Abstract

We studied cascaded optical rectification processes for intense terahertz (THz) pulse generation in electro-optic crystals using simulations based on one-dimensional coupled propagation equations of THz and optical fields. We found that under ideal conditions of perfect phase matching and no absorption, cascaded optical rectification processes produce intense THz pulses with efficiencies exceeding the Manley-Rowe limit. Large red shifting of the pump light spectrum was observed. Effects of finite optical and THz absorption, phase mismatches, and pulse width were examined using parameters of a ZnTe crystal pumped by 800 nm pulses. THz field enhancement by multiple pulse pumping was also studied.

© 2007 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  4. D. J. Cook, J. X. Chen, E. A. Morlino, and R. M. Hochstrasser, "Terahertz-field-induced second-harmonic generation measurements of liquid dynamics," Chem. Phys. Lett. 309, 221-228 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  27. C. Kolleck, "Cascaded second-order contribution to the third-order nonlinear susceptibility," Phys. Rev. A 69, 053812 (2004).
    [CrossRef]
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  29. S. Casalbuoni, H. Schlarb, B. Schmidt, P. Schmüser, B. Steffen, and A. Winter, "Numerical studies on the electrooptic sampling of relativistic electron bubches," TESLA Report 2005-11 (2005).
  30. 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]
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    [CrossRef]

2006 (4)

2005 (4)

A. G. Stepanov, J. Kuhl, I. Z. Kozma, E. Riedle, G. Almási, and J. Hebling, "Scaling up the energy of THz pulses created by optical rectification," Opt. Express 13, 5762-5768 (2005).
[CrossRef] [PubMed]

T . Löffler, T. Hahn, M . Thomson, F. Jacob, and H. G. Roskos, "Large-area electro-optic ZnTe terahertz emitters," Opt. Express 13, 5353-5362 (2005).
[CrossRef] [PubMed]

R. Rungsawang, A. Mochiduki, S. Ookuma, and T. Hattori, "1-kHz real-time imaging using a half-cycle terahertz electromagnetic pulse," Jpn. J. Appl. Phys. 44, L288-L291 (2005).
[CrossRef]

T. Löffler, M. Kreß, M. Thomson, T. Hahn, N. Hasegawa, and H. G. Roskos, "Comparative performance of terahertz emitters in amplifier-laser-based systems," Semicond. Sci. Technol. 20, S134-141 (2005).
[CrossRef]

2004 (5)

C. Luo, K. Reimann, M. Woerner, and T. Elsaesser, "Nonlinear terahertz spectroscopy of semiconductor nanostructures," Appl. Phys. A 78, 435-440 (2004).
[CrossRef]

M. Nagai, K. Tanaka, H. Ohtake, T. Bessho, T. Sugiura, T. Hirosumi, and M. Yoshida, "Generation and detection of terahertz radiation by electro-optic process in GaAs using 1.56 μm fiber laser pulses," Appl. Phys. Lett. 85, 3974-3976 (2004).
[CrossRef]

M. Cronin-Golomb, "Cascaded nonlinear difference-frequency generation of enhanced terahertz wave generation," Opt. Lett. 29, 2046-2048 (2004).
[CrossRef] [PubMed]

J. Hebling, A. G. Stepanov, G. Almási, B. Bartal and J. Kuhl, "Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts," Appl. Phys. B 78, 593-599 (2004).
[CrossRef]

C. Kolleck, "Cascaded second-order contribution to the third-order nonlinear susceptibility," Phys. Rev. A 69, 053812 (2004).
[CrossRef]

2003 (1)

2002 (2)

B. Ferguson and X. -C. Zhang, "Materials for terahertz science and technology," Nature Materials 1, 26-33 (2002).
[CrossRef]

J. -P. Caumes, L. Videau, C. Rouyer, and E. Freysz, "Ker-like nonlinearity induced via terahertz generation and the electro-optical effect in zinc blende crystals," Phys. Rev. Lett. 89, 047401 (2002).
[CrossRef] [PubMed]

2001 (2)

T. Hattori, K. Tukamoto, and H. Nakatsuka, "Time-resolved study of intense terahertz pulses generated by a large-aperture photoconductive antenna," Jpn. J. Appl. Phys. 40, 4907-4912 (2001).
[CrossRef]

M. Schall, M. Walther, and P. Uhd. Jepsen, "Fundamental and second-order phonon processes in CdTe and ZnTe," Phys. Rev. B 64, 094301 (2001).
[CrossRef]

2000 (1)

