Abstract

In this Letter, we introduce a new method of estimation of the terahertz (THz) field amplitude. This method uses second-harmonic generation (SHG) in the presence of THz and DC fields in gaseous media. We take into account contributions from both nonionized molecules and free plasma electrons to the nonlinear process of SHG. We analyze the applicability of this method of detection to obtaining correct information on the waveform and amplitude of broadband THz pulses.

© 2014 Optical Society of America

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References

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  1. Y.-S. Lee, Principles of Terahertz Science and Technology (Springer Science, 2008).
  2. X. Lu, N. Karpowicz, and X.-C. Zhang, J. Opt. Soc. Am. B 26, A66 (2009).
    [CrossRef]
  3. R. S. Finn and J. F. Ward, Phys. Rev. Lett. 26, 285 (1971).
    [CrossRef]
  4. P. D. Maker and R. W. Terhune, Phys. Rev. 137, A801 (1965).
    [CrossRef]
  5. A. A. Frolov, A. V. Borodin, M. N. Esaulkov, I. I. Kuritsyn, and A. P. Shkurinov, J. Exp. Theor. Phys. 141, 893 (2012).
    [CrossRef]
  6. R. W. Boyd, Nonlinear Optics (Academic, 2003).
  7. A. V. Borodin, M. N. Esaulkov, I. I. Kuritsyn, I. A. Kotelnikov, and A. P. Shkurinov, J. Opt. Soc. Am. B 29, 1911 (2012).
    [CrossRef]
  8. P. Klarskov, A. Strikwerda, K. Iwaszczuk, and P. U. Jepsen, New J. Phys. 15, 075012 (2013).
    [CrossRef]
  9. A. V. Borodin, N. A. Panov, O. G. Kosareva, V. A. Andreeva, M. N. Esaulkov, V. A. Makarov, A. P. Shkurinov, S. L. Chin, and X.-C. Zhang, Opt. Lett. 38, 1906 (2013).
    [CrossRef]

2013

2012

A. A. Frolov, A. V. Borodin, M. N. Esaulkov, I. I. Kuritsyn, and A. P. Shkurinov, J. Exp. Theor. Phys. 141, 893 (2012).
[CrossRef]

A. V. Borodin, M. N. Esaulkov, I. I. Kuritsyn, I. A. Kotelnikov, and A. P. Shkurinov, J. Opt. Soc. Am. B 29, 1911 (2012).
[CrossRef]

2009

1971

R. S. Finn and J. F. Ward, Phys. Rev. Lett. 26, 285 (1971).
[CrossRef]

1965

P. D. Maker and R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Andreeva, V. A.

Borodin, A. V.

Boyd, R. W.

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

Chin, S. L.

Esaulkov, M. N.

Finn, R. S.

R. S. Finn and J. F. Ward, Phys. Rev. Lett. 26, 285 (1971).
[CrossRef]

Frolov, A. A.

A. A. Frolov, A. V. Borodin, M. N. Esaulkov, I. I. Kuritsyn, and A. P. Shkurinov, J. Exp. Theor. Phys. 141, 893 (2012).
[CrossRef]

Iwaszczuk, K.

P. Klarskov, A. Strikwerda, K. Iwaszczuk, and P. U. Jepsen, New J. Phys. 15, 075012 (2013).
[CrossRef]

Jepsen, P. U.

P. Klarskov, A. Strikwerda, K. Iwaszczuk, and P. U. Jepsen, New J. Phys. 15, 075012 (2013).
[CrossRef]

Karpowicz, N.

Klarskov, P.

P. Klarskov, A. Strikwerda, K. Iwaszczuk, and P. U. Jepsen, New J. Phys. 15, 075012 (2013).
[CrossRef]

Kosareva, O. G.

Kotelnikov, I. A.

Kuritsyn, I. I.

A. V. Borodin, M. N. Esaulkov, I. I. Kuritsyn, I. A. Kotelnikov, and A. P. Shkurinov, J. Opt. Soc. Am. B 29, 1911 (2012).
[CrossRef]

A. A. Frolov, A. V. Borodin, M. N. Esaulkov, I. I. Kuritsyn, and A. P. Shkurinov, J. Exp. Theor. Phys. 141, 893 (2012).
[CrossRef]

Lee, Y.-S.

Y.-S. Lee, Principles of Terahertz Science and Technology (Springer Science, 2008).

Lu, X.

Makarov, V. A.

Maker, P. D.

P. D. Maker and R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Panov, N. A.

Shkurinov, A. P.

Strikwerda, A.

