Abstract

We propose a generally applicable velocity matching method for THz-pulse generation by optical rectification in the range below the phonon frequency of the nonlinear material. Velocity matching is based on pulse front tilting of the ultrashort excitation pulse and is able to produce a large-area THz beam. Tuning of the THz radiation by changing the tilt angle is experimentally demonstrated for a narrow line in the range between 0.8-0.97 times the phonon frequency. According to model calculations broadband THz radiation can be generated at lower frequencies. Advantages of the new velocity matching technique in comparison to the electro-optic Cherenkov effect and non-collinear beam mixing are discussed.

© 2002 Optical Society of America

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References

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  1. D. H. Auston, K.P. Cheung, J. A. Valdmanis and D. A. Kleinman, �??Cherenkov radiation from femtosecond optical pulses in electro-optic media,�?? Phys. Rev. Lett. 53, 1555-1558 (1984).
    [CrossRef]
  2. A. Nahata, A.S. Weling and T.F. Heinz, �??A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,�?? Appl. Phys. Lett. 69, 2321-2323 (1996).
    [CrossRef]
  3. Q. Wu and X.-C. Zhang, �??Free-space electro-optic sampling of mid-infrared pulses,�?? Appl. Phys. Lett. 71, 1285-1286 (1997).
    [CrossRef]
  4. D. Grischkowsky, S. Keiding, M. van Exter and C. Fattinger, �??Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,�?? J. Opt. Soc. Am. B 7, 2006-2015 (1990).
    [CrossRef]
  5. M. C. Nuss, P. M. Mankiewich, M. L. O�??Malley, E. H. Westerwick and P. B. Littlewood, �??Dynamic conductivity and coherence peak in YBa2Cu3O7 superconductors,�?? Phys. Rev. Lett. 66, 3305-3308 (1991).
    [CrossRef] [PubMed]
  6. A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss and W. H. Knox, �??Femtosecond charge transport in polar semiconductors,�?? Phys. Rev. Lett. 82, 5140-5143 (1999).
    [CrossRef]
  7. B. E. Cole, J. B. Williams, B. T. King, M. S. Sherwin and C. R. Stanley, �??Coherent manipulation of semiconductor quantum bits with terahertz radiation,�?? Nature 410, 60-63 (2001).
    [CrossRef] [PubMed]
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  9. R. Huber, A. Brodschelm, F. Tauser and A. Leitenstorfer, �??Generation and field-resolved detection of femtosecond electromagnetic pulses tunable up to 41 THz,�?? Appl. Phys. Lett. 76, 3191-3193 (2000).
    [CrossRef]
  10. A.S. Barker and R. Loudon, �??Response function in the theory of Raman scattering by vibrational and polariton modes in dielectric crystals,�?? Rev. Mod. Phys. 44, 18-47 (1972).
    [CrossRef]
  11. H.J. Bakker, G.C. Cho, H. Kurz, Q. Wu and X.-C. Zhang, �??Distortion of terahertz pulses in electro-optic sampling,�?? J. Opt. Soc. Am. B 15, 1795-1801 (1998).
    [CrossRef]
  12. T. E. Stevens, J. K. Wahlstrand, J. Kuhl and R. Merlin, �??Cherenkov radiation at speeds below the light threshold: Phonon assisted phase matching,�?? Science 291, 627-630 (2001).
    [CrossRef] [PubMed]
  13. D. A. Kleinman and D. H. Auston, �??Theory of electrooptic shock radiation in nonlinear optical media,�?? IEEE J. Quantum Electron. 20, 964-970 (1984).
    [CrossRef]
  14. Zs. Bor and B. Racz, �??Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation,�?? Opt. Commun. 54, 165-170 (1985).
    [CrossRef]
  15. J. Hebling, �??Derivation of the pulse front tilt caused by angular dispersion,�?? Opt. Quantum Electron. 28, 1759-1763 (1996).
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  16. P.A. Tipler, Physics for scientists and engineers (W.H. Freeman and Company, 1999).
  17. S. Ushioda and J.D. McMullen, �??Measurement of the frequency dependence of the phonon damping function by Raman scattering from polaritons in GaP,�?? Solid State Commun. 11, 299-304 (1972).
    [CrossRef]
  18. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

Appl. Phys. Lett. (3)

A. Nahata, A.S. Weling and T.F. Heinz, �??A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling,�?? Appl. Phys. Lett. 69, 2321-2323 (1996).
[CrossRef]

Q. Wu and X.-C. Zhang, �??Free-space electro-optic sampling of mid-infrared pulses,�?? Appl. Phys. Lett. 71, 1285-1286 (1997).
[CrossRef]

