Abstract

We study theoretically confinement related effects in the optical response of thin plasmonic films of controlled variable thickness. While being constant for relatively thick films, the plasma frequency is shown to acquire spatial dispersion typical of two-dimensional materials such as graphene, gradually shifting to the red with the film thickness reduction. The dissipative loss, while decreasing at any fixed frequency, gradually goes up at the plasma frequency as it shifts to the red with the film thickness reduced. These features offer a controllable way to tune spatial dispersion and related optical properties of plasmonic films and metasurfaces on demand, by precisely controlling their thickness, material composition, and by choosing deposition substrates and coating layers appropriately.

© 2017 Optical Society of America

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    [Crossref]

2017 (2)

D. Shah, H. Reddy, N. Kinsey, V. M. Shalaev, and A. Boltasseva, “Optical properties of plasmonic ultrathin TiN films,” Adv. Optical Mater. 5, 1700065 (2017).
[Crossref]

C. David and J. Christensen, “Extraordinary optical transmission through nonlocal holey metal films,” Appl. Phys. Lett 110, 261110 (2017).
[Crossref]

2016 (3)

K. F. Mak and J. Shan, “Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides,” Nature Phot. 10, 216–226 (2016).
[Crossref]

O. V. Polischuk, V. S. Melnikova, and V. V. Popov, “Giant cross-polarization conversion of terahertz radiation by plasmons in an active graphene metasurface,” Appl. Phys. Lett. 109, 131101 (2016).
[Crossref]

H. Reddy, U. Guler, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Temperature-dependent optical properties of gold thin films,” Opt. Mater. Express 6, 2776–2802 (2016).
[Crossref]

2015 (4)

E. Yoxall, M. Schnell, A. Y. Nikitin, O. Txoperena, A. Woessner, M. B. Lundeberg, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Direct observation of ultraslow hyperbolic polariton propagation with negative phase velocity,” Nature Phot. 9, 674–678 (2015).
[Crossref]

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nature Nanotechn. 10, 682–686 (2015).
[Crossref]

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nature Commun. 6, 6963 (2015).
[Crossref]

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, J. García de Abajo, V. Pruneri, and H. Altug, “Mid-infrared plasmonic biosensing with graphene,” Science 349, 165–168 (2015).
[Crossref] [PubMed]

2014 (6)

A. Manjavacas and F. J. García de Abajo, “Tunable plasmons in atomically thin gold nanodisks,” Nature Commun. 5, 3548 (2014).
[Crossref]

A. Chernikov, T. C. Berkelbach, H. M. Hill, A. Rigosi, Y. Li, O. B. Aslan, D. R. Reichman, M. S. Hybertsen, and T. F. Heinz, “Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2,” Phys. Rev. Lett. 113, 076802 (2014).
[Crossref]

D. N. Basov, M. M. Fogler, A. Lanzara, F. Wang, and Y. Zhang, “Colloquium: Graphene spectroscopy,” Rev. Mod. Phys. 86, 959–994 (2014).
[Crossref]

F. H. L. Koppens, T. Mueller, Ph. Avouris, A. C. Ferrari, M. S. Vitiello, and M. Polini, “Photodetectors based on graphene, other two-dimensional materials and hybrid systems,” Nature Nanotechn. 9, 780–793 (2014).
[Crossref]

C. David and F. J. García de Abajo, “Surface plasmon dependence on the electron density profile at metal surfaces,” ACS Nano 8, 9558–9566 (2014).
[Crossref] [PubMed]

T. Stauber, “Plasmonics in Dirac systems: From graphene to topological insulators,” J. Phys.: Condens. Matter 26123201 (2014).

2013 (5)

T. Stauber, G. Gómez-Santos, and L. Brey, “Spin-charge separation of plasmonic excitations in thin topological insulators,” Phys. Rev. B 88, 205427 (2013).
[Crossref]

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1232009 (2013).
[Crossref] [PubMed]

C. David, N. A. Mortensen, and J. Christensen, “Perfect imaging, epsilon-near zero phenomena and waveguiding in the scope of nonlocal effects,” Sci. Rep. 3, 2526 (2013).
[Crossref] [PubMed]

W. Yan, N. A. Mortensen, and M. Wubs, “Hyperbolic metamaterial lens with hydrodynamic nonlocal response,” Optics Express 21, 15026–15036 (2013).
[Crossref] [PubMed]