P. Klarskov, A. Strikwerda, K. Iwaszczuk, and P. U. Jepsen, New J. Phys. 15, 075012 (2013).
[CrossRef]

Terhune, R. W.

P. D. Maker and R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Ward, J. F.

R. S. Finn and J. F. Ward, Phys. Rev. Lett. 26, 285 (1971).
[CrossRef]

Zhang, X.-C.

J. Exp. Theor. Phys.

A. A. Frolov, A. V. Borodin, M. N. Esaulkov, I. I. Kuritsyn, and A. P. Shkurinov, J. Exp. Theor. Phys. 141, 893 (2012).
[CrossRef]

J. Opt. Soc. Am. B

New J. Phys.

P. Klarskov, A. Strikwerda, K. Iwaszczuk, and P. U. Jepsen, New J. Phys. 15, 075012 (2013).
[CrossRef]

Opt. Lett.

Phys. Rev.

P. D. Maker and R. W. Terhune, Phys. Rev. 137, A801 (1965).
[CrossRef]

Phys. Rev. Lett.

R. S. Finn and J. F. Ward, Phys. Rev. Lett. 26, 285 (1971).
[CrossRef]

Other

Y.-S. Lee, Principles of Terahertz Science and Technology (Springer Science, 2008).

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

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Figures (3)

Fig. 1.
Fig. 1.

Schematic representation of the experimental setup.

Fig. 2.
Fig. 2.

Spectral integrated signal acquired by EFISH method compared with THz signal intensity measured by the Golay cell.

Fig. 3.
Fig. 3.

Total SH intensity versus DC-bias voltage for blocked THz beam (black squares) and open THz beam with two polarities of DC field (open and filled gray circles). Solid line is an approximation of experimental data using Eq. (17).

Equations (21)

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W2ω(Δ)=WDC+WTHz,DC(Δ)+WTHz(Δ),
WDC=GDC·ωp2τ2kp2d2VE416c4EDC2πRL2cτ162JDC,
WTHz,DC(Δ)=GTHz,DC·ωp2τ2kp2d2VE416c4×EDCRL2c4ΔdξET(ξ)e2(ξΔ)2τ2JTHz,DC,
WTHz(Δ)=GTHz·ωp2τ2kp2d2VE416c4RL2c2τ2×Δdξ|ΔξdξET(ξ)|2e2(ξΔ)2τ2JTHz.
GDC=(e0eL)2+1/8,GTHz,DC=(eTeL)(e0eL)+1/8(e0eT),GTHz=(eTeL)2+1/8,
JDC=14d2|dddze3iωp2z/(4cω)1+iz/zL|2,JTHz=14d2|dddze3iωp2z/(4cω)(1+iz/zL)(1+iz/zT)|2,
JTHz,DC=18d2(dddze3iωp2z/(4cω)1+iz/zL×dddze3iωp2z/(4cω)(1iz/zL)(1iz/zT)+c.c.).
WTHz,DC(Δ)=GTHz,DCGDCJTHz,DCJDC×42WDCτπEDCΔdξET(ξ)e2(ξΔ)2τ2.
W+=WDC+WTHz,DC(Δ=0)+WTHz(Δ=0),W=WDCWTHz,DC(Δ=0)+WTHz(Δ=0).
WTHz,DC(Δ=0)=W0=W+W2.
WTHz,DC(Δ)=W+W2F(Δ).
ET(Δ)=GDCGTHz,DCJDCJTHz,DCEDC2W+W2WDCF(Δ).
E2ω=4πiωncχ(3)Eω2(αEDC+βET),
α=+dzeiΔkz1+iz/zL,β=+dzeiΔkz(1+iz/zL)(1+iz/zT).
I2ω=c8π|4πωncχ(3)|2|Eω4|×[|α|2EDC2+|β|2ET2+(αβ*+α*β)EDCET].
W2ω(Δ)=|4πωncχ(3)|2cRL2E0L416+dξe2(ξΔ)2τ2×[|α|2EDC2+|β|2ET2(ξ)+(αβ*+α*β)EDCET(ξ)].
WDC=|4πωncχ(3)|2π2|α|2τcRL2E0L4EDC216.
WTHz,DC(Δ)=αβ*+α*β|α|2WDCEDCET(Δ).
ET(Δ)=|α|2αβ*+α*βEDCW+W2WDCF(Δ).
ET(r,ξ,z)=eTET(ξ)1+iz/zTexp((r|z|tgα)22RT2(1+iz/zT)),
Pav=c8πETHz2dtS1τrep.rate,

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