R. Huber, A. Brodschelm, F. Tauser and A. Leitenstorfer, �??Generation and field-resolved detection of femtosecond electromagnetic pulses tunable up to 41 THz,�?? Appl. Phys. Lett. 76, 3191-3193 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. A. Kleinman and D. H. Auston, �??Theory of electrooptic shock radiation in nonlinear optical media,�?? IEEE J. Quantum Electron. 20, 964-970 (1984).
[CrossRef]

J. Opt. Soc. Am. B (2)

Nature (1)

B. E. Cole, J. B. Williams, B. T. King, M. S. Sherwin and C. R. Stanley, �??Coherent manipulation of semiconductor quantum bits with terahertz radiation,�?? Nature 410, 60-63 (2001).
[CrossRef] [PubMed]

Opt. Commun. (1)

Zs. Bor and B. Racz, �??Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation,�?? Opt. Commun. 54, 165-170 (1985).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

J. Hebling, �??Derivation of the pulse front tilt caused by angular dispersion,�?? Opt. Quantum Electron. 28, 1759-1763 (1996).
[CrossRef]

Phys. Rev. Lett. (3)

M. C. Nuss, P. M. Mankiewich, M. L. O�??Malley, E. H. Westerwick and P. B. Littlewood, �??Dynamic conductivity and coherence peak in YBa2Cu3O7 superconductors,�?? Phys. Rev. Lett. 66, 3305-3308 (1991).
[CrossRef] [PubMed]

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss and W. H. Knox, �??Femtosecond charge transport in polar semiconductors,�?? Phys. Rev. Lett. 82, 5140-5143 (1999).
[CrossRef]

D. H. Auston, K.P. Cheung, J. A. Valdmanis and D. A. Kleinman, �??Cherenkov radiation from femtosecond optical pulses in electro-optic media,�?? Phys. Rev. Lett. 53, 1555-1558 (1984).
[CrossRef]

Rev. Mod. Phys. (1)

A.S. Barker and R. Loudon, �??Response function in the theory of Raman scattering by vibrational and polariton modes in dielectric crystals,�?? Rev. Mod. Phys. 44, 18-47 (1972).
[CrossRef]

Science (1)

T. E. Stevens, J. K. Wahlstrand, J. Kuhl and R. Merlin, �??Cherenkov radiation at speeds below the light threshold: Phonon assisted phase matching,�?? Science 291, 627-630 (2001).
[CrossRef] [PubMed]

Solid State Commun. (1)

S. Ushioda and J.D. McMullen, �??Measurement of the frequency dependence of the phonon damping function by Raman scattering from polaritons in GaP,�?? Solid State Commun. 11, 299-304 (1972).
[CrossRef]

Other (2)

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

P.A. Tipler, Physics for scientists and engineers (W.H. Freeman and Company, 1999).

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Figures (4)

Fig. 1.
Fig. 1.

Two different schemes of THz excitation. For the usual Cherenkov geometry (a), the THz radiation is emitted as a cone characterized by the angle ΘC. Velocity matching (see Eq. 4) is satisfied, but the exciting beam has to be very narrow (see Eq. 3). Velocity matching by pulse front tilting (b) creates a plane THz wave without any upper limit for the exciting beam cross-section.

Fig. 2.
Fig. 2.

Measured differential transmission versus probe delay for γ = 39.3° tilt angle. The inset shows the corresponding spectrum of the radiation. Its peak at 10.16 THz is in good agreement with the 10.12 THz calculated from Eq. 4. Changing γ, we were able to tune the spectrum from 9.0-10.7 THz.

Fig. 3.
Fig. 3.

Calculated dependence of the THz field amplitude spectrum on the GaP crystal length for velocities adjusted to generate a narrow spectrum at 9 THz (a), and 6 THz (b), respectively. During the calculations the excitation pulse duration and the polariton linewidth were supposed to be 30 fs and 1.1 cm-1, respectively.

Fig. 4.
Fig. 4.

Illustration of phase-matching (wave-vector conservation) for THz generation (a). Application of two ultrashort pulses without pulse front tilt for mixing achieves only partial overlap of the beam cross-sections, (b). For a beam with tilted pulse front (see Fig. 1b), the spectral components overlap across the whole cross-section of the beam, resulting in efficient THz generation.

Equations (6)

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v vis gr = v THz ph
w v vis gr τ ,
Θ C = cos 1 ( v THz ph v vis gr ) .
v vis gr cos γ = v THz ph .
Δ k = k vis + THz k vis k THz = 0 ,
tan γ = n n g r ω d Θ d ω , where n g r = n ω d n d ω = c v vis g r

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