Abstract

A new electro-optic (EO) sampling scheme, which we refer to as “heterodyne EO sampling”, for detection of pulsed terahertz (THz) waves is proposed and experimentally demonstrated. In this heterodyne EO sampling scheme, the intensity change in the optical probe pulse induced by a THz field in a nonlinear crystal is measured without any polarization optics. Applied in combination with the non-collinear Cherenkov velocity matching technique, this method allows one to detect pulsed THz waves efficiently and easily using a simpler optical setup as compared to the conventional ellipsometric EO sampling method.

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  1. Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett.67(24), 3523–3525 (1995).
    [CrossRef]
  2. D. H. Auston, K. P. Cheung, and P. R. Smith, “Picosecond photoconducting Hertzian dipoles,” Appl. Phys. Lett.45(3), 284–286 (1984).
    [CrossRef]
  3. M. Tani, S. Matsuura, K. Sakai, and S. Nakashima, “Emission characteristics of photoconductive antennas based on low-temperature-grown GaAs and semi-insulating GaAs,” Appl. Opt.36(30), 7853–7859 (1997).
    [CrossRef] [PubMed]
  4. M. Tani, K. Horita, T. Kinoshita, C. T. Que, E. Estacio, K. Yamamoto, and M. I. Bakunov, “Efficient electro-optic sampling detection of terahertz radiation via Cherenkov phase matching,” Opt. Express19(21), 19901–19906 (2011).
    [CrossRef] [PubMed]
  5. P. Y. Han, M. Tani, F. Pan, and X.-C. Zhang, “Use of the organic crystal DAST for terahertz beam applications,” Opt. Lett.25(9), 675–677 (2000).
    [CrossRef] [PubMed]
  6. S. P. Kovalev and G. Kh. Kitaeva, “Two alternative approaches to electro-optical detection of terahertz pulses,” JETP Lett.94(2), 91–96 (2011).
    [CrossRef]
  7. G. Kh. Kitaeva, “Frequency conversion in aperiodic quasi-phase-matched structures,” Phys. Rev. A76(4), 043841 (2007).
    [CrossRef]
  8. G. Kh. Kitaeva, S. P. Kovalev, I. I. Naumova, R. A. Akhmedzhanov, I. E. Ilyakov, B. V. Shishkin, and E. V. Suvorov, “Quasi-phase-matched probe-energy electro-optic sampling as a method of narrowband terahertz detection,” Appl. Phys. Lett.96(7), 071106 (2010).
    [CrossRef]
  9. G. Gallot and D. Grischkowsky, “Electro-optic detection of terahertz radiation,” J. Opt. Soc. Am. B16(8), 1204–1212 (1999).
    [CrossRef]
  10. D. E. Zelmon, D. L. Small, and D. Jundt, “Infrared corrected Sellmeier coefficients for congruently grown lithium niobate and 5 mol.% magnesium oxide-doped lithium niobate,” J. Opt. Soc. Am. B14(12), 3319–3322 (1997).
    [CrossRef]
  11. L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgar, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys.97(12), 123505 (2005).
    [CrossRef]
  12. D. F. Edwards, “Silicon (Si),” in Handbook of Optical Constant of Solids, E. D. Palik, ed. (Academic, 1985).
  13. C. Winnewisser, P. Uhd Jepsen, M. Schall, V. Schyja, and H. Helm, “Electro-optic detection of THz radiation in LiTaO3, LiNbO3 and ZnTe,” Appl. Phys. Lett.70(23), 3069–3071 (1997).
    [CrossRef]
  14. M. Tani, S. Matsuura, K. Sakai, and S. Nakashima, “Emission characteristics of photoconductive antennas based on low-temperature-grown GaAs and semi-insulating GaAs,” Appl. Opt.36(30), 7853–7859 (1997).
    [CrossRef] [PubMed]
  15. T. Nagase, T. Kinoshita, S. Ozawa, K. Kawase, M. I. Bakunov, K. Yamamoto, and M. Tani,“Detection of THz radiation by using optical waveguide structure in Cherenkov-phase-matched EO sampling,” in Proceedings of International Symposium on Frontiers in Terahertz Technology (FTT 2012), N. Hiromoto Ed. (Electronically published by FTT 2012 Secretariat, 2012), paper Pos1.26.

