Abstract

We demonstrate the use of optical pulse-shaping technique in conjunction with difference frequency generation in a non-linear optoelectronic crystal for generating synthesized waveforms at terahertz frequencies. Spectral phase modulations, programmed using Gerchberg-Saxton algorithm and prepared in a spatial light Fourier filter, produce tailored terahertz pulses, including chirped pulses, zero-area pulses, and trains of multiple pulses for tunable narrow-band terahertz radiation up to 2.0 THz.

© 2003 Optical Society of America

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References

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  1. J. M. Chamberlain, and R. E. Miles, New Directions in Terahertz Technology (NATO Asi Series. Series E, Applied Sciences, Vol 334), (Boston, Kluwer Academic Publishers, 1997).
  2. L. Xu, X.-C. Zhang, and D. H. Auston, �??Terahertz beam generation by femtosecond optical pulses in eletro-optic materials,�?? Appl. Phys. Lett. 61, 1784-1786 (1992).
    [CrossRef]
  3. D. You, R. R. Jones, D. R. Dykaar, and P. H. Bucksbaum, �??Generation of High-Power Half-Cycle 500 Femtosecond Electromagnetic Pulses,�?? Opt. Lett. 18, 290 (1993).
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  4. 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, 3191-93 (2000).
    [CrossRef]
  5. C. Winnewisser, P. Uhd Jepson, M. Schall, V. Schyja, and H. Helm, �??Electro-optic detection of THz radiation in LiTaO3, LiNbO3, and ZnTe,�?? Appl. Phys. Lett. 70, 3069 (1997).
    [CrossRef]
  6. Q. Chen, and X.-C. Zhang, �??Polarization modulation in optoelectronic generation and detection of terahertz baams,�?? Appl. Phys. Lett. 74, 3435 (1999).
    [CrossRef]
  7. B. E. Cole, J. B. Willams, B. T. King, M. S. Sherwin, C. R. Stanley, �??Coherent manipulation of semiconductor quantum bits with terahertz information,�?? Nature 410, 60 (2001).
    [CrossRef] [PubMed]
  8. R. Huber, F. Tauser, A. Brodschelm, M. Bichler, G. Abstreiter, and A. Leitenstorfer, �??How many-particle intersactions develop after ultrafast excitation of an electron-hole plasma,�?? Nature 414, 289 (2001).
    [CrossRef]
  9. D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Kock, �??Recent Advances in terahertz imaging,�?? Appl. Phys. B 68, 1085-1094 (1999).
    [CrossRef]
  10. D. G. Tilley, and D. J. Yemc, �??Wave domain processing of synthetic aperture radar signals,�?? Johns Hopkins APL technical Digest 15, 224-36 (1994).
  11. J. Ahn, D. N. Hutchinson, C. Rangan, and P. H. Bucksbaum, �??Quantum phase retrieval of a Rydberg wave packet using a half-cycle pulse,�?? Phys. Rev. Lett. 86, 1179-82 (2001).
    [CrossRef] [PubMed]
  12. Y. Nakamura, Yu. A. Pashkin, and J. S. Tsai, �??Coherent control of macroscopic quantum states in a single-Cooper-pair box,�?? Nature 398, 786-788 (1999).
