Abstract

We report the development of a light modulator using the Pockels effect of water in a nanometer-thick electric double layer on an electrode surface. The modulator comprises a transparent-oxide electrode on a glass substrate immersed in an aqueous electrolyte solution. When an optical beam is incident such that it is totally reflected at the electrode-water interface, the light is modulated at a specific wavelength with a near-100% modulation depth synchronized with the frequency of the applied AC voltage. This result was reproduced by a calculation that assumes a change in the refractive index of −0.1 in a 2-nm electric double layer and of −0.0031 in a 30-nm space-charge layer formed at the interface between the electrolyte aqueous solution and the transparent electrode. This is the first report of an optical modulator that uses the interfacial Pockels effect of a material that does not allow for the Pockels effect in the bulk. The principle of giant optical modulation is explained by invoking the large Pockels coefficient of interfacial water and a Fabry–Perot-resonance effect in the transparent thin-film electrode.

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

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2018 (3)

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. V. Campenhout, C. Huyghebaert, I. Goykhman, A. K. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

C. Haffner, D. Chelladurai, Y. Fedoryshyn, A. Josten, B. Baeuerle, W. Heni, T. Watanabe, T. Cui, B. Cheng, S. Saha, D. L. Elder, L. R. Dalton, A. Boltasseva, V. M. Shalaev, N. Kinsey, and J. Leuthold, “Low-loss plasmon-assisted electro-optic modulator,” Nature 556(7702), 483–486 (2018).
[Crossref]

S. Yukita, Y. Suzuki, N. Shiokawa, T. Kobayashi, and E. Tokunaga, “Mechanisms of the anomalous Pockels effect in bulk water,” Opt. Rev. 25(2), 205–214 (2018).
[Crossref]

2017 (2)

K. Takagi, S. V. Nair, R. Watanabe, K. Seto, T. Kobayashi, and E. Tokunaga, “Surface Plasmon Polariton Resonance of Gold, Silver, and Copper Studied in the Kretschmann Geometry: Dependence on Wavelength, Angle of Incidence, and Film Thickness,” J. Phys. Soc. Jpn. 86(12), 124721 (2017).
[Crossref]

H. Kanemaru, S. Yukita, H. Namiki, Y. Nosaka, T. Kobayashi, and E. Tokunaga, “Giant Pockels effect of polar organic solvents and water in the electric double layer on a transparent electrode,” RSC Adv. 7(72), 45682–45690 (2017).
[Crossref]

2016 (1)

Y. Suzuki, K. Osawa, S. Yukita, T. Kobayashi, and E. Tokunaga, “Anomalously large electro-optic Pockels effect at the air-water interface with an electric field applied parallel to the interface,” Appl. Phys. Lett. 108(19), 191103 (2016).
[Crossref]

2015 (2)

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic Mach–Zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9(8), 525–528 (2015).
[Crossref]

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

2014 (4)

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. Van Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

R. Burt, G. Birkett, and X. S. Zhao, “A review of molecular modelling of electric double layer capacitors,” Phys. Chem. Chem. Phys. 16(14), 6519–6538 (2014).
[Crossref]

K. Ueno, H. Shimotani, H. Yuan, J. Ye, M. Kawasaki, and Y. Iwasa, “Field-Induced Superconductivity in Electric Double Layer Transistors,” J. Phys. Soc. Jpn. 83(3), 032001 (2014).
[Crossref]

K. Mawatari, Y. Kazoe, H. Shimizu, Y. Pihosh, and T. Kitamori, “Extended-Nanofluidics: Fundamental Technologies, Unique Liquid Properties, and Application in Chemical and Bio Analysis Methods and Devices,” Anal. Chem. 86(9), 4068–4077 (2014).
[Crossref]

2012 (1)

S. Yukita, N. Shiokawa, H. Kanemaru, H. Namiki, T. Kobayashi, and E. Tokunaga, “Deflection switching of a laser beam by the Pockels effect of water,” Appl. Phys. Lett. 100(17), 171108 (2012).
[Crossref]

2011 (1)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

2010 (2)