2011

2010

G. Kh. Kitaeva, S. P. Kovalev, I. I. Naumova, R. A. Akhmedzhanov, I. E. Ilyakov, B. V. Shishkin, and E. V. Suvorov, “Quasi-phase-matched probe-energy electro-optic sampling as a method of narrowband terahertz detection,” Appl. Phys. Lett.96(7), 071106 (2010).
[CrossRef]

2007

G. Kh. Kitaeva, “Frequency conversion in aperiodic quasi-phase-matched structures,” Phys. Rev. A76(4), 043841 (2007).
[CrossRef]

2005

L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgar, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys.97(12), 123505 (2005).
[CrossRef]

2000

1999

1997

1995

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett.67(24), 3523–3525 (1995).
[CrossRef]

1984

D. H. Auston, K. P. Cheung, and P. R. Smith, “Picosecond photoconducting Hertzian dipoles,” Appl. Phys. Lett.45(3), 284–286 (1984).
[CrossRef]

Akhmedzhanov, R. A.

G. Kh. Kitaeva, S. P. Kovalev, I. I. Naumova, R. A. Akhmedzhanov, I. E. Ilyakov, B. V. Shishkin, and E. V. Suvorov, “Quasi-phase-matched probe-energy electro-optic sampling as a method of narrowband terahertz detection,” Appl. Phys. Lett.96(7), 071106 (2010).
[CrossRef]

Auston, D. H.

D. H. Auston, K. P. Cheung, and P. R. Smith, “Picosecond photoconducting Hertzian dipoles,” Appl. Phys. Lett.45(3), 284–286 (1984).
[CrossRef]

Bakunov, M. I.

Cheung, K. P.

D. H. Auston, K. P. Cheung, and P. R. Smith, “Picosecond photoconducting Hertzian dipoles,” Appl. Phys. Lett.45(3), 284–286 (1984).
[CrossRef]

Estacio, E.

Gallot, G.

Grischkowsky, D.

Han, P. Y.

Hebling, J.

L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgar, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys.97(12), 123505 (2005).
[CrossRef]

Helm, H.

C. Winnewisser, P. Uhd Jepsen, M. Schall, V. Schyja, and H. Helm, “Electro-optic detection of THz radiation in LiTaO3, LiNbO3 and ZnTe,” Appl. Phys. Lett.70(23), 3069–3071 (1997).
[CrossRef]

Horita, K.

Ilyakov, I. E.

G. Kh. Kitaeva, S. P. Kovalev, I. I. Naumova, R. A. Akhmedzhanov, I. E. Ilyakov, B. V. Shishkin, and E. V. Suvorov, “Quasi-phase-matched probe-energy electro-optic sampling as a method of narrowband terahertz detection,” Appl. Phys. Lett.96(7), 071106 (2010).
[CrossRef]

Jundt, D.

Kinoshita, T.

Kitaeva, G. Kh.

S. P. Kovalev and G. Kh. Kitaeva, “Two alternative approaches to electro-optical detection of terahertz pulses,” JETP Lett.94(2), 91–96 (2011).
[CrossRef]

G. Kh. Kitaeva, S. P. Kovalev, I. I. Naumova, R. A. Akhmedzhanov, I. E. Ilyakov, B. V. Shishkin, and E. V. Suvorov, “Quasi-phase-matched probe-energy electro-optic sampling as a method of narrowband terahertz detection,” Appl. Phys. Lett.96(7), 071106 (2010).
[CrossRef]

G. Kh. Kitaeva, “Frequency conversion in aperiodic quasi-phase-matched structures,” Phys. Rev. A76(4), 043841 (2007).
[CrossRef]

Kovalev, S. P.

S. P. Kovalev and G. Kh. Kitaeva, “Two alternative approaches to electro-optical detection of terahertz pulses,” JETP Lett.94(2), 91–96 (2011).
[CrossRef]

G. Kh. Kitaeva, S. P. Kovalev, I. I. Naumova, R. A. Akhmedzhanov, I. E. Ilyakov, B. V. Shishkin, and E. V. Suvorov, “Quasi-phase-matched probe-energy electro-optic sampling as a method of narrowband terahertz detection,” Appl. Phys. Lett.96(7), 071106 (2010).
[CrossRef]

Kuhl, J.

L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgar, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys.97(12), 123505 (2005).
[CrossRef]

Matsuura, S.

Nakashima, S.

Naumova, I. I.