    [CrossRef]
  13. C. W. Siders, J. L. W. Siders, A. J. Taylor, S.-G. Park, and A. M. Weiner, �??Efficient high-energy pulse-train generation using a 2n-pulse Michelson interferometer,�?? Appl. Opt. 37, 5302 (1998).
    [CrossRef]
  14. A. M. Weiner, �??Femtosecond pulse shaping using spatial light modulators,�?? Rev. Sci. Instru. 71, 1929 (2000)
    [CrossRef]
  15. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, D. J. Kane, �??Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,�?? Rev. Sci. Instru. 68, 3277-95 (1997).
    [CrossRef]
  16. Y. Liu, S.-G. Park, and A. M.Weiner, �??Terahertz waveform synthesis via optical pulse shaping,�?? IEEE J. Quantum Electron. 2, 709 (1996).
    [CrossRef]
  17. S.-G. Park, A. M. Weiner, M. R. Melloch, C. W. SIder, J. L. Sider, and A. J. Taylor, �??High-power narrow-band terahertz generation using large-aperture photoconductors,�?? IEEE J. Quantum Electron. 35, 1257-68 (1999).
    [CrossRef]
  18. . G. Gallot and D. Grischkowsky, �??Electro-optic detection of terahertz radiation,�?? J. Opt. Soc. America B 16, 1204-1212 (1999).
    [CrossRef]
  19. J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, �??Kerr-Like nonlinearity induced via terahertz generation and the elctro-optical effect in Zinc blend crystals�??, Phys. Rev. Lett. 89, 047401 (2002).
    [CrossRef] [PubMed]
  20. . A. Nahata, A. S. Weling, and T. F. Heinz, �??A windeband coherent terhaertz spectroscopy system using optical rectification and electro-optic sampling,�?? Apl. Phys. Lett. 69, 2321 (1996).
    [CrossRef]
  21. .R. W. Gerchberg and W. O. Saxton, �??Phase determination from image and diffraction plane pictures in the electron microscope,�?? Optik 35, 237-246 (1972).
  22. A. Rundquist, A. V. Efimov, and D. H. Reitze, �??Pulse shaping with the Gerchberg-Saxton algorithm,�?? J. Opt. Soc. Am. B 19, 2468 (2002).
    [CrossRef]
  23. Y.-S. Lee, N. Amer, and W. C. Hurlbut, �??Terahertz pulse shaping via optical rectification in poled lithium niobate,�?? Appl. Phys. Lett. 82, 170 (2003).
    [CrossRef]
  24. J. Y. Sohn, Y. H. Ahn, D. J. Park, E. Oh, and D. S. Kim, �??Tunable terahertz generation using femtosecond pulse shaping,�?? Appl. Phys. Lett. 81, 13 (2002).
    [CrossRef]
  25. Our GaAs data is consistent with the spectral tunning data shown in Fig. 8 of Ref. [16].
  26. C. W. Siders, J. L. W. Siders, A. J. Taylor, S.-G. Park, M. R. Mellock, and A. M. Weiner, �??Generation and characterization of terahertz pulse trains from biased, large-aperture photoconductors,�?? Opt. Letter 24, 241 (1999).
    [CrossRef]
  27. Y.-S. Lee, T. Meade, T. B. Norris, and A. Galvanauskas, �??Tunable narrow-band terahertz generation from periodically poled lithium niobate,�?? Appl. Phys. Lett. 78, 3583 (2001).
    [CrossRef]