H. Kanemaru, Y. Nosaka, A. Hirako, K. Ohkawa, T. Kobayashi, and E. Tokunaga, “Electrooptic effect of water in electric double layer at interface of GaN electrode,” Opt. Rev. 17(3), 352–356 (2010).
[Crossref]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent Perfect Absorbers: Time-Reversed Lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[Crossref]

2008 (1)

Y. Nosaka, M. Hirabayashi, T. Kobayashi, and E. Tokunaga, “Gigantic optical Pockels effect in water within the electric double layer at the electrode-solution interface,” Phys. Rev. B 77(24), 241401 (2008).
[Crossref]

2007 (2)

E. Tokunaga, Y. Nosaka, M. Hirabayashi, and T. Kobayashi, “Pockels effect of water in the electric double layer at the interface between water and transparent electrode,” Surf. Sci. 601(3), 735–741 (2007).
[Crossref]

H. Hosono, “Recent progress in transparent oxide semiconductors: Materials and device application,” Thin Solid Films 515(15), 6000–6014 (2007).
[Crossref]

2005 (2)

S. Liu, Q. Pu, L. Gao, C. Korzeniewski, and C. Matzke, “From Nanochannel-Induced Proton Conduction Enhancement to a Nanochannel-Based Fuel Cell,” Nano Lett. 5(7), 1389–1393 (2005).
[Crossref]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref]

1999 (1)

G. E. Brown, V. E. Henrich, W. H. Casey, D. L. Clark, C. Eggleston, A. Felmy, D. W. Goodman, M. Grätzel, G. Maciel, M. I. McCarthy, K. H. Nealson, D. A. Sverjensky, M. F. Toney, and J. M. Zachara, “Metal Oxide Surfaces and Their Interactions with Aqueous Solutions and Microbial Organisms,” Chem. Rev. 99(1), 77–174 (1999).
[Crossref]

1983 (1)

1971 (1)

E. Kretschmann, “Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflachenplasmaschwingungen,” Z. Phys. A: Hadrons Nucl. 241(4), 313–324 (1971).
[Crossref]

Alexander, R. W.

Alloatti, L.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. Van Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

Asanovic, K.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

Asselberghs, I.

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. V. Campenhout, C. Huyghebaert, I. Goykhman, A. K. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

Atabaki, A. H.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

Avizienis, R. R.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

Baeuerle, B.

C. Haffner, D. Chelladurai, Y. Fedoryshyn, A. Josten, B. Baeuerle, W. Heni, T. Watanabe, T. Cui, B. Cheng, S. Saha, D. L. Elder, L. R. Dalton, A. Boltasseva, V. M. Shalaev, N. Kinsey, and J. Leuthold, “Low-loss plasmon-assisted electro-optic modulator,” Nature 556(7702), 483–486 (2018).
[Crossref]

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic Mach–Zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9(8), 525–528 (2015).
[Crossref]

Bell, R. J.

Bell, R. R.

Bell, S. E.

Bhatia, A. B.

M. Born, E. Wolf, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, “Principles of Optics by Max Born,” /core/books/principles-of-optics/D12868B8AE26B83D6D3C2193E94FFC32.

Birkett, G.

R. Burt, G. Birkett, and X. S. Zhao, “A review of molecular modelling of electric double layer capacitors,” Phys. Chem. Chem. Phys. 16(14), 6519–6538 (2014).
[Crossref]

Boltasseva, A.

C. Haffner, D. Chelladurai, Y. Fedoryshyn, A. Josten, B. Baeuerle, W. Heni, T. Watanabe, T. Cui, B. Cheng, S. Saha, D. L. Elder, L. R. Dalton, A. Boltasseva, V. M. Shalaev, N. Kinsey, and J. Leuthold, “Low-loss plasmon-assisted electro-optic modulator,” Nature 556(7702), 483–486 (2018).
[Crossref]

Born, M.

M. Born, E. Wolf, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, “Principles of Optics by Max Born,” /core/books/principles-of-optics/D12868B8AE26B83D6D3C2193E94FFC32.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Elsevier, 2008).

Brown, G. E.