M. Schall and P. Uhd. Jepsen, "Freeze-out of difference-phonon modes in ZnTe and its application in detection of THz pulses," Appl. Phys. Lett. 77, 2801-2803 (2000).
[CrossRef]

1999 (2)

G. Gallot, J. Zhang, R. W. McGowan, T. -I. Jeon, and D. Grischkowsky, "Measurements of the THz absorption and dispersion of ZnTe and their relevance to the electro-optic detection of THz radiation," Appl. Phys. Lett. 74, 3450-3452 (1999).
[CrossRef]

D. J. Cook, J. X. Chen, E. A. Morlino, and R. M. Hochstrasser, "Terahertz-field-induced second-harmonic generation measurements of liquid dynamics," Chem. Phys. Lett. 309, 221-228 (1999).
[CrossRef]

1996 (2)

E. Budiarto, J. Margolies, S. Jeong, J. Son, and J. Bokor, "High-intensity terahertz pulses at 1-kHz repetition rate," IEEE J. Quantum Electron. 32, 1839-1846 (1996).
[CrossRef]

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]

1995 (3)

Ch. Bosshard, R. Spreiter, M. Zgonik, and P. Günter, "Kerr nonlinearity via cascaded optical rectification and the linear electro-optic effect," Phys. Rev. Lett. 74, 2816-2819 (1995).
[CrossRef] [PubMed]

B. B. Hu and M. C. Nuss, "Imaging with terahertz waves," Opt. Lett. 20, 1716-1718 (1995).
[CrossRef] [PubMed]

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, "Generation of terahertz radiation using electro-optic crystal mosaics," Appl. Phys. Lett. 66,10-12 (1995).
[CrossRef]

1993 (1)

1967 (1)

R. E. Nahory and H. Y. Fan, "Optical properties of zinc telluride," Phys. Rev. 156, 825-833 (1967).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. A (1)

C. Luo, K. Reimann, M. Woerner, and T. Elsaesser, "Nonlinear terahertz spectroscopy of semiconductor nanostructures," Appl. Phys. A 78, 435-440 (2004).
[CrossRef]

Appl. Phys. B (1)

J. Hebling, A. G. Stepanov, G. Almási, B. Bartal and J. Kuhl, "Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts," Appl. Phys. B 78, 593-599 (2004).
[CrossRef]

Appl. Phys. Lett. (5)

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]

T. J. Carrig, G. Rodriguez, T. S. Clement, A. J. Taylor, and K. R. Stewart, "Generation of terahertz radiation using electro-optic crystal mosaics," Appl. Phys. Lett. 66,10-12 (1995).
[CrossRef]

M. Nagai, K. Tanaka, H. Ohtake, T. Bessho, T. Sugiura, T. Hirosumi, and M. Yoshida, "Generation and detection of terahertz radiation by electro-optic process in GaAs using 1.56 μm fiber laser pulses," Appl. Phys. Lett. 85, 3974-3976 (2004).
[CrossRef]

G. Gallot, J. Zhang, R. W. McGowan, T. -I. Jeon, and D. Grischkowsky, "Measurements of the THz absorption and dispersion of ZnTe and their relevance to the electro-optic detection of THz radiation," Appl. Phys. Lett. 74, 3450-3452 (1999).
[CrossRef]

M. Schall and P. Uhd. Jepsen, "Freeze-out of difference-phonon modes in ZnTe and its application in detection of THz pulses," Appl. Phys. Lett. 77, 2801-2803 (2000).
[CrossRef]

Chem. Phys. Lett. (1)

D. J. Cook, J. X. Chen, E. A. Morlino, and R. M. Hochstrasser, "Terahertz-field-induced second-harmonic generation measurements of liquid dynamics," Chem. Phys. Lett. 309, 221-228 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

E. Budiarto, J. Margolies, S. Jeong, J. Son, and J. Bokor, "High-intensity terahertz pulses at 1-kHz repetition rate," IEEE J. Quantum Electron. 32, 1839-1846 (1996).
[CrossRef]

Jpn. J. Appl. Phys. (3)

T. Hattori, K. Tukamoto, and H. Nakatsuka, "Time-resolved study of intense terahertz pulses generated by a large-aperture photoconductive antenna," Jpn. J. Appl. Phys. 40, 4907-4912 (2001).
[CrossRef]

T. Hattori, K. Egawa, S. Ookuma, and T. Itatani, "Intense terahertz pulses from large-aperture antenna with interdigitated electrodes," Jpn. J. Appl. Phys. 45, L422-L424 (2006).
[CrossRef]