Apl. Phys. Lett.

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

Appl. Opt

C. W. Siders, J. L. W. Siders, A. J. Taylor, S.-G. Park, and A. M. Weiner, �??Efficient high-energy pulse-train generation using a 2n-pulse Michelson interferometer,�?? Appl. Opt. 37, 5302 (1998).
[CrossRef]

Appl. Phys. B

D. M. Mittleman, M. Gupta, R. Neelamani, R. G. Baraniuk, J. V. Rudd, and M. Kock, �??Recent Advances in terahertz imaging,�?? Appl. Phys. B 68, 1085-1094 (1999).
[CrossRef]

Appl. Phys. Lett

Y.-S. Lee, T. Meade, T. B. Norris, and A. Galvanauskas, �??Tunable narrow-band terahertz generation from periodically poled lithium niobate,�?? Appl. Phys. Lett. 78, 3583 (2001).
[CrossRef]

Appl. Phys. Lett.

L. Xu, X.-C. Zhang, and D. H. Auston, �??Terahertz beam generation by femtosecond optical pulses in eletro-optic materials,�?? Appl. Phys. Lett. 61, 1784-1786 (1992).
[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, 3191-93 (2000).
[CrossRef]

C. Winnewisser, P. Uhd Jepson, M. Schall, V. Schyja, and H. Helm, �??Electro-optic detection of THz radiation in LiTaO3, LiNbO3, and ZnTe,�?? Appl. Phys. Lett. 70, 3069 (1997).
[CrossRef]

Q. Chen, and X.-C. Zhang, �??Polarization modulation in optoelectronic generation and detection of terahertz baams,�?? Appl. Phys. Lett. 74, 3435 (1999).
[CrossRef]

Y.-S. Lee, N. Amer, and W. C. Hurlbut, �??Terahertz pulse shaping via optical rectification in poled lithium niobate,�?? Appl. Phys. Lett. 82, 170 (2003).
[CrossRef]

J. Y. Sohn, Y. H. Ahn, D. J. Park, E. Oh, and D. S. Kim, �??Tunable terahertz generation using femtosecond pulse shaping,�?? Appl. Phys. Lett. 81, 13 (2002).
[CrossRef]

Applied Sciences

J. M. Chamberlain, and R. E. Miles, New Directions in Terahertz Technology (NATO Asi Series. Series E, Applied Sciences, Vol 334), (Boston, Kluwer Academic Publishers, 1997).

IEEE J. Quantum Electron

S.-G. Park, A. M. Weiner, M. R. Melloch, C. W. SIder, J. L. Sider, and A. J. Taylor, �??High-power narrow-band terahertz generation using large-aperture photoconductors,�?? IEEE J. Quantum Electron. 35, 1257-68 (1999).
[CrossRef]

IEEE J. Quantum Electron.

Y. Liu, S.-G. Park, and A. M.Weiner, �??Terahertz waveform synthesis via optical pulse shaping,�?? IEEE J. Quantum Electron. 2, 709 (1996).
[CrossRef]

J. Opt. Soc. Am. B

J. Opt. Soc. America B

. G. Gallot and D. Grischkowsky, �??Electro-optic detection of terahertz radiation,�?? J. Opt. Soc. America B 16, 1204-1212 (1999).
[CrossRef]

Johns Hopkins APL technical Digest

D. G. Tilley, and D. J. Yemc, �??Wave domain processing of synthetic aperture radar signals,�?? Johns Hopkins APL technical Digest 15, 224-36 (1994).

Nature

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

R. Huber, F. Tauser, A. Brodschelm, M. Bichler, G. Abstreiter, and A. Leitenstorfer, �??How many-particle intersactions develop after ultrafast excitation of an electron-hole plasma,�?? Nature 414, 289 (2001).
[CrossRef]

Y. Nakamura, Yu. A. Pashkin, and J. S. Tsai, �??Coherent control of macroscopic quantum states in a single-Cooper-pair box,�?? Nature 398, 786-788 (1999).
[CrossRef]

Opt. Lett.

Opt. Letter

C. W. Siders, J. L. W. Siders, A. J. Taylor, S.-G. Park, M. R. Mellock, and A. M. Weiner, �??Generation and characterization of terahertz pulse trains from biased, large-aperture photoconductors,�?? Opt. Letter 24, 241 (1999).
[CrossRef]

Optik

.R. W. Gerchberg and W. O. Saxton, �??Phase determination from image and diffraction plane pictures in the electron microscope,�?? Optik 35, 237-246 (1972).

Phys. Rev. Lett

J.-P. Caumes, L. Videau, C. Rouyer, and E. Freysz, �??Kerr-Like nonlinearity induced via terahertz generation and the elctro-optical effect in Zinc blend crystals�??, Phys. Rev. Lett. 89, 047401 (2002).
[CrossRef] [PubMed]

Phys. Rev. Lett.

J. Ahn, D. N. Hutchinson, C. Rangan, and P. H. Bucksbaum, �??Quantum phase retrieval of a Rydberg wave packet using a half-cycle pulse,�?? Phys. Rev. Lett. 86, 1179-82 (2001).
[CrossRef] [PubMed]

Rev. Sci. Instru

A. M. Weiner, �??Femtosecond pulse shaping using spatial light modulators,�?? Rev. Sci. Instru. 71, 1929 (2000)
[CrossRef]

Rev. Sci. Instru.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, D. J. Kane, �??Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,�?? Rev. Sci. Instru. 68, 3277-95 (1997).
[CrossRef]

Other

Our GaAs data is consistent with the spectral tunning data shown in Fig. 8 of Ref. [16].

