Abstract

A novel technique for the terahertz (THz) tomography of a photo-induced carrier that is based on optical-pump THz-probe time-resolved reflection spectroscopy using counterpropagation geometry of the pump and probe pulses has been proposed. Transient reflection due to the photo-induced carrier provides information about the physical properties and spatial distribution separately. We have experimentally demonstrated this method using a silicon wafer. The obtained complex reflection can be reproduced by the exact solution of Maxwell’s equations, assuming an exponential distribution of the photo-induced carrier density.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]

2011 (1)

P. U. Jepsen, D. G. Cooke, and M. Koch, Laser Photon. Rev. 5, 124 (2011), and references therein.
[CrossRef]

2009 (1)

D. G. Cooke and P. U. Jepsen, Appl. Phys. Lett. 94, 241118 (2009).
[CrossRef]

2004 (2)

F. Kadlec, H. Němec, and P. Kužel, Phys. Rev. B 70, 125205 (2004).
[CrossRef]

X. C. Zhang, Phil. Trans. R. Soc. A 362, 283 (2004).
[CrossRef]

2002 (3)

T. Bauer, J. S. Kolb, T. Loffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, J. Appl. Phys. 92, 2210 (2002).
[CrossRef]

M. Nagai and M. Kuwata-Gonokami, J. Phys. Soc. Jpn. 71, 2276 (2002).
[CrossRef]

J. Hebling, G. Almási, I. Z. Kozma, and J. Kuhl, Opt. Express 10, 1161 (2002).

2000 (2)

M. Schall and P. U. Jepsen, Opt. Lett. 25, 13 (2000).
[CrossRef]

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, Phys. Rev. B 62, 15764 (2000).
[CrossRef]

1996 (3)

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[CrossRef]

Q. Wu and X. C. Zhang, IEEE J. Sel. Top. Quantum Electron. 2, 693 (1996).
[CrossRef]

J. Zielbauer and M. Wegener, Appl. Phys. Lett. 68, 1223 (1996).
[CrossRef]

1994 (1)

1992 (1)

P. N. Saeta, J. F. Federici, B. I. Greene, and D. R. Dykaar, Appl. Phys. Lett. 60, 1477 (1992).
[CrossRef]

1990 (1)

1987 (1)

H. M. van Driel, Phys. Rev. B 35, 8166 (1987).
[CrossRef]

1984 (1)

J. Y. Vinet, M. Combescot, and C. Tanguy, Solid State Commun. 51, 171 (1984).
[CrossRef]

1979 (1)

H. A. Weakliem and D. Redfield, J. Appl. Phys. 50, 1491 (1979).
[CrossRef]

Almási, G.

Bauer, T.

T. Bauer, J. S. Kolb, T. Loffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, J. Appl. Phys. 92, 2210 (2002).
[CrossRef]

Beard, M. C.

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, Phys. Rev. B 62, 15764 (2000).
[CrossRef]

Combescot, M.

J. Y. Vinet, M. Combescot, and C. Tanguy, Solid State Commun. 51, 171 (1984).
[CrossRef]

Cooke, D. G.

P. U. Jepsen, D. G. Cooke, and M. Koch, Laser Photon. Rev. 5, 124 (2011), and references therein.
[CrossRef]

D. G. Cooke and P. U. Jepsen, Appl. Phys. Lett. 94, 241118 (2009).
[CrossRef]

Dykaar, D. R.

P. N. Saeta, J. F. Federici, B. I. Greene, and D. R. Dykaar, Appl. Phys. Lett. 60, 1477 (1992).
[CrossRef]

Fattinger, C.

Federici, J. F.

P. N. Saeta, J. F. Federici, B. I. Greene, and D. R. Dykaar, Appl. Phys. Lett. 60, 1477 (1992).
[CrossRef]

Greene, B. I.

P. N. Saeta, J. F. Federici, B. I. Greene, and D. R. Dykaar, Appl. Phys. Lett. 60, 1477 (1992).
[CrossRef]

Grischkowsky, D.

