Abstract

We investigate the nonlinear response of terahertz (THz) metamaterial perfect absorbers consisting of electric split ring resonators on GaAs integrated with a polyimide spacer and gold ground plane. These perfect absorbers on bulk semi-insulating GaAs are characterized using high-field THz time-domain spectroscopy. The resonance frequency redshifts 20 GHz and the absorbance is reduced by 30% as the incident peak field is increased from 30 to 300 kV/cm. The nonlinear response arises from THz field driven interband transitions and intervalley scattering in the GaAs. To eliminate the Fresnel losses from the GaAs substrate, we design and fabricate a flexible metamaterial saturable perfect absorber. The ability to create nonlinear absorbers enables appealing applications such as optical limiting and self-focusing.

© 2016 Chinese Laser Press

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    [Crossref]
  23. H. Hirori, K. Shinokita, M. Shirai, S. Tani, Y. Kadoya, and K. Tanaka, “Extraordinary carrier multiplication gated by a picosecond electric field pulse,” Nat. Commun. 2, 594 (2011).
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    [Crossref]
  26. L. Huang, D. R. Chowdhury, S. Ramani, M. T. Reiten, S.-N. Luo, A. K. Azad, A. J. Taylor, and H.-T. Chen, “Impact of resonator geometry and its coupling with ground plane on ultrathin metamaterial perfect absorbers,” Appl. Phys. Lett. 101, 101102 (2012).
    [Crossref]
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  28. K.-H. Lin, C. A. Werley, and K. A. Nelson, “Nonlinear terahertz devices utilizing semiconducting plasmonic metamaterials,” Appl. Phys. Lett. 95, 103304 (2009).
    [Crossref]
  29. H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006).
    [Crossref]
  30. H. R. Seren, G. R. Keiser, L. Cao, J. Zhang, A. C. Strikwerda, K. Fan, G. D. Metcalfe, M. Wraback, X. Zhang, and R. D. Averitt, “Optically modulated multiband terahertz perfect absorber,” Adv. Opt. Mater. 2, 1221–1226 (2014).
    [Crossref]
  31. http://www.axt.com/site/index.php?q=node/38 .
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    [Crossref]
  34. H. Bergner, V. Brückner, M. Lenzner, and R. Strobel, “Investigation of the field-dependent carrier mobility in GaAs by picosecond photoconductivity measurements,” Phys. Stat. Sol. B 150, 885–889 (1988).
    [Crossref]
  35. X. Zhao, K. Fan, J. Zhang, H. R. Seren, G. D. Metcalfe, M. Wraback, R. D. Averitt, and X. Zhang, “Optically tunable metamaterial perfect absorber on highly flexible substrate,” Sens. Actuators A 231, 74–80 (2015).
    [Crossref]

2015 (6)

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, 379–383 (2015).
[Crossref]

J. Zhang, X. Zhao, K. Fan, X. Wang, G.-F. Zhang, K. Geng, X. Zhang, and R. D. Averitt, “Terahertz radiation-induced sub-cycle field electron emission across a split-gap dipole antenna,” Appl. Phys. Lett. 107, 231101 (2015).
[Crossref]

A. T. Tarekegne, K. Iwaszczuk, M. Zalkovskij, A. C. Strikwerda, and P. U. Jepsen, “Impact ionization in high resistivity silicon induced by an intense terahertz field enhanced by an antenna array,” New J. Phys. 17, 043002 (2015).
[Crossref]

X. Zhao, K. Fan, J. Zhang, H. R. Seren, G. D. Metcalfe, M. Wraback, R. D. Averitt, and X. Zhang, “Optically tunable metamaterial perfect absorber on highly flexible substrate,” Sens. Actuators A 231, 74–80 (2015).
[Crossref]

K. Iwaszczuk, M. Zalkovskij, A. C. Strikwerda, and P. U. Jepsen, “Nitrogen plasma formation through terahertz-induced ultrafast electron field emission,” Optica 2, 116–123 (2015).
[Crossref]

A. C. Strikwerda, M. Zalkovskij, K. Iwaszczuk, D. L. Lorenzen, and P. U. Jepsen, “Permanently reconfigured metamaterials due to terahertz induced mass transfer of gold,” Opt. Express 23, 11586–11599 (2015).
[Crossref]

2014 (3)

H. R. Seren, G. R. Keiser, L. Cao, J. Zhang, A. C. Strikwerda, K. Fan, G. D. Metcalfe, M. Wraback, X. Zhang, and R. D. Averitt, “Optically modulated multiband terahertz perfect absorber,” Adv. Opt. Mater. 2, 1221–1226 (2014).
[Crossref]

C. Lange, T. Maag, M. Hohenleutner, S. Baierl, O. Schubert, E. Edwards, D. Bougeard, G. Woltersdorf, and R. Huber, “Extremely nonperturbative nonlinearities in GaAs driven by atomically strong terahertz fields in gold metamaterials,” Phys. Rev. Lett. 113, 227401 (2014).
[Crossref]

M. Lapine, I. V. Shadrivov, and Y. S. Kivshar, “Colloquium: nonlinear metamaterials,” Rev. Mod. Phys. 86, 1093–1123 (2014).
[Crossref]

2013 (3)

G. Keiser, K. Fan, X. Zhang, and R. Averitt, “Towards dynamic, tunable, and nonlinear metamaterials via near field interactions: a review,” J. Infrared Millim. Terahertz Waves 34, 709–723 (2013).
[Crossref]

