Abstract

We demonstrate a simple quasi-optical technique for spatiotemporal shaping of half-cycle terahertz-radiation pulses. We show, both experimentally and theoretically, that properly polarized half-cycle pulses can be modulated temporally by diffraction through a conductive aperture of finite thickness. We use the finite-difference time-domain method to solve Maxwell’s equations for such a geometry and show that it can explain all the experimentally observed features. In the case of a thick aperture, a planar waveguide model can also be used to describe the propagation of the pulse through the aperture, with excellent agreement with the experimental results.

[Optical Society of America ]

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References

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  1. A. Baltuska , Z. Wei , M. Pshenichnikov , and D. Wiersma , Optical pulse compression to 5 fs at a 1-MHz repetition rate , Opt. Lett. OPLEDP 22 , 102 ( 1997
    [CrossRef] [PubMed]
  2. R. L. Fork , C. H. Brito Cruz , P. C. Becker , and C. V. Shank , Compression of optical pulses to six femtoseconds by using cubic phase compensation , Opt. Lett. OPLEDP 12 , 483 ( 1987
    [CrossRef] [PubMed]
  3. D. H. Auston , K. P. Cheung , and P. R. Smith , Picosecond photoconducting Hertzian dipoles , Appl. Phys. Lett. APPLAB 45 , 284 ( 1984
    [CrossRef]
  4. D. R. Dykaar , B. I. Greene , J. F. Federici , A. F. J. Levi , L. N. Pfeiffer , and R. F. Kopf , Log-periodic antennas for pulsed terahertz radiation , Appl. Phys. Lett. APPLAB 59 , 262 ( 1991
    [CrossRef]
  5. J. T. Darrow , B. B. Hu , X.-C. Zhang , and D. H. Auston , Subpicosecond electromagnetic pulses from large-aperture photoconducting antennas , Opt. Lett. OPLEDP 15 , 323 ( 1990
    [CrossRef] [PubMed]
  6. X.-C. Zhang , B. B. Hu , J. T. Darrow , and D. H. Auston , Generation of femtosecond electromagnetic pulses from semiconductor surfaces , Appl. Phys. Lett. APPLAB 56 , 1011 ( 1990
    [CrossRef]
  7. L. Xu , X.-C. Zhang , D. H. Auston , and B. Jahali , Terahertz radiation from large aperture Si p-i-n diodes , Appl. Phys. Lett. APPLAB 59 , 3357 ( 1991
    [CrossRef]
  8. X.-C. Zhang , B. B. Hu , S. Xin , and D. H. Auston , Optically induced femtosecond electromagnetic pulses from GaSb/AlSb strained-layer superlattice , Appl. Phys. Lett. APPLAB 57 , 753 ( 1990
    [CrossRef]
  9. A. S. Weling , B. B. Hu , N. M. Froberg , and D. H. Auston , Generation of tunable narrow-band THz radiation from large aperture photoconducting antennas , Appl. Phys. Lett. APPLAB 64 , 137 ( 1994
    [CrossRef]
  10. S. R. Keiding , THz spectroscopy in atomic, molecular and optical physics , Comments At. Mol. Phys. CAMPBS 30 , 37 ( 1994
  11. B. B. Hu and M. C. Nuss , Imaging with terahertz waves , Opt. Lett. OPLEDP 20 , 1716 ( 1995
    [CrossRef] [PubMed]
  12. R. R. Jones , Creating and probing electronic wave packets using half-cycle pulses , Phys. Rev. Lett. PRLTAO 76 , 3927 ( 1996
    [CrossRef] [PubMed]
  13. J. Wenbin , S. Diechi , and L. Fuming , Distortion of femtosecond optical pulses with Gaussian spatial distribution propagating in free space , Chin. Phys. CHPHD2 10 , 168 ( 1990
  14. D. You and P. H. Bucksbaum , Propagation of half-cycle FIR pulses , J. Opt. Soc. Am. B JOBPDE 14 , 1651 ( 1997
    [CrossRef]
  15. N. M. Froberg , B. B. Hu , X.-C. Zhang , and D. H. Auston , Terahertz radiation from a photoconducting antenna array , IEEE J. Quantum Electron. IEJQA7 28 , 2291 ( 1992
    [CrossRef]
  16. J. O. White , C. Ludwig , and J. Kuhl , Response of grating pairs to single-cycle electromagnetic pulses , J. Opt. Soc. Am. B JOBPDE 12 , 1687 ( 1995
    [CrossRef]
  17. A. Taflove and M. Brodwin , Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell s equations , IEEE Trans. Microwave Theory Tech. IETMAB MTT-23 , 623 ( 1975
    [CrossRef]

