Abstract

We present a method for the generation of THz pulses with tailored temporal shape from nonlinear metasurfaces. The method is based on single-cycle THz emission by the metasurface inclusions. We show that the spatial amplitude and phase structure of the nonlinear response is mapped to the temporal shape of pulses emitted at certain angles. We specifically show a method for reconstruction of desired pulses, generation of few-cycles pulses with tailored carrier-envelope and all-optical control over the pulse shape by the pump pulse characteristics.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  4. T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mährlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent terahertz control of antiferromagnetic spin waves,” Nat. Photonics 5(1), 31–34 (2011).
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    [Crossref]
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    [Crossref]
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  38. M. Tymchenko, J. S. Gomez-Diaz, J. Lee, M. A. Belkin, and A. Alù, “Highly-efficient THz generation using nonlinear plasmonic metasurfaces,” J. Opt. 19(10), 104001 (2017).
    [Crossref]
  39. M. Fang, N.-H. Shen, W. E. I. Sha, Z. Huang, T. Koschny, and C. M. Soukoulis, “Nonlinearity in the Dark: Broadband Terahertz Generation with Extremely High Efficiency,” Phys. Rev. Lett. 122(2), 027401 (2019).
    [Crossref]

2019 (2)

S. Keren-Zur, M. Tal, S. Fleischer, D. M. Mittleman, and T. Ellenbogen, “Generation of spatiotemporally tailored terahertz wavepackets by nonlinear metasurfaces,” Nat. Commun. 10(1), 1778 (2019).
[Crossref]

M. Fang, N.-H. Shen, W. E. I. Sha, Z. Huang, T. Koschny, and C. M. Soukoulis, “Nonlinearity in the Dark: Broadband Terahertz Generation with Extremely High Efficiency,” Phys. Rev. Lett. 122(2), 027401 (2019).
[Crossref]

2018 (2)

2017 (5)

L. Gingras and D. G. Cooke, “Direct temporal shaping of terahertz light pulses,” Optica 4(11), 1416 (2017).
[Crossref]

J. Lu, X. Li, H. Y. Hwang, B. K. Ofori-Okai, T. Kurihara, T. Suemoto, and K. A. Nelson, “Coherent Two-Dimensional Terahertz Magnetic Resonance Spectroscopy of Collective Spin Waves,” Phys. Rev. Lett. 118(20), 207204 (2017).
[Crossref]

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, M. A. Belkin, and A. Alù, “Highly-efficient THz generation using nonlinear plasmonic metasurfaces,” J. Opt. 19(10), 104001 (2017).
[Crossref]

L. Michaeli, S. Keren-Zur, O. Avayu, H. Suchowski, and T. Ellenbogen, “Nonlinear Surface Lattice Resonance in Plasmonic Nanoparticle Arrays,” Phys. Rev. Lett. 118(24), 243904 (2017).
[Crossref]

G. R. Keiser, N. Karl, P. Q. Liu, C. Tulloss, H.-T. Chen, A. J. Taylor, I. Brener, J. L. Reno, and D. M. Mittleman, “Nonlinear terahertz metamaterials with active electrical control,” Appl. Phys. Lett. 111(12), 121101 (2017).
[Crossref]

2016 (3)

J. Yang, C. Gong, L. Sun, P. Chen, L. Lin, and W. Liu, “Tunable reflecting terahertz filter based on chirped metamaterial structure,” Sci. Rep. 6(1), 38732 (2016).
[Crossref]

S. Keren-Zur, O. Avayu, L. Michaeli, and T. Ellenbogen, “Nonlinear Beam Shaping with Plasmonic Metasurfaces,” ACS Photonics 3(1), 117–123 (2016).
[Crossref]

I. A. Finneran, R. Welsch, M. A. Allodi, T. F. Miller, and G. A. Blake, “Coherent two-dimensional terahertz-terahertz-Raman spectroscopy,” Proc. Natl. Acad. Sci. U. S. A. 113(25), 6857–6861 (2016).
[Crossref]

2015 (3)

J. Lu, H. Y. Hwang, X. Li, S.-H. Lee, O.-P. Kwon, and K. A. Nelson, “Tunable multi-cycle THz generation in organic crystal HMQ-TMS,” Opt. Express 23(17), 22723 (2015).
[Crossref]

