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Controlling polarization-dependent optical absorption of graphene through its thickness
Optik 137 (2017) 59–64
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Original research article
Controlling polarization-dependent optical absorption of graphene through its thickness Liyun Ding a , Chuang Xu a , Zhilin Xia b,∗ , Bing Xu a , Jun Huang a a b
National Engineering Laboratory for Fiber Optic Sensing Technology, Wuhan University of Technology, Wuhan, 430070, China School of Materials Science and Engineering, Wuhan University of Technology, Wuhan, 430070, China
a r t i c l e
i n f o
Article history: Received 23 September 2016 Received in revised form 14 February 2017 Accepted 14 February 2017 Keywords: Graphene Polarization-dependent absorption Polarizer
a b s t r a c t Graphene, a promising material with unique electric and photonic properties, has been reported to show polarization-dependent optical absorption in the visible spectral range. Here, we study further on it and demonstrate that this polarization-dependent optical absorption is highly related with the thickness of graphene, i.e., the number of graphene layers. Numerical simulation result shows the extinction ratio of the three-layer graphene polarizer, which is switchable to be s-polarized pass or p-polarized pass, is remarkably high, indicating a great potential in many applications such as broadband polarizer and optical sensor. © 2017 Elsevier GmbH. All rights reserved.
1. Introduction Graphene, a two-dimensional form of carbon, has unique mechanical, electric, magnetic and thermal properties with a multitude of exciting applications [1–3]. It is a rising star in optics and photonics, and studies on interaction between electromagnetic wave and graphene mainly concentrate on graphene plasmonics, corresponding to the wavelength range from infrared to terahertz [4–8]. Photons in this wavelength domain can be readily coupled to surface plasmons in graphene [9], exciting a surface plasmon polariton (SPP) wave with many appealing properties such as extreme confinement, tunability via electrical gating or chemical doping, and low losses [4]. Unlike noble metals such as Au and Ag, graphene supports a tunable SPP wave, because of its complex dynamic conductivity [10]. That makes graphene an attractive alternative to traditional noble metal as plasmonic material. Bao et al. [11] have demonstrated a graphene TE (s-polarized)-pass polarizer with an extinction ratio up to 27 dB in the telecommunications band, and if graphene’s chemical potential is modulated relatively high (|| > ω/2) by electrical gating or chemical doping, making the interband conductivity imaginary and the intraband contribution dominant, the TE-pass polarizer can be switched to a TM (p-polarized) -pass polarizer. As for researches on graphene in the visible region, optical conductivity of graphene is a universal constant equal to e2 / 2h, from which one can infer that graphene’s optical transmittance is also universal and given by T = (1 + ˛/2)-2 ≈ 1 − ˛ ≈ 97.7%, where ˛ = e2 /(4ε0 c) ≈ 1/137 is the fine structure constant [12], and this result was experimentally confirmed [13]. However, reports on polarization-dependent absorption of graphene in the visible domain are very few. Recently, a research group of Nankai University has demonstrated, theoretically and experimentally, that graphene exhibited strong polarizationdependent optical absorption (for s-polarized wave) under total internal reflection (TIR) in the visible spectral range [14,15].
∗ Corresponding author. E-mail address: [email protected] (Z. Xia). http://dx.doi.org/10.1016/j.ijleo.2017.02.048 0030-4026/© 2017 Elsevier GmbH. All rights reserved.
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L. Ding et al. / Optik 137 (2017) 59–64
Fig. 1. Diagram of the Kretschmann configuration for simulation.
Fig. 2. Principle of the multilayer matrix method.
In this letter, we study the polarization-dependent optical absorption of graphene under TIR in the visible spectral range further, using multilayer matrix method [16,17], and numerically reveal that graphene’s selective absorption of s-polarized wave or p-polarized wave can be controlled through its thickness. We then propose a switchable graphene polarizer and calculate the extinction ratios for different polarization directions (s- and p-polarized) in the visible wavelength domain. 2. Theory We adopted a traditional Kretschmann configuration [18] (Fig. 1), which is generally used in surface plasmon resonance (SPR) measurements, to carry out our numerical simulation process. The three-layer configuration consists of a prism, graphene, and air with refractive index of n1 , nG and n2 , respectively. The matrix method for a multilayer optical system based on boundary conditions for electromagnetic field [19] is used to calculate the reflectance of the incident light with different polarization directions. The principle of the multilayer matrix method is shown in Fig. 2. Suppose that the incident light is s-polarized, then E1 , H1 , E2 , H2 are linked by certain numerical relationship in a matrix form:
E1 H1
=
A
B
C
D
E2 H2
⎡
=⎣
⎤
cos ıG −iG sin ıG
−
i E2 sin ıG G ⎦ , H2 cos ı
(1)
G
where Ek and Hk (k = 1, 2), are the electric and magnetic fields at the kth boundary, respectively, with ıG , G given by: ıG =
2 nG h cos t1
G =
ε0 nG cos t1 0
(2)
(3)
where h, are the thickness of graphene and the wavelength of the incident light in vacuum, respectively and ε0 and 0 are the dielectric constant and permeability of vacuum, respectively. then one can derive the coefficient of reflection: rs =
A1 + B1 2 − C − D2 A1 + B1 2 + C + D2
(4)
L. Ding et al. / Optik 137 (2017) 59–64
61
Fig. 3. Reflectance spectra with N changes in low(a)/high(b) number range.
