Abstract

The behavior of the TE and TM electromagnetic waves in graphene at the interface between two semi-infinite dielectric media is studied. The dramatic influence on the TE waves propagation even at very small changes in the optical contrast between the two dielectric media is predicted. Frequencies of the TE waves are found to lie only in the window determined by the contrast. We consider this effect in connection with the design of graphene-based optical gas sensor. Near the frequency, where the imaginary part of the conductivity of graphene becomes zero, ultrahigh refractive index sensitivity and very low detection limit are revealed. The considered graphene-based optical gas sensor outperforms characteristics of modern volume refractive index sensors by several orders of magnitude.

© 2013 OSA

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2013

V. G.  Kravets, F.  Schedin, R.  Jalil, L.  Britnell, R. V.  Gorbachev, D.  Ansell, B.  Thackray, K. S.  Novoselov, A. K.  Geim, A. V.  Kabashin, A. N.  Grigorenko, “Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection,” Nat. Mater. 12(4), 304–309 (2013).
[CrossRef] [PubMed]

I.  Iorsh, I.  Shadrivov, P.  Belov, Y.  Kivshar, “Tunable hybrid surface waves supported by a graphene layer,” JETP Lett. 97, 287–290 (2013).

A. V.  Gorbach, “Nonlinear graphene plasmonics: amplitude equation for surface plasmons,” Phys. Rev. A 87(1), 013830 (2013).
[CrossRef]

J.  Hodgkinson R. P.  Tatam, “Optical gas sensing: a review,” Meas. Sci. Technol. 24(1), 012004 (2013).
[CrossRef]

2012

J. S.  Gómez-Díaz J.  Perruisseau-Carrier, “Propagation of hybrid transverse magnetic-transverse electric plasmons on magnetically biased graphene sheets,” J. Appl. Phys. 112(12), 124906 (2012).
[CrossRef]

B.  Wang, X.  Zhang, F. J.  García-Vidal, X.  Yuan, J.  Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[CrossRef] [PubMed]

Y.  Zou, P.  Tassin, T.  Koschny, C. M.  Soukoulis, “Interaction between graphene and metamaterials: split rings vs. wire pairs,” Opt. Express 20(11), 12198–12204 (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]

R.  Yan, B.  Sensale-Rodriguez, L.  Liu, D.  Jena, H. G.  Xing, “A new class of electrically tunable metamaterial terahertz modulators,” Opt. Express 20(27), 28664–28671 (2012).
[CrossRef] [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]

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]

T.  Stauber G.  Gomez-Santos, “Plasmons and near-field amplification in double-layer graphene,” Phys. Rev. B 85(7), 075410 (2012).
[CrossRef]

T.  Stauber G.  Gomez-Santos, “Graphene plasmons and retardation: Strong light-matter coupling,” Europhys. Lett. 99(2), 27006 (2012).
[CrossRef]

T.  Stauber G.  Gomez-Santos, “Plasmons in layered structures including graphene,” New J. Phys. 14(10), 105018 (2012).
[CrossRef]

A.  Ferreira, N. M. R.  Peres, A. H.  Castro Neto, “Confined magneto-optical waves in graphene,” Phys. Rev. B 85(20), 205426 (2012).
[CrossRef]

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

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

Q.  Bao K. P.  Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6(5), 3677–3694 (2012).
[CrossRef] [PubMed]

Yu. V.  Bludov, M. I.  Vasilevskiy, N. M. R.  Peres, “Graphene-based polaritonic crystal,” Phys. Rev. B 85(24), 245409 (2012).
[CrossRef]

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

W.  Gao, J.  Shu, C.  Qiu, Q.  Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
[CrossRef] [PubMed]

A.  Ferreira N. M. R.  Peres, “Complete light absorption in graphene-metamaterial corrugated structures,” Phys. Rev. B 86(20), 205401 (2012).
[CrossRef]

A. Yu.  Nikitin, F.  Guinea, F. J.  García-Vidal, L.  Martín-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85, 081405(R) (2012).

A. Yu.  Nikitin, F.  Guinea, L.  Martín-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101(15), 151119 (2012).
[CrossRef]

Z.  Fang, Y.  Wang, Z.  Liu, A.  Schlather, P. M.  Ajayan, F. H. L.  Koppens, P.  Nordlander, N. J.  Halas, “Plasmon-induced doping of graphene,” ACS Nano 6(11), 10222–10228 (2012).
[CrossRef] [PubMed]

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]

J.  Christensen, A.  Manjavacas, S.  Thongrattanasiri, F. H. L.  Koppens, F. J.  de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[CrossRef] [PubMed]

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]

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]

2011

A.  Vakil N.  Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[CrossRef] [PubMed]

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]

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Figures (7)

Fig. 1
Fig. 1

Schematic representation of TM (a) and TE (b) waves in 2D electron system (e.g., graphene layer) depicted by dotted line. (a) The charge density oscillations for TM waves can be represented in terms of electric dipole wave. (b) Self-sustained oscillations of the current in the case of TE waves can be described in terms of magnetic dipole wave where electric field is always directed opposite to the current.