H. Y. Hwang, S. Fleischer, N. C. Brandt, B. G. Perkins, M. Liu, K. Fan, A. Sternbach, X. Zhang, R. D. Averitt, and K. A. Nelson, “A review of non-linear terahertz spectroscopy with ultrashort tabletop-laser pulses,” J. Mod. Opt. 62(18), 1447–1479 (2015).
[Crossref]

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
[Crossref]

2014 (2)

L. Liu, X. Zhang, M. Kenney, X. Su, N. Xu, C. Ouyang, Y. Shi, J. Han, W. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26(29), 5031–5036 (2014).
[Crossref]

L. Luo, I. Chatzakis, J. Wang, F. B. P. Niesler, M. Wegener, T. Koschny, and C. M. Soukoulis, “Broadband terahertz generation from metamaterials,” Nat. Commun. 5(1), 3055 (2014).
[Crossref]

2013 (3)

M. Sato, T. Higuchi, N. Kanda, K. Konishi, K. Yoshioka, T. Suzuki, K. Misawa, and M. Kuwata-Gonokami, “Terahertz polarization pulse shaping with arbitrary field control,” Nat. Photonics 7(9), 724–731 (2013).
[Crossref]

M. Woerner, W. Kuehn, P. Bowlan, K. Reimann, and T. Elsaesser, “Ultrafast two-dimensional terahertz spectroscopy of elementary excitations in solids,” New J. Phys. 15(2), 025039 (2013).
[Crossref]

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7(12), 977–981 (2013).
[Crossref]

2012 (1)

S. Linden, F. B. P. Niesler, J. Förstner, Y. Grynko, T. Meier, and M. Wegener, “Collective Effects in Second-Harmonic Generation from Split-Ring-Resonator Arrays,” Phys. Rev. Lett. 109(1), 015502 (2012).
[Crossref]

2011 (4)

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref]

A. M. Weiner, “Ultrafast optical pulse shaping: A tutorial review,” Opt. Commun. 284(15), 3669–3692 (2011).
[Crossref]

T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mährlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent terahertz control of antiferromagnetic spin waves,” Nat. Photonics 5(1), 31–34 (2011).
[Crossref]

S. Fleischer, Y. Zhou, R. W. Field, and K. A. Nelson, “Molecular Orientation and Alignment by Intense Single-Cycle THz Pulses,” Phys. Rev. Lett. 107(16), 163603 (2011).
[Crossref]

2010 (1)

2009 (1)

Y. Silberberg, “Quantum Coherent Control for Nonlinear Spectroscopy and Microscopy,” Annu. Rev. Phys. Chem. 60(1), 277–292 (2009).
[Crossref]

2008 (1)

2004 (2)

2003 (2)

J. Ahn, A. Efimov, R. Averitt, and A. Taylor, “Terahertz waveform synthesis via optical rectification of shaped ultrafast laser pulses,” Opt. Express 11(20), 2486 (2003).
[Crossref]

Y.-S. Lee, N. Amer, and W. C. Hurlbut, “Terahertz pulse shaping via optical rectification in poled lithium niobate,” Appl. Phys. Lett. 82(2), 170–172 (2003).
[Crossref]

2002 (2)

2001 (2)

D. E. Leaird and A. M. Weiner, “Femtosecond direct space-to-time pulse shaping,” IEEE J. Quantum Electron. 37(4), 494–504 (2001).
[Crossref]

B. E. Cole, J. B. Williams, B. T. King, M. S. Sherwin, and C. R. Stanley, “Coherent manipulation of semiconductor quantum bits with terahertz radiation,” Nature 410(6824), 60–63 (2001).
[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(3), 709–719 (1996).
[Crossref]

Ahn, J.

Allodi, M. A.

I. A. Finneran, R. Welsch, M. A. Allodi, T. F. Miller, and G. A. Blake, “Coherent two-dimensional terahertz-terahertz-Raman spectroscopy,” Proc. Natl. Acad. Sci. U. S. A. 113(25), 6857–6861 (2016).
[Crossref]

Alù, A.

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, M. A. Belkin, and A. Alù, “Highly-efficient THz generation using nonlinear plasmonic metasurfaces,” J. Opt. 19(10), 104001 (2017).
[Crossref]

Ambacher, O.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7(12), 977–981 (2013).
[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(2), 170–172 (2003).
[Crossref]

Andrés, P.