G. E. Brown, V. E. Henrich, W. H. Casey, D. L. Clark, C. Eggleston, A. Felmy, D. W. Goodman, M. Grätzel, G. Maciel, M. I. McCarthy, K. H. Nealson, D. A. Sverjensky, M. F. Toney, and J. M. Zachara, “Metal Oxide Surfaces and Their Interactions with Aqueous Solutions and Microbial Organisms,” Chem. Rev. 99(1), 77–174 (1999).
[Crossref]

Burt, R.

R. Burt, G. Birkett, and X. S. Zhao, “A review of molecular modelling of electric double layer capacitors,” Phys. Chem. Chem. Phys. 16(14), 6519–6538 (2014).
[Crossref]

Campenhout, J. V.

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. V. Campenhout, C. Huyghebaert, I. Goykhman, A. K. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

Cao, H.

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent Perfect Absorbers: Time-Reversed Lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[Crossref]

Casey, W. H.

G. E. Brown, V. E. Henrich, W. H. Casey, D. L. Clark, C. Eggleston, A. Felmy, D. W. Goodman, M. Grätzel, G. Maciel, M. I. McCarthy, K. H. Nealson, D. A. Sverjensky, M. F. Toney, and J. M. Zachara, “Metal Oxide Surfaces and Their Interactions with Aqueous Solutions and Microbial Organisms,” Chem. Rev. 99(1), 77–174 (1999).
[Crossref]

Chelladurai, D.

C. Haffner, D. Chelladurai, Y. Fedoryshyn, A. Josten, B. Baeuerle, W. Heni, T. Watanabe, T. Cui, B. Cheng, S. Saha, D. L. Elder, L. R. Dalton, A. Boltasseva, V. M. Shalaev, N. Kinsey, and J. Leuthold, “Low-loss plasmon-assisted electro-optic modulator,” Nature 556(7702), 483–486 (2018).
[Crossref]

Chen, B.

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. Van Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

Chen, Y.-H.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

Cheng, B.

C. Haffner, D. Chelladurai, Y. Fedoryshyn, A. Josten, B. Baeuerle, W. Heni, T. Watanabe, T. Cui, B. Cheng, S. Saha, D. L. Elder, L. R. Dalton, A. Boltasseva, V. M. Shalaev, N. Kinsey, and J. Leuthold, “Low-loss plasmon-assisted electro-optic modulator,” Nature 556(7702), 483–486 (2018).
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Chong, Y. D.

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K. Takagi, S. V. Nair, R. Watanabe, K. Seto, T. Kobayashi, and E. Tokunaga, “Surface Plasmon Polariton Resonance of Gold, Silver, and Copper Studied in the Kretschmann Geometry: Dependence on Wavelength, Angle of Incidence, and Film Thickness,” J. Phys. Soc. Jpn. 86(12), 124721 (2017).
[Crossref]

Taylor, A. M.

M. Born, E. Wolf, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, “Principles of Optics by Max Born,” /core/books/principles-of-optics/D12868B8AE26B83D6D3C2193E94FFC32.

Tokunaga, E.

S. Yukita, Y. Suzuki, N. Shiokawa, T. Kobayashi, and E. Tokunaga, “Mechanisms of the anomalous Pockels effect in bulk water,” Opt. Rev. 25(2), 205–214 (2018).
[Crossref]

H. Kanemaru, S. Yukita, H. Namiki, Y. Nosaka, T. Kobayashi, and E. Tokunaga, “Giant Pockels effect of polar organic solvents and water in the electric double layer on a transparent electrode,” RSC Adv. 7(72), 45682–45690 (2017).
[Crossref]

K. Takagi, S. V. Nair, R. Watanabe, K. Seto, T. Kobayashi, and E. Tokunaga, “Surface Plasmon Polariton Resonance of Gold, Silver, and Copper Studied in the Kretschmann Geometry: Dependence on Wavelength, Angle of Incidence, and Film Thickness,” J. Phys. Soc. Jpn. 86(12), 124721 (2017).
[Crossref]

Y. Suzuki, K. Osawa, S. Yukita, T. Kobayashi, and E. Tokunaga, “Anomalously large electro-optic Pockels effect at the air-water interface with an electric field applied parallel to the interface,” Appl. Phys. Lett. 108(19), 191103 (2016).
[Crossref]