K. Fan, H. Y. Hwang, M. Liu, A. C. Strikwerda, A. Sternbach, J. Zhang, X. Zhao, X. Zhang, K. A. Nelson, and R. D. Averitt, “Nonlinear terahertz metamaterials via field-enhanced carrier dynamics in GaAs,” Phys. Rev. Lett. 110, 217404 (2013).
[Crossref]

A. P. Slobozhanyuk, M. Lapine, D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, R. C. McPhedran, and P. A. Belov, “Flexible helices for nonlinear metamaterials,” Adv. Mater. 25, 3409–3412 (2013).
[Crossref]

2012 (8)

J. Zhou, D. R. Chowdhury, R. Zhao, A. K. Azad, H.-T. Chen, C. M. Soukoulis, A. J. Taylor, and J. F. O’Hara, “Terahertz chiral metamaterials with giant and dynamically tunable optical activity,” Phys. Rev. B 86, 035448 (2012).
[Crossref]

N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater. 11, 917–924 (2012).
[Crossref]

M. Lapine, I. V. Shadrivov, D. A. Powell, and Y. S. Kivshar, “Magnetoelastic metamaterials,” Nat. Mater. 11, 30-33 (2012).
[Crossref]

A. Minovich, J. Farnell, D. N. Neshev, I. McKerracher, F. Karouta, J. Tian, D. A. Powell, I. V. Shadrivov, H. H. Tan, and C. Jagadish, “Liquid crystal based nonlinear fishnet metamaterials,” Appl. Phys. Lett. 100, 121113 (2012).
[Crossref]

L. Huang, D. R. Chowdhury, S. Ramani, M. T. Reiten, S.-N. Luo, A. K. Azad, A. J. Taylor, and H.-T. Chen, “Impact of resonator geometry and its coupling with ground plane on ultrathin metamaterial perfect absorbers,” Appl. Phys. Lett. 101, 101102 (2012).
[Crossref]

M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, and J. Lu, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487, 345–348 (2012).
[Crossref]

H.-T. Chen, “Interference theory of metamaterial perfect absorbers,” Opt. Express 20, 7165–7172 (2012).
[Crossref]

C. A. Werley, K. Fan, A. C. Strikwerda, S. M. Teo, X. Zhang, R. D. Averitt, and K. A. Nelson, “Time-resolved imaging of near-fields in THz antennas and direct quantitative measurement of field enhancements,” Opt. Express 20, 8551–8567 (2012).
[Crossref]

2011 (1)

H. Hirori, K. Shinokita, M. Shirai, S. Tani, Y. Kadoya, and K. Tanaka, “Extraordinary carrier multiplication gated by a picosecond electric field pulse,” Nat. Commun. 2, 594 (2011).
[Crossref]

2010 (2)

H.-T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105, 073901 (2010).

W. Kuehn, P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, and R. Hey, “Terahertz-induced interband tunneling of electrons in GaAs,” Phys. Rev. B 82, 075204 (2010).
[Crossref]

2009 (3)

M. Seo, H. Park, S. Koo, D. Park, J. Kang, O. Suwal, S. Choi, P. Planken, G. Park, and N. Park, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3, 152–156 (2009).
[Crossref]

F. Su, F. Blanchard, G. Sharma, L. Razzari, A. Ayesheshim, T. Cocker, L. Titova, T. Ozaki, J.-C. Kieffer, and R. Morandotti, “Terahertz pulse induced intervalley scattering in photoexcited GaAs,” Opt. Express 17, 9620–9629 (2009).
[Crossref]

K.-H. Lin, C. A. Werley, and K. A. Nelson, “Nonlinear terahertz devices utilizing semiconducting plasmonic metamaterials,” Appl. Phys. Lett. 95, 103304 (2009).
[Crossref]

2008 (1)

I. V. Shadrivov, A. B. Kozyrev, D. W. van der Weide, and Y. S. Kivshar, “Tunable transmission and harmonic generation in nonlinear metamaterials,” Appl. Phys. Lett. 93, 161903 (2008).
[Crossref]

2006 (2)

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313, 502–504 (2006).
[Crossref]

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006).
[Crossref]

1999 (1)

J. B. Pendry, A. J. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

1988 (1)

H. Bergner, V. Brückner, M. Lenzner, and R. Strobel, “Investigation of the field-dependent carrier mobility in GaAs by picosecond photoconductivity measurements,” Phys. Stat. Sol. B 150, 885–889 (1988).
[Crossref]

1972 (1)

C. L. Anderson and C. R. Crowell, “Threshold energies for electron-hole pair production by impact ionization in semiconductors,” Phys. Rev. B 5, 2267–2272 (1972).
[Crossref]

1965 (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

Anderson, C. L.

C. L. Anderson and C. R. Crowell, “Threshold energies for electron-hole pair production by impact ionization in semiconductors,” Phys. Rev. B 5, 2267–2272 (1972).
[Crossref]

Averitt, R.

G. Keiser, K. Fan, X. Zhang, and R. Averitt, “Towards dynamic, tunable, and nonlinear metamaterials via near field interactions: a review,” J. Infrared Millim. Terahertz Waves 34, 709–723 (2013).
[Crossref]

Averitt, R. D.