G. Mínguez-Vega, O. Mendoza-Yero, J. Lancis, R. Gisbert, and P. Andrés, Diffractive Optics for Quasi-Direct Space-to-Time Pulse Shaping (2008), Vol. 16.

Antes, J.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7(12), 977–981 (2013).
[Crossref]

Avayu, O.

L. Michaeli, S. Keren-Zur, O. Avayu, H. Suchowski, and T. Ellenbogen, “Nonlinear Surface Lattice Resonance in Plasmonic Nanoparticle Arrays,” Phys. Rev. Lett. 118(24), 243904 (2017).
[Crossref]

S. Keren-Zur, O. Avayu, L. Michaeli, and T. Ellenbogen, “Nonlinear Beam Shaping with Plasmonic Metasurfaces,” ACS Photonics 3(1), 117–123 (2016).
[Crossref]

Averitt, R.

Averitt, R. D.

H. Y. Hwang, S. Fleischer, N. C. Brandt, B. G. Perkins, M. Liu, K. Fan, A. Sternbach, X. Zhang, R. D. Averitt, and K. A. Nelson, “A review of non-linear terahertz spectroscopy with ultrashort tabletop-laser pulses,” J. Mod. Opt. 62(18), 1447–1479 (2015).
[Crossref]

Bechtel, H. A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref]

Belkin, M. A.

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, M. A. Belkin, and A. Alù, “Highly-efficient THz generation using nonlinear plasmonic metasurfaces,” J. Opt. 19(10), 104001 (2017).
[Crossref]

Blake, G. A.

I. A. Finneran, R. Welsch, M. A. Allodi, T. F. Miller, and G. A. Blake, “Coherent two-dimensional terahertz-terahertz-Raman spectroscopy,” Proc. Natl. Acad. Sci. U. S. A. 113(25), 6857–6861 (2016).
[Crossref]

Boes, F.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7(12), 977–981 (2013).
[Crossref]

Bowlan, P.

M. Woerner, W. Kuehn, P. Bowlan, K. Reimann, and T. Elsaesser, “Ultrafast two-dimensional terahertz spectroscopy of elementary excitations in solids,” New J. Phys. 15(2), 025039 (2013).
[Crossref]

Brandt, N. C.

H. Y. Hwang, S. Fleischer, N. C. Brandt, B. G. Perkins, M. Liu, K. Fan, A. Sternbach, X. Zhang, R. D. Averitt, and K. A. Nelson, “A review of non-linear terahertz spectroscopy with ultrashort tabletop-laser pulses,” J. Mod. Opt. 62(18), 1447–1479 (2015).
[Crossref]

Brener, I.

G. R. Keiser, N. Karl, P. Q. Liu, C. Tulloss, H.-T. Chen, A. J. Taylor, I. Brener, J. L. Reno, and D. M. Mittleman, “Nonlinear terahertz metamaterials with active electrical control,” Appl. Phys. Lett. 111(12), 121101 (2017).
[Crossref]

Chatzakis, I.

L. Luo, I. Chatzakis, J. Wang, F. B. P. Niesler, M. Wegener, T. Koschny, and C. M. Soukoulis, “Broadband terahertz generation from metamaterials,” Nat. Commun. 5(1), 3055 (2014).
[Crossref]

Chen, H.-T.

G. R. Keiser, N. Karl, P. Q. Liu, C. Tulloss, H.-T. Chen, A. J. Taylor, I. Brener, J. L. Reno, and D. M. Mittleman, “Nonlinear terahertz metamaterials with active electrical control,” Appl. Phys. Lett. 111(12), 121101 (2017).
[Crossref]

Chen, P.

J. Yang, C. Gong, L. Sun, P. Chen, L. Lin, and W. Liu, “Tunable reflecting terahertz filter based on chirped metamaterial structure,” Sci. Rep. 6(1), 38732 (2016).
[Crossref]

Cole, B. E.

B. E. Cole, J. B. Williams, B. T. King, M. S. Sherwin, and C. R. Stanley, “Coherent manipulation of semiconductor quantum bits with terahertz radiation,” Nature 410(6824), 60–63 (2001).
[Crossref]

Cooke, D. G.

