Abstract

Terahertz pulse shaping technique is used to adaptively design terahertz waveforms of enhanced spectral correlation to particular materials among a given set of materials. In a proof-of-principle experiment performed with a two-dimensional image target consisted of meta-materials of distinctive resonance frequencies, the as-designed waveforms are used to demonstrate terahertz substance imaging. It is hoped that this material-specific terahertz waveforms may enable single- or few-shot terahertz material classification when being used in conjunction with terahertz power measurement.

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  2. D. Grischkowsky, S. Keiding, M. van Exter, and Ch. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B7, 2006 (1990).
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    [CrossRef] [PubMed]
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    [CrossRef]
  9. S. Lee, J. Lim, J. Ahn, V. Hakobyan, and S. Guerin, “Strong-field two-level two-photon transition by phase shaping,” Phys. Rev. A82, 023408 (2010).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. J. Y. Sohn, Y. H. Ahn, D. J. Park, E. Oh, and D. S. Kim, “Tunable terahertz generation using femtosecond pulse shaping,” Appl. Phys. Lett.81, 13–15 (2002).
    [CrossRef]
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  24. M. Mitchell, An Introduction to Genetic Algorithms (MIT Press, 1996).

2011 (1)

J. Lim, H.-g. Lee, S. Lee, and J. Ahn, “Quantum control in two-dimensional Fourier transform spectroscopy,” Phys. Rev. A84, 013425 (2011).
[CrossRef]

2010 (2)

S. Lee, J. Lim, J. Ahn, V. Hakobyan, and S. Guerin, “Strong-field two-level two-photon transition by phase shaping,” Phys. Rev. A82, 023408 (2010).
[CrossRef]

S. Vidal, J. Degert, J. Oberlè, and E. Freysz, “Femtosecond optical pulse shaping for tunable terahertz pulse generation,” J. Opt. Soc. Am. B27, 1044–1050 (2010).
[CrossRef]

2009 (3)

2008 (1)

M. Yi, K. Hee Lee, I. Maeng, J.-H. Son, R. D. Averitt, and J. Ahn, “Tailoring the spectra of terahertz emission from CdTe and ZnTe electro-optic crystals,” Jpn. J. Appl. Phys.47, 202–204 (2008).
[CrossRef]

2007 (2)

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, “Electrically resonant terahertz metamaterials: Theoretical and experimental investigations,” Phys. Rev. B75, 041102(R) (2007).
[CrossRef]

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photon.1, 97105 (2007).
[CrossRef]

2006 (1)

2003 (3)

2002 (2)

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater.1, 26–33 (2002).
[CrossRef]

J. Y. Sohn, Y. H. Ahn, D. J. Park, E. Oh, and D. S. Kim, “Tunable terahertz generation using femtosecond pulse shaping,” Appl. Phys. Lett.81, 13–15 (2002).
[CrossRef]

2000 (2)

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped pulse optimization of coherent emission of high-harmonic soft X-rays,” Nature406, 164–166 (2000).
[CrossRef] [PubMed]

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum.71, 1929–1960 (2000).
[CrossRef]

1998 (1)

D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature396, 239–242 (1998).
[CrossRef]

1996 (1)

Y. Liu, S.-G. Park, and A. M. Weiner, “Terahertz waveform synthesis via optical pulse shaping,” IEEE J. Sel. Top. Quantum Electron.2, 709–719 (1996).
[CrossRef]

1990 (1)

1988 (1)

Ahn, J.

J. Lim, H.-g. Lee, S. Lee, and J. Ahn, “Quantum control in two-dimensional Fourier transform spectroscopy,” Phys. Rev. A84, 013425 (2011).
[CrossRef]

S. Lee, J. Lim, J. Ahn, V. Hakobyan, and S. Guerin, “Strong-field two-level two-photon transition by phase shaping,” Phys. Rev. A82, 023408 (2010).
[CrossRef]

M. Yi, K. Hee Lee, I. Maeng, J.-H. Son, R. D. Averitt, and J. Ahn, “Tailoring the spectra of terahertz emission from CdTe and ZnTe electro-optic crystals,” Jpn. J. Appl. Phys.47, 202–204 (2008).
[CrossRef]

J. Ahn, A. Efimov, R. Averitt, and A. Taylor, “Terahertz waveform synthesis via optical rectification of shaped ultrafast laser pulses,” Opt. Express11, 2486–2496 (2003).
[CrossRef] [PubMed]

Ahn, Y. H.

J. Y. Sohn, Y. H. Ahn, D. J. Park, E. Oh, and D. S. Kim, “Tunable terahertz generation using femtosecond pulse shaping,” Appl. Phys. Lett.81, 13–15 (2002).
[CrossRef]

Amer, N.

