Abstract

Transverse-electric (TE) plasmons are a unique and unusual aspect of graphene’s plasmonic response that are predicted to manifest when the sign of imaginary part of conductivity changes to negative near the spectral onset of interband transitions. Although thus far, a feasible platform for the direct experimental detection of TE plasmons at finite temperature is yet to be suggested. Here we analyze the dynamics of Otto-Kretschmann excitation of TE plasmons in graphene. We show that TE plasmons supported by graphene in an Otto configuration unusually exhibit a cutoff thickness between the coupling prism and the graphene layer that forbids their efficient coupling to an incident wave in the case of a single-layer graphene at typical finite temperatures. In contrast, significantly increased coupling in the case of an N-layer graphene insulator stack, owing to an N-fold increase of the effective graphene conductivity as the insulator thickness approaches zero, is predicted to provide a TE plasmon resonance that is easily detectable at room temperature.

© 2014 Optical Society of America

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2013 (10)

G. Pirruccio, L. Martín Moreno, G. Lozano, J. Gómez Rivas, “Coherent and broadband enhanced optical absorption in graphene,” ACS Nano 7(6), 4810–4817 (2013).
[CrossRef] [PubMed]

X. Wang, Z. Cheng, K. Xu, H. K. Tsang, J. B. Xu, “High-responsivity graphene/silicon-heterostructure waveguide photodetectors,” Nat. Photonics 7(11), 888–891 (2013).
[CrossRef]

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[CrossRef]

X. Gan, R. J. Shiue, Y. Gao, I. Meric, T. F. Heinz, K. Shepard, J. Hone, S. Assefa, D. Englund, “Chip-integrated ultrafast graphene photodetector with high responsivity,” Nat. Photonics 7(11), 883–887 (2013).
[CrossRef]

S. Thongrattanasiri, F. J. García de Abajo, “Optical field enhancement by strong plasmon interaction in graphene nanostructures,” Phys. Rev. Lett. 110(18), 187401 (2013).
[CrossRef] [PubMed]

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13(6), 2541–2547 (2013).
[CrossRef] [PubMed]

Yu. V. Bludov, A. Ferreira, N. M. R. Peres, M. I. Vasilevskiy, “A primer on surface plasmon-polaritons in graphene,” Int. J. Mod. Phys. B 27(10), 1341001 (2013).
[CrossRef]

I. H. Baek, K. J. Ahn, B. J. Kang, S. Bae, B. H. Hong, D. I. Yeom, K. Lee, Y. U. Jeong, F. Rotermund, “Terahertz transmission and sheet conductivity of randomly stacked multi-layer graphene,” Appl. Phys. Lett. 102(19), 191109 (2013).
[CrossRef]

M. A. K. Othman, C. Guclu, F. Capolino, “Graphene–dielectric composite metamaterials: evolution from elliptic to hyperbolic wavevector dispersion and the transverse epsilon-near-zero condition,” J. Nanophotonics 7(1), 073089 (2013).
[CrossRef]

O. V. Kotov, M. A. Kol’chenko, Y. E. Lozovik, “Ultrahigh refractive index sensitivity of TE-polarized electromagnetic waves in graphene at the interface between two dielectric media,” Opt. Express 21(11), 13533–13546 (2013).
[CrossRef] [PubMed]

2012 (14)

C. C. Lee, S. Suzuki, W. Xie, T. R. Schibli, “Broadband graphene electro-optic modulators with sub-wavelength thickness,” Opt. Express 20(5), 5264–5269 (2012).
[CrossRef] [PubMed]

R. Alaee, M. Farhat, C. Rockstuhl, F. Lederer, “A perfect absorber made of a graphene micro-ribbon metamaterial,” Opt. Express 20(27), 28017–28024 (2012).
[CrossRef] [PubMed]

C. Cocchi, D. Prezzi, A. Ruini, E. Benassi, M. J. Caldas, S. Corni, E. Molinari, “Optical excitations and field enhancement in short graphene nanoribbons,” J. Phys. Chem. Lett. 3(7), 924–929 (2012).
[CrossRef]

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
[PubMed]

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[PubMed]

M. Liu, X. Yin, X. Zhang, “Double-layer graphene optical modulator,” Nano Lett. 12(3), 1482–1485 (2012).
[CrossRef] [PubMed]

S. J. Koester, M. Li, “High-speed waveguide-coupled graphene-on-graphene optical modulators,” Appl. Phys. Lett. 100(17), 171107 (2012).
[CrossRef]

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[CrossRef] [PubMed]