Fig. 2
Fig. 2

The real and imaginary parts of the dynamic conductivity of graphene, in units of σ 0 = e 2 / 4 as a function of frequency Ω= ω / E F at zero and room temperatures. The parameters of graphene are set as E F =1eV , τ=0.5 10 13 s .

Fig. 3
Fig. 3

The possible registration system of graphene-based optical gas sensor (see the text). (a) Graphene is surrounded by media with equal refractive index n 1 = n 2 =1 . (b) After the appearance of the investigated gas refractive index below the graphene layer is increased by n x (i.e. n 1 =1 and n 2 =1+ n x ).

Fig. 4
Fig. 4

The function of refractive index change n x (Ω) (inset: the same near Ω= Ω 0 ) (a), common logarithm of the minimal detection limit as a function of carrier relaxation time (b) and common logarithm of the refractive index sensitivity in units RIU 1 as a function of frequency Ω= ω / E F (c) at zero and room temperatures. The parameters of graphene are set as E F =1eV , τ=0.5 10 13 s (for (a) and (c)).

Fig. 5
Fig. 5

The dispersion of TE (a) and TM (b) waves. (a) For n x =0 (black line), n x = 10 6 RIU (red line), n x = 10 5 RIU (blue line). (b) For n x =0 (black line), n x =0.1RIU (red line), n x =0.2RIU (blue line). The parameters of graphene are set as E F =1eV , τ=0.5 10 13 s .

Fig. 6
Fig. 6

The normalized transverse wave vectors K 1,2z of TE waves in graphene as a function of frequency. (a) Real and imaginary parts of K 1,2z for n x =0 at zero and room temperatures. (b) Real part of K 1,2z (expressing wave confinement) at T=300K for: n x =0 (black (1)), n x =6.6 10 7 RIU (green (2)), n x = 10 5 RIU (red (3)) and n x =3 10 5 RIU (blue (4)). The parameters of graphene are set as E F =1eV , τ=0.5 10 13 s .

Fig. 7
Fig. 7

TE wave decay length in graphene L z (blue lines) at n x = 0 and common logarithm of the refractive index sensitivity S λ [ nm / RIU ] (red lines) as a function of wavelength at T = 0 K (dashed lines) and at T = 300 K (solid lines) for wavelengths near the sensitivity point (a) and for wavelengths near the damping region (b). The parameters of graphene are set as E F = 1 e V , τ = 0.5 10 13 s .

Equations (11)

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ε q 2 ε ( ω/c ) 2 = 2πσ(ω) iω ( TM waves ),
q 2 ε ( ω/c ) 2 = 2πσ(ω)ω i c 2 ( TE waves ),
n 1 2 K x 2 n 1 2 + n 2 2 K x 2 n 2 2 =f ( TM waves ),    
K x 2 n 1 2 + K x 2 n 2 2 =f ( TE waves ),
σ(Ω) σ 0 =Θ( Ω2 )+ i π ( 4 ( Ω+iΓ ) ln| Ω+iΓ+2 Ω+iΓ2 | )
σ(Ω,t) σ 0 = 1 2 + 1 π arctan( Ω2 2t )+ i π ( 8tln( 2cosh( 1 2t ) ) ( Ω+iΓ ) 1 2 ln( ( Ω+iΓ+2 ) 2 ( Ω+iΓ2 ) 2 + ( 2t ) 2 ) )
{ K 1z + K 2z =f, K 1z 2 + n 1 2 = K 2z 2 + n 2 2 .
K 1z = Ref( | f | 2 +( n 2 2 n 1 2 ) ) 2 | f | 2 +i Imf( | f | 2 ( n 2 2 n 1 2 ) ) 2 | f | 2 ,
K 2z = Ref( | f | 2 ( n 2 2 n 1 2 ) ) 2 | f | 2 +i Imf( | f | 2 +( n 2 2 n 1 2 ) ) 2 | f | 2 .
n x (Ω)= 1+ | f(Ω) | 2 1 | f(Ω) | 2 /2 .
Q( Ω )=Ω v F c ( ReF( K 1z )+| F( K 1z ) | 2 +i ImF( K 1z ) 2( ReF( K 1z )+| F( K 1z ) | ) ),

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