Y.-S. Lee, N. Amer, and W. C. Hurlbut, “Terahertz pulse shaping via optical rectification in poled lithium niobate,” Appl. Phys. Lett.82, 170–172 (2003).
[CrossRef]

Aronsson, M. T.

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, “Electrically resonant terahertz metamaterials: Theoretical and experimental investigations,” Phys. Rev. B75, 041102(R) (2007).
[CrossRef]

Averitt, R.

Averitt, R. D.

M. Yi, K. Hee Lee, I. Maeng, J.-H. Son, R. D. Averitt, and J. Ahn, “Tailoring the spectra of terahertz emission from CdTe and ZnTe electro-optic crystals,” Jpn. J. Appl. Phys.47, 202–204 (2008).
[CrossRef]

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, “Electrically resonant terahertz metamaterials: Theoretical and experimental investigations,” Phys. Rev. B75, 041102(R) (2007).
[CrossRef]

Backus, S.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped pulse optimization of coherent emission of high-harmonic soft X-rays,” Nature406, 164–166 (2000).
[CrossRef] [PubMed]

Bartels, R.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped pulse optimization of coherent emission of high-harmonic soft X-rays,” Nature406, 164–166 (2000).
[CrossRef] [PubMed]

Beaurepaire, E.

Chatterjee, S.

Christov, I. P.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped pulse optimization of coherent emission of high-harmonic soft X-rays,” Nature406, 164–166 (2000).
[CrossRef] [PubMed]

D’Amico, C.

Das, J.

Débarre, D.

Degert, J.

Efimov, A.

Fattinger, Ch.

Ferguson, B.

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater.1, 26–33 (2002).
[CrossRef]

Freysz, E.

Grischkowsky, D.

Guerin, S.

S. Lee, J. Lim, J. Ahn, V. Hakobyan, and S. Guerin, “Strong-field two-level two-photon transition by phase shaping,” Phys. Rev. A82, 023408 (2010).
[CrossRef]

Hakobyan, V.

S. Lee, J. Lim, J. Ahn, V. Hakobyan, and S. Guerin, “Strong-field two-level two-photon transition by phase shaping,” Phys. Rev. A82, 023408 (2010).
[CrossRef]

Hecht, E.

E. Hecht, Optics4th ed. (Addison Wesley, 2002).

Hee Lee, K.

M. Yi, K. Hee Lee, I. Maeng, J.-H. Son, R. D. Averitt, and J. Ahn, “Tailoring the spectra of terahertz emission from CdTe and ZnTe electro-optic crystals,” Jpn. J. Appl. Phys.47, 202–204 (2008).
[CrossRef]

Heritage, J. P.

Highstrete, C.

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, “Electrically resonant terahertz metamaterials: Theoretical and experimental investigations,” Phys. Rev. B75, 041102(R) (2007).
[CrossRef]

Hurlbut, W. C.

Y.-S. Lee, N. Amer, and W. C. Hurlbut, “Terahertz pulse shaping via optical rectification in poled lithium niobate,” Appl. Phys. Lett.82, 170–172 (2003).
[CrossRef]

Inoue, H.

Joffre, M.

Kapteyn, H. C.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped pulse optimization of coherent emission of high-harmonic soft X-rays,” Nature406, 164–166 (2000).
[CrossRef] [PubMed]

Kawase, K.

Keiding, S.

Kim, D. S.

J. Y. Sohn, Y. H. Ahn, D. J. Park, E. Oh, and D. S. Kim, “Tunable terahertz generation using femtosecond pulse shaping,” Appl. Phys. Lett.81, 13–15 (2002).
[CrossRef]

Kohli, K. K.

Lee, H.-g.

J. Lim, H.-g. Lee, S. Lee, and J. Ahn, “Quantum control in two-dimensional Fourier transform spectroscopy,” Phys. Rev. A84, 013425 (2011).
[CrossRef]

Lee, M.

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, “Electrically resonant terahertz metamaterials: Theoretical and experimental investigations,” Phys. Rev. B75, 041102(R) (2007).
[CrossRef]

Lee, S.

J. Lim, H.-g. Lee, S. Lee, and J. Ahn, “Quantum control in two-dimensional Fourier transform spectroscopy,” Phys. Rev. A84, 013425 (2011).
[CrossRef]

S. Lee, J. Lim, J. Ahn, V. Hakobyan, and S. Guerin, “Strong-field two-level two-photon transition by phase shaping,” Phys. Rev. A82, 023408 (2010).
[CrossRef]

Lee, Y.-S.

Y.-S. Lee, N. Amer, and W. C. Hurlbut, “Terahertz pulse shaping via optical rectification in poled lithium niobate,” Appl. Phys. Lett.82, 170–172 (2003).
[CrossRef]

Y.-S. Lee, Principles of Terahertz Science and Technology (Springer, USA, 2009).