Cui, W.

Dekorsy, T.

T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mährlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent terahertz control of antiferromagnetic spin waves,” Nat. Photonics 5(1), 31–34 (2011).
[Crossref]

Efimov, A.

Ellenbogen, T.

S. Keren-Zur, M. Tal, S. Fleischer, D. M. Mittleman, and T. Ellenbogen, “Generation of spatiotemporally tailored terahertz wavepackets by nonlinear metasurfaces,” Nat. Commun. 10(1), 1778 (2019).
[Crossref]

L. Michaeli, S. Keren-Zur, O. Avayu, H. Suchowski, and T. Ellenbogen, “Nonlinear Surface Lattice Resonance in Plasmonic Nanoparticle Arrays,” Phys. Rev. Lett. 118(24), 243904 (2017).
[Crossref]

S. Keren-Zur, O. Avayu, L. Michaeli, and T. Ellenbogen, “Nonlinear Beam Shaping with Plasmonic Metasurfaces,” ACS Photonics 3(1), 117–123 (2016).
[Crossref]

Elsaesser, T.

M. Woerner, W. Kuehn, P. Bowlan, K. Reimann, and T. Elsaesser, “Ultrafast two-dimensional terahertz spectroscopy of elementary excitations in solids,” New J. Phys. 15(2), 025039 (2013).
[Crossref]

Fan, K.

H. Y. Hwang, S. Fleischer, N. C. Brandt, B. G. Perkins, M. Liu, K. Fan, A. Sternbach, X. Zhang, R. D. Averitt, and K. A. Nelson, “A review of non-linear terahertz spectroscopy with ultrashort tabletop-laser pulses,” J. Mod. Opt. 62(18), 1447–1479 (2015).
[Crossref]

Fang, M.