S. Raza, T. Christensen, M. Wubs, S. I. Bozhevolnyi, and N. A. Mortensen, “Nonlocal response in thin-film waveguides: Loss versus nonlocality and breaking of complementarity,” Phys. Rev. B 88, 115401 (2013).
[Crossref]

2011 (3)

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic systems due to nonlocal response,” Phys. Rev. B 84, 121412 (2011).
[Crossref]

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: A platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref] [PubMed]

M. W. Knight, H. Sobhani, P. Nordlander, and N. Halas, “Photodetection with active optical antennas,” Science 332, 702–704 (2011).
[Crossref] [PubMed]

2010 (2)

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nature Mater. 9, 205–213 (2010).
[Crossref]

J.-S. Huang, V. Callegari, P. Geisler, C. Brüning, J. Kern, J. C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, U. Sennhauser, and B. Hecht, “Atomically flat single-crystalline gold nanostructures for plasmonic nanocircuitrys,” Nature Commun. 1, 150 (2010).
[Crossref]

2009 (1)

J. Deslippe, M. Dipoppa, D. Prendergast, M. V. O. Moutinho, R. B. Capaz, and S. G. Louie, “Electron-hole interaction in carbon nanotubes: novel screening and exciton excitation spectra,” Nano Lett. 9, 1330–1334 (2009).
[Crossref] [PubMed]

2008 (1)

M. Grzelczak, J. Pérez-Juste, P. Mulvaney, and L. M. Liz-Marzán, “Shape control in gold nanoparticle synthesis,” Chem. Soc. Rev. 37, 1783–1791 (2008).
[Crossref] [PubMed]

2007 (1)

N. Stokes, A. M. McDonagh, and M. B. Cortie, “Preparation of nanoscale gold structures by nanolithography,” Gold Bull. 40/4, 310–320 (2007).
[Crossref]

2004 (1)

D. P. O’Neal, L. R. Hirsch, N. J. Halas, J. D. Payne, and J. L. West, “Photo-thermal tumor ablation in mice using near infrared-absorbing nanoparticles,” Cancer Lett. 209, 171–176 (2004).
[Crossref]

2002 (1)

F. Léonard and J. Tersoff, “Dielectric response of semiconducting carbon nanotubes,” Appl. Phys. Lett. 81, 4835 (2002).
[Crossref]

1979 (1)

L. V. Keldysh, “Coulomb interaction in thin semiconductor and semimetal films,” Pis’ma Zh. Eksp. Teor. Fiz. 29, 716–719 (1979)

1957 (1)

R. H. Ritchie, “Plasma losses by fast electrons in thin films,” Phys. Rev. 106, 874–881 (1957).
[Crossref]

1952 (2)

D. Bohm and D. Pines, “A collective description of electron interactions: II. Collective vs individual particle aspects of the interactions,” Phys. Rev. 85, 338–353 (1952).
[Crossref]

D. Pines and D. Bohm, “A collective description of electron interactions: III. Coulomb interactions in a degenerate electron gas,” Phys. Rev. 92, 609–625 (1952).

1951 (1)

D. Bohm and D. Pines, “A collective description of electron interactions: I. Magnetic interactions,” Phys. Rev. 82, 625–634 (1951).
[Crossref]

Altug, H.

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, J. García de Abajo, V. Pruneri, and H. Altug, “Mid-infrared plasmonic biosensing with graphene,” Science 349, 165–168 (2015).
[Crossref] [PubMed]

Andersen, T.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nature Nanotechn. 10, 682–686 (2015).
[Crossref]

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nature Commun. 6, 6963 (2015).
[Crossref]

Aslan, O. B.

A. Chernikov, T. C. Berkelbach, H. M. Hill, A. Rigosi, Y. Li, O. B. Aslan, D. R. Reichman, M. S. Hybertsen, and T. F. Heinz, “Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2,” Phys. Rev. Lett. 113, 076802 (2014).
[Crossref]

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nature Mater. 9, 205–213 (2010).
[Crossref]

Avouris, Ph.

F. H. L. Koppens, T. Mueller, Ph. Avouris, A. C. Ferrari, M. S. Vitiello, and M. Polini, “Photodetectors based on graphene, other two-dimensional materials and hybrid systems,” Nature Nanotechn. 9, 780–793 (2014).
[Crossref]

Basov, D. N.