Lim, J.

J. Lim, H.-g. Lee, S. Lee, and J. Ahn, “Quantum control in two-dimensional Fourier transform spectroscopy,” Phys. Rev. A84, 013425 (2011).
[CrossRef]

S. Lee, J. Lim, J. Ahn, V. Hakobyan, and S. Guerin, “Strong-field two-level two-photon transition by phase shaping,” Phys. Rev. A82, 023408 (2010).
[CrossRef]

Liu, Y.

Y. Liu, S.-G. Park, and A. M. Weiner, “Terahertz waveform synthesis via optical pulse shaping,” IEEE J. Sel. Top. Quantum Electron.2, 709–719 (1996).
[CrossRef]

Maeng, I.

M. Yi, K. Hee Lee, I. Maeng, J.-H. Son, R. D. Averitt, and J. Ahn, “Tailoring the spectra of terahertz emission from CdTe and ZnTe electro-optic crystals,” Jpn. J. Appl. Phys.47, 202–204 (2008).
[CrossRef]

Martin, J.-L.

Meshulach, D.

D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature396, 239–242 (1998).
[CrossRef]

Misoguti, L.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped pulse optimization of coherent emission of high-harmonic soft X-rays,” Nature406, 164–166 (2000).
[CrossRef] [PubMed]

Mitchell, M.

M. Mitchell, An Introduction to Genetic Algorithms (MIT Press, 1996).

Murnane, M. M.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped pulse optimization of coherent emission of high-harmonic soft X-rays,” Nature406, 164–166 (2000).
[CrossRef] [PubMed]

Oberlè, J.

Ogawa, Y.

Ogilvie, J. P.

Oh, E.

J. Y. Sohn, Y. H. Ahn, D. J. Park, E. Oh, and D. S. Kim, “Tunable terahertz generation using femtosecond pulse shaping,” Appl. Phys. Lett.81, 13–15 (2002).
[CrossRef]

Padilla, W. J.

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, “Electrically resonant terahertz metamaterials: Theoretical and experimental investigations,” Phys. Rev. B75, 041102(R) (2007).
[CrossRef]

Park, D. J.

J. Y. Sohn, Y. H. Ahn, D. J. Park, E. Oh, and D. S. Kim, “Tunable terahertz generation using femtosecond pulse shaping,” Appl. Phys. Lett.81, 13–15 (2002).
[CrossRef]

Park, S.-G.

Y. Liu, S.-G. Park, and A. M. Weiner, “Terahertz waveform synthesis via optical pulse shaping,” IEEE J. Sel. Top. Quantum Electron.2, 709–719 (1996).
[CrossRef]

Rühle, W. W.

Salehi, J. A.

Silberberg, Y.

D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature396, 239–242 (1998).
[CrossRef]

Sohn, J. Y.

J. Y. Sohn, Y. H. Ahn, D. J. Park, E. Oh, and D. S. Kim, “Tunable terahertz generation using femtosecond pulse shaping,” Appl. Phys. Lett.81, 13–15 (2002).
[CrossRef]

Solinas, X.

Son, J.-H.

M. Yi, K. Hee Lee, I. Maeng, J.-H. Son, R. D. Averitt, and J. Ahn, “Tailoring the spectra of terahertz emission from CdTe and ZnTe electro-optic crystals,” Jpn. J. Appl. Phys.47, 202–204 (2008).
[CrossRef]

Taylor, A.

Taylor, A. J.

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, “Electrically resonant terahertz metamaterials: Theoretical and experimental investigations,” Phys. Rev. B75, 041102(R) (2007).
[CrossRef]

Tondusson, M.

Tonouchi, M.

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photon.1, 97105 (2007).
[CrossRef]

van Exter, M.

Vaupel, A.

Vdovin, G.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped pulse optimization of coherent emission of high-harmonic soft X-rays,” Nature406, 164–166 (2000).
[CrossRef] [PubMed]

Vidal, S.

Watanabe, Y.

Weiner, A. M.

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum.71, 1929–1960 (2000).
[CrossRef]

Y. Liu, S.-G. Park, and A. M. Weiner, “Terahertz waveform synthesis via optical pulse shaping,” IEEE J. Sel. Top. Quantum Electron.2, 709–719 (1996).
[CrossRef]

A. M. Weiner, J. P. Heritage, and J. A. Salehi, “Encoding and decoding of femtosecond pulses,” Opt. Lett.13, 300–302 (1988).
[CrossRef] [PubMed]

Yamaguchi, M.

Yi, M.

