Abstract

The interest in plasmonic electro-optical modulators with nanoscale footprint and ultrafast low-energy performance has generated a demand for precise multiphysics modeling of the electrical and optical properties of plasmonic nanostructures. We perform combined simulations that account for the interaction of highly confined nearfields with charge accumulation and depletion on the nanoscale. Validation of our numerical model is done by comparison to a recently published reflective meta-absorber. The simulations show excellent agreement to the experimental mid-infrared data. We then use our model to propose electro-optical modulation of the extinction cross-section of a gold dimer nanoantenna at the telecom wavelength of 1550 nm. An ITO gap-loaded nanoantenna structure allows us to achieve a normalized modulation of 45% at 1550 nm, where the gap-load design circumvents resonance pinning of the structure. Resonance pinning limits the performance of simplistic designs such as a uniform coating of the nanoantenna with a sheet of indium tin oxide, which we also present for comparison. This large value is reached by a reduction of the capacitive coupling of the antenna arms, which breaks the necessity of a large volume overlap between the charge distribution and the optical nearfield. A parameter exploration shows a weak reliance on the exact device dimensions, as long as strong coupling inside the antenna gap is ensured. These results open the way for a new method in electro-optical tuning of plasmonic structures and can readily be adapted to plasmonic waveguides, metasurfaces and other electro-optical modulators.

© 2017 Optical Society of America

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References

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2017 (1)

J. Park, J. Kang, S. J. Kim, X. Liu, and M. L. Brongersma, “Dynamic reflection phase and polarization control in metasurfaces,” Nano Lett. 17 (1), 407–413 (2017).
[Crossref]

2016 (4)

Y. Huang, H. Wai, H. Lee, R. Sokhoyan, R. A. Pala, Krishnan Thyagarajan, Seunghoon Han, Din Ping Tsai, and Harry A. Atwater, “Gate-tunable conducting oxide metasurfaces,” Nano Lett. 16 (9), 5319–5325 (2016).
[Crossref] [PubMed]

P. Guo, R. D. Schaller, J. B. Ketterson, and R. P. H. Chang, “Ultrafast switching of tunable infrared plasmons in indium tin oxide nanorod arrays with large absolute amplitude,” Nat. Photonics 10, 267–273 (2016).
[Crossref]

U. Koch, C. Hoessbacher, J. Niegemann, C. Hafner, and J. Leuthold, “Digital plasmonic absorption modulator exploiting epsilon-near-zero in transparent conducting oxides,” IEEE Photon. J. 1 (1), 4800813 (2016).

J. Kim, A. Dutta, G. V. Naik, A. J. Giles, F. J. Bezares, C. T. Ellis, J. G. Tischler, A. M. Mahmoud, H. Caglayan, O. J. Glembocki, A. V. Kildishev, J. D. Caldwell, A. Boltasseva, and N. Engheta, “Role of epsilon-near-zero substrates in the optical response of plasmonic antennas,” Optica 3, 339–346 (2016).
[Crossref]

2015 (6)

J. Kern, R. Kullock, J. Prangsma, M. Emmerling, M. Kamp, and B. Hecht, “Electrically driven optical antennas,” Nat. Photonics 9, 582–586 (2015).
[Crossref]

K. Dopf, C. Moosmann, S. W. Kettlitz, P. M. Schwab, K. Ilin, M. Siegel, U. Lemmer, and H.-J. Eisler, “Coupled T-shaped optical antennas with two resonances localized in a common nanogap,” ACS Photon. 2 (11), 1644–1651 (2015).
[Crossref]

A. Olivieri, C. Chen, S. Hassan, E. Lisicka-Skrzek, R. Niall Tait, and P. Berini, “Plasmonic nanostructured metal-oxide-semiconductor reflection modulators,” Nano Lett. 15 (4), 2304–2311 (2015).
[Crossref] [PubMed]

C. Lin and A. S. Helmy., “Dynamically reconfigurable nanoscale modulators utilizing coupled hybrid plasmonics,” Sci. Rep. 5, 12313 (2015).
[Crossref] [PubMed]

V. E. Babicheva, A. Boltasseva, and A. V. Lavrinenko, “Transparent conducting oxides for electro-optical plasmonic modulators,” Nanophotonics 4 (1), 165–185 (2015).
[Crossref]