Groeneveld, R. H. M.

Hebling, J.

Heinz, T. F.

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[CrossRef]

Jepsen, P. U.

P. U. Jepsen, D. G. Cooke, and M. Koch, Laser Photon. Rev. 5, 124 (2011), and references therein.
[CrossRef]

D. G. Cooke and P. U. Jepsen, Appl. Phys. Lett. 94, 241118 (2009).
[CrossRef]

M. Schall and P. U. Jepsen, Opt. Lett. 25, 13 (2000).
[CrossRef]

Kadlec, F.

F. Kadlec, H. Němec, and P. Kužel, Phys. Rev. B 70, 125205 (2004).
[CrossRef]

Keiding, S.

Koch, M.

P. U. Jepsen, D. G. Cooke, and M. Koch, Laser Photon. Rev. 5, 124 (2011), and references therein.
[CrossRef]

Kolb, J. S.

T. Bauer, J. S. Kolb, T. Loffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, J. Appl. Phys. 92, 2210 (2002).
[CrossRef]

Kozma, I. Z.

Kuhl, J.

Kuwata-Gonokami, M.

M. Nagai and M. Kuwata-Gonokami, J. Phys. Soc. Jpn. 71, 2276 (2002).
[CrossRef]

Kužel, P.

F. Kadlec, H. Němec, and P. Kužel, Phys. Rev. B 70, 125205 (2004).
[CrossRef]

Loffler, T.

T. Bauer, J. S. Kolb, T. Loffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, J. Appl. Phys. 92, 2210 (2002).
[CrossRef]

Mohler, E.

T. Bauer, J. S. Kolb, T. Loffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, J. Appl. Phys. 92, 2210 (2002).
[CrossRef]

Nagai, M.

M. Nagai and M. Kuwata-Gonokami, J. Phys. Soc. Jpn. 71, 2276 (2002).
[CrossRef]

Nahata, A.

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[CrossRef]

Nemec, H.

F. Kadlec, H. Němec, and P. Kužel, Phys. Rev. B 70, 125205 (2004).
[CrossRef]

Pernisz, U. C.

T. Bauer, J. S. Kolb, T. Loffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, J. Appl. Phys. 92, 2210 (2002).
[CrossRef]

Redfield, D.

H. A. Weakliem and D. Redfield, J. Appl. Phys. 50, 1491 (1979).
[CrossRef]

Roskos, H. G.

T. Bauer, J. S. Kolb, T. Loffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, J. Appl. Phys. 92, 2210 (2002).
[CrossRef]

Saeta, P. N.

P. N. Saeta, J. F. Federici, B. I. Greene, and D. R. Dykaar, Appl. Phys. Lett. 60, 1477 (1992).
[CrossRef]

Schall, M.

Schmuttenmaer, C. A.

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, Phys. Rev. B 62, 15764 (2000).
[CrossRef]

Tanguy, C.

J. Y. Vinet, M. Combescot, and C. Tanguy, Solid State Commun. 51, 171 (1984).
[CrossRef]

Turner, G. M.

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, Phys. Rev. B 62, 15764 (2000).
[CrossRef]

van Driel, H. M.

H. M. van Driel, Phys. Rev. B 35, 8166 (1987).
[CrossRef]

Vanexter, M.

Vinet, J. Y.

J. Y. Vinet, M. Combescot, and C. Tanguy, Solid State Commun. 51, 171 (1984).
[CrossRef]

Weakliem, H. A.

H. A. Weakliem and D. Redfield, J. Appl. Phys. 50, 1491 (1979).
[CrossRef]

Wegener, M.

J. Zielbauer and M. Wegener, Appl. Phys. Lett. 68, 1223 (1996).
[CrossRef]

Weling, A. S.

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[CrossRef]

Wu, Q.

Q. Wu and X. C. Zhang, IEEE J. Sel. Top. Quantum Electron. 2, 693 (1996).
[CrossRef]

Zhang, X. C.