R. Rungsawang, A. Mochiduki, S. Ookuma, and T. Hattori, "1-kHz real-time imaging using a half-cycle terahertz electromagnetic pulse," Jpn. J. Appl. Phys. 44, L288-L291 (2005).
[CrossRef]

Nature Materials (1)

B. Ferguson and X. -C. Zhang, "Materials for terahertz science and technology," Nature Materials 1, 26-33 (2002).
[CrossRef]

Opt. Express (4)

Opt. Lett. (4)

Phys. Rev. (1)

R. E. Nahory and H. Y. Fan, "Optical properties of zinc telluride," Phys. Rev. 156, 825-833 (1967).
[CrossRef]

Phys. Rev. A (1)

C. Kolleck, "Cascaded second-order contribution to the third-order nonlinear susceptibility," Phys. Rev. A 69, 053812 (2004).
[CrossRef]

Phys. Rev. B (1)

M. Schall, M. Walther, and P. Uhd. Jepsen, "Fundamental and second-order phonon processes in CdTe and ZnTe," Phys. Rev. B 64, 094301 (2001).
[CrossRef]

Phys. Rev. Lett. (2)

Ch. Bosshard, R. Spreiter, M. Zgonik, and P. Günter, "Kerr nonlinearity via cascaded optical rectification and the linear electro-optic effect," Phys. Rev. Lett. 74, 2816-2819 (1995).
[CrossRef] [PubMed]

J. -P. Caumes, L. Videau, C. Rouyer, and E. Freysz, "Ker-like nonlinearity induced via terahertz generation and the electro-optical effect in zinc blende crystals," Phys. Rev. Lett. 89, 047401 (2002).
[CrossRef] [PubMed]

Semicond. Sci. Technol. (1)

T. Löffler, M. Kreß, M. Thomson, T. Hahn, N. Hasegawa, and H. G. Roskos, "Comparative performance of terahertz emitters in amplifier-laser-based systems," Semicond. Sci. Technol. 20, S134-141 (2005).
[CrossRef]

Other (3)

F. G. Sun, W. Ji, and X. -C. Zhang, "Two-photon absorption induced saturation of THz radiation in ZnTe," in Conference on Lasers and Electro-Optics, OSA Technichal Digest (Optical Society of America, Wasgington DC, 2000), 479-480.

R. W. Boyd, Nonlinear Optics (Academic, San Diego, 2003).

S. Casalbuoni, H. Schlarb, B. Schmidt, P. Schmüser, B. Steffen, and A. Winter, "Numerical studies on the electrooptic sampling of relativistic electron bubches," TESLA Report 2005-11 (2005).

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Figures (15)

Fig. 1.
Fig. 1.

Dispersion relation of ZnTe in the (a) THz and (b) optical regions. Red horizontal line in (a) shows the group refractive index at 375 THz (i.e., 800 nm).

Fig. 2.
Fig. 2.

Power spectra of (a) THz and (b) optical fields under perfect phase matching and no absorption conditions at propagation distances in the ZnTe crystal from 0 to 5 mm by a step of 0.25 mm. Each spectrum is shifted upward by 0.1.

Fig. 3.
Fig. 3.

Peak frequency of the optical spectrum as a function of propagation distance obtained under perfect phase matching and no absorption conditions.

Fig. 4.
Fig. 4.

Black line shows peak field of THz pulses in time domain as a function of propagation distance under perfect phase matching and no absorption conditions. Red line is a straight line that is obtained assuming no pump light change.

Fig. 5.
Fig. 5.

Photon conversion ratio from optical to THz photons under perfect phase matching and no absorption conditions. Red line shows the level of unity, which corresponds to the Manley-Rowe limit.

Fig. 6.
Fig. 6.

Black lines: Temporal waveforms of THz field obtained under perfect phase matching and no absorption conditions. Red line: Temporal shape of the incident pump light pulse intensity.

Fig. 7.
Fig. 7.

Power spectra of (a) THz and (b) optical fields under realistic phase mismatches and no absorption conditions at propagation distances in the ZnTe crystal from 0 to 5 mm by a step of 0.25 mm. Each spectrum is shifted upward by 0.1.

Fig. 8.
Fig. 8.

Temporal waveforms of THz pulses obtained under realistic phase mismatches and no absorption conditions. Temporal shape of the incident pump pulse intensity is also shown.

Fig. 9.
Fig. 9.

Photon conversion ratio obtained under realistic phase mismatches and no absorption conditions. Red line shows the level of unity, which corresponds to the Manley-Rowe limit.