X. Zhao, K. Fan, J. Zhang, H. R. Seren, G. D. Metcalfe, M. Wraback, R. D. Averitt, and X. Zhang, “Optically tunable metamaterial perfect absorber on highly flexible substrate,” Sens. Actuators A 231, 74–80 (2015).
[Crossref]

J. Zhang, X. Zhao, K. Fan, X. Wang, G.-F. Zhang, K. Geng, X. Zhang, and R. D. Averitt, “Terahertz radiation-induced sub-cycle field electron emission across a split-gap dipole antenna,” Appl. Phys. Lett. 107, 231101 (2015).
[Crossref]

H. R. Seren, G. R. Keiser, L. Cao, J. Zhang, A. C. Strikwerda, K. Fan, G. D. Metcalfe, M. Wraback, X. Zhang, and R. D. Averitt, “Optically modulated multiband terahertz perfect absorber,” Adv. Opt. Mater. 2, 1221–1226 (2014).
[Crossref]

K. Fan, H. Y. Hwang, M. Liu, A. C. Strikwerda, A. Sternbach, J. Zhang, X. Zhao, X. Zhang, K. A. Nelson, and R. D. Averitt, “Nonlinear terahertz metamaterials via field-enhanced carrier dynamics in GaAs,” Phys. Rev. Lett. 110, 217404 (2013).
[Crossref]

C. A. Werley, K. Fan, A. C. Strikwerda, S. M. Teo, X. Zhang, R. D. Averitt, and K. A. Nelson, “Time-resolved imaging of near-fields in THz antennas and direct quantitative measurement of field enhancements,” Opt. Express 20, 8551–8567 (2012).
[Crossref]

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006).
[Crossref]

H. R. Seren, J. Zhang, G. R. Keiser, S. J. Maddox, X. Zhao, K. Fan, S. R. Bank, X. Zhang, and R. D. Averitt, “Nonlinear terahertz devices utilizing semiconducting plasmonic metamaterials,” arXiv: 1508.03183 (2015).

Ayesheshim, A.

Azad, A. K.

J. Zhou, D. R. Chowdhury, R. Zhao, A. K. Azad, H.-T. Chen, C. M. Soukoulis, A. J. Taylor, and J. F. O’Hara, “Terahertz chiral metamaterials with giant and dynamically tunable optical activity,” Phys. Rev. B 86, 035448 (2012).
[Crossref]

L. Huang, D. R. Chowdhury, S. Ramani, M. T. Reiten, S.-N. Luo, A. K. Azad, A. J. Taylor, and H.-T. Chen, “Impact of resonator geometry and its coupling with ground plane on ultrathin metamaterial perfect absorbers,” Appl. Phys. Lett. 101, 101102 (2012).
[Crossref]

H.-T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105, 073901 (2010).

Baierl, S.

C. Lange, T. Maag, M. Hohenleutner, S. Baierl, O. Schubert, E. Edwards, D. Bougeard, G. Woltersdorf, and R. Huber, “Extremely nonperturbative nonlinearities in GaAs driven by atomically strong terahertz fields in gold metamaterials,” Phys. Rev. Lett. 113, 227401 (2014).
[Crossref]

Bank, S. R.

H. R. Seren, J. Zhang, G. R. Keiser, S. J. Maddox, X. Zhao, K. Fan, S. R. Bank, X. Zhang, and R. D. Averitt, “Nonlinear terahertz devices utilizing semiconducting plasmonic metamaterials,” arXiv: 1508.03183 (2015).

Belov, P. A.

A. P. Slobozhanyuk, M. Lapine, D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, R. C. McPhedran, and P. A. Belov, “Flexible helices for nonlinear metamaterials,” Adv. Mater. 25, 3409–3412 (2013).
[Crossref]

Bergner, H.

H. Bergner, V. Brückner, M. Lenzner, and R. Strobel, “Investigation of the field-dependent carrier mobility in GaAs by picosecond photoconductivity measurements,” Phys. Stat. Sol. B 150, 885–889 (1988).
[Crossref]

Blanchard, F.

Bougeard, D.

C. Lange, T. Maag, M. Hohenleutner, S. Baierl, O. Schubert, E. Edwards, D. Bougeard, G. Woltersdorf, and R. Huber, “Extremely nonperturbative nonlinearities in GaAs driven by atomically strong terahertz fields in gold metamaterials,” Phys. Rev. Lett. 113, 227401 (2014).
[Crossref]

Brückner, V.

H. Bergner, V. Brückner, M. Lenzner, and R. Strobel, “Investigation of the field-dependent carrier mobility in GaAs by picosecond photoconductivity measurements,” Phys. Stat. Sol. B 150, 885–889 (1988).
[Crossref]

Cao, L.

H. R. Seren, G. R. Keiser, L. Cao, J. Zhang, A. C. Strikwerda, K. Fan, G. D. Metcalfe, M. Wraback, X. Zhang, and R. D. Averitt, “Optically modulated multiband terahertz perfect absorber,” Adv. Opt. Mater. 2, 1221–1226 (2014).
[Crossref]

Chen, F.

H.-T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105, 073901 (2010).

Chen, H.-T.