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nature Commun. 6, 6963 (2015).
[Crossref]

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nature Nanotechn. 10, 682–686 (2015).
[Crossref]

D. N. Basov, M. M. Fogler, A. Lanzara, F. Wang, and Y. Zhang, “Colloquium: Graphene spectroscopy,” Rev. Mod. Phys. 86, 959–994 (2014).
[Crossref]

Berkelbach, T. C.

A. Chernikov, T. C. Berkelbach, H. M. Hill, A. Rigosi, Y. Li, O. B. Aslan, D. R. Reichman, M. S. Hybertsen, and T. F. Heinz, “Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2,” Phys. Rev. Lett. 113, 076802 (2014).
[Crossref]

Biagioni, P.

J.-S. Huang, V. Callegari, P. Geisler, C. Brüning, J. Kern, J. C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, U. Sennhauser, and B. Hecht, “Atomically flat single-crystalline gold nanostructures for plasmonic nanocircuitrys,” Nature Commun. 1, 150 (2010).
[Crossref]

Bohm, D.

D. Bohm and D. Pines, “A collective description of electron interactions: II. Collective vs individual particle aspects of the interactions,” Phys. Rev. 85, 338–353 (1952).
[Crossref]

D. Pines and D. Bohm, “A collective description of electron interactions: III. Coulomb interactions in a degenerate electron gas,” Phys. Rev. 92, 609–625 (1952).

D. Bohm and D. Pines, “A collective description of electron interactions: I. Magnetic interactions,” Phys. Rev. 82, 625–634 (1951).
[Crossref]

Boltasseva, A.

D. Shah, H. Reddy, N. Kinsey, V. M. Shalaev, and A. Boltasseva, “Optical properties of plasmonic ultrathin TiN films,” Adv. Optical Mater. 5, 1700065 (2017).
[Crossref]

H. Reddy, U. Guler, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Temperature-dependent optical properties of gold thin films,” Opt. Mater. Express 6, 2776–2802 (2016).
[Crossref]

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1232009 (2013).
[Crossref] [PubMed]

Bozhevolnyi, S. I.

S. Raza, T. Christensen, M. Wubs, S. I. Bozhevolnyi, and N. A. Mortensen, “Nonlocal response in thin-film waveguides: Loss versus nonlocality and breaking of complementarity,” Phys. Rev. B 88, 115401 (2013).
[Crossref]

Brey, L.

T. Stauber, G. Gómez-Santos, and L. Brey, “Spin-charge separation of plasmonic excitations in thin topological insulators,” Phys. Rev. B 88, 205427 (2013).
[Crossref]

Brüning, C.

J.-S. Huang, V. Callegari, P. Geisler, C. Brüning, J. Kern, J. C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, U. Sennhauser, and B. Hecht, “Atomically flat single-crystalline gold nanostructures for plasmonic nanocircuitrys,” Nature Commun. 1, 150 (2010).
[Crossref]

Callegari, V.

J.-S. Huang, V. Callegari, P. Geisler, C. Brüning, J. Kern, J. C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, U. Sennhauser, and B. Hecht, “Atomically flat single-crystalline gold nanostructures for plasmonic nanocircuitrys,” Nature Commun. 1, 150 (2010).
[Crossref]

Capaz, R. B.

J. Deslippe, M. Dipoppa, D. Prendergast, M. V. O. Moutinho, R. B. Capaz, and S. G. Louie, “Electron-hole interaction in carbon nanotubes: novel screening and exciton excitation spectra,” Nano Lett. 9, 1330–1334 (2009).
[Crossref] [PubMed]

Casanova, F.

E. Yoxall, M. Schnell, A. Y. Nikitin, O. Txoperena, A. Woessner, M. B. Lundeberg, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Direct observation of ultraslow hyperbolic polariton propagation with negative phase velocity,” Nature Phot. 9, 674–678 (2015).
[Crossref]

Chang, D. E.

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: A platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref] [PubMed]

Chernikov, A.

A. Chernikov, T. C. Berkelbach, H. M. Hill, A. Rigosi, Y. Li, O. B. Aslan, D. R. Reichman, M. S. Hybertsen, and T. F. Heinz, “Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2,” Phys. Rev. Lett. 113, 076802 (2014).
[Crossref]

Christensen, J.

