Abstract

Three methods for distortion-free enhancement of electro-optic sampling measurements of terahertz signals are tested. In the first part of this two-paper series [J. Opt. Soc. Am B31, 904–910 (2014)], the theoretical framework for describing the signal enhancement was presented and discussed. As the applied optical bias is decreased, individual signal traces become enhanced but distorted. Here we experimentally show that nonlinear signal components that distort the terahertz electric field measurement can be removed by subtracting traces recorded with opposite optical bias values. In all three methods tested, we observe up to an order of magnitude increase in distortion-free signal enhancement, in agreement with the theory, making possible measurements of small terahertz-induced transient birefringence signals with increased signal-to-noise ratio.

© 2014 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. R. Torre, Time-Resolved Spectropscopy in Complex Liquids: An Experimental Perspective (Springer, 2007).
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    [CrossRef]
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2014 (1)

2013 (1)

Y. Minami, Y. Hayashi, J. Takeda, and I. Katayama, “Single-shot measurement of a terahertz electric-field waveform using a reflective echelon mirror,” Appl. Phys. Lett. 103, 051103 (2013).
[CrossRef]

2012 (1)

2011 (2)

C. A. Werley, S. M. Teo, and K. A. Nelson, “Pulsed laser noise analysis and pump-probe signal detection with a data acquisition card,” Rev. Sci. Instrum. 82, 123108 (2011).
[CrossRef]

N. H. Matlis, G. R. Plateau, J. van Tilborg, and W. P. Leemans, “Single-shot spatiotemporal measurements of ultrashort THz waveforms using temporal electric-field cross correlation,” J. Opt. Soc. Am. B 28, 23–27 (2011).
[CrossRef]

2008 (1)

2004 (1)

2001 (1)

1997 (1)

Q. Wu and X.-C. Zhang, “7 terahertz broadband GaP electro-optic sensor,” Appl. Phys. Lett. 70, 1784–1786 (1997).
[CrossRef]

1996 (2)

Q. Wu and X.-C. Zhang, “Ultrafast electro-optic field sensors,” Appl. Phys. Lett. 68, 1604–1606 (1996).
[CrossRef]

C. A. Gautier, J. C. Loulergue, and J. Etchpare, “Homodyne and heterodyne impulsive Raman Kerr nonlinearities in crystal: application to E-symmetry polariton modes in PbTiO3,” Solid State Commun. 100, 133–136 (1996).

1991 (1)

D. McMorrow and W. T. Lotshaw, “Intermolecular dynamics in acetonitrile probed with femtosecond Fourier transform Raman spectroscopy,” J. Phys. Chem. 95, 10395–10406 (1991).
[CrossRef]

1989 (1)

Y. Berozashvili, S. Machavariani, A. Natsvlishvili, and A. Chirakadze, “Dispersion of the linear electro-optic coefficients and the non-linear susceptibility in GaP,” J. Phys. D 22, 682–686 (1989).
[CrossRef]

1987 (1)

Y. Yan and K. A. Nelson, “Impulsive stimulated light scattering. I. General theory,” J. Chem. Phys. 87, 6240–6256 (1987).
[CrossRef]

Bakker, H. J.

Berozashvili, Y.

Y. Berozashvili, S. Machavariani, A. Natsvlishvili, and A. Chirakadze, “Dispersion of the linear electro-optic coefficients and the non-linear susceptibility in GaP,” J. Phys. D 22, 682–686 (1989).
[CrossRef]

Brunner, F. D. J.

Chirakadze, A.

Y. Berozashvili, S. Machavariani, A. Natsvlishvili, and A. Chirakadze, “Dispersion of the linear electro-optic coefficients and the non-linear susceptibility in GaP,” J. Phys. D 22, 682–686 (1989).
[CrossRef]

Etchpare, J.

C. A. Gautier, J. C. Loulergue, and J. Etchpare, “Homodyne and heterodyne impulsive Raman Kerr nonlinearities in crystal: application to E-symmetry polariton modes in PbTiO3,” Solid State Commun. 100, 133–136 (1996).

Ferrer, A.

Feurer, T.

Gautier, C. A.

C. A. Gautier, J. C. Loulergue, and J. Etchpare, “Homodyne and heterodyne impulsive Raman Kerr nonlinearities in crystal: application to E-symmetry polariton modes in PbTiO3,” Solid State Commun. 100, 133–136 (1996).

Grübel, S.

Günter, P.

Hauri, C. P.

Hayashi, Y.

Y. Minami, Y. Hayashi, J. Takeda, and I. Katayama, “Single-shot measurement of a terahertz electric-field waveform using a reflective echelon mirror,” Appl. Phys. Lett. 103, 051103 (2013).
[CrossRef]

Jazbinšek, M.