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Figures (8)

Fig. 1.
Fig. 1.

Terahertz spectrum and coherence length in ZnTe. Terahertz spectra(upper figure) for three different pump laser wavelengths (810, 790, and 750 nm) are shown compared with the coherence lengths (lower figure) defined as lc =πk. The thickness of the ZnTe crystal, indicated under the thick line, is chosen to separate the coherent bands in the spectrum for 790 nm and 750 nm.

Fig. 2.
Fig. 2.

Measured terahertz spectra(left panel) and their far-field waveforms(right panel) at three different excitation wavelengths : (a) λ=810 nm; (b) λ=790 nm; (c) λ=750 nm.

Fig. 3.
Fig. 3.

Schematic diagram of experimental arrangement. Pump laser pulses enter the apparatus from the left and are spectrally dispersed in an optical pulse shaper which has a computer-controlled array of optical masks before combined without spatial dispersion. The programmed optical pulses now generate the shaped terahertz pulses. The shape of the terahertz pulses are recorded as the phase modulation in the electro-optic ellipsometer, and analyzed via a fast lock-in detection.

Fig. 4.
Fig. 4.

Demonstration of the chirped terahertz pulse and the zero-area terahertz pulse. The optical pulse trains programmed via Gerchberg-Saxton algorithm for chirped pulse (a) and zero-area pulse (e) (dots - experimental cross-correlations, lines - numerical targets), terahertz waveforms designed and measured for the designed chirped pulse (b,c) and the zeroarea pulse (f,g), the calculated (line) and measured (hexagon) spectra of chirped pulse (d) and zero-area pulse (h).

Fig. 5.
Fig. 5.

Digital pulse demonstration. The terahertz binary signal is represented by the negative amplitudes of the electric field pulse. From the top of the figure, the binary numbers (11111), (01111), (10111), (11011),(11101), and (11110) are encoded.

Fig. 6.
Fig. 6.

Temporal and spectral shapes of designed terahertz pulses for demonstrating the narrowing of the spectral width. From top to bottom, 1, 3, 5, 7, 9, and 11 cycle pulses are programmed. The intensity of the optical pulses, the temporal shapes, and the spectra of the terahertz pulses are shown in the left, the middle, and the right panels, respectively. The oscillatory pulse trains are prepared by weaving multiple impulsive terahertz pulses.

Fig. 7.
Fig. 7.

Tuning of the terahertz spectrum from 0.5 THz to 2.0 THz generated from a thick ZnTe material with programmed optical pulse trains. The temporal intensity (the left column), terahertz waveforms(the middle column), and the spectral shapes (the right column) are shown. The temporal window of 10 ps (except the top experiment for 2.0 THz) was used to program a narrow-band tunable terahertz source. The frequency changes from 0.5 THz (bottom) to 2.0 THz(top).

Fig. 8.
Fig. 8.

Terahertz waveforms tuning the THz spectrum from 0.5 THz to 1.0 THz generated from a biased GaAs material with programmed optical pulse trains. The frequency changes from 0.5 THz (top) to 1.3 THz (bottom)

Equations (4)

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2 z 2 E THz ( z , ω ) + ε ( ω ) ω 2 c 2 E THz ( z , ω ) = 4 π ω 2 c 2 P ( 2 ) ( z , ω ) ,
P ( 2 ) ( z , ω ) = χ ( 2 ) ( ω ) I ˜ ( ω ) exp ( i ω z v g ) ,
E THz ( z , ω ) ω 2 χ ( 2 ) ( ω ) I ˜ ( ω ) z sinc ( Δ k THz z 2 ) ,
l c ( ω ; λ ) = c 2 f n o ( λ ) λ d n o ( λ ) d λ n t ( ω ) .

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