C. David and J. Christensen, “Extraordinary optical transmission through nonlocal holey metal films,” Appl. Phys. Lett 110, 261110 (2017).
[Crossref]

C. David, N. A. Mortensen, and J. Christensen, “Perfect imaging, epsilon-near zero phenomena and waveguiding in the scope of nonlocal effects,” Sci. Rep. 3, 2526 (2013).
[Crossref] [PubMed]

Christensen, T.

S. Raza, T. Christensen, M. Wubs, S. I. Bozhevolnyi, and N. A. Mortensen, “Nonlocal response in thin-film waveguides: Loss versus nonlocality and breaking of complementarity,” Phys. Rev. B 88, 115401 (2013).
[Crossref]

Cortie, M. B.

N. Stokes, A. M. McDonagh, and M. B. Cortie, “Preparation of nanoscale gold structures by nanolithography,” Gold Bull. 40/4, 310–320 (2007).
[Crossref]

Dai, S.

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nature Commun. 6, 6963 (2015).
[Crossref]

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J.-S. Huang, V. Callegari, P. Geisler, C. Brüning, J. Kern, J. C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, U. Sennhauser, and B. Hecht, “Atomically flat single-crystalline gold nanostructures for plasmonic nanocircuitrys,” Nature Commun. 1, 150 (2010).
[Crossref]

Prendergast, D.

J. Deslippe, M. Dipoppa, D. Prendergast, M. V. O. Moutinho, R. B. Capaz, and S. G. Louie, “Electron-hole interaction in carbon nanotubes: novel screening and exciton excitation spectra,” Nano Lett. 9, 1330–1334 (2009).
[Crossref] [PubMed]

Pruneri, V.

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, J. García de Abajo, V. Pruneri, and H. Altug, “Mid-infrared plasmonic biosensing with graphene,” Science 349, 165–168 (2015).
[Crossref] [PubMed]

Raza, S.

S. Raza, T. Christensen, M. Wubs, S. I. Bozhevolnyi, and N. A. Mortensen, “Nonlocal response in thin-film waveguides: Loss versus nonlocality and breaking of complementarity,” Phys. Rev. B 88, 115401 (2013).
[Crossref]

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic systems due to nonlocal response,” Phys. Rev. B 84, 121412 (2011).
[Crossref]

Reddy, H.

D. Shah, H. Reddy, N. Kinsey, V. M. Shalaev, and A. Boltasseva, “Optical properties of plasmonic ultrathin TiN films,” Adv. Optical Mater. 5, 1700065 (2017).
[Crossref]

H. Reddy, U. Guler, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Temperature-dependent optical properties of gold thin films,” Opt. Mater. Express 6, 2776–2802 (2016).
[Crossref]

Reichman, D. R.

A. Chernikov, T. C. Berkelbach, H. M. Hill, A. Rigosi, Y. Li, O. B. Aslan, D. R. Reichman, M. S. Hybertsen, and T. F. Heinz, “Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2,” Phys. Rev. Lett. 113, 076802 (2014).
[Crossref]

Rigosi, A.

A. Chernikov, T. C. Berkelbach, H. M. Hill, A. Rigosi, Y. Li, O. B. Aslan, D. R. Reichman, M. S. Hybertsen, and T. F. Heinz, “Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2,” Phys. Rev. Lett. 113, 076802 (2014).
[Crossref]

Ritchie, R. H.

R. H. Ritchie, “Plasma losses by fast electrons in thin films,” Phys. Rev. 106, 874–881 (1957).
[Crossref]

Rodrigo, D.

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, J. García de Abajo, V. Pruneri, and H. Altug, “Mid-infrared plasmonic biosensing with graphene,” Science 349, 165–168 (2015).
[Crossref] [PubMed]

Schnell, M.

E. Yoxall, M. Schnell, A. Y. Nikitin, O. Txoperena, A. Woessner, M. B. Lundeberg, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Direct observation of ultraslow hyperbolic polariton propagation with negative phase velocity,” Nature Phot. 9, 674–678 (2015).
[Crossref]

Sennhauser, U.

J.-S. Huang, V. Callegari, P. Geisler, C. Brüning, J. Kern, J. C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, U. Sennhauser, and B. Hecht, “Atomically flat single-crystalline gold nanostructures for plasmonic nanocircuitrys,” Nature Commun. 1, 150 (2010).
[Crossref]

Shah, D.