L. Huang, D. R. Chowdhury, S. Ramani, M. T. Reiten, S.-N. Luo, A. K. Azad, A. J. Taylor, and H.-T. Chen, “Impact of resonator geometry and its coupling with ground plane on ultrathin metamaterial perfect absorbers,” Appl. Phys. Lett. 101, 101102 (2012).
[Crossref]

J. Zhou, D. R. Chowdhury, R. Zhao, A. K. Azad, H.-T. Chen, C. M. Soukoulis, A. J. Taylor, and J. F. O’Hara, “Terahertz chiral metamaterials with giant and dynamically tunable optical activity,” Phys. Rev. B 86, 035448 (2012).
[Crossref]

H.-T. Chen, “Interference theory of metamaterial perfect absorbers,” Opt. Express 20, 7165–7172 (2012).
[Crossref]

H.-T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105, 073901 (2010).

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006).
[Crossref]

Choi, S.

M. Seo, H. Park, S. Koo, D. Park, J. Kang, O. Suwal, S. Choi, P. Planken, G. Park, and N. Park, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3, 152–156 (2009).
[Crossref]

Chowdhury, D. R.

L. Huang, D. R. Chowdhury, S. Ramani, M. T. Reiten, S.-N. Luo, A. K. Azad, A. J. Taylor, and H.-T. Chen, “Impact of resonator geometry and its coupling with ground plane on ultrathin metamaterial perfect absorbers,” Appl. Phys. Lett. 101, 101102 (2012).
[Crossref]

J. Zhou, D. R. Chowdhury, R. Zhao, A. K. Azad, H.-T. Chen, C. M. Soukoulis, A. J. Taylor, and J. F. O’Hara, “Terahertz chiral metamaterials with giant and dynamically tunable optical activity,” Phys. Rev. B 86, 035448 (2012).
[Crossref]

Cocker, T.

Crowell, C. R.

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A. P. Slobozhanyuk, M. Lapine, D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, R. C. McPhedran, and P. A. Belov, “Flexible helices for nonlinear metamaterials,” Adv. Mater. 25, 3409–3412 (2013).
[Crossref]

A. Minovich, J. Farnell, D. N. Neshev, I. McKerracher, F. Karouta, J. Tian, D. A. Powell, I. V. Shadrivov, H. H. Tan, and C. Jagadish, “Liquid crystal based nonlinear fishnet metamaterials,” Appl. Phys. Lett. 100, 121113 (2012).
[Crossref]

M. Lapine, I. V. Shadrivov, D. A. Powell, and Y. S. Kivshar, “Magnetoelastic metamaterials,” Nat. Mater. 11, 30-33 (2012).
[Crossref]

I. V. Shadrivov, A. B. Kozyrev, D. W. van der Weide, and Y. S. Kivshar, “Tunable transmission and harmonic generation in nonlinear metamaterials,” Appl. Phys. Lett. 93, 161903 (2008).
[Crossref]

Sharma, G.

Shinokita, K.

H. Hirori, K. Shinokita, M. Shirai, S. Tani, Y. Kadoya, and K. Tanaka, “Extraordinary carrier multiplication gated by a picosecond electric field pulse,” Nat. Commun. 2, 594 (2011).
[Crossref]

Shirai, M.

H. Hirori, K. Shinokita, M. Shirai, S. Tani, Y. Kadoya, and K. Tanaka, “Extraordinary carrier multiplication gated by a picosecond electric field pulse,” Nat. Commun. 2, 594 (2011).
[Crossref]

Slobozhanyuk, A. P.

A. P. Slobozhanyuk, M. Lapine, D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, R. C. McPhedran, and P. A. Belov, “Flexible helices for nonlinear metamaterials,” Adv. Mater. 25, 3409–3412 (2013).
[Crossref]

Soukoulis, C. M.

J. Zhou, D. R. Chowdhury, R. Zhao, A. K. Azad, H.-T. Chen, C. M. Soukoulis, A. J. Taylor, and J. F. O’Hara, “Terahertz chiral metamaterials with giant and dynamically tunable optical activity,” Phys. Rev. B 86, 035448 (2012).
[Crossref]

Sternbach, A.

K. Fan, H. Y. Hwang, M. Liu, A. C. Strikwerda, A. Sternbach, J. Zhang, X. Zhao, X. Zhang, K. A. Nelson, and R. D. Averitt, “Nonlinear terahertz metamaterials via field-enhanced carrier dynamics in GaAs,” Phys. Rev. Lett. 110, 217404 (2013).
[Crossref]

Sternbach, A. J.

M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, and J. Lu, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487, 345–348 (2012).
[Crossref]

Stewart, W.

J. B. Pendry, A. J. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

Strikwerda, A. C.

K. Iwaszczuk, M. Zalkovskij, A. C. Strikwerda, and P. U. Jepsen, “Nitrogen plasma formation through terahertz-induced ultrafast electron field emission,” Optica 2, 116–123 (2015).
[Crossref]

A. C. Strikwerda, M. Zalkovskij, K. Iwaszczuk, D. L. Lorenzen, and P. U. Jepsen, “Permanently reconfigured metamaterials due to terahertz induced mass transfer of gold,” Opt. Express 23, 11586–11599 (2015).
[Crossref]

A. T. Tarekegne, K. Iwaszczuk, M. Zalkovskij, A. C. Strikwerda, and P. U. Jepsen, “Impact ionization in high resistivity silicon induced by an intense terahertz field enhanced by an antenna array,” New J. Phys. 17, 043002 (2015).
[Crossref]

H. R. Seren, G. R. Keiser, L. Cao, J. Zhang, A. C. Strikwerda, K. Fan, G. D. Metcalfe, M. Wraback, X. Zhang, and R. D. Averitt, “Optically modulated multiband terahertz perfect absorber,” Adv. Opt. Mater. 2, 1221–1226 (2014).
[Crossref]