Fig. 10.
Fig. 10.

Power spectra of THz and optical fields under realistic phase mismatches and absorption at propagation distances in the ZnTe crystal from 0 to 5 mm by a step of 0.25 mm. Each spectrum is shifted upward by 0.1. (a) THz spectra at 300 MW/cm2 pump; (b) optical spectra at 300 MW/cm2 pump; (c) THz spectra at 800 MW/cm2 pump; and (d) optical spectra at 800 MW/cm2 pump.

Fig. 11.
Fig. 11.

Propagation distance dependence of the peak field of the THz temporal waveform at pump intensities of 300 to 800 MW/cm2.

Fig. 12.
Fig. 12.

Pulse width dependence of the THz power spectra under perfect phase matching and no loss conditions.

Fig. 13.
Fig. 13.

Temporal waveform of THz pulse obtained at 1.66 mm when pumped by a 180 fs single pulse. Time zero is set at the peak time.

Fig. 14.
Fig. 14.

Peak THz field obtained by multiple pulse pumping. Black circles and green triangles show results obtained by pumping with in-phase and out-of-phase pulse trains, respectively. Red squares are summations of peaks of the THz waveform obtained by single pulse pumping.

Fig. 15.
Fig. 15.

Waveforms and power spectra of THz pulses obtained by multiple pulse pumping.

Equations (30)

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

ε ( v ) = ε el + S 0 v 0 2 v 0 2 v 2 i Γ 0 v ,
n ( λ ) = ( 4.27 + 3.01 λ 2 λ 2 0.142 ) 1 2 .
n ( ω T ) = n g ( ω opt ) ,
d eff = 2 3 d 14 .
d 14 = ε 0 n 0 4 r 41 2 ,
2 E z t z 2 εμ 2 E z t t 2 μσ E z t t = μ 2 z t t 2 .
E z t = E L z t + E T z t
P z t = 2 d eff [ E z t ] 2
E L ( z , t ) = 1 2 e L z t exp ( i ω 0 t ) + c . c. ,
e L z t = E L z ω exp [ ik ( ω + ω 0 ) z iωt ] .
E T z t = E T z ω T exp [ ik ( ω T ) z i ω T t ] T .
z E L z ω = α L 2 E L z ω + i 2 μd eff ( ω + ω 0 ) 2 k ( ω + ω 0 ) E L ( z , ω ω T ) E T z ω T exp ( i Δ k L z ) T ,
z E T z ω T = α T 2 E T z ω T + i μd eff ω T 2 2 k ( ω T ) E L ( z , ω + ω T ) E L * z ω exp ( i Δ k T z ) .
Δ k L k ( ω + ω 0 ω T ) + k ( ω T ) k ( ω + ω 0 ) ,
Δ k T k ( ω + ω 0 + ω T ) k ( ω + ω 0 ) k ( ω T ) .
E T z ω T = i μd eff ω T 2 2 k ( ω T ) dωE L ( ω + ω T ) E L * ( ω ) e ( i Δ k T α L ) z e α TZ 2 ( α T 2 ) α L + i Δ k T ,
E T z ω T = i μd eff ω T 2 z 2 k ( ω T ) dωE L ( ω + ω T ) E L * ( ω )
= i μcd eff ω T z 2 n T ( ω T ) dωE L ( ω + ω T ) E L * ( ω ) ,
E T z t = μcd eff z 2 n T t e L ( t ) 2 ,
e L 0 t = E 0 exp ( 2 ln 2 t 2 δt 2 ) ,
E L 0 ω = E 0 δt 2 2 π ln 2 exp ( δt 2 8 ln 2 ω 2 ) .
r E = 2 E T z ω T 2 T E L 0 ω 2 ,
r p = 2 E T z ω T 2 ω T d ω T E L 0 ω 2 ω + ω 0 .
E T z ω T = i μd eff cδtω T 8 π ln 2 n T ( ω T ) E 2 0 z exp ( δt 2 16 ln 2 ω T 2 ) ,
2 E T z ω T 2 ω T T = 1 4 π ( μ d eff c n T E 0 2 z ) 2 ,
E L 0 ω 2 ω + ω 0 = δt 2 8 π ln 2 E 0 2 1 ω + ω 0 exp ( δt 2 4 ln 2 ω 2 )
= δt 4 π ln 2 ω 0 E 0 2 .
ω + ω 0 ω 0
z c = n T μd eff cE 0 δt ω 0 π ln 2 .
z a = 1 ( α T 2 ) α L ln ( α T 2 α L ) .

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