D. Shah, H. Reddy, N. Kinsey, V. M. Shalaev, and A. Boltasseva, “Optical properties of plasmonic ultrathin TiN films,” Adv. Optical Mater. 5, 1700065 (2017).
[Crossref]

Shalaev, V. M.

D. Shah, H. Reddy, N. Kinsey, V. M. Shalaev, and A. Boltasseva, “Optical properties of plasmonic ultrathin TiN films,” Adv. Optical Mater. 5, 1700065 (2017).
[Crossref]

H. Reddy, U. Guler, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Temperature-dependent optical properties of gold thin films,” Opt. Mater. Express 6, 2776–2802 (2016).
[Crossref]

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1232009 (2013).
[Crossref] [PubMed]

Shan, J.

K. F. Mak and J. Shan, “Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides,” Nature Phot. 10, 216–226 (2016).
[Crossref]

Sobhani, H.

M. W. Knight, H. Sobhani, P. Nordlander, and N. Halas, “Photodetection with active optical antennas,” Science 332, 702–704 (2011).
[Crossref] [PubMed]

Stauber, T.

T. Stauber, “Plasmonics in Dirac systems: From graphene to topological insulators,” J. Phys.: Condens. Matter 26123201 (2014).

T. Stauber, G. Gómez-Santos, and L. Brey, “Spin-charge separation of plasmonic excitations in thin topological insulators,” Phys. Rev. B 88, 205427 (2013).
[Crossref]

Stokes, N.

N. Stokes, A. M. McDonagh, and M. B. Cortie, “Preparation of nanoscale gold structures by nanolithography,” Gold Bull. 40/4, 310–320 (2007).
[Crossref]

Taniguchi, T.

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nature Commun. 6, 6963 (2015).
[Crossref]

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nature Nanotechn. 10, 682–686 (2015).
[Crossref]

Tersoff, J.

F. Léonard and J. Tersoff, “Dielectric response of semiconducting carbon nanotubes,” Appl. Phys. Lett. 81, 4835 (2002).
[Crossref]

Thiemens, M.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nature Nanotechn. 10, 682–686 (2015).
[Crossref]

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nature Commun. 6, 6963 (2015).
[Crossref]

Toscano, G.

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic systems due to nonlocal response,” Phys. Rev. B 84, 121412 (2011).
[Crossref]

Txoperena, O.

E. Yoxall, M. Schnell, A. Y. Nikitin, O. Txoperena, A. Woessner, M. B. Lundeberg, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Direct observation of ultraslow hyperbolic polariton propagation with negative phase velocity,” Nature Phot. 9, 674–678 (2015).
[Crossref]

Vitiello, M. S.

F. H. L. Koppens, T. Mueller, Ph. Avouris, A. C. Ferrari, M. S. Vitiello, and M. Polini, “Photodetectors based on graphene, other two-dimensional materials and hybrid systems,” Nature Nanotechn. 9, 780–793 (2014).
[Crossref]

Wagner, M.

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nature Commun. 6, 6963 (2015).
[Crossref]

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nature Nanotechn. 10, 682–686 (2015).
[Crossref]

Wang, F.

D. N. Basov, M. M. Fogler, A. Lanzara, F. Wang, and Y. Zhang, “Colloquium: Graphene spectroscopy,” Rev. Mod. Phys. 86, 959–994 (2014).
[Crossref]

Watanabe, K.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nature Nanotechn. 10, 682–686 (2015).
[Crossref]

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nature Commun. 6, 6963 (2015).
[Crossref]

Weinmann, P.

J.-S. Huang, V. Callegari, P. Geisler, C. Brüning, J. Kern, J. C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, U. Sennhauser, and B. Hecht, “Atomically flat single-crystalline gold nanostructures for plasmonic nanocircuitrys,” Nature Commun. 1, 150 (2010).
[Crossref]

West, J. L.

D. P. O’Neal, L. R. Hirsch, N. J. Halas, J. D. Payne, and J. L. West, “Photo-thermal tumor ablation in mice using near infrared-absorbing nanoparticles,” Cancer Lett. 209, 171–176 (2004).
[Crossref]

Woessner, A.

E. Yoxall, M. Schnell, A. Y. Nikitin, O. Txoperena, A. Woessner, M. B. Lundeberg, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Direct observation of ultraslow hyperbolic polariton propagation with negative phase velocity,” Nature Phot. 9, 674–678 (2015).
[Crossref]

Wu, X.