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H. Y. Hwang, S. Fleischer, N. C. Brandt, B. G. Perkins, M. Liu, K. Fan, A. Sternbach, X. Zhang, R. D. Averitt, and K. A. Nelson, “A review of non-linear terahertz spectroscopy with ultrashort tabletop-laser pulses,” J. Mod. Opt. 62(18), 1447–1479 (2015).
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J. Lu, H. Y. Hwang, X. Li, S.-H. Lee, O.-P. Kwon, and K. A. Nelson, “Tunable multi-cycle THz generation in organic crystal HMQ-TMS,” Opt. Express 23(17), 22723 (2015).
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S. Fleischer, Y. Zhou, R. W. Field, and K. A. Nelson, “Molecular Orientation and Alignment by Intense Single-Cycle THz Pulses,” Phys. Rev. Lett. 107(16), 163603 (2011).
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L. Luo, I. Chatzakis, J. Wang, F. B. P. Niesler, M. Wegener, T. Koschny, and C. M. Soukoulis, “Broadband terahertz generation from metamaterials,” Nat. Commun. 5(1), 3055 (2014).
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S. Linden, F. B. P. Niesler, J. Förstner, Y. Grynko, T. Meier, and M. Wegener, “Collective Effects in Second-Harmonic Generation from Split-Ring-Resonator Arrays,” Phys. Rev. Lett. 109(1), 015502 (2012).
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K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
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L. Liu, X. Zhang, M. Kenney, X. Su, N. Xu, C. Ouyang, Y. Shi, J. Han, W. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26(29), 5031–5036 (2014).
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S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7(12), 977–981 (2013).
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Y. Liu, S.-G. Park, and A. M. Weiner, “Terahertz waveform synthesis via optical pulse shaping,” IEEE J. Sel. Top. Quantum Electron. 2(3), 709–719 (1996).
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T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mährlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent terahertz control of antiferromagnetic spin waves,” Nat. Photonics 5(1), 31–34 (2011).
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H. Y. Hwang, S. Fleischer, N. C. Brandt, B. G. Perkins, M. Liu, K. Fan, A. Sternbach, X. Zhang, R. D. Averitt, and K. A. Nelson, “A review of non-linear terahertz spectroscopy with ultrashort tabletop-laser pulses,” J. Mod. Opt. 62(18), 1447–1479 (2015).
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M. Woerner, W. Kuehn, P. Bowlan, K. Reimann, and T. Elsaesser, “Ultrafast two-dimensional terahertz spectroscopy of elementary excitations in solids,” New J. Phys. 15(2), 025039 (2013).
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G. R. Keiser, N. Karl, P. Q. Liu, C. Tulloss, H.-T. Chen, A. J. Taylor, I. Brener, J. L. Reno, and D. M. Mittleman, “Nonlinear terahertz metamaterials with active electrical control,” Appl. Phys. Lett. 111(12), 121101 (2017).
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K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
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L. Liu, X. Zhang, M. Kenney, X. Su, N. Xu, C. Ouyang, Y. Shi, J. Han, W. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26(29), 5031–5036 (2014).
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L. Liu, X. Zhang, M. Kenney, X. Su, N. Xu, C. Ouyang, Y. Shi, J. Han, W. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26(29), 5031–5036 (2014).
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L. Michaeli, S. Keren-Zur, O. Avayu, H. Suchowski, and T. Ellenbogen, “Nonlinear Surface Lattice Resonance in Plasmonic Nanoparticle Arrays,” Phys. Rev. Lett. 118(24), 243904 (2017).
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K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
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J. Lu, X. Li, H. Y. Hwang, B. K. Ofori-Okai, T. Kurihara, T. Suemoto, and K. A. Nelson, “Coherent Two-Dimensional Terahertz Magnetic Resonance Spectroscopy of Collective Spin Waves,” Phys. Rev. Lett. 118(20), 207204 (2017).
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J. Yang, C. Gong, L. Sun, P. Chen, L. Lin, and W. Liu, “Tunable reflecting terahertz filter based on chirped metamaterial structure,” Sci. Rep. 6(1), 38732 (2016).
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S. Keren-Zur, M. Tal, S. Fleischer, D. M. Mittleman, and T. Ellenbogen, “Generation of spatiotemporally tailored terahertz wavepackets by nonlinear metasurfaces,” Nat. Commun. 10(1), 1778 (2019).
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G. R. Keiser, N. Karl, P. Q. Liu, C. Tulloss, H.-T. Chen, A. J. Taylor, I. Brener, J. L. Reno, and D. M. Mittleman, “Nonlinear terahertz metamaterials with active electrical control,” Appl. Phys. Lett. 111(12), 121101 (2017).
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M. Tymchenko, J. S. Gomez-Diaz, J. Lee, M. A. Belkin, and A. Alù, “Highly-efficient THz generation using nonlinear plasmonic metasurfaces,” J. Opt. 19(10), 104001 (2017).
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L. Luo, I. Chatzakis, J. Wang, F. B. P. Niesler, M. Wegener, T. Koschny, and C. M. Soukoulis, “Broadband terahertz generation from metamaterials,” Nat. Commun. 5(1), 3055 (2014).
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M. Woerner, W. Kuehn, P. Bowlan, K. Reimann, and T. Elsaesser, “Ultrafast two-dimensional terahertz spectroscopy of elementary excitations in solids,” New J. Phys. 15(2), 025039 (2013).
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L. Liu, X. Zhang, M. Kenney, X. Su, N. Xu, C. Ouyang, Y. Shi, J. Han, W. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26(29), 5031–5036 (2014).
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J. Yang, C. Gong, L. Sun, P. Chen, L. Lin, and W. Liu, “Tunable reflecting terahertz filter based on chirped metamaterial structure,” Sci. Rep. 6(1), 38732 (2016).
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K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
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M. Sato, T. Higuchi, N. Kanda, K. Konishi, K. Yoshioka, T. Suzuki, K. Misawa, and M. Kuwata-Gonokami, “Terahertz polarization pulse shaping with arbitrary field control,” Nat. Photonics 7(9), 724–731 (2013).
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L. Liu, X. Zhang, M. Kenney, X. Su, N. Xu, C. Ouyang, Y. Shi, J. Han, W. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26(29), 5031–5036 (2014).
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K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
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H. Y. Hwang, S. Fleischer, N. C. Brandt, B. G. Perkins, M. Liu, K. Fan, A. Sternbach, X. Zhang, R. D. Averitt, and K. A. Nelson, “A review of non-linear terahertz spectroscopy with ultrashort tabletop-laser pulses,” J. Mod. Opt. 62(18), 1447–1479 (2015).
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L. Liu, X. Zhang, M. Kenney, X. Su, N. Xu, C. Ouyang, Y. Shi, J. Han, W. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26(29), 5031–5036 (2014).
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Zhou, Y.