J. Park, J. Kang, X. Liu, and M. L. Brongersma, “Electrically tunable epsilon-near-zero (ENZ) metafilm absorbers,” Sci. Rep. 5, 15754 (2015).
[Crossref] [PubMed]

2014 (4)

Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14 (11), 6526–6532 (2014).
[Crossref] [PubMed]

X. Liu, J. Park, J. Kang, H. Yuan, Y. Cui, H. Y. Hwang, and M. L. Brongersma, “Quantification and impact of nonparabolicity of the conduction band of indium tin oxide on its plasmonic properties,” Appl. Phys. 105, 181117 (2014).

H. W. Lee, G. Papadakis, S. P. Burgos, K. Chander, A. Kriesch, R. Pala, U. Peschel, and H. A. Atwater, “Nanoscale conducting oxide PlasMOStor,” Nano Lett. 14 (1), 6463–6468 (2014).
[Crossref] [PubMed]

M. Abb, Y. Wang, C.H. de Groot, and O. L. Muskens, “Hotspot-mediated ultrafast nonlinear control of multifrequency plasmonic nanoantennas,” Nat. Commun. 5, 4869 (2014).
[Crossref] [PubMed]

2013 (1)

Y. Wang, M. Abb, S. A. Boden, J. Aizpurua, C.H. de Groot, and O. L. Muskens, “Ultrafast nonlinear control of progressively loaded, single plasmonic nanoantennas fabricated using helium ion milling,” Nano Lett. 13 (11), 5647–5653 (2013).
[Crossref] [PubMed]

2012 (2)

J. C. Prangsma, J. Kern, A. G. Knapp, S. Grossmann, M. Emmerling, M. Kamp, and B. Hecht, “Electrically connected resonant optical antennas,” Nano Lett. 12, 3915–3919 (2012).
[Crossref] [PubMed]

V. J. Sorger, N. D. Lanzillotti-Kimura, R. M. Ma, and X. Zhang, “Ultra-compact silicon nanophotonic modulator with broadband response,” Nanophotonics 1 (1), 17–22 (2012).
[Crossref]

2011 (1)

2010 (2)

E. Feigenbaum, K. Diest, and H. A. Atwater, “Unity-order index change in transparent conducting oxides at visible frequencies,” Nano Lett. 10 (6), 2111–2116 (2010).
[Crossref] [PubMed]

N. Large, M. Abb, J. Aizpurua, and O. L. Muskens, “Photoconductively loaded plasmonic nanoantenna as building block for ultracompact optical switches,” Nano Lett. 10, 1741–1746 (2010).
[Crossref] [PubMed]

2009 (1)

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: A metal-oxide-si field effect plasmonic modulator,” Nano Lett. 9 (2), 897–902 (2009).
[Crossref] [PubMed]

2007 (3)

R. Kirchain and L. Kimerling, “A roadmap for nanophotonics,” Nat. Photonics 1, 303–305 (2007).
[Crossref]

C. Sire, S. Blonkowski, M. J. Gordon, and T. Baron, “Statistics of electrical breakdown field in HfO2 and SiO2 films from millimeter to nanometer length scales,” Appl. Phys. Lett. 5, 2822420 (2007).

H. A. Mohamed, “The effect of annealing and ZnO dopant on the optoelectronic properties of ITO thin films,” J. Phys. D: ApplṖhys. 404234–4240 (2007).
[Crossref]

2005 (1)

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 10, 1607–1609 (2005).
[Crossref]

2001 (1)

G. D. Wilk, R. M. Wallace, and J. M. Anthony, “High-κ gate dielectrics: Current status and materials properties considerations,” Appl. Phys. 89 (10), 5243–5275 (2001).
[Crossref]

1999 (2)

M. D. Losego, A. Y. Efremenko, C. L. Rhodes, M. G. Cerruti, S. Franzen, and J. Maria, “Conductive oxide thin films: Model systems for understanding and controlling surface plasmon resonance,” Appl. Phys. 106, 024903 (1999).
[Crossref]

J. S. Kim, F. Cacialli, A. Cola, G. Gigli, and R. Cingolani, “Increase of charge carriers density and reduction of Hall mobilities in oxygen-plasma treated indium-tin-oxide anodes,” Appl. Phys. Lett. 75, 19–21 (1999).
[Crossref]

1990 (1)

1982 (1)

G. Frank and H. Köstlin, “Electrical properties and defect model of tin-doped indium oxide layers,” Appl. Phys. A 27 (4), 197–206 (1982).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6 (12), 4370–4379 (1972).
[Crossref]

Abb, M.