G. Kh. Kitaeva, S. P. Kovalev, I. I. Naumova, R. A. Akhmedzhanov, I. E. Ilyakov, B. V. Shishkin, and E. V. Suvorov, “Quasi-phase-matched probe-energy electro-optic sampling as a method of narrowband terahertz detection,” Appl. Phys. Lett.96(7), 071106 (2010).
[CrossRef]

Pálfalvi, L.

L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgar, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys.97(12), 123505 (2005).
[CrossRef]

Pan, F.

Peter, A.

L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgar, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys.97(12), 123505 (2005).
[CrossRef]

Polgar, K.

L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgar, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys.97(12), 123505 (2005).
[CrossRef]

Que, C. T.

Sakai, K.

Schall, M.

C. Winnewisser, P. Uhd Jepsen, M. Schall, V. Schyja, and H. Helm, “Electro-optic detection of THz radiation in LiTaO3, LiNbO3 and ZnTe,” Appl. Phys. Lett.70(23), 3069–3071 (1997).
[CrossRef]

Schyja, V.

C. Winnewisser, P. Uhd Jepsen, M. Schall, V. Schyja, and H. Helm, “Electro-optic detection of THz radiation in LiTaO3, LiNbO3 and ZnTe,” Appl. Phys. Lett.70(23), 3069–3071 (1997).
[CrossRef]

Shishkin, B. V.

G. Kh. Kitaeva, S. P. Kovalev, I. I. Naumova, R. A. Akhmedzhanov, I. E. Ilyakov, B. V. Shishkin, and E. V. Suvorov, “Quasi-phase-matched probe-energy electro-optic sampling as a method of narrowband terahertz detection,” Appl. Phys. Lett.96(7), 071106 (2010).
[CrossRef]

Small, D. L.

Smith, P. R.

D. H. Auston, K. P. Cheung, and P. R. Smith, “Picosecond photoconducting Hertzian dipoles,” Appl. Phys. Lett.45(3), 284–286 (1984).
[CrossRef]

Suvorov, E. V.

G. Kh. Kitaeva, S. P. Kovalev, I. I. Naumova, R. A. Akhmedzhanov, I. E. Ilyakov, B. V. Shishkin, and E. V. Suvorov, “Quasi-phase-matched probe-energy electro-optic sampling as a method of narrowband terahertz detection,” Appl. Phys. Lett.96(7), 071106 (2010).
[CrossRef]

Tani, M.

Uhd Jepsen, P.

C. Winnewisser, P. Uhd Jepsen, M. Schall, V. Schyja, and H. Helm, “Electro-optic detection of THz radiation in LiTaO3, LiNbO3 and ZnTe,” Appl. Phys. Lett.70(23), 3069–3071 (1997).
[CrossRef]

Winnewisser, C.

C. Winnewisser, P. Uhd Jepsen, M. Schall, V. Schyja, and H. Helm, “Electro-optic detection of THz radiation in LiTaO3, LiNbO3 and ZnTe,” Appl. Phys. Lett.70(23), 3069–3071 (1997).
[CrossRef]

Wu, Q.

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett.67(24), 3523–3525 (1995).
[CrossRef]

Yamamoto, K.

Zelmon, D. E.

Zhang, X.-C.

P. Y. Han, M. Tani, F. Pan, and X.-C. Zhang, “Use of the organic crystal DAST for terahertz beam applications,” Opt. Lett.25(9), 675–677 (2000).
[CrossRef] [PubMed]

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett.67(24), 3523–3525 (1995).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

C. Winnewisser, P. Uhd Jepsen, M. Schall, V. Schyja, and H. Helm, “Electro-optic detection of THz radiation in LiTaO3, LiNbO3 and ZnTe,” Appl. Phys. Lett.70(23), 3069–3071 (1997).
[CrossRef]

Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett.67(24), 3523–3525 (1995).
[CrossRef]

D. H. Auston, K. P. Cheung, and P. R. Smith, “Picosecond photoconducting Hertzian dipoles,” Appl. Phys. Lett.45(3), 284–286 (1984).
[CrossRef]

G. Kh. Kitaeva, S. P. Kovalev, I. I. Naumova, R. A. Akhmedzhanov, I. E. Ilyakov, B. V. Shishkin, and E. V. Suvorov, “Quasi-phase-matched probe-energy electro-optic sampling as a method of narrowband terahertz detection,” Appl. Phys. Lett.96(7), 071106 (2010).
[CrossRef]

J. Appl. Phys.

L. Pálfalvi, J. Hebling, J. Kuhl, A. Peter, and K. Polgar, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys.97(12), 123505 (2005).
[CrossRef]

J. Opt. Soc. Am. B

JETP Lett.