Other (17)

D. H. Auston , K. P. Cheung , and P. R. Smith , Picosecond photoconducting Hertzian dipoles , Appl. Phys. Lett. APPLAB 45 , 284 ( 1984
[CrossRef]

D. R. Dykaar , B. I. Greene , J. F. Federici , A. F. J. Levi , L. N. Pfeiffer , and R. F. Kopf , Log-periodic antennas for pulsed terahertz radiation , Appl. Phys. Lett. APPLAB 59 , 262 ( 1991
[CrossRef]

X.-C. Zhang , B. B. Hu , J. T. Darrow , and D. H. Auston , Generation of femtosecond electromagnetic pulses from semiconductor surfaces , Appl. Phys. Lett. APPLAB 56 , 1011 ( 1990
[CrossRef]

L. Xu , X.-C. Zhang , D. H. Auston , and B. Jahali , Terahertz radiation from large aperture Si p-i-n diodes , Appl. Phys. Lett. APPLAB 59 , 3357 ( 1991
[CrossRef]

X.-C. Zhang , B. B. Hu , S. Xin , and D. H. Auston , Optically induced femtosecond electromagnetic pulses from GaSb/AlSb strained-layer superlattice , Appl. Phys. Lett. APPLAB 57 , 753 ( 1990
[CrossRef]

A. S. Weling , B. B. Hu , N. M. Froberg , and D. H. Auston , Generation of tunable narrow-band THz radiation from large aperture photoconducting antennas , Appl. Phys. Lett. APPLAB 64 , 137 ( 1994
[CrossRef]

S. R. Keiding , THz spectroscopy in atomic, molecular and optical physics , Comments At. Mol. Phys. CAMPBS 30 , 37 ( 1994

R. R. Jones , Creating and probing electronic wave packets using half-cycle pulses , Phys. Rev. Lett. PRLTAO 76 , 3927 ( 1996
[CrossRef] [PubMed]

J. Wenbin , S. Diechi , and L. Fuming , Distortion of femtosecond optical pulses with Gaussian spatial distribution propagating in free space , Chin. Phys. CHPHD2 10 , 168 ( 1990

N. M. Froberg , B. B. Hu , X.-C. Zhang , and D. H. Auston , Terahertz radiation from a photoconducting antenna array , IEEE J. Quantum Electron. IEJQA7 28 , 2291 ( 1992
[CrossRef]

A. Taflove and M. Brodwin , Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell s equations , IEEE Trans. Microwave Theory Tech. IETMAB MTT-23 , 623 ( 1975
[CrossRef]

R. L. Fork , C. H. Brito Cruz , P. C. Becker , and C. V. Shank , Compression of optical pulses to six femtoseconds by using cubic phase compensation , Opt. Lett. OPLEDP 12 , 483 ( 1987
[CrossRef] [PubMed]

J. T. Darrow , B. B. Hu , X.-C. Zhang , and D. H. Auston , Subpicosecond electromagnetic pulses from large-aperture photoconducting antennas , Opt. Lett. OPLEDP 15 , 323 ( 1990
[CrossRef] [PubMed]

J. O. White , C. Ludwig , and J. Kuhl , Response of grating pairs to single-cycle electromagnetic pulses , J. Opt. Soc. Am. B JOBPDE 12 , 1687 ( 1995
[CrossRef]