M. Abb, Y. Wang, C.H. de Groot, and O. L. Muskens, “Hotspot-mediated ultrafast nonlinear control of multifrequency plasmonic nanoantennas,” Nat. Commun. 5, 4869 (2014).
[Crossref] [PubMed]

Y. Wang, M. Abb, S. A. Boden, J. Aizpurua, C.H. de Groot, and O. L. Muskens, “Ultrafast nonlinear control of progressively loaded, single plasmonic nanoantennas fabricated using helium ion milling,” Nano Lett. 13 (11), 5647–5653 (2013).
[Crossref] [PubMed]

N. Large, M. Abb, J. Aizpurua, and O. L. Muskens, “Photoconductively loaded plasmonic nanoantenna as building block for ultracompact optical switches,” Nano Lett. 10, 1741–1746 (2010).
[Crossref] [PubMed]

Aizpurua, J.

Y. Wang, M. Abb, S. A. Boden, J. Aizpurua, C.H. de Groot, and O. L. Muskens, “Ultrafast nonlinear control of progressively loaded, single plasmonic nanoantennas fabricated using helium ion milling,” Nano Lett. 13 (11), 5647–5653 (2013).
[Crossref] [PubMed]

N. Large, M. Abb, J. Aizpurua, and O. L. Muskens, “Photoconductively loaded plasmonic nanoantenna as building block for ultracompact optical switches,” Nano Lett. 10, 1741–1746 (2010).
[Crossref] [PubMed]

Anthony, J. M.

G. D. Wilk, R. M. Wallace, and J. M. Anthony, “High-κ gate dielectrics: Current status and materials properties considerations,” Appl. Phys. 89 (10), 5243–5275 (2001).
[Crossref]

Atwater, H. A.

H. W. Lee, G. Papadakis, S. P. Burgos, K. Chander, A. Kriesch, R. Pala, U. Peschel, and H. A. Atwater, “Nanoscale conducting oxide PlasMOStor,” Nano Lett. 14 (1), 6463–6468 (2014).
[Crossref] [PubMed]

E. Feigenbaum, K. Diest, and H. A. Atwater, “Unity-order index change in transparent conducting oxides at visible frequencies,” Nano Lett. 10 (6), 2111–2116 (2010).
[Crossref] [PubMed]

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: A metal-oxide-si field effect plasmonic modulator,” Nano Lett. 9 (2), 897–902 (2009).
[Crossref] [PubMed]

Atwater, Harry A.

Y. Huang, H. Wai, H. Lee, R. Sokhoyan, R. A. Pala, Krishnan Thyagarajan, Seunghoon Han, Din Ping Tsai, and Harry A. Atwater, “Gate-tunable conducting oxide metasurfaces,” Nano Lett. 16 (9), 5319–5325 (2016).
[Crossref] [PubMed]

Babicheva, V. E.

V. E. Babicheva, A. Boltasseva, and A. V. Lavrinenko, “Transparent conducting oxides for electro-optical plasmonic modulators,” Nanophotonics 4 (1), 165–185 (2015).
[Crossref]

Baron, T.

C. Sire, S. Blonkowski, M. J. Gordon, and T. Baron, “Statistics of electrical breakdown field in HfO2 and SiO2 films from millimeter to nanometer length scales,” Appl. Phys. Lett. 5, 2822420 (2007).

Berini, P.

A. Olivieri, C. Chen, S. Hassan, E. Lisicka-Skrzek, R. Niall Tait, and P. Berini, “Plasmonic nanostructured metal-oxide-semiconductor reflection modulators,” Nano Lett. 15 (4), 2304–2311 (2015).
[Crossref] [PubMed]

Bezares, F. J.

Blonkowski, S.

C. Sire, S. Blonkowski, M. J. Gordon, and T. Baron, “Statistics of electrical breakdown field in HfO2 and SiO2 films from millimeter to nanometer length scales,” Appl. Phys. Lett. 5, 2822420 (2007).