K. Fan, H. Y. Hwang, M. Liu, A. C. Strikwerda, A. Sternbach, J. Zhang, X. Zhao, X. Zhang, K. A. Nelson, and R. D. Averitt, “Nonlinear terahertz metamaterials via field-enhanced carrier dynamics in GaAs,” Phys. Rev. Lett. 110, 217404 (2013).
[Crossref]

C. A. Werley, K. Fan, A. C. Strikwerda, S. M. Teo, X. Zhang, R. D. Averitt, and K. A. Nelson, “Time-resolved imaging of near-fields in THz antennas and direct quantitative measurement of field enhancements,” Opt. Express 20, 8551–8567 (2012).
[Crossref]

M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, and J. Lu, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487, 345–348 (2012).
[Crossref]

Strobel, R.

H. Bergner, V. Brückner, M. Lenzner, and R. Strobel, “Investigation of the field-dependent carrier mobility in GaAs by picosecond photoconductivity measurements,” Phys. Stat. Sol. B 150, 885–889 (1988).
[Crossref]

Su, F.

Suchowski, H.

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, 379–383 (2015).
[Crossref]

Suwal, O.

M. Seo, H. Park, S. Koo, D. Park, J. Kang, O. Suwal, S. Choi, P. Planken, G. Park, and N. Park, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3, 152–156 (2009).
[Crossref]

Tan, H. H.

A. Minovich, J. Farnell, D. N. Neshev, I. McKerracher, F. Karouta, J. Tian, D. A. Powell, I. V. Shadrivov, H. H. Tan, and C. Jagadish, “Liquid crystal based nonlinear fishnet metamaterials,” Appl. Phys. Lett. 100, 121113 (2012).
[Crossref]

Tanaka, K.

H. Hirori, K. Shinokita, M. Shirai, S. Tani, Y. Kadoya, and K. Tanaka, “Extraordinary carrier multiplication gated by a picosecond electric field pulse,” Nat. Commun. 2, 594 (2011).
[Crossref]

Tani, S.

H. Hirori, K. Shinokita, M. Shirai, S. Tani, Y. Kadoya, and K. Tanaka, “Extraordinary carrier multiplication gated by a picosecond electric field pulse,” Nat. Commun. 2, 594 (2011).
[Crossref]

Tao, H.

M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, and J. Lu, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487, 345–348 (2012).
[Crossref]

Tarekegne, A. T.

A. T. Tarekegne, K. Iwaszczuk, M. Zalkovskij, A. C. Strikwerda, and P. U. Jepsen, “Impact ionization in high resistivity silicon induced by an intense terahertz field enhanced by an antenna array,” New J. Phys. 17, 043002 (2015).
[Crossref]

Taylor, A. J.

J. Zhou, D. R. Chowdhury, R. Zhao, A. K. Azad, H.-T. Chen, C. M. Soukoulis, A. J. Taylor, and J. F. O’Hara, “Terahertz chiral metamaterials with giant and dynamically tunable optical activity,” Phys. Rev. B 86, 035448 (2012).
[Crossref]

L. Huang, D. R. Chowdhury, S. Ramani, M. T. Reiten, S.-N. Luo, A. K. Azad, A. J. Taylor, and H.-T. Chen, “Impact of resonator geometry and its coupling with ground plane on ultrathin metamaterial perfect absorbers,” Appl. Phys. Lett. 101, 101102 (2012).
[Crossref]

H.-T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105, 073901 (2010).

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006).
[Crossref]

Teo, S. M.

Tian, J.

A. Minovich, J. Farnell, D. N. Neshev, I. McKerracher, F. Karouta, J. Tian, D. A. Powell, I. V. Shadrivov, H. H. Tan, and C. Jagadish, “Liquid crystal based nonlinear fishnet metamaterials,” Appl. Phys. Lett. 100, 121113 (2012).
[Crossref]

Titova, L.

van der Weide, D. W.

I. V. Shadrivov, A. B. Kozyrev, D. W. van der Weide, and Y. S. Kivshar, “Tunable transmission and harmonic generation in nonlinear metamaterials,” Appl. Phys. Lett. 93, 161903 (2008).
[Crossref]

Wang, X.

J. Zhang, X. Zhao, K. Fan, X. Wang, G.-F. Zhang, K. Geng, X. Zhang, and R. D. Averitt, “Terahertz radiation-induced sub-cycle field electron emission across a split-gap dipole antenna,” Appl. Phys. Lett. 107, 231101 (2015).
[Crossref]

Wegener, M.

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313, 502–504 (2006).
[Crossref]

Werley, C. A.

West, K. G.

M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, and J. Lu, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487, 345–348 (2012).
[Crossref]

Woerner, M.

W. Kuehn, P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, and R. Hey, “Terahertz-induced interband tunneling of electrons in GaAs,” Phys. Rev. B 82, 075204 (2010).
[Crossref]

Woltersdorf, G.

C. Lange, T. Maag, M. Hohenleutner, S. Baierl, O. Schubert, E. Edwards, D. Bougeard, G. Woltersdorf, and R. Huber, “Extremely nonperturbative nonlinearities in GaAs driven by atomically strong terahertz fields in gold metamaterials,” Phys. Rev. Lett. 113, 227401 (2014).
[Crossref]

Wraback, M.