Johnson, J. A.

Johnson, S. L.

Katayama, I.

Y. Minami, Y. Hayashi, J. Takeda, and I. Katayama, “Single-shot measurement of a terahertz electric-field waveform using a reflective echelon mirror,” Appl. Phys. Lett. 103, 051103 (2013).
[CrossRef]

Kwon, O.-P.

Kwon, S.-J.

Leemans, W. P.

Lotshaw, W. T.

D. McMorrow and W. T. Lotshaw, “Intermolecular dynamics in acetonitrile probed with femtosecond Fourier transform Raman spectroscopy,” J. Phys. Chem. 95, 10395–10406 (1991).
[CrossRef]

Loulergue, J. C.

C. A. Gautier, J. C. Loulergue, and J. Etchpare, “Homodyne and heterodyne impulsive Raman Kerr nonlinearities in crystal: application to E-symmetry polariton modes in PbTiO3,” Solid State Commun. 100, 133–136 (1996).

Machavariani, S.

Y. Berozashvili, S. Machavariani, A. Natsvlishvili, and A. Chirakadze, “Dispersion of the linear electro-optic coefficients and the non-linear susceptibility in GaP,” J. Phys. D 22, 682–686 (1989).
[CrossRef]

Matlis, N. H.

McMorrow, D.

D. McMorrow and W. T. Lotshaw, “Intermolecular dynamics in acetonitrile probed with femtosecond Fourier transform Raman spectroscopy,” J. Phys. Chem. 95, 10395–10406 (1991).
[CrossRef]

Minami, Y.

Y. Minami, Y. Hayashi, J. Takeda, and I. Katayama, “Single-shot measurement of a terahertz electric-field waveform using a reflective echelon mirror,” Appl. Phys. Lett. 103, 051103 (2013).
[CrossRef]

Natsvlishvili, A.

Y. Berozashvili, S. Machavariani, A. Natsvlishvili, and A. Chirakadze, “Dispersion of the linear electro-optic coefficients and the non-linear susceptibility in GaP,” J. Phys. D 22, 682–686 (1989).
[CrossRef]

Nelson, K. A.

C. A. Werley, S. M. Teo, and K. A. Nelson, “Pulsed laser noise analysis and pump-probe signal detection with a data acquisition card,” Rev. Sci. Instrum. 82, 123108 (2011).
[CrossRef]

Y. Yan and K. A. Nelson, “Impulsive stimulated light scattering. I. General theory,” J. Chem. Phys. 87, 6240–6256 (1987).
[CrossRef]

Nienhuys, H.-K.

Planken, P. C. M.

Plateau, G. R.

Ruchert, C.

Schneider, A.

Takeda, J.

Y. Minami, Y. Hayashi, J. Takeda, and I. Katayama, “Single-shot measurement of a terahertz electric-field waveform using a reflective echelon mirror,” Appl. Phys. Lett. 103, 051103 (2013).
[CrossRef]

Teo, S. M.

C. A. Werley, S. M. Teo, and K. A. Nelson, “Pulsed laser noise analysis and pump-probe signal detection with a data acquisition card,” Rev. Sci. Instrum. 82, 123108 (2011).
[CrossRef]

Torre, R.

R. Torre, Time-Resolved Spectropscopy in Complex Liquids: An Experimental Perspective (Springer, 2007).

van der Valk, N. C. J.

van Tilborg, J.

Vicario, C.

Wecnkebach, T.

Wenckebach, T.

Werley, C. A.

C. A. Werley, S. M. Teo, and K. A. Nelson, “Pulsed laser noise analysis and pump-probe signal detection with a data acquisition card,” Rev. Sci. Instrum. 82, 123108 (2011).
[CrossRef]

Wu, Q.

Q. Wu and X.-C. Zhang, “7 terahertz broadband GaP electro-optic sensor,” Appl. Phys. Lett. 70, 1784–1786 (1997).
[CrossRef]

Q. Wu and X.-C. Zhang, “Ultrafast electro-optic field sensors,” Appl. Phys. Lett. 68, 1604–1606 (1996).
[CrossRef]

Yan, Y.

Y. Yan and K. A. Nelson, “Impulsive stimulated light scattering. I. General theory,” J. Chem. Phys. 87, 6240–6256 (1987).
[CrossRef]

Zhang, X.-C.