S. Yukita, N. Shiokawa, H. Kanemaru, H. Namiki, T. Kobayashi, and E. Tokunaga, “Deflection switching of a laser beam by the Pockels effect of water,” Appl. Phys. Lett. 100(17), 171108 (2012).
[Crossref]

H. Kanemaru, Y. Nosaka, A. Hirako, K. Ohkawa, T. Kobayashi, and E. Tokunaga, “Electrooptic effect of water in electric double layer at interface of GaN electrode,” Opt. Rev. 17(3), 352–356 (2010).
[Crossref]

Y. Nosaka, M. Hirabayashi, T. Kobayashi, and E. Tokunaga, “Gigantic optical Pockels effect in water within the electric double layer at the electrode-solution interface,” Phys. Rev. B 77(24), 241401 (2008).
[Crossref]

E. Tokunaga, Y. Nosaka, M. Hirabayashi, and T. Kobayashi, “Pockels effect of water in the electric double layer at the interface between water and transparent electrode,” Surf. Sci. 601(3), 735–741 (2007).
[Crossref]

Toney, M. F.

G. E. Brown, V. E. Henrich, W. H. Casey, D. L. Clark, C. Eggleston, A. Felmy, D. W. Goodman, M. Grätzel, G. Maciel, M. I. McCarthy, K. H. Nealson, D. A. Sverjensky, M. F. Toney, and J. M. Zachara, “Metal Oxide Surfaces and Their Interactions with Aqueous Solutions and Microbial Organisms,” Chem. Rev. 99(1), 77–174 (1999).
[Crossref]

Ueno, K.

K. Ueno, H. Shimotani, H. Yuan, J. Ye, M. Kawasaki, and Y. Iwasa, “Field-Induced Superconductivity in Electric Double Layer Transistors,” J. Phys. Soc. Jpn. 83(3), 032001 (2014).
[Crossref]

Ulin-Avila, E.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

Van Thourhout, D.

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. Van Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

Wade, M. T.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

Wang, F.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

Ward, C. A.

Watanabe, R.

K. Takagi, S. V. Nair, R. Watanabe, K. Seto, T. Kobayashi, and E. Tokunaga, “Surface Plasmon Polariton Resonance of Gold, Silver, and Copper Studied in the Kretschmann Geometry: Dependence on Wavelength, Angle of Incidence, and Film Thickness,” J. Phys. Soc. Jpn. 86(12), 124721 (2017).
[Crossref]

Watanabe, T.

C. Haffner, D. Chelladurai, Y. Fedoryshyn, A. Josten, B. Baeuerle, W. Heni, T. Watanabe, T. Cui, B. Cheng, S. Saha, D. L. Elder, L. R. Dalton, A. Boltasseva, V. M. Shalaev, N. Kinsey, and J. Leuthold, “Low-loss plasmon-assisted electro-optic modulator,” Nature 556(7702), 483–486 (2018).
[Crossref]

Waterman, A. S.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

Wayman, P. A.

M. Born, E. Wolf, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, “Principles of Optics by Max Born,” /core/books/principles-of-optics/D12868B8AE26B83D6D3C2193E94FFC32.

Wilcock, W. L.

M. Born, E. Wolf, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, “Principles of Optics by Max Born,” /core/books/principles-of-optics/D12868B8AE26B83D6D3C2193E94FFC32.

Wolf, E.

M. Born, E. Wolf, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, “Principles of Optics by Max Born,” /core/books/principles-of-optics/D12868B8AE26B83D6D3C2193E94FFC32.

Xu, Q.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref]

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, 1989).

Ye, J.

K. Ueno, H. Shimotani, H. Yuan, J. Ye, M. Kawasaki, and Y. Iwasa, “Field-Induced Superconductivity in Electric Double Layer Transistors,” J. Phys. Soc. Jpn. 83(3), 032001 (2014).
[Crossref]

Yin, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

Yuan, H.