F. Xing, Z. B. Liu, Z. C. Deng, X. T. Kong, X. Q. Yan, X. D. Chen, Q. Ye, C. P. Zhang, Y. S. Chen, J. G. Tian, “Sensitive real-time monitoring of refractive indexes using a novel graphene-based optical sensor,” Sci Rep 2, 908 (2012).
[CrossRef] [PubMed]

Y. V. Bludov, M. I. Vasilevskiy, N. M. R. Peres, “Tunable graphene-based polarizer,” J. Appl. Phys. 112(8), 084320 (2012).
[CrossRef]

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
[CrossRef] [PubMed]

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85(8), 081405(R) (2012).
[CrossRef]

S. Thongrattanasiri, F. H. L. Koppens, F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012).
[CrossRef] [PubMed]

A. N. Grigorenko, M. Polini, K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[CrossRef]

2011 (8)

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

F. H. L. Koppens, D. E. Chang, F. J. García de Abajo, “Graphene plasmonics: A platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[CrossRef] [PubMed]

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

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[CrossRef]

G. W. Hanson, A. B. Yakovlev, A. Mafi, “Excitation of discrete and continuous spectrum for a surface conductivity model of graphene,” J. Appl. Phys. 110(11), 114305 (2011).
[CrossRef]

M. Jablan, H. Buljan, M. Soljačić, “Transverse electric plasmons in bilayer graphene,” Opt. Express 19(12), 11236–11241 (2011).
[CrossRef] [PubMed]

G. Gómez-Santos, T. Stauber, “Fluorescence quenching in graphene: A fundamental ruler and evidence for transverse plasmons,” Phys. Rev. B 84(16), 165438 (2011).
[CrossRef]

A. Yu. Nikitin, F. Guinea, F. J. Garcia-Vidal, L. Martin-Moreno, “Fields radiated by a nanoemitter in a graphene sheet,” Phys. Rev. B 84(19), 195446 (2011).
[CrossRef]

2010 (2)

Y. W. Song, S. Y. Jang, W. S. Han, M. K. Bae, “Graphene mode-lockers for fiber lasers functioned with evanescent field interaction,” Appl. Phys. Lett. 96(5), 051122 (2010).
[CrossRef]

F. Bonaccorso, Z. Sun, T. Hasan, A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[CrossRef]

2009 (5)

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
[CrossRef] [PubMed]

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).
[CrossRef]

F. Xia, T. Mueller, Y. M. Lin, A. Valdes-Garcia, P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4(12), 839–843 (2009).
[CrossRef] [PubMed]

M. Jablan, H. Buljan, M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[CrossRef]

2008 (5)

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008).
[CrossRef]

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[CrossRef] [PubMed]

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, Y. R. Shen, “Gate-Variable Optical Transitions in Graphene,” Science 320(5873), 206–209 (2008).
[CrossRef] [PubMed]

J. Hass, F. Varchon, J. E. Millán-Otoya, M. Sprinkle, N. Sharma, W. A. de Heer, C. Berger, P. N. First, L. Magaud, E. H. Conrad, “Why multilayer graphene on 4H-SiC(0001[over ]) behaves like a single sheet of graphene,” Phys. Rev. Lett. 100(12), 125504 (2008).
[CrossRef] [PubMed]

L. A. Falkovsky, “Optical properties of graphene,” J. Phys. Conf. Ser. 129, 012004 (2008).
[CrossRef]

2007 (2)

E. H. Hwang, S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75(20), 205418 (2007).
[CrossRef]

S. A. Mikhailov, K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99(1), 016803 (2007).
[CrossRef] [PubMed]

2006 (1)

B. Wunsch, T. Stauber, F. Sols, F. Guinea, “Dynamical polarization of graphene at finite doping,” New J. Phys. 8(12), 318 (2006).
[CrossRef]

2005 (1)

R. Naraoka, K. Kajikawa, “Phase detection of surface plasmon resonance using rotating analyzer method,” Sensor Actuat. Biol. Chem. 107, 952–956 (2005).

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[CrossRef] [PubMed]

1999 (1)

1996 (1)

E. Y. Yeatman, “Resolution and sensitivity in surface plasmon microscopy and sensing,” Biosens. Bioelectron. 11(6-7), 635–649 (1996).
[CrossRef]

1968 (1)

A. Otto, “Excitation of nonradiative surface waves in silver by the method of frustrated total reflection,” Z. Phys. 216(4), 398–410 (1968).
[CrossRef]

Ahn, K. J.