M. Yi, K. Hee Lee, I. Maeng, J.-H. Son, R. D. Averitt, and J. Ahn, “Tailoring the spectra of terahertz emission from CdTe and ZnTe electro-optic crystals,” Jpn. J. Appl. Phys.47, 202–204 (2008).
[CrossRef]

Zeek, E.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped pulse optimization of coherent emission of high-harmonic soft X-rays,” Nature406, 164–166 (2000).
[CrossRef] [PubMed]

Zhang, X.-C.

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater.1, 26–33 (2002).
[CrossRef]

Appl. Phys. Lett. (2)

J. Y. Sohn, Y. H. Ahn, D. J. Park, E. Oh, and D. S. Kim, “Tunable terahertz generation using femtosecond pulse shaping,” Appl. Phys. Lett.81, 13–15 (2002).
[CrossRef]

Y.-S. Lee, N. Amer, and W. C. Hurlbut, “Terahertz pulse shaping via optical rectification in poled lithium niobate,” Appl. Phys. Lett.82, 170–172 (2003).
[CrossRef]

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

Y. Liu, S.-G. Park, and A. M. Weiner, “Terahertz waveform synthesis via optical pulse shaping,” IEEE J. Sel. Top. Quantum Electron.2, 709–719 (1996).
[CrossRef]

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

Jpn. J. Appl. Phys. (1)

M. Yi, K. Hee Lee, I. Maeng, J.-H. Son, R. D. Averitt, and J. Ahn, “Tailoring the spectra of terahertz emission from CdTe and ZnTe electro-optic crystals,” Jpn. J. Appl. Phys.47, 202–204 (2008).
[CrossRef]

Nat. Mater. (1)

B. Ferguson and X.-C. Zhang, “Materials for terahertz science and technology,” Nat. Mater.1, 26–33 (2002).
[CrossRef]

Nat. Photon. (1)

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photon.1, 97105 (2007).
[CrossRef]

Nature (2)

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped pulse optimization of coherent emission of high-harmonic soft X-rays,” Nature406, 164–166 (2000).
[CrossRef] [PubMed]

D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature396, 239–242 (1998).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. A (2)

S. Lee, J. Lim, J. Ahn, V. Hakobyan, and S. Guerin, “Strong-field two-level two-photon transition by phase shaping,” Phys. Rev. A82, 023408 (2010).
[CrossRef]

J. Lim, H.-g. Lee, S. Lee, and J. Ahn, “Quantum control in two-dimensional Fourier transform spectroscopy,” Phys. Rev. A84, 013425 (2011).
[CrossRef]

Phys. Rev. B (1)

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, “Electrically resonant terahertz metamaterials: Theoretical and experimental investigations,” Phys. Rev. B75, 041102(R) (2007).
[CrossRef]

Rev. Sci. Instrum. (1)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum.71, 1929–1960 (2000).
[CrossRef]

Other (3)

E. Hecht, Optics4th ed. (Addison Wesley, 2002).

M. Mitchell, An Introduction to Genetic Algorithms (MIT Press, 1996).

Y.-S. Lee, Principles of Terahertz Science and Technology (Springer, USA, 2009).

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Figures (4)

Fig. 1
Fig. 1

Meta-material samples ETM1 and ETM2. (a, b) Electric field norms plotted at their resonance frequencies. (c, d) Microscope images of the fabricated samples. (e, f) Measured transmitted amplitude spectra of unshaped THz pulses. (Dotted lines indicate the calculated resonance frequencies.)

Fig. 2
Fig. 2

(a) Schematic experimental diagram of THz pulse shaping with a spatial light modulator. (b) Adaptive feed-back loop implemented for the THz pulse profile optimization.

Fig. 3
Fig. 3

(a,d) Measured correlation difference C1 vs. the iteration number for the recognition of ETM1 and ETM2 substances, respectively. Measurement of the final THz waveforms (b,e) and their THz spectra (c,f).

Fig. 4
Fig. 4

(a) An imaging target consists of two different THz meta-material regions, where the left half square is filled with ETM1 of 0.5 THz resonance frequency and the right half with the other with 0.8 THz. (b–d) Measured THz power images with three different THz pulses: (b) the near zero, (c) the biggest positive, and (d) the biggest negative correlation-difference phase-mask arrays, respectively. (e,f) Measured THz power (red) along the lateral X-positions marked with dashed lines in (c,d), respectively, where the reference measurement (blue) is from (b).

Equations (2)

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C 1 ( { E ( ω ) } ) = ( | t 1 ( ω ) E ( ω ) | 2 | t 2 ( ω ) E ( ω ) | 2 ) d ω ,
C i ( { E ( ω ) } ) = 2 | t i ( ω ) E ( ω ) | 2 d ω j = 1 M | t j ( ω ) E ( ω ) | 2 d ω ,

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