B. B. Hu and M. C. Nuss , Imaging with terahertz waves , Opt. Lett. OPLEDP 20 , 1716 ( 1995
[CrossRef] [PubMed]

D. You and P. H. Bucksbaum , Propagation of half-cycle FIR pulses , J. Opt. Soc. Am. B JOBPDE 14 , 1651 ( 1997
[CrossRef]

A. Baltuska , Z. Wei , M. Pshenichnikov , and D. Wiersma , Optical pulse compression to 5 fs at a 1-MHz repetition rate , Opt. Lett. OPLEDP 22 , 102 ( 1997
[CrossRef] [PubMed]

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Figures (9)

Fig. 1
Fig. 1

(a) Experimental setup and (b) measured THz pulse incident upon the conducting aperture.

Fig. 2
Fig. 2

Measured (solid curves) and FDTD calculated THz pulse shapes for thin (left) and thick (right) apertures: (a) 300-μm, (b) 500-μm, (c) 700-μm widths.

Fig. 3
Fig. 3

Diffraction from a conductive slit: FDTD (dashed curves) versus measured (solid curves) field. The scattering geometry (inset) is defined by d=0.5 mm, D=3 mm, s=7 mm, and l=1.7 mm. The incident pulse shape (measured) is used in all subsequent FDTD simulations.

Fig. 4
Fig. 4

TE (left) versus TM diffraction: Pulse propagation is tracked as it penetrates the aperture in time increments of 1.5 ps. The solid curves are the on-axis pulse profiles.

Fig. 5
Fig. 5

Measured slit transfer function (d=0.5 mm). Dashed curve, phase as predicted by the waveguide model.

Fig. 6
Fig. 6

Cutoff frequency for the thick conductive slit with TM polarization: waveguide prediction (solid curve) versus measured cutoff frequencies (points).

Fig. 7
Fig. 7

TM diffraction: thin (left, l=0.1 mm) versus thick (right, l=1.7 mm) conductive apertures. The aperture width is d=0.5 mm in both cases.

Fig. 8
Fig. 8

TM pulse shaping in variable-thickness conductive apertures: the 0.5-mm-wide aperture thickness is increased from 283 μm (thin) to 1698 μm (thick).

Fig. 9
Fig. 9

TM pulse shaping in variable-width apertures: the 1.7-mm-thick aperture width is 300 μm (upper row), 700 μm (middle row), and 1100 μm (bottom row).

Equations (13)

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Hxn+1/2(i, j+1/2)
=Hxn-1/2(i, j+1/2)+Δtμ(i, j+1/2)ΔL× [Ezn(i, j)-Ezn(i, j+1)],
Hyn+1/2(i+1/2, j)
=Hyn-1/2(i+1/2,j)+Δtμ(i+1/2,j)ΔL×[Ezn(i+1,j)-Ezn(i, j)],
Ezn+1(i, j)
=Ezn(i, j)+Δtε(i+1/2,j)ΔL [Hyn+1/2(i+1/2,j)-Hyn+1/2(i-1/2,j)+Hxn+1/2(i, j-1/2)-Hxn+1/2(i, j+1/2)],
Exn+1(i+1/2,j)
=Exn(i+1/2,j)+Δtε(i+1/2,j)ΔL×[Hzn+1/2(i+1/2,j+1/2)-Hzn+1/2(i+1/2,j-1/2)],
Eyn+1(i, j+1/2)
=Eyn(i, j+1/2)+Δtε(i, j+1/2)ΔL×[Hzn+1/2(i-1/2,j+1/2)-Hzn+1/2(i+1/2,j+1/2)],
Hzn+1/2(i+1/2,j+1/2)
=Hzn-1/2(i+1/2,j+1/2)+Δtμ(i+1/2,j+1/2)ΔL [Exn(i+1/2,j+1)-Exn(i+1/2,j)+Eyn(i, j+1/2)-Eyn(i+1,j+1/2)].
β(ν)=πd [(ν/νc)2-1]1/2ν>νci πd [1-(ν/νc)2]1/2ννc,

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