K. Ueno, H. Shimotani, H. Yuan, J. Ye, M. Kawasaki, and Y. Iwasa, “Field-Induced Superconductivity in Electric Double Layer Transistors,” J. Phys. Soc. Jpn. 83(3), 032001 (2014).
[Crossref]

Yukita, S.

S. Yukita, Y. Suzuki, N. Shiokawa, T. Kobayashi, and E. Tokunaga, “Mechanisms of the anomalous Pockels effect in bulk water,” Opt. Rev. 25(2), 205–214 (2018).
[Crossref]

H. Kanemaru, S. Yukita, H. Namiki, Y. Nosaka, T. Kobayashi, and E. Tokunaga, “Giant Pockels effect of polar organic solvents and water in the electric double layer on a transparent electrode,” RSC Adv. 7(72), 45682–45690 (2017).
[Crossref]

Y. Suzuki, K. Osawa, S. Yukita, T. Kobayashi, and E. Tokunaga, “Anomalously large electro-optic Pockels effect at the air-water interface with an electric field applied parallel to the interface,” Appl. Phys. Lett. 108(19), 191103 (2016).
[Crossref]

S. Yukita, N. Shiokawa, H. Kanemaru, H. Namiki, T. Kobayashi, and E. Tokunaga, “Deflection switching of a laser beam by the Pockels effect of water,” Appl. Phys. Lett. 100(17), 171108 (2012).
[Crossref]

Zachara, J. M.

G. E. Brown, V. E. Henrich, W. H. Casey, D. L. Clark, C. Eggleston, A. Felmy, D. W. Goodman, M. Grätzel, G. Maciel, M. I. McCarthy, K. H. Nealson, D. A. Sverjensky, M. F. Toney, and J. M. Zachara, “Metal Oxide Surfaces and Their Interactions with Aqueous Solutions and Microbial Organisms,” Chem. Rev. 99(1), 77–174 (1999).
[Crossref]

Zentgraf, T.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

Zhang, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

Zhao, X. S.

R. Burt, G. Birkett, and X. S. Zhao, “A review of molecular modelling of electric double layer capacitors,” Phys. Chem. Chem. Phys. 16(14), 6519–6538 (2014).
[Crossref]

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Y. Suzuki, K. Osawa, S. Yukita, T. Kobayashi, and E. Tokunaga, “Anomalously large electro-optic Pockels effect at the air-water interface with an electric field applied parallel to the interface,” Appl. Phys. Lett. 108(19), 191103 (2016).
[Crossref]

S. Yukita, N. Shiokawa, H. Kanemaru, H. Namiki, T. Kobayashi, and E. Tokunaga, “Deflection switching of a laser beam by the Pockels effect of water,” Appl. Phys. Lett. 100(17), 171108 (2012).
[Crossref]

Chem. Rev. (1)

G. E. Brown, V. E. Henrich, W. H. Casey, D. L. Clark, C. Eggleston, A. Felmy, D. W. Goodman, M. Grätzel, G. Maciel, M. I. McCarthy, K. H. Nealson, D. A. Sverjensky, M. F. Toney, and J. M. Zachara, “Metal Oxide Surfaces and Their Interactions with Aqueous Solutions and Microbial Organisms,” Chem. Rev. 99(1), 77–174 (1999).
[Crossref]

J. Phys. Soc. Jpn. (2)

K. Ueno, H. Shimotani, H. Yuan, J. Ye, M. Kawasaki, and Y. Iwasa, “Field-Induced Superconductivity in Electric Double Layer Transistors,” J. Phys. Soc. Jpn. 83(3), 032001 (2014).
[Crossref]

K. Takagi, S. V. Nair, R. Watanabe, K. Seto, T. Kobayashi, and E. Tokunaga, “Surface Plasmon Polariton Resonance of Gold, Silver, and Copper Studied in the Kretschmann Geometry: Dependence on Wavelength, Angle of Incidence, and Film Thickness,” J. Phys. Soc. Jpn. 86(12), 124721 (2017).
[Crossref]

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S. Liu, Q. Pu, L. Gao, C. Korzeniewski, and C. Matzke, “From Nanochannel-Induced Proton Conduction Enhancement to a Nanochannel-Based Fuel Cell,” Nano Lett. 5(7), 1389–1393 (2005).
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[Crossref]