X. C. Zhang, Phil. Trans. R. Soc. A 362, 283 (2004).
[CrossRef]

Q. Wu and X. C. Zhang, IEEE J. Sel. Top. Quantum Electron. 2, 693 (1996).
[CrossRef]

Zielbauer, J.

J. Zielbauer and M. Wegener, Appl. Phys. Lett. 68, 1223 (1996).
[CrossRef]

Appl. Phys. Lett. (4)

P. N. Saeta, J. F. Federici, B. I. Greene, and D. R. Dykaar, Appl. Phys. Lett. 60, 1477 (1992).
[CrossRef]

A. Nahata, A. S. Weling, and T. F. Heinz, Appl. Phys. Lett. 69, 2321 (1996).
[CrossRef]

J. Zielbauer and M. Wegener, Appl. Phys. Lett. 68, 1223 (1996).
[CrossRef]

D. G. Cooke and P. U. Jepsen, Appl. Phys. Lett. 94, 241118 (2009).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

Q. Wu and X. C. Zhang, IEEE J. Sel. Top. Quantum Electron. 2, 693 (1996).
[CrossRef]

J. Appl. Phys. (2)

H. A. Weakliem and D. Redfield, J. Appl. Phys. 50, 1491 (1979).
[CrossRef]

T. Bauer, J. S. Kolb, T. Loffler, E. Mohler, H. G. Roskos, and U. C. Pernisz, J. Appl. Phys. 92, 2210 (2002).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. Soc. Jpn. (1)

M. Nagai and M. Kuwata-Gonokami, J. Phys. Soc. Jpn. 71, 2276 (2002).
[CrossRef]

Laser Photon. Rev. (1)

P. U. Jepsen, D. G. Cooke, and M. Koch, Laser Photon. Rev. 5, 124 (2011), and references therein.
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phil. Trans. R. Soc. A (1)

X. C. Zhang, Phil. Trans. R. Soc. A 362, 283 (2004).
[CrossRef]

Phys. Rev. B (3)

F. Kadlec, H. Němec, and P. Kužel, Phys. Rev. B 70, 125205 (2004).
[CrossRef]

M. C. Beard, G. M. Turner, and C. A. Schmuttenmaer, Phys. Rev. B 62, 15764 (2000).
[CrossRef]

H. M. van Driel, Phys. Rev. B 35, 8166 (1987).
[CrossRef]

Solid State Commun. (1)

J. Y. Vinet, M. Combescot, and C. Tanguy, Solid State Commun. 51, 171 (1984).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Schematic of (a) copropagation and (b) counterpropagation geometries. Vertical axis shows the frequency of the THz probe pulse.

Fig. 2.
Fig. 2.

(a) Schematic of pulse propagation and detection employed in this study. (b) Example of the THz waveform transmitted from the Si wafer. (c) Pump-probe delay time dependence of Pulse B when the Si wafer was excited by the optical pump with an energy density of 360μJ/cm2. The insert values show the pump-probe delay times. The dashed lines indicate the equivalent phase position of the reflected pulses.

Fig. 3.
Fig. 3.

Relative reflectivity R/R0 and phase shift Δϕ=ϕϕ0 measured at the pump-probe delay time of 3 ps as a function of the THz frequency. The solid and dashed lines show the observed and calculated results, respectively.

Equations (3)

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

ε(ω,z)=εb[1ωp(z)2ω(ω+iτ1)]=εb4πNe2exp(z/D*)mω(ω+iτ1),
rsigrref=εb+1εb1Γ(1+i2D*α)Γ(1i2D*α)BA(βD*)i4D*α=RR0ei(ϕϕ0),
BA={(1εb)Ii2D*α1(2βD*)(1+εb)Ii2D*α+1(2βD*)}/{(1+εb)Ii2D*α1(2βD*)(1εb)Ii2D*α+1(2βD*)}.

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