X. Zhao, K. Fan, J. Zhang, H. R. Seren, G. D. Metcalfe, M. Wraback, R. D. Averitt, and X. Zhang, “Optically tunable metamaterial perfect absorber on highly flexible substrate,” Sens. Actuators A 231, 74–80 (2015).
[Crossref]

H. R. Seren, G. R. Keiser, L. Cao, J. Zhang, A. C. Strikwerda, K. Fan, G. D. Metcalfe, M. Wraback, X. Zhang, and R. D. Averitt, “Optically modulated multiband terahertz perfect absorber,” Adv. Opt. Mater. 2, 1221–1226 (2014).
[Crossref]

Yin, X.

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, 379–383 (2015).
[Crossref]

Zalkovskij, M.

Zhang, G.-F.

J. Zhang, X. Zhao, K. Fan, X. Wang, G.-F. Zhang, K. Geng, X. Zhang, and R. D. Averitt, “Terahertz radiation-induced sub-cycle field electron emission across a split-gap dipole antenna,” Appl. Phys. Lett. 107, 231101 (2015).
[Crossref]

Zhang, J.

J. Zhang, X. Zhao, K. Fan, X. Wang, G.-F. Zhang, K. Geng, X. Zhang, and R. D. Averitt, “Terahertz radiation-induced sub-cycle field electron emission across a split-gap dipole antenna,” Appl. Phys. Lett. 107, 231101 (2015).
[Crossref]

X. Zhao, K. Fan, J. Zhang, H. R. Seren, G. D. Metcalfe, M. Wraback, R. D. Averitt, and X. Zhang, “Optically tunable metamaterial perfect absorber on highly flexible substrate,” Sens. Actuators A 231, 74–80 (2015).
[Crossref]

H. R. Seren, G. R. Keiser, L. Cao, J. Zhang, A. C. Strikwerda, K. Fan, G. D. Metcalfe, M. Wraback, X. Zhang, and R. D. Averitt, “Optically modulated multiband terahertz perfect absorber,” Adv. Opt. Mater. 2, 1221–1226 (2014).
[Crossref]

K. Fan, H. Y. Hwang, M. Liu, A. C. Strikwerda, A. Sternbach, J. Zhang, X. Zhao, X. Zhang, K. A. Nelson, and R. D. Averitt, “Nonlinear terahertz metamaterials via field-enhanced carrier dynamics in GaAs,” Phys. Rev. Lett. 110, 217404 (2013).
[Crossref]

H. R. Seren, J. Zhang, G. R. Keiser, S. J. Maddox, X. Zhao, K. Fan, S. R. Bank, X. Zhang, and R. D. Averitt, “Nonlinear terahertz devices utilizing semiconducting plasmonic metamaterials,” arXiv: 1508.03183 (2015).

Zhang, X.

J. Zhang, X. Zhao, K. Fan, X. Wang, G.-F. Zhang, K. Geng, X. Zhang, and R. D. Averitt, “Terahertz radiation-induced sub-cycle field electron emission across a split-gap dipole antenna,” Appl. Phys. Lett. 107, 231101 (2015).
[Crossref]

X. Zhao, K. Fan, J. Zhang, H. R. Seren, G. D. Metcalfe, M. Wraback, R. D. Averitt, and X. Zhang, “Optically tunable metamaterial perfect absorber on highly flexible substrate,” Sens. Actuators A 231, 74–80 (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, 379–383 (2015).
[Crossref]

H. R. Seren, G. R. Keiser, L. Cao, J. Zhang, A. C. Strikwerda, K. Fan, G. D. Metcalfe, M. Wraback, X. Zhang, and R. D. Averitt, “Optically modulated multiband terahertz perfect absorber,” Adv. Opt. Mater. 2, 1221–1226 (2014).
[Crossref]

K. Fan, H. Y. Hwang, M. Liu, A. C. Strikwerda, A. Sternbach, J. Zhang, X. Zhao, X. Zhang, K. A. Nelson, and R. D. Averitt, “Nonlinear terahertz metamaterials via field-enhanced carrier dynamics in GaAs,” Phys. Rev. Lett. 110, 217404 (2013).
[Crossref]

G. Keiser, K. Fan, X. Zhang, and R. Averitt, “Towards dynamic, tunable, and nonlinear metamaterials via near field interactions: a review,” J. Infrared Millim. Terahertz Waves 34, 709–723 (2013).
[Crossref]

C. A. Werley, K. Fan, A. C. Strikwerda, S. M. Teo, X. Zhang, R. D. Averitt, and K. A. Nelson, “Time-resolved imaging of near-fields in THz antennas and direct quantitative measurement of field enhancements,” Opt. Express 20, 8551–8567 (2012).
[Crossref]

H. R. Seren, J. Zhang, G. R. Keiser, S. J. Maddox, X. Zhao, K. Fan, S. R. Bank, X. Zhang, and R. D. Averitt, “Nonlinear terahertz devices utilizing semiconducting plasmonic metamaterials,” arXiv: 1508.03183 (2015).

Zhao, R.

J. Zhou, D. R. Chowdhury, R. Zhao, A. K. Azad, H.-T. Chen, C. M. Soukoulis, A. J. Taylor, and J. F. O’Hara, “Terahertz chiral metamaterials with giant and dynamically tunable optical activity,” Phys. Rev. B 86, 035448 (2012).
[Crossref]

Zhao, X.