I. H. Baek, K. J. Ahn, B. J. Kang, S. Bae, B. H. Hong, D. I. Yeom, K. Lee, Y. U. Jeong, F. Rotermund, “Terahertz transmission and sheet conductivity of randomly stacked multi-layer graphene,” Appl. Phys. Lett. 102(19), 191109 (2013).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Real (blue) and Imaginary (red) parts of the graphene conductivity in the spectral transition region at Fermi energies EF = 0.1eV (dotted), 0.5eV (dashed), and 1eV (solid), and at temperatures T = 300K (a), and T = 80K (b). The electron mobility is μ = 1 × 104cm2(Vs)−1.

Fig. 2
Fig. 2

(a) Schematic of the Otto excitation structure. A1 and B1 are the electric field amplitudes of the incident and reflected TE (y-polarized) plane waves, θ is the angle of incidence and reflection, d is the thickness of the film between the n1|n2 interface and the graphene layer, and n1 (n2) is the refractive index of the high-index (low-index) medium. (b) Staggered plot of angular reflectance distributions R(θ) at d/λ = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, 30 (curves from bottom-to-top). We note that R(θ = 48.593) ≈Rmax = 0.966, and the actual reflectance is indicated by the green scale bar. The dashed blue line coincides with the cutoff d, dcut/λ ≈7. The graphene conductivity is σ = 0.5σuu. (c) R(θ) for case of TE (solid curves) and TM (dashed curve) incident wave polarization and positive/negative sign of Im(σ); σ = 0.5σu ± u and d/λ = 7. (d) d-dependence of normalized angular deviation of θTE (solid curves) and θmin (dashed curves) from the critical angle θc.

Fig. 3
Fig. 3

(a) d-dependence of TE plasmon internal (qint″; colored curves) and radiative (qrad″; dashed black curve) propagation loss. (b) d-dependence of minimum reflectance Rmin) (solid curves) and RTE) (black dashed curves). Colors in (a,b) indicate conductivities as noted. (c,d) Electric field intensity profile of asymmetric TE plasmons illustrating cutoff behavior: (c) Otto configuration at indicated d. (d) Asymmetric semi-infinite structure at indicated values of na and nb. The dashed line x = 0 marks the position of the graphene layer.

Fig. 4
Fig. 4

(a) d-dependence of minimum reflectance Rmin). (b) Angular reflectance distributions R(θ) corresponding to indicated values of d. Colors in (a,b) indicate conductivities as given in inset of (a). All other parameters are the same as for Fig. 2(b).

Fig. 5
Fig. 5

(a) d-dependent normalized effective index deviation of even (dashed) and odd (dot-dashed) TE plasmon coupled-modes of an Otto system with two single-layer graphenes at indicated values of the inter-layer distance, Δ. The conductivity of each single-layer graphene is σ ~0.5σuu. The solid blue and red curves correspond to a single layer Otto system with the graphene conductivity σ ~2(0.5σuu), and σ ~0.5σuu, respectively. The thick red dashed curve corresponds to the semi-infinite symmetric structure. (b) Angular reflectance distributions R(θ) for an Otto system with an N-layer graphene stack (Δ/λ = 0.001) at respective d = dcut(N) and with σ ~0.5σuu (solid curves; T ~80K) and σ ~0.5σui0.5σu (dashed red curve; T ~300K). Inset: wide-angle comparison of single-layer and 20-layer reflectance distributions over 0 < θ < 90 (deg) with σ ~0.5σuu.

Equations (5)

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σ(ω)=ln[ 2cosh( E F 2 k B T ) ] 2 e 2 k B T π 2 i ω+i/τ + e 2 4 { H( ω/2 )+ 4iω π 0 dx H( x )H( ω/2 ) ω 2 4 x 2 },
H(x)= sinh( x/ k B T ) cosh( E F / k B T )+cosh( x/ k B T ) ,
E 1 ( x )= A 1 exp( i k 1 x )+ B 1 exp( i k 1 x ),x<0; E 2 ( x )= A 2 exp( κ[ xd ] )+ B 2 exp( κ[ xd ] ),0<x<d; E 3 ( x )= A 3 exp( κ[ xd ] )+ B 3 exp( κ[ xd ] ),x>d.
r= κ[ Λcosh( κd )+κsinh( κd ) ]+i k 1 [ κcosh( κd )+Λsinh( κd ) ] κ[ Λcosh( κd )+κsinh( κd ) ]i k 1 [ κcosh( κd )+Λsinh( κd ) ] ,
exp( 2κd )= k 1 +iκ k 1 iκ i2κ+ω μ 0 σ ω μ 0 σ .

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