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. Van Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
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C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic Mach–Zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9(8), 525–528 (2015).
[Crossref]

Nature (4)

C. Haffner, D. Chelladurai, Y. Fedoryshyn, A. Josten, B. Baeuerle, W. Heni, T. Watanabe, T. Cui, B. Cheng, S. Saha, D. L. Elder, L. R. Dalton, A. Boltasseva, V. M. Shalaev, N. Kinsey, and J. Leuthold, “Low-loss plasmon-assisted electro-optic modulator,” Nature 556(7702), 483–486 (2018).
[Crossref]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref]

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

Opt. Rev. (2)

S. Yukita, Y. Suzuki, N. Shiokawa, T. Kobayashi, and E. Tokunaga, “Mechanisms of the anomalous Pockels effect in bulk water,” Opt. Rev. 25(2), 205–214 (2018).
[Crossref]

H. Kanemaru, Y. Nosaka, A. Hirako, K. Ohkawa, T. Kobayashi, and E. Tokunaga, “Electrooptic effect of water in electric double layer at interface of GaN electrode,” Opt. Rev. 17(3), 352–356 (2010).
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R. Burt, G. Birkett, and X. S. Zhao, “A review of molecular modelling of electric double layer capacitors,” Phys. Chem. Chem. Phys. 16(14), 6519–6538 (2014).
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Y. Nosaka, M. Hirabayashi, T. Kobayashi, and E. Tokunaga, “Gigantic optical Pockels effect in water within the electric double layer at the electrode-solution interface,” Phys. Rev. B 77(24), 241401 (2008).
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Figures (8)

Fig. 1.
Fig. 1. Schematic illustration of the optical configuration of relevant multilayer structure with and without electric field for (a) the conventional normal-incidence method and (b) the proposed total-reflection method. The ITO substrate comprised 330-nm ITO (In2O3 doped with SnO2) thin film on glass substrate (1.1-nm thick soda-lime glass); the TCO substrate was made of soda-lime glass (1.1 mm)/ITO (300 nm)/SnO2 (100 nm). The experimental systems in both panels (a) and (b) are properly modeled by three layers with the electric field off: a semi-infinite glass substrate, bulk ITO, and semi-infinite (bulk) water; and five layers with electric field on: a semi-infinite glass substrate, bulk ITO, SCL in ITO, EDL in water, and semi-infinite (bulk) water. (c) Definition of angle of incidence in experiment: the angle in air between the incident light beam with respect to the surface normal of the transparent conductive substrate in the water cell.
Fig. 2.
Fig. 2. Experimental setup: LDLS: Laser-driven light source (Xe lamp); SQ F50: 30-mm diameter, 50-mm focal-length synthetic quartz plano-convex lens; Pinhole: 40-µm diameter pinhole, Fiber: 1-mm core, 1.25-mm cladding multimode quartz fiber, Sample: aqueous electrolyte solution (NaCl) cell in which transparent conductive oxide and Pt electrodes are positioned as depicted.
Fig. 3.
Fig. 3. (a), (b) Complex refractive index n +  of transparent electrode ITO and change in complex refractive index of SCL in ITO used for calculation (almost the same functions as used for simulating the experimental results in Refs. [11,12,15]).
Fig. 4.
Fig. 4. Spectra of relative difference transmittance and reflectance for 330-nm thick ITO in 0.1-M NaCl aqueous solution. (a) Spectrum of relative difference transmittance obtained by using the conventional method with 0° incidence, 2 V, 20 Hz. (b) Spectra of relative difference reflectance obtained by using the new method with 85° incidence in air, 1–5 V, 223 Hz, S polarization. Calculated spectra for 330-nm thick ITO for (c) 0° incidence and for (d) 87° incidence in glass. For both calculations, $\Delta n ={-} 0.1$ in 2-nm thick EDL and $\Delta n ={-} 0.0031$ at 500 nm in 30-nm thick SCL, which corresponds to the experimental conditions of a peak AC voltage of 2 V at 1 Hz.
Fig. 5.
Fig. 5. Relative difference reflectance for 400-nm thick TCO in 0.1-M NaCl aqueous solution, obtained by using the proposed method. (a) Experimental difference reflectance spectra for 87° incidence in air, with S polarization and peak voltages of 1–4 V at 223 Hz. (b) Calculated difference reflectance spectra for 89° incidence in glass assuming $\Delta n ={-} 0.1$ in 2-nm-thick EDL and $\Delta n ={-} 0.0031$ at 500 nm in 30-nm-thick SCL, which corresponds to the experimental condition of 2 V at 1 Hz.
Fig. 6.
Fig. 6. Reflectance spectra and difference reflectance spectra (a) measured experimentally (87° incidence in air, 30 Hz, 2V) and (b) calculated (plot shows the average of results for 87°, 88°, and 89° incidence in glass) for S (black curves) and P (red curves) polarization in total-reflection configuration. The change in refractive index is the same as in Figs. 4 and 5.
Fig. 7.
Fig. 7. Single-layer model to explain principle of giant optical modulation.
Fig. 8.
Fig. 8. Calculated reflectance and difference reflectance spectra (62°incidence, nearly critical angle, in glass) for S- and P-polarized light in total-reflection configuration. We assume the same change in refractive index as in Figs. 4, 5, and 6.