J. Zhang, X. Zhao, K. Fan, X. Wang, G.-F. Zhang, K. Geng, X. Zhang, and R. D. Averitt, “Terahertz radiation-induced sub-cycle field electron emission across a split-gap dipole antenna,” Appl. Phys. Lett. 107, 231101 (2015).
[Crossref]

X. Zhao, K. Fan, J. Zhang, H. R. Seren, G. D. Metcalfe, M. Wraback, R. D. Averitt, and X. Zhang, “Optically tunable metamaterial perfect absorber on highly flexible substrate,” Sens. Actuators A 231, 74–80 (2015).
[Crossref]

K. Fan, H. Y. Hwang, M. Liu, A. C. Strikwerda, A. Sternbach, J. Zhang, X. Zhao, X. Zhang, K. A. Nelson, and R. D. Averitt, “Nonlinear terahertz metamaterials via field-enhanced carrier dynamics in GaAs,” Phys. Rev. Lett. 110, 217404 (2013).
[Crossref]

H. R. Seren, J. Zhang, G. R. Keiser, S. J. Maddox, X. Zhao, K. Fan, S. R. Bank, X. Zhang, and R. D. Averitt, “Nonlinear terahertz devices utilizing semiconducting plasmonic metamaterials,” arXiv: 1508.03183 (2015).

Zheludev, N. I.

N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater. 11, 917–924 (2012).
[Crossref]

Zhou, J.

J. Zhou, D. R. Chowdhury, R. Zhao, A. K. Azad, H.-T. Chen, C. M. Soukoulis, A. J. Taylor, and J. F. O’Hara, “Terahertz chiral metamaterials with giant and dynamically tunable optical activity,” Phys. Rev. B 86, 035448 (2012).
[Crossref]

H.-T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105, 073901 (2010).

Zide, J. M. O.

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006).
[Crossref]

Adv. Mater. (1)

A. P. Slobozhanyuk, M. Lapine, D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, R. C. McPhedran, and P. A. Belov, “Flexible helices for nonlinear metamaterials,” Adv. Mater. 25, 3409–3412 (2013).
[Crossref]

Adv. Opt. Mater. (1)

H. R. Seren, G. R. Keiser, L. Cao, J. Zhang, A. C. Strikwerda, K. Fan, G. D. Metcalfe, M. Wraback, X. Zhang, and R. D. Averitt, “Optically modulated multiband terahertz perfect absorber,” Adv. Opt. Mater. 2, 1221–1226 (2014).
[Crossref]

Appl. Phys. Lett. (5)

L. Huang, D. R. Chowdhury, S. Ramani, M. T. Reiten, S.-N. Luo, A. K. Azad, A. J. Taylor, and H.-T. Chen, “Impact of resonator geometry and its coupling with ground plane on ultrathin metamaterial perfect absorbers,” Appl. Phys. Lett. 101, 101102 (2012).
[Crossref]

K.-H. Lin, C. A. Werley, and K. A. Nelson, “Nonlinear terahertz devices utilizing semiconducting plasmonic metamaterials,” Appl. Phys. Lett. 95, 103304 (2009).
[Crossref]

I. V. Shadrivov, A. B. Kozyrev, D. W. van der Weide, and Y. S. Kivshar, “Tunable transmission and harmonic generation in nonlinear metamaterials,” Appl. Phys. Lett. 93, 161903 (2008).
[Crossref]

A. Minovich, J. Farnell, D. N. Neshev, I. McKerracher, F. Karouta, J. Tian, D. A. Powell, I. V. Shadrivov, H. H. Tan, and C. Jagadish, “Liquid crystal based nonlinear fishnet metamaterials,” Appl. Phys. Lett. 100, 121113 (2012).
[Crossref]

J. Zhang, X. Zhao, K. Fan, X. Wang, G.-F. Zhang, K. Geng, X. Zhang, and R. D. Averitt, “Terahertz radiation-induced sub-cycle field electron emission across a split-gap dipole antenna,” Appl. Phys. Lett. 107, 231101 (2015).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

J. Infrared Millim. Terahertz Waves (1)

G. Keiser, K. Fan, X. Zhang, and R. Averitt, “Towards dynamic, tunable, and nonlinear metamaterials via near field interactions: a review,” J. Infrared Millim. Terahertz Waves 34, 709–723 (2013).
[Crossref]

Nat. Commun. (1)

H. Hirori, K. Shinokita, M. Shirai, S. Tani, Y. Kadoya, and K. Tanaka, “Extraordinary carrier multiplication gated by a picosecond electric field pulse,” Nat. Commun. 2, 594 (2011).
[Crossref]

Nat. Mater. (3)

N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nat. Mater. 11, 917–924 (2012).
[Crossref]

M. Lapine, I. V. Shadrivov, D. A. Powell, and Y. S. Kivshar, “Magnetoelastic metamaterials,” Nat. Mater. 11, 30-33 (2012).
[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, 379–383 (2015).
[Crossref]

Nat. Photonics (1)

M. Seo, H. Park, S. Koo, D. Park, J. Kang, O. Suwal, S. Choi, P. Planken, G. Park, and N. Park, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3, 152–156 (2009).
[Crossref]

Nature (2)

M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, and J. Lu, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487, 345–348 (2012).
[Crossref]

H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444, 597–600 (2006).
[Crossref]

New J. Phys. (1)