S. Fleischer, Y. Zhou, R. W. Field, and K. A. Nelson, “Molecular Orientation and Alignment by Intense Single-Cycle THz Pulses,” Phys. Rev. Lett. 107(16), 163603 (2011).
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S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7(12), 977–981 (2013).
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ACS Photonics (1)

S. Keren-Zur, O. Avayu, L. Michaeli, and T. Ellenbogen, “Nonlinear Beam Shaping with Plasmonic Metasurfaces,” ACS Photonics 3(1), 117–123 (2016).
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Adv. Mater. (1)

L. Liu, X. Zhang, M. Kenney, X. Su, N. Xu, C. Ouyang, Y. Shi, J. Han, W. Zhang, and S. Zhang, “Broadband metasurfaces with simultaneous control of phase and amplitude,” Adv. Mater. 26(29), 5031–5036 (2014).
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Annu. Rev. Phys. Chem. (1)

Y. Silberberg, “Quantum Coherent Control for Nonlinear Spectroscopy and Microscopy,” Annu. Rev. Phys. Chem. 60(1), 277–292 (2009).
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Appl. Phys. Lett. (2)

Y.-S. Lee, N. Amer, and W. C. Hurlbut, “Terahertz pulse shaping via optical rectification in poled lithium niobate,” Appl. Phys. Lett. 82(2), 170–172 (2003).
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G. R. Keiser, N. Karl, P. Q. Liu, C. Tulloss, H.-T. Chen, A. J. Taylor, I. Brener, J. L. Reno, and D. M. Mittleman, “Nonlinear terahertz metamaterials with active electrical control,” Appl. Phys. Lett. 111(12), 121101 (2017).
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IEEE J. Quantum Electron. (1)

D. E. Leaird and A. M. Weiner, “Femtosecond direct space-to-time pulse shaping,” IEEE J. Quantum Electron. 37(4), 494–504 (2001).
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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(3), 709–719 (1996).
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J. Mod. Opt. (1)

H. Y. Hwang, S. Fleischer, N. C. Brandt, B. G. Perkins, M. Liu, K. Fan, A. Sternbach, X. Zhang, R. D. Averitt, and K. A. Nelson, “A review of non-linear terahertz spectroscopy with ultrashort tabletop-laser pulses,” J. Mod. Opt. 62(18), 1447–1479 (2015).
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J. Opt. (1)

M. Tymchenko, J. S. Gomez-Diaz, J. Lee, M. A. Belkin, and A. Alù, “Highly-efficient THz generation using nonlinear plasmonic metasurfaces,” J. Opt. 19(10), 104001 (2017).
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Nat. Commun. (2)

S. Keren-Zur, M. Tal, S. Fleischer, D. M. Mittleman, and T. Ellenbogen, “Generation of spatiotemporally tailored terahertz wavepackets by nonlinear metasurfaces,” Nat. Commun. 10(1), 1778 (2019).
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Nat. Mater. (1)

K. O’Brien, H. Suchowski, J. Rho, A. Salandrino, B. Kante, X. Yin, and X. Zhang, “Predicting nonlinear properties of metamaterials from the linear response,” Nat. Mater. 14(4), 379–383 (2015).
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L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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Nat. Photonics (3)

T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mährlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent terahertz control of antiferromagnetic spin waves,” Nat. Photonics 5(1), 31–34 (2011).
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[Crossref]

M. Sato, T. Higuchi, N. Kanda, K. Konishi, K. Yoshioka, T. Suzuki, K. Misawa, and M. Kuwata-Gonokami, “Terahertz polarization pulse shaping with arbitrary field control,” Nat. Photonics 7(9), 724–731 (2013).
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Nature (1)

B. E. Cole, J. B. Williams, B. T. King, M. S. Sherwin, and C. R. Stanley, “Coherent manipulation of semiconductor quantum bits with terahertz radiation,” Nature 410(6824), 60–63 (2001).
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New J. Phys. (1)

M. Woerner, W. Kuehn, P. Bowlan, K. Reimann, and T. Elsaesser, “Ultrafast two-dimensional terahertz spectroscopy of elementary excitations in solids,” New J. Phys. 15(2), 025039 (2013).
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Opt. Commun. (1)