J.-S. Huang, V. Callegari, P. Geisler, C. Brüning, J. Kern, J. C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, U. Sennhauser, and B. Hecht, “Atomically flat single-crystalline gold nanostructures for plasmonic nanocircuitrys,” Nature Commun. 1, 150 (2010).
[Crossref]

Wubs, M.

W. Yan, N. A. Mortensen, and M. Wubs, “Hyperbolic metamaterial lens with hydrodynamic nonlocal response,” Optics Express 21, 15026–15036 (2013).
[Crossref] [PubMed]

S. Raza, T. Christensen, M. Wubs, S. I. Bozhevolnyi, and N. A. Mortensen, “Nonlocal response in thin-film waveguides: Loss versus nonlocality and breaking of complementarity,” Phys. Rev. B 88, 115401 (2013).
[Crossref]

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic systems due to nonlocal response,” Phys. Rev. B 84, 121412 (2011).
[Crossref]

Yan, W.

W. Yan, N. A. Mortensen, and M. Wubs, “Hyperbolic metamaterial lens with hydrodynamic nonlocal response,” Optics Express 21, 15026–15036 (2013).
[Crossref] [PubMed]

Yoxall, E.

E. Yoxall, M. Schnell, A. Y. Nikitin, O. Txoperena, A. Woessner, M. B. Lundeberg, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Direct observation of ultraslow hyperbolic polariton propagation with negative phase velocity,” Nature Phot. 9, 674–678 (2015).
[Crossref]

Zhang, Y.

D. N. Basov, M. M. Fogler, A. Lanzara, F. Wang, and Y. Zhang, “Colloquium: Graphene spectroscopy,” Rev. Mod. Phys. 86, 959–994 (2014).
[Crossref]

Zhu, S-E.

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nature Nanotechn. 10, 682–686 (2015).
[Crossref]

Ziegler, J.

J.-S. Huang, V. Callegari, P. Geisler, C. Brüning, J. Kern, J. C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, U. Sennhauser, and B. Hecht, “Atomically flat single-crystalline gold nanostructures for plasmonic nanocircuitrys,” Nature Commun. 1, 150 (2010).
[Crossref]

ACS Nano (1)

C. David and F. J. García de Abajo, “Surface plasmon dependence on the electron density profile at metal surfaces,” ACS Nano 8, 9558–9566 (2014).
[Crossref] [PubMed]

Adv. Optical Mater. (1)

D. Shah, H. Reddy, N. Kinsey, V. M. Shalaev, and A. Boltasseva, “Optical properties of plasmonic ultrathin TiN films,” Adv. Optical Mater. 5, 1700065 (2017).
[Crossref]

Appl. Phys. Lett (1)

C. David and J. Christensen, “Extraordinary optical transmission through nonlocal holey metal films,” Appl. Phys. Lett 110, 261110 (2017).
[Crossref]

Appl. Phys. Lett. (2)

O. V. Polischuk, V. S. Melnikova, and V. V. Popov, “Giant cross-polarization conversion of terahertz radiation by plasmons in an active graphene metasurface,” Appl. Phys. Lett. 109, 131101 (2016).
[Crossref]

F. Léonard and J. Tersoff, “Dielectric response of semiconducting carbon nanotubes,” Appl. Phys. Lett. 81, 4835 (2002).
[Crossref]

Cancer Lett. (1)

D. P. O’Neal, L. R. Hirsch, N. J. Halas, J. D. Payne, and J. L. West, “Photo-thermal tumor ablation in mice using near infrared-absorbing nanoparticles,” Cancer Lett. 209, 171–176 (2004).
[Crossref]

Chem. Soc. Rev. (1)

M. Grzelczak, J. Pérez-Juste, P. Mulvaney, and L. M. Liz-Marzán, “Shape control in gold nanoparticle synthesis,” Chem. Soc. Rev. 37, 1783–1791 (2008).
[Crossref] [PubMed]

Gold Bull. (1)

N. Stokes, A. M. McDonagh, and M. B. Cortie, “Preparation of nanoscale gold structures by nanolithography,” Gold Bull. 40/4, 310–320 (2007).
[Crossref]

J. Phys.: Condens. Matter (1)

T. Stauber, “Plasmonics in Dirac systems: From graphene to topological insulators,” J. Phys.: Condens. Matter 26123201 (2014).