Boden, S. A.

Y. Wang, M. Abb, S. A. Boden, J. Aizpurua, C.H. de Groot, and O. L. Muskens, “Ultrafast nonlinear control of progressively loaded, single plasmonic nanoantennas fabricated using helium ion milling,” Nano Lett. 13 (11), 5647–5653 (2013).
[Crossref] [PubMed]

Boltasseva, A.

Brongersma, M. L.

J. Park, J. Kang, S. J. Kim, X. Liu, and M. L. Brongersma, “Dynamic reflection phase and polarization control in metasurfaces,” Nano Lett. 17 (1), 407–413 (2017).
[Crossref]

J. Park, J. Kang, X. Liu, and M. L. Brongersma, “Electrically tunable epsilon-near-zero (ENZ) metafilm absorbers,” Sci. Rep. 5, 15754 (2015).
[Crossref] [PubMed]

X. Liu, J. Park, J. Kang, H. Yuan, Y. Cui, H. Y. Hwang, and M. L. Brongersma, “Quantification and impact of nonparabolicity of the conduction band of indium tin oxide on its plasmonic properties,” Appl. Phys. 105, 181117 (2014).

Burgos, S. P.

H. W. Lee, G. Papadakis, S. P. Burgos, K. Chander, A. Kriesch, R. Pala, U. Peschel, and H. A. Atwater, “Nanoscale conducting oxide PlasMOStor,” Nano Lett. 14 (1), 6463–6468 (2014).
[Crossref] [PubMed]

Cacialli, F.

J. S. Kim, F. Cacialli, A. Cola, G. Gigli, and R. Cingolani, “Increase of charge carriers density and reduction of Hall mobilities in oxygen-plasma treated indium-tin-oxide anodes,” Appl. Phys. Lett. 75, 19–21 (1999).
[Crossref]

Caglayan, H.

Caldwell, J. D.

Capasso, F.

Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14 (11), 6526–6532 (2014).
[Crossref] [PubMed]

Cerruti, M. G.

M. D. Losego, A. Y. Efremenko, C. L. Rhodes, M. G. Cerruti, S. Franzen, and J. Maria, “Conductive oxide thin films: Model systems for understanding and controlling surface plasmon resonance,” Appl. Phys. 106, 024903 (1999).
[Crossref]

Chander, K.

H. W. Lee, G. Papadakis, S. P. Burgos, K. Chander, A. Kriesch, R. Pala, U. Peschel, and H. A. Atwater, “Nanoscale conducting oxide PlasMOStor,” Nano Lett. 14 (1), 6463–6468 (2014).
[Crossref] [PubMed]

Chang, R. P. H.

P. Guo, R. D. Schaller, J. B. Ketterson, and R. P. H. Chang, “Ultrafast switching of tunable infrared plasmons in indium tin oxide nanorod arrays with large absolute amplitude,” Nat. Photonics 10, 267–273 (2016).
[Crossref]

Chen, C.

A. Olivieri, C. Chen, S. Hassan, E. Lisicka-Skrzek, R. Niall Tait, and P. Berini, “Plasmonic nanostructured metal-oxide-semiconductor reflection modulators,” Nano Lett. 15 (4), 2304–2311 (2015).
[Crossref] [PubMed]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6 (12), 4370–4379 (1972).
[Crossref]

Cingolani, R.

J. S. Kim, F. Cacialli, A. Cola, G. Gigli, and R. Cingolani, “Increase of charge carriers density and reduction of Hall mobilities in oxygen-plasma treated indium-tin-oxide anodes,” Appl. Phys. Lett. 75, 19–21 (1999).
[Crossref]

Cola, A.

J. S. Kim, F. Cacialli, A. Cola, G. Gigli, and R. Cingolani, “Increase of charge carriers density and reduction of Hall mobilities in oxygen-plasma treated indium-tin-oxide anodes,” Appl. Phys. Lett. 75, 19–21 (1999).
[Crossref]

Cui, Y.

X. Liu, J. Park, J. Kang, H. Yuan, Y. Cui, H. Y. Hwang, and M. L. Brongersma, “Quantification and impact of nonparabolicity of the conduction band of indium tin oxide on its plasmonic properties,” Appl. Phys. 105, 181117 (2014).

de Groot, C.H.