S. P. Kovalev and G. Kh. Kitaeva, “Two alternative approaches to electro-optical detection of terahertz pulses,” JETP Lett.94(2), 91–96 (2011).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

G. Kh. Kitaeva, “Frequency conversion in aperiodic quasi-phase-matched structures,” Phys. Rev. A76(4), 043841 (2007).
[CrossRef]

Other

D. F. Edwards, “Silicon (Si),” in Handbook of Optical Constant of Solids, E. D. Palik, ed. (Academic, 1985).

T. Nagase, T. Kinoshita, S. Ozawa, K. Kawase, M. I. Bakunov, K. Yamamoto, and M. Tani,“Detection of THz radiation by using optical waveguide structure in Cherenkov-phase-matched EO sampling,” in Proceedings of International Symposium on Frontiers in Terahertz Technology (FTT 2012), N. Hiromoto Ed. (Electronically published by FTT 2012 Secretariat, 2012), paper Pos1.26.

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Figures (6)

Fig. 1
Fig. 1

The Cherenkov velocity matching scheme for heterodyne EO sampling.

Fig. 2
Fig. 2

Wave vector diagrams for non-collinear (a) SFG and (b) DFG processes.

Fig. 3
Fig. 3

Schematic of the experimental setup.

Fig. 4
Fig. 4

(a) THz waveforms measured with the LN/Si-prism structure in the heterodyne and ellipsometric schemes. (b) Corresponding Fourier transformed amplitude spectra

Fig. 5
Fig. 5

The heterodyne EO sampling signal for different positions Δ of the photo-detector across the expanded probe beam (Δ is measured from the center of the beam).

Fig. 6
Fig. 6

(a) THz waveforms detected by the balanced (red line) and single-beam (blue and black lines) heterodyne EO sampling. (b) Corresponding Fourier transformed amplitude spectra

Equations (29)