A. T. Tarekegne, K. Iwaszczuk, M. Zalkovskij, A. C. Strikwerda, and P. U. Jepsen, “Impact ionization in high resistivity silicon induced by an intense terahertz field enhanced by an antenna array,” New J. Phys. 17, 043002 (2015).
[Crossref]

Opt. Express (4)

Optica (1)

Phys. Rev. B (3)

C. L. Anderson and C. R. Crowell, “Threshold energies for electron-hole pair production by impact ionization in semiconductors,” Phys. Rev. B 5, 2267–2272 (1972).
[Crossref]

W. Kuehn, P. Gaal, K. Reimann, M. Woerner, T. Elsaesser, and R. Hey, “Terahertz-induced interband tunneling of electrons in GaAs,” Phys. Rev. B 82, 075204 (2010).
[Crossref]

J. Zhou, D. R. Chowdhury, R. Zhao, A. K. Azad, H.-T. Chen, C. M. Soukoulis, A. J. Taylor, and J. F. O’Hara, “Terahertz chiral metamaterials with giant and dynamically tunable optical activity,” Phys. Rev. B 86, 035448 (2012).
[Crossref]

Phys. Rev. Lett. (3)

C. Lange, T. Maag, M. Hohenleutner, S. Baierl, O. Schubert, E. Edwards, D. Bougeard, G. Woltersdorf, and R. Huber, “Extremely nonperturbative nonlinearities in GaAs driven by atomically strong terahertz fields in gold metamaterials,” Phys. Rev. Lett. 113, 227401 (2014).
[Crossref]

K. Fan, H. Y. Hwang, M. Liu, A. C. Strikwerda, A. Sternbach, J. Zhang, X. Zhao, X. Zhang, K. A. Nelson, and R. D. Averitt, “Nonlinear terahertz metamaterials via field-enhanced carrier dynamics in GaAs,” Phys. Rev. Lett. 110, 217404 (2013).
[Crossref]

H.-T. Chen, J. Zhou, J. F. O’Hara, F. Chen, A. K. Azad, and A. J. Taylor, “Antireflection coating using metamaterials and identification of its mechanism,” Phys. Rev. Lett. 105, 073901 (2010).

Phys. Stat. Sol. B (1)

H. Bergner, V. Brückner, M. Lenzner, and R. Strobel, “Investigation of the field-dependent carrier mobility in GaAs by picosecond photoconductivity measurements,” Phys. Stat. Sol. B 150, 885–889 (1988).
[Crossref]

Rev. Mod. Phys. (1)

M. Lapine, I. V. Shadrivov, and Y. S. Kivshar, “Colloquium: nonlinear metamaterials,” Rev. Mod. Phys. 86, 1093–1123 (2014).
[Crossref]

Science (1)

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-harmonic generation from magnetic metamaterials,” Science 313, 502–504 (2006).
[Crossref]

Sens. Actuators A (1)

X. Zhao, K. Fan, J. Zhang, H. R. Seren, G. D. Metcalfe, M. Wraback, R. D. Averitt, and X. Zhang, “Optically tunable metamaterial perfect absorber on highly flexible substrate,” Sens. Actuators A 231, 74–80 (2015).
[Crossref]

Sov. Phys. JETP (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

Other (2)

http://www.axt.com/site/index.php?q=node/38 .

H. R. Seren, J. Zhang, G. R. Keiser, S. J. Maddox, X. Zhao, K. Fan, S. R. Bank, X. Zhang, and R. D. Averitt, “Nonlinear terahertz devices utilizing semiconducting plasmonic metamaterials,” arXiv: 1508.03183 (2015).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic of the MPA on the GaAs substrate; (b) simulated transmission (T), reflection (R), and absorption (A) spectra; (c) microscope image of the ESRR array of the MPA (inset: close-up view of a unit cell); (d) simulated time domain field strength of the incident THz pulse ( 10 × ) and the electric field in the middle of the capacitive gap [inset: the 2D map of the electric field enhancement factor ( f E )].

Fig. 2.
Fig. 2.

Simulated time-domain response of (a) the MPA and (b) the reference demonstrates the multi-reflection effect of the GaAs substrate. The second pulse (gray shaded area) is the internal absorption response that is considered in our analysis.

Fig. 3.
Fig. 3.

(a) Measured reflection spectra of the nonlinear MPA under different THz field strengths, (b) calculated nonlinear absorbance spectra, (c) the resonance frequency versus the incident THz peak field, (d) the absorbance at 0.68 THz versus the incident THz peak field.

Fig. 4.
Fig. 4.

(a) Simulated spatial distribution of the field enhancement across the gap at depths of 0.1 and 0.5 μm (inset: the cross section of the MPA), (b) simulated reflection spectra with different carrier densities and mobilities.

Fig. 5.
Fig. 5.

(a) Illustration of the flexible MPA, (b) the fabricated MPA wrapped on a plastic vein [top inset: pristine unit cell; bottom inset: the unit cell damaged by the high field (the white circle highlights the damaged area)], (c) the field enhancement spectra of the flexible and solid MPAs, (d) measured absorbance at different field strengths.

Equations (4)

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A = 1 | t | 2 | r | 2 .
r = ř 12 ť 12 ť 21 e i 2 β 1 + ř 21 e i 2 β ,
r z = e 2 E n 2 m r 1 / 2 18 π 2 E g 1 / 2 exp ( π m r 1 / 2 E g 3 / 2 2 e E n ) ,
ϵ GaAs = ϵ ω p 2 ω ( ω + i γ ) ,

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