Nano Lett. (2)

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: A platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
[Crossref] [PubMed]

J. Deslippe, M. Dipoppa, D. Prendergast, M. V. O. Moutinho, R. B. Capaz, and S. G. Louie, “Electron-hole interaction in carbon nanotubes: novel screening and exciton excitation spectra,” Nano Lett. 9, 1330–1334 (2009).
[Crossref] [PubMed]

Nature Commun. (3)

A. Manjavacas and F. J. García de Abajo, “Tunable plasmons in atomically thin gold nanodisks,” Nature Commun. 5, 3548 (2014).
[Crossref]

J.-S. Huang, V. Callegari, P. Geisler, C. Brüning, J. Kern, J. C. Prangsma, X. Wu, T. Feichtner, J. Ziegler, P. Weinmann, M. Kamp, A. Forchel, P. Biagioni, U. Sennhauser, and B. Hecht, “Atomically flat single-crystalline gold nanostructures for plasmonic nanocircuitrys,” Nature Commun. 1, 150 (2010).
[Crossref]

S. Dai, Q. Ma, T. Andersen, A. S. Mcleod, Z. Fei, M. K. Liu, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material,” Nature Commun. 6, 6963 (2015).
[Crossref]

Nature Mater. (1)

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nature Mater. 9, 205–213 (2010).
[Crossref]

Nature Nanotechn. (2)

F. H. L. Koppens, T. Mueller, Ph. Avouris, A. C. Ferrari, M. S. Vitiello, and M. Polini, “Photodetectors based on graphene, other two-dimensional materials and hybrid systems,” Nature Nanotechn. 9, 780–793 (2014).
[Crossref]

S. Dai, Q. Ma, M. K. Liu, T. Andersen, Z. Fei, M. D. Goldflam, M. Wagner, K. Watanabe, T. Taniguchi, M. Thiemens, F. Keilmann, G. C. A. M. Janssen, S-E. Zhu, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, “Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial,” Nature Nanotechn. 10, 682–686 (2015).
[Crossref]

Nature Phot. (2)

E. Yoxall, M. Schnell, A. Y. Nikitin, O. Txoperena, A. Woessner, M. B. Lundeberg, F. Casanova, L. E. Hueso, F. H. L. Koppens, and R. Hillenbrand, “Direct observation of ultraslow hyperbolic polariton propagation with negative phase velocity,” Nature Phot. 9, 674–678 (2015).
[Crossref]

K. F. Mak and J. Shan, “Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides,” Nature Phot. 10, 216–226 (2016).
[Crossref]

Opt. Mater. Express (1)

Optics Express (1)

W. Yan, N. A. Mortensen, and M. Wubs, “Hyperbolic metamaterial lens with hydrodynamic nonlocal response,” Optics Express 21, 15026–15036 (2013).
[Crossref] [PubMed]

Phys. Rev. (4)

D. Bohm and D. Pines, “A collective description of electron interactions: I. Magnetic interactions,” Phys. Rev. 82, 625–634 (1951).
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D. Pines and D. Bohm, “A collective description of electron interactions: III. Coulomb interactions in a degenerate electron gas,” Phys. Rev. 92, 609–625 (1952).

R. H. Ritchie, “Plasma losses by fast electrons in thin films,” Phys. Rev. 106, 874–881 (1957).
[Crossref]

Phys. Rev. B (3)

S. Raza, G. Toscano, A.-P. Jauho, M. Wubs, and N. A. Mortensen, “Unusual resonances in nanoplasmonic systems due to nonlocal response,” Phys. Rev. B 84, 121412 (2011).
[Crossref]

S. Raza, T. Christensen, M. Wubs, S. I. Bozhevolnyi, and N. A. Mortensen, “Nonlocal response in thin-film waveguides: Loss versus nonlocality and breaking of complementarity,” Phys. Rev. B 88, 115401 (2013).
[Crossref]

T. Stauber, G. Gómez-Santos, and L. Brey, “Spin-charge separation of plasmonic excitations in thin topological insulators,” Phys. Rev. B 88, 205427 (2013).
[Crossref]

Phys. Rev. Lett. (1)

A. Chernikov, T. C. Berkelbach, H. M. Hill, A. Rigosi, Y. Li, O. B. Aslan, D. R. Reichman, M. S. Hybertsen, and T. F. Heinz, “Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2,” Phys. Rev. Lett. 113, 076802 (2014).
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L. V. Keldysh, “Coulomb interaction in thin semiconductor and semimetal films,” Pis’ma Zh. Eksp. Teor. Fiz. 29, 716–719 (1979)