Equations (26)

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r = r 01 + r 12 e 2 i Φ 1 + r 01 r 12 e 2 i Φ ,
n 0 sin θ 0 = n 1 sin θ 1 = ( n + i κ ) sin θ 1 ,
n 0 sin θ 0 = ( n + i κ ) sin ( x + i y ) = 1 2 { [ κ ( e y e y ) cos x + n ( e y + e y ) sin x ] + i [ κ ( e y + e y ) sin x n ( e y e y ) cos x ] } .
n 0 sin θ 0 = 1 2 [ n 2 + κ 2 n ( e y + e y ) sin x ] n sin x .
k 1 x = ( n + i κ ) k sin θ 1 = n 0 k sin θ 0 ,
k 1 z = ( n + i κ ) k cos θ 1 = ( n + i κ ) k ( 1 sin 2 θ 1 ) 1 / 2 = ( n + i κ ) k [ 1 ( n 0 n + i κ sin θ 0 ) 2 ] 1 / 2 = k [ ( n 2 κ 2 n 0 2 sin 2 θ 0 ) + 2 i n κ ] 1 / 2 k [ ( n 2 n 0 2 sin 2 θ 0 ) + 2 i n κ ] 1 / 2 = k ( n 2 n 0 2 sin 2 θ 0 ) 1 / 2 [ 1 + 2 i n κ ( n 2 n 0 2 sin 2 θ 0 ) ] 1 / 2 k ( n 2 n 0 2 sin 2 θ 0 ) 1 / 2 [ 1 + i n κ ( n 2 n 0 2 sin 2 θ 0 ) ] = k [ ( n 2 n 0 2 sin 2 θ 0 ) 1 / 2 + i n κ ( n 2 n 0 2 sin 2 θ 0 ) 1 / 2 ] k ( n cos x + i κ cos x ) .
r 01 S = n 0 cos θ 0 n 1 cos θ 1 n 0 cos θ 0 + n 1 cos θ 1 , r 01 P = n 1 cos θ 0 n 0 cos θ 1 n 1 cos θ 0 + n 0 cos θ 1 ,
r 12 S = n 1 cos θ 1 n 2 cos θ 2 n 1 cos θ 1 + n 2 cos θ 2 ,     r 12 P = n 2 cos θ 1 n 1 cos θ 2 n 2 cos θ 1 + n 1 cos θ 2 .
l r 01 S = n 0 cos θ 0 n 1 cos θ 1 n 0 cos θ 0 + n 1 cos θ 1 1.52 cos 61.04 2 cos 41.68 1.52 cos 61.04 + 2 cos 41.68 = 0.758 2.23 = 0.340
r 01 P = n 1 cos θ 1 n 0 cos θ 1 n 1 cos θ 0 + n 0 cos θ 1 2 cos 61.04 1.52 cos 41.68 2 cos 61.04 + 1.52 cos 41.68 = 0.167 2.10 = 0.0795
n 0 sin θ 0 = n 1 sin θ 1 1.52 sin 89 2 sin θ 1 θ 1 = 49.5
1 0 r 10S = n 1 cos θ 1 n 0 cos θ 0 n 1 cos θ 1 + n 0 cos θ 0 2 cos 49.5 1.52 cos 89 2 cos 49.5 + 1.52 cos 89 = 1.272 1.325 = 0.960 ,