M. Abb, Y. Wang, C.H. de Groot, and O. L. Muskens, “Hotspot-mediated ultrafast nonlinear control of multifrequency plasmonic nanoantennas,” Nat. Commun. 5, 4869 (2014).
[Crossref] [PubMed]

Y. Wang, M. Abb, S. A. Boden, J. Aizpurua, C.H. de Groot, and O. L. Muskens, “Ultrafast nonlinear control of progressively loaded, single plasmonic nanoantennas fabricated using helium ion milling,” Nano Lett. 13 (11), 5647–5653 (2013).
[Crossref] [PubMed]

Diest, K.

E. Feigenbaum, K. Diest, and H. A. Atwater, “Unity-order index change in transparent conducting oxides at visible frequencies,” Nano Lett. 10 (6), 2111–2116 (2010).
[Crossref] [PubMed]

J. A. Dionne, K. Diest, L. A. Sweatlock, and H. A. Atwater, “PlasMOStor: A metal-oxide-si field effect plasmonic modulator,” Nano Lett. 9 (2), 897–902 (2009).
[Crossref] [PubMed]

Dionne, J. A.

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Figures (6)

Fig. 1
Fig. 1

Transition wavelength of ITO as a function of carrier concentration according to Eq. 3.

Fig. 2
Fig. 2

Schematic and nearfield distribution at resonance of the structure by Park et. al [10]. The gold grating consists of infinitely long wires with 600 nm width and 750 nm period. (b) Simulated carrier distribution in a vertical line cut through the ITO using the software Lumerical DEVICE. (c) Induced refractive index change by changing the applied voltage from −5 V to +5 V as a function of wavelength and distance from the ITO-HfO2 interface. At 3000 nm, the refractive index comes near zero close to the interface.

Fig. 3
Fig. 3

Comparison between the measured and simulated reflectance of a reflective meta-absorber. (a) Measured optical reflectance using an FTIR, taken from [10] (under the Creative Commons License 4.0 http://creativecommons.org/licenses/by/4.0/). (b) Simulated reflectance from combined Lumerical DEVICE and FDTD simulations, showing good agreement with the experimental spectra.

Fig. 4
Fig. 4

(a) Schematic representation of a gold dimer antenna whose arms are electrically addressable by thin wires. (b) Cross-sectional view of the gold dimer antenna, coated by 2 nm of HfO2 and 100 nm ITO. (c) Charge distribution inside the ITO upon the application biases from −2 V to +2 V. (d) Optical nearfield distribution of the proposed structure. The field enhancement (FE) is strongest in the gap and at the antenna ends. (e) Simulated extinction spectra of the depicted design, using an antenna with 500 nm arm length. (f) Normalized modulation from −2 V to +2 V by the same structure.

Fig. 5
Fig. 5

(a) Cross-sectional view of the gap-loaded structure, where the substrate is coated by a back contact consisting of 100 nm low-doped ITO and 30 nm of HfO2. The gold dimer antenna serves as top electrode and has a gap load of 50 nm high ITO. The top-view of the structure is the same as in Fig. 4(a). (b) Carrier distribution inside the ITO gap-load as a function of voltage. The accumulated carriers reach 3 × 1021 cm−3. (c) Simulated extinction spectra of the depicted design, for antennas with 210 nm and 160 nm arm lengths. (d) Relative modulation of the same antennas normalized to the unperturbed cross-section spectrum. (e) Transmission and reflection spectra of a periodic structure with 250 nm transverse spacing between the antenna arms. (f) Normalized modulation of the spectra in (e).

Fig. 6
Fig. 6

(a) Normalized modulation spectra as a function of the carrier concentration of the gap load. The spectra show two main peaks, marked A in black and B in red. (b) Influence of the HfO2 thickness on the peak modulation. (c) Influence of the antenna gap width on the modulation strength. (d) The modulation spectra with and without the inclusion of charge modulation in the low-doped ITO back contact.

Equations (3)

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

ε = ε + j ε ε ( ω ) = ε ω p 2 ω 2 + Γ 2 .
ω p 2 = N e 2 m * ε 0 and Γ = e m * μ ,
λ trans = 2 π c 0 ω p × ε .

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