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E y (0,t)=Re[ A 0 ( t ) e i ω 0 t ]= + dω A ˜ 0 ( ω ) e iωt .
E y ( x,t )= dω E ˜ y ( x,ω ) e iωt , E ˜ y ( x,ω )= A ˜ 0 ( ω ) e ik(ω)x ,
E y THz ( x,z,t+τ )= dΩ E ˜ y THz ( x,z,τ,Ω ) e iΩt = dΩ A ˜ THz ( Ω ) e iΩ( t+τ )+i K x ( Ω )x+i K z ( Ω )z ,
P ˜ y NL ( x,z,ω )=2 ε 0 χ eff (2) 0 dΩ [ E ˜ y ( x,ωΩ ) E ˜ y THz ( x,z,Ω )+ E ˜ y ( x,ω+Ω ) E ˜ y THz ( x,z,Ω ) ],
2 E ˜ y x 2 + 2 E ˜ y z 2 + k 2 (ω) E ˜ y = μ 0 ω 2 P ˜ y NL ( x,z,ω ),
1 2π dz e i( g K z )z =δ[ g K z ( Ω ) ] = 1 K z δ( Ω Ω g ),
2 E ˜ y x 2 + k x 2 E ˜ y = 2 ω 2 c 2 K z χ eff (2) [ A ˜ 0 ( ω Ω g ) A ˜ THz ( Ω g ) e ik( ω Ω g )x+i K x ( Ω g )xi Ω g τ + A ˜ 0 ( ω+ Ω g ) A ˜ THz ( Ω g ) e ik( ω+ Ω g )xi K x ( Ω g )x+i Ω g τ ],
E ˜ y = A ˜ ( x,g,ω ) e i k x x .
A ˜ x = i ω 2 c 2 k x K z χ eff (2) [ A ˜ 0 ( ω Ω g ) A ˜ THz ( Ω g ) e i (Δk) + xi Ω g τ + A ˜ 0 ( ω+ Ω g ) A ˜ THz ( Ω g ) e i (Δk) x+i Ω g τ ],
A ˜ ( L,g,ω )= A ˜ 0 ( ω )δ( g )+ i ω 2 L c 2 k x K z χ eff (2) { A ˜ 0 ( ω Ω g ) A ˜ THz ( Ω g )sinc[ ( Δk ) + L 2 ] e i ( Δk ) + L /2 i Ω g τ + A ˜ 0 ( ω+ Ω g ) A ˜ THz ( Ω g )sinc[ ( Δk ) L 2 ] e i ( Δk ) L /2 +i Ω g τ }.
E ˜ y ( x,z,ω )= A ˜ 0 ( ω ) e ik( ω )x + i ω 2 L c 2 χ eff (2) 0 dΩ e i k x x k x { A ˜ 0 ( ωΩ ) A ˜ THz ( Ω )sinc[ ( Δk ) + L 2 ] e i K z z+i ( Δk ) + L /2 iΩτ + A ˜ 0 ( ω+Ω ) A ˜ THz ( Ω )sinc[ ( Δk ) L 2 ] e i K z zi ( Δk ) L /2 +iΩτ }.
( Δk ) ± K x ( Ω ) Ω V ± K z 2 2k = Ω c ( n Si sinα n g )± K z 2 2k .
E y ( x,z,t )= dω[ A ˜ 0 ( ω )+Δ A ˜ ( L,z,ω ) ] e iωt+ik( ω )x .
ΔI= dt[ E y ( x,t ) H z ( x,t ) E y ( 0,t ) H z ( 0,t ) ] ,
dt e i( ω ω )t =2πδ( ω ω )
ΔI=2π ε 0 L χ eff (2) 0 dΩ{ i A ˜ THz ( Ω )sinc[ ( Δk ) + L 2 ] e i K z z+i ( Δk ) + L /2 iΩτ dωω A ˜ 0 ( ωΩ ) A ˜ 0 ( ω ) +i A ˜ THz ( Ω )sinc[ ( Δk ) L 2 ] e i K z zi ( Δk ) L /2 +iΩτ dωω A ˜ 0 ( ω+Ω ) A ˜ 0 ( ω ) +c.c. }
dωω A ˜ 0 ( ω±Ω ) A ˜ 0 ( ω ) ω 0 C( Ω ),
C( Ω )= dω A ˜ 0 ( ω±Ω ) A ˜ 0 ( ω ) .
ΔI=2π ε 0 L ω 0 χ eff (2) 0 dΩC( Ω ){ i A ˜ THz ( Ω )sinc[ ( Δk ) + L 2 ] e i K z z+i ( Δk ) + L /2 iΩτ +i A ˜ THz ( Ω )sinc[ ( Δk ) L 2 ] e i K z zi ( Δk ) L /2 +iΩτ +c.c. }.
ΔI=8π ε 0 L ω 0 χ eff (2) 0 dΩC( Ω )sinc( K z 2 L 4 k 0 )sin( K z 2 L 4 k 0 )Re[ A ˜ THz ( Ω ) e iΩτ+i K z z ] .
Δ I SFG =4π ε 0 L ω 0 χ eff (2) 0 dΩC( Ω )sinc[ ( Δk ) + L 2 ]Im[ A ˜ THz ( Ω ) e iΩτ+i ( Δk ) + L /2 +i K z z ] ,
Δ I DFG =4π ε 0 L ω 0 χ eff (2) 0 dΩC( Ω )sinc[ ( Δk ) L 2 ]Im[ A ˜ THz ( Ω ) e iΩτi ( Δk ) L /2 i K z z ] .
Δ I SFG I 0 2L ω 0 c n opt χ eff (2) 0 dΩsinc( K z 2 L 4 k 0 )Im[ A ˜ THz ( Ω ) e iΩτ+i K z 2 L / ( 4 k 0 ) +i K z z ] ,
Δ I SFG I 0 2L ω 0 c n opt χ eff (2) 0 dΩsinc( K z 2 L 4 k 0 )Im[ A ˜ THz ( Ω ) e iΩτi K z 2 L / ( 4 k 0 ) +i K z z ] .
Δ I SFG I 0 Δ I DFG I 0 ω 0 L n e 3 r 33 c 0 dΩIm[ A ˜ THz ( Ω ) e iΩτ+i K z z ] .
Δ I SFG I 0 Δ I DFG I 0 ω 0 L n e 3 r 33 c 0 dΩ| A ˜ THz ( Ω ) |sin[ Ωτ K z zφ( Ω ) ] .
E y THz ( 0,z,τ )=2 0 dΩ| A ˜ THz ( Ω ) |cos[ Ωτ K z zφ( Ω ) ] .
Δ I SFG I 0 Δ I DFG I 0 ω 0 L n e 3 r 33 2c Η[ E y THz ( 0,z,τ ) ].
ΔI I 0 ( n e 3 r 33 n o 3 r 13 ) ω 0 L 2c E y THz ( τ ),

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