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Opt. Express (5)

Opt. Lett. (4)

Optica (1)

Phys. Rev. Lett. (5)

S. Linden, F. B. P. Niesler, J. Förstner, Y. Grynko, T. Meier, and M. Wegener, “Collective Effects in Second-Harmonic Generation from Split-Ring-Resonator Arrays,” Phys. Rev. Lett. 109(1), 015502 (2012).
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[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. (a) Working principle of THz-DST pulse shaping with NLMS. A near infrared ultrashort pulse (NIR) excites a NLMS consisted of nonlinear meta-atom. Consequently, each meta-atom emits a single-cycle THz pulse as a point source. When measured in the far-field at an angle $\theta $ (i.e., collected and collimated after a slit), a train of single-cycle pulses is formed. The train of pulses is formed according to the spatial distribution of the meta-atoms on the meta-surface, and the nonlinear response of each emitter. (b) THz emission spectrum from a NLMS based on SRRs as was experimentally measured before [26]. (c) Temporal form of THz pulse emitted from the NLMS.
Fig. 2.
Fig. 2. (a) Structure of NLMS constructed of two separated regions of uniform arrays of SRRs, marked I and II. (b) Real part (Re) and absolute value (Abs) of calculated pulse shape for θ=15° according to simulation (sim) and convolution (con) as described in Eq. (10). Pulses are associated with regions I and II (c) Angular dependent emission pattern as simulated by broadband beam propagation technique. Dashed line corresponds with (b).
Fig. 3.
Fig. 3. (a) Illustration of methods to manipulate the local nonlinear response of the NLMS. The changes of the SRR array structure are shown at the top with the effect on the emitted pulse shown at the bottom. (b) Nonlinear response of studied two phase and amplitude modulated NLMS. (c) Simulated pulse shape emitted at 15° from NLMS structures presented in (b).
Fig. 4.
Fig. 4. (a) Reconstruction of desired pulse (blue) by deconvolution with the kernel pulse (purple) to calculate the required NLMS structure (yellow) for pulse emission at 30°. Red curve is the beam propagation simulated pulse. (b) Reconstruction of a desired pulse exceeding the bandwidth limitations.
Fig. 5.
Fig. 5. (a) Design of a NLMS for generation of two consecutive pulses with different carrier frequency and envelope shape. (b) Emitted THz pulse at 30° from the NLMS described in (a).
Fig. 6.
Fig. 6. (a) Structure of a NLMS consisted of two perpendicular oriented SRRs. (b) Emitted THz pulse from the NLMS described in (a), at 15° for various pump polarization. (c) Nonlinear coefficient dependency on NIR pump wavelength. Different resonant behavior is shown for two SRRs with different geometry. (d) NLMS structure consisted of two SRRs with different geometry and resonance frequency, as described in (c). (e) Emitted THz pulse from the NLMS described in (d) at 15°, for various pump wavelengths.

Equations (13)

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E ( x , z = 0 ) s ( x )
S ( k x ) = 1 2 π s ( x ) e i k x x d x
s ( x ) = 1 2 π S ( k x ) e i k x x d k x
F ( ω ) = 1 2 π f ( t ) e i ω t d t
f ( t ) = 1 2 π F ( ω ) e i ω t d ω
E ( x , t , z = 0 ) s ( x ) f ( t ) = 1 2 π d ω d k x S ( k x ) F ( ω ) e i ( k x x ω t )
E ( x , t , z ) 1 2 π d ω d k x S ( k x ) F ( ω ) e i ( k x x ω t ) e i ( ω c ) 2 k x 2 z
E ( x , t , z ) 1 2 π d ω d k x S ( k x ) F ( ω ) e i ( k x x ω t ) e i ( ω c ) 2 k x 2 z δ ( k x ω c s i n θ )
E ( x = z t a n θ , t , z ) 1 2 π d ω S ( ω c s i n θ ) F ( ω ) e i ω ( t z c c o s θ )
E ( x = z t a n θ , t , z ) = s ( c t s i n θ ) f ( t t 0 )
s ( x ) = F T 1 [ F T [ E ( x c s i n θ ) ] F T [ f ( x c s i n θ t 0 ) ] ]
Λ = c ν s i n θ
s i n θ = ± λ Λ