Carey, J. Zawadzka, D. A. Jaroszynski, and K. Wynne, “Noncausal time response in frustrated total internal reflection,” Phys. Rev. Lett. 84, 1431–1434 (2000).
[CrossRef] [PubMed]

Zawadzka, J.

J. J. Carey, J. Zawadzka, D. A. Jaroszynski, and K. Wynne, “Noncausal time response in frustrated total internal reflection,” Phys. Rev. Lett. 84, 1431–1434 (2000).
[CrossRef] [PubMed]

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

Opt. Commun. (1)

A. K. Ghatak, M. R. Shenoy, I. C. Goyal, and K. Thyagarajan, “Beam propagation under frustrated total internal reflection,” Opt. Commun. 56, 313–317 (1986).
[CrossRef]

Phys. Rev. E (1)

M. T. Reiten, D. Grischkowsky, and R. A. Cheville, Phys. Rev. E 64, 036604 (2001).
[CrossRef]

Phys. Rev. Lett. (2)

Ph. Balcou and L. Dutriaux, “Dual optical tunneling times is frustrated total internal reflection,” Phys. Rev. Lett. 78, 851–854 (1997).
[CrossRef]

J. J. Carey, J. Zawadzka, D. A. Jaroszynski, and K. Wynne, “Noncausal time response in frustrated total internal reflection,” Phys. Rev. Lett. 84, 1431–1434 (2000).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

R. Landauer and Th. Martin, “Barrier interaction time in tunneling,” Rev. Mod. Phys. 66, 217–221 (1994).
[CrossRef]

Other (2)

R. Y. Chiao and A. M. Steinberg, “Tunneling times and superluminality,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1997), Vol. 37 pp. 345–405.
[CrossRef]

L. Brillouin, Wave Propagation and Group Velocity (Academic, New York, 1960).

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Figures (3)

Fig. 1
Fig. 1

(a) Experimental schematic of a fiber-coupled THz receiver (FCTR). The lines represent the propagation path (dashed line, Δ=0 μm; solid line, Δ=1000 μm). Contour plots: (b) E0x,t with 15-pA contour spacing, (c) ETx,t with 5-pA spacing.

Fig. 2
Fig. 2

(a) Normalized E0ϕ,ω,Δ=0 μm. (b) ETϕ,ω,Δ=1000 μm normalized to E0ϕ,ω. The contour line spacing is 0.05, and the vertical line is θc. (c) Hϕ,ω. The dashed lines are constant ϕ values of Fig.  3, and the dotted curve represents the thick–thin barrier boundary.

Fig. 3
Fig. 3

(a) Semilog plot of Hϕ,ω and (b) linear plot of Φϕ,ω for ϕ=-0.15°,0°,+0.15°.

Equations (3)

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

Ekx,ω0=-Er,ω0exp-ikxxx,
ETϕ,ωE0ϕ,ω=Hϕ,ω=Hϕ,ωexpiΦϕ,ω.
τΦ=Φω,τL=-lnHϕ,ωω.

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