1 0 r 10P = n 0 cos θ 1 n 1 cos θ 0 n 0 cos θ 1 + n 1 cos θ 0 1.52 cos 49.5 2 cos 89 1.52 cos 49.5 + 2 cos 89 = 0.952 1.022 = 0.932.
r = r 01 + e i ( 2 Φ + Ω X ) 1 + r 01 e i ( 2 Φ + Ω X ) = r 01 + e i ( 2 ( p + i q ) + Ω X ) 1 + r 01 e i ( 2 ( p + i q ) + Ω X ) = r 01 + e i ( 2 p + Ω X ) 2 q 1 + r 01 e i ( 2 p + Ω X ) 2 q
r 01 = e i ( 2 p + Ω X ) 2 q and e i ( 2 p + Ω X ) = 1.
2 p + Ω X = 2 k n d cos x + Ω X = 2 m π m = 0 , 1 , 2
r 01 = e 2 q .
R = | r | 2 = r 01 + e 2 q e i ( 2 p + Ω X ) 1 + r 01 e 2 q e i ( 2 p + Ω X ) r 01 + e 2 q e i ( 2 p + Ω X ) 1 + r 01 e 2 q e i ( 2 p + Ω X ) = r 01 2 + e 4 q + 2 r 01 e 2 q cos ( 2 p + Ω X ) 1 + r 01 2 e 4 q + 2 r 01 e 2 q cos ( 2 p + Ω X ) 4 r 01 2 ( 1 r 01 2 ) 2 ( n 2 + κ 2 ) d 2 Δ k 2 around R = 0 with the coefficient of finesse: F = 4 r 01 2 ( 1 r 01 2 ) 2
r = r 01 + e i Ω X e 2 i Φ 1 + r 01 e i Ω X e 2 i Φ X = P or S ,
tan Ω P 2 = sin 2 θ 1 ( n 2 / n 1 ) 2 ( n 2 / n 1 ) 2 cos θ 1 ,
tan Ω S 2 = sin 2 θ 1 ( n 2 / n 1 ) 2 cos θ 1 ,
Δ Ω P = sin Ω P [ n 2 / n 1 sin 2 θ 1 ( n 2 / n 1 ) 2 + 2 ( n 1 / n 2 ) ] Δ ( n 2 / n 1 ) = 2 cos 2 Ω P 2 Δ ( n 2 / n 1 ) ( n 2 / n 1 ) cos θ 1 [ sin 2 θ 1 ( n 2 / n 1 ) 2 ] 1 / 2 2 ( n 1 / n 2 ) sin Ω P Δ ( n 2 / n 1 )
Δ Ω S = sin Ω S [ n 2 / n 1 sin 2 θ 1 ( n 2 / n 1 ) 2 ] Δ ( n 2 / n 1 ) = 2 cos 2 Ω S 2 Δ ( n 2 / n 1 ) ( n 2 / n 1 ) cos θ 1 [ sin 2 θ 1 ( n 2 / n 1 ) 2 ] 1 / 2 .
cos θ 2 = ( 1 sin 2 θ 2 ) 1 / 2 = ( 1 ( n 1 n 2 ) 2 sin 2 θ 1 ) 1 / 2 = ± i [ ( n 1 n 2 ) 2 sin 2 θ 1 1 ] 1 / 2 .
exp ( i k 2 z z ) = exp ( i k cos θ 2 z ) = exp ( k [ ( n 1 n 2 ) 2 sin 2 θ 1 1 ] 1 / 2 z )
k 2 z 1 = λ 2 π [ ( n 1 n 2 ) 2 sin 2 θ 1 1 ] 1 / 2 .