Rev. Mod. Phys. (1)

D. N. Basov, M. M. Fogler, A. Lanzara, F. Wang, and Y. Zhang, “Colloquium: Graphene spectroscopy,” Rev. Mod. Phys. 86, 959–994 (2014).
[Crossref]

Sci. Rep. (1)

C. David, N. A. Mortensen, and J. Christensen, “Perfect imaging, epsilon-near zero phenomena and waveguiding in the scope of nonlocal effects,” Sci. Rep. 3, 2526 (2013).
[Crossref] [PubMed]

Science (3)

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339, 1232009 (2013).
[Crossref] [PubMed]

D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, J. García de Abajo, V. Pruneri, and H. Altug, “Mid-infrared plasmonic biosensing with graphene,” Science 349, 165–168 (2015).
[Crossref] [PubMed]

M. W. Knight, H. Sobhani, P. Nordlander, and N. Halas, “Photodetection with active optical antennas,” Science 332, 702–704 (2011).
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Figures (4)

Fig. 1
Fig. 1

(a,b) Schematic to show the geometry notations and the normalized electrostatic (Keldysh) potential for the Coulomb interaction of the two point charges e and e′ confined in a planar thin film of finite thickness.

Fig. 2
Fig. 2

(a) The ratio ω p / ω p 3 D given by Eq. (11) as a function of the dimensionless variables kd and (ε1 + ε2)/ε. (b) The contour plot of the same ratio as a function of kd obtained by cutting the graph in (a) with parallel vertical planes of constant (ε1 + ε2)/ε. The thick vertical blue arrow shows the direction of the (ε1 + ε2)/ε increase.

Fig. 3
Fig. 3

(a) Real (red) and imaginary (green) parts of Eq. (13) as functions of the dimensionless variables ω p / ω p 3 D and (ε1 + ε2)/εkd. (b) The contour plot one obtains by cutting the graph in (a) with parallel vertical planes of constant (ε1 + ε2)/εkd. The thick horizontal blue arrow shows the direction of the (ε1 + ε2)/εkd increase.

Fig. 4
Fig. 4

Plasmon resonance peak behavior given by −Im[ε/ε(k, ω)] of Eq. (13) as a function of the dimensionless variables ω p / ω p 3 D and (ε1 + ε2)/εkd.

Equations (14)

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

V ( ρ ) = π e e ε d [ H 0 ( ε 1 + ε 2 ε ρ d ) N 0 ( ε 1 + ε 2 ε ρ d ) ] ,
V ( ρ ) V 1 ( ρ ) = 2 e e ε d [ ln ( 2 ε ε 1 + ε 2 d ρ ) C ] ,
V ( ρ ) V 2 ( ρ ) = 2 e e ( ε 1 + ε 2 ) ρ ,
V ( ρ j ) = 4 π e 2 ε L 2 l , k   exp ( i k ρ j l ) k [ k d + ( ε 1 + ε 2 ) / ε ] .
ρ ¨ j = i 4 π e 2 ε m * L 2 l , k k exp ( i k ρ j l ) k [ k d + ( ε 1 + ε 2 ) / ε ] .
n ( ρ ) = l δ ( ρ ρ l ) = k n k exp ( i k ρ )
n k = 1 L 2 l exp ( i k ρ l ) , n k = 0 = N 2 D
n ¨ k = 4 π e 2 ε m * q   ( k q ) n q n k q q [ q d + ( ε 1 + ε 2 ) / ε ] 1 L 2 l ( k ρ ˙ l ) 2 exp ( i k ρ l ) .
n ¨ k + ω p 2 n k = 1 L 2 l ( k ρ ˙ l ) 2 exp ( i k ρ l )
ω p = ω p ( k ) = 4 π e 2 k N 2 D ε m * ( k d + ( ε 1 + ε 2 ) / ε ) .
ω p 3 D = 4 π e 2 N 3 D ε m *
ω p = ω p ( k ) = ω p 3 D 1 + ( ε 1 + ε 2 ) / ε k d .
ω p = ω p 2 D ( k ) = 4 π e 2 N 2 D k ( ε 1 + ε 2 ) m *
ε ( k , ω ) ε = 1 ω p 2 ω ( ω + i γ ) ,