Q. Wu and X.-C. Zhang, “7 terahertz broadband GaP electro-optic sensor,” Appl. Phys. Lett. 70, 1784–1786 (1997).
[CrossRef]

Q. Wu and X.-C. Zhang, “Ultrafast electro-optic field sensors,” Appl. Phys. Lett. 68, 1604–1606 (1996).
[CrossRef]

Appl. Phys. Lett. (3)

Q. Wu and X.-C. Zhang, “Ultrafast electro-optic field sensors,” Appl. Phys. Lett. 68, 1604–1606 (1996).
[CrossRef]

Q. Wu and X.-C. Zhang, “7 terahertz broadband GaP electro-optic sensor,” Appl. Phys. Lett. 70, 1784–1786 (1997).
[CrossRef]

Y. Minami, Y. Hayashi, J. Takeda, and I. Katayama, “Single-shot measurement of a terahertz electric-field waveform using a reflective echelon mirror,” Appl. Phys. Lett. 103, 051103 (2013).
[CrossRef]

J. Chem. Phys. (1)

Y. Yan and K. A. Nelson, “Impulsive stimulated light scattering. I. General theory,” J. Chem. Phys. 87, 6240–6256 (1987).
[CrossRef]

J. Opt. Soc. Am. B (4)

J. Phys. Chem. (1)

D. McMorrow and W. T. Lotshaw, “Intermolecular dynamics in acetonitrile probed with femtosecond Fourier transform Raman spectroscopy,” J. Phys. Chem. 95, 10395–10406 (1991).
[CrossRef]

J. Phys. D (1)

Y. Berozashvili, S. Machavariani, A. Natsvlishvili, and A. Chirakadze, “Dispersion of the linear electro-optic coefficients and the non-linear susceptibility in GaP,” J. Phys. D 22, 682–686 (1989).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

C. A. Werley, S. M. Teo, and K. A. Nelson, “Pulsed laser noise analysis and pump-probe signal detection with a data acquisition card,” Rev. Sci. Instrum. 82, 123108 (2011).
[CrossRef]

Solid State Commun. (1)

C. A. Gautier, J. C. Loulergue, and J. Etchpare, “Homodyne and heterodyne impulsive Raman Kerr nonlinearities in crystal: application to E-symmetry polariton modes in PbTiO3,” Solid State Commun. 100, 133–136 (1996).

Other (2)

R. Torre, Time-Resolved Spectropscopy in Complex Liquids: An Experimental Perspective (Springer, 2007).

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985), Vol. V, Chap. 2, p. 21.

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the transient birefringence setup. A high-quality polarizer P1 sets the probe polarization. Optical bias is applied by either using a variable wave plate (VWP) or a QWP after P1. Either the VWP, the QWP, or P1 can be rotated to vary the level of optical bias, as described in the text. Another high-quality polarizer (P2) serves as analyzer, here depicted as a Wollaston prism as in the current measurements. Lens L1 focuses the probe beam to the EO crystal, and L2 collimates it after. Detectors monitor the perpendicular and parallel channels, each of which has a variable attenuator (VA). An off-axis parabolic mirror focuses the terahertz to the EO crystal or the sample, collinearly with the probe beam.

Fig. 2.
Fig. 2.

Terahertz-induced EO transient birefringence data collected for different P1 angles with QWP fixed at 0°. (a) The normalized difference signal for positive optical biases corresponding to Γ0=2ϕ shown in the key. (b) The normalized difference signal for negative optical biases shown in the key.

Fig. 3.
Fig. 3.

(a) Difference between the positive and negative optical bias traces from Fig. 2. (b) The same traces as in (a), normalized and overlaid.

Fig. 4.
Fig. 4.

(a) Signal enhancement, averaged for many delay times (identical for each trace) and normalized to the 90° optical bias values (the VWP data was normalized to the 80° optical bias value). Circles are for rotating P1 (case 1), squares are for adjusting the VWP (case 3), and triangles are for rotating the QWP (case 2). The solid lines are the theoretical enhancement in the absence of a scattering background (b=0). (b) Theoretical and fitted values for A and B parameters (respectively, the linear and quadratic raw signal component amplitudes as described in the text). As in (a), circles are for rotating P1, squares are for adjusting the VWP, and triangles are for rotating the QWP.

Fig. 5.
Fig. 5.

Ratio ΔB(Γ0,ΔΓ0)/2A(Γ0) plotted with errors in the negative optical bias of ΔΓ0=0.05° and 0.01° when rotating P1 or using a VWP. The relative quadratic signal magnitude reaches 10% at 3.74° and 1.68° for ΔΓ0=0.05° and 0.01°, respectively.

Equations (6)

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

S(ETHz,Γ0)=TI(ETHz,Γ0)TI(ETHz,Γ0)TI(0,Γ0)+TI(0,Γ0),
gP1/VWP(Γ0)=1sinΓ0,
gQWP(θ)=1sin(2θ)(1+cos2θ),
S=AΓTHz+BΓTHz2,
BP1/VWP(Γ0)=g2cotΓ0
BQWP(θ)=cot22θ2(1+cos22θ),

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