where
1 =
2 =
ε0 n1 cos i1 0
(5)
ε0 n2 cos t2 0
(6)
finally, we get the reflectance: Rs = |rs |2
(7)
As for p-polarized light, we can also get the reflectance by replacing the transfer matrix and parameters with
A
B
C
D
1 =
⎡
=⎣
cos ıG −
−iG sin ıG
i sin ıG G
⎤ ⎦
0 cos i1 /n1 , G = ε0
0 cos t1 /nG , 2 = ε0
and Rp = |rp |2 where rp =
D 1 D1
(8)
cos ıG
0 cos t2 /n2 , ε0
(9) (10)
+ C1 2 + C1 2
− B + B
− A2 + A2
.
(11)
3. Results and discussions The structure parameters of the three-layer configuration are set as follows: n1 = 1.5, nG = 3 + i**5.446(m−1 )/3 [20], n2 = 1, =600 m, and the thickness of graphene, h = N × 0.34 nm, where 0.34 nm is the thickness of a single layer of graphene and N is the number of graphene layers, from 0 to 150. The reflectance spectra with N changes in low/high number range are shown in Fig. 3(a) and (b), respectively. When N = 0, i.e., there is no graphene layer between prism and air, the reflectance
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L. Ding et al. / Optik 137 (2017) 59–64
Fig. 4. Extinction ratio of the graphene polarizer with different graphene layers number around 35(a)/123(b).
curves of p-polarized wave and s-polarized wave are typical examples of TIR, that the reflectance, Rp and Rs are both equal to 1 as the incident angle is greater than the critical angle. However, as N increases, Rs becomes smaller than Rp under TIR. Since the absorbance of graphene is given by 1-R-T, where T, the transmittance is 0 under TIR, graphene has greater absorption for s-polarized wave than for p-polarized wave. What’s more, it’s possible for Rs to approach zero as long as the incident angle is around 57.76◦ and N is around 35, while Rp still holds a relatively high value. In contrast, if N becomes much larger (larger than 53 at least according to our simulation), then Rp curves lies below Rs curves at the large incident angle region, indicating that graphene has greater absorption for p-polarized wave than for s-polarized wave. Similarly, if N is around 123, Rp can approach zero at the incident angle around 78.5◦ , while Rs still holds a relatively high value, and this switchable absorption for p- and s-polarized wave of graphene makes it possible to design a polarizer based on this three-layer configuration to selectively let s- or p-polarized wave pass. Although the configuration we adopted is generally used for SPR, the polarization-dependent optical absorption of graphene is not based on SPR, because according to the refractive index of graphene, the real part of its relative dielectric constant is positive, which doesn’t satisfy the prerequisite of SPR, e.g. εr εm < 0, where εr , εm are the relative dielectric constants of materials on whose boundary SPR happens. We think the optical absorption of graphene can be attributed to the light energy loss in graphene due to its imaginary part of refractive index. To evaluate the potential extinction ability of the graphene polarizer based on this three-layer configuration, we calculated extinction ratios for different layers of graphene. Fig. 4(a) and (b) depicts the extinction ratios of the graphene polarizer with different graphene layers number around 35 and 123, respectively. Obviously, graphene of 35 layers shows the most intense absorption for s-polarized wave at 57.75◦ , with an extinction ratio (−10 × lg(Rs /Rp )) of 37.48 dB, and graphene of 123 layers shows the most intense absorption for p-polarized wave at 78.51◦ , with an extinction ratio (−10 × lg(Rp /Rs )) of 47.06 dB. That is to say, we can get highly polarized light of either polarization direction(s-polarized or p-polarized) just by changing the number of graphene layers and the incident angle, which provides a new approach besides chemical doping and electrical gating, to fabricate a switchable graphene polarizer. In addition, we investigated the polarization-dependent optical absorption of this configuration in a broadband wavelength range from 450 nm to 750 nm, in which the refractive index of graphene extracted from [20] is valid. To realize a total absorption of s- or p-polarized wave of different wavelength, appropriate number of graphene layers(N) and incident angle() are necessary, as shown in Fig. 5(a) and (b). As the wavelength of incident light increases, the number of graphene layers(N) should increase and the incident angle() should decrease appropriately to gain total absorption, or high extinc-
L. Ding et al. / Optik 137 (2017) 59–64
63
Fig. 5. N and for incident light from 450 nm to 750 nm to totally absorb s- (a) and p-polarized wave (b).
Fig. 6. Extinction ratio at different wavelength in s- and p-polarized pass situation.
tion ratio of either s- or p-polarized wave. Both N and show good linear relationships with the wavelength of incident light, so it’s easy to determine the proper N and for a certain wavelength. The extinction ratios of the graphene polarizer at different wavelength in s- and p-polarized pass situation are shown in Fig. 6. With small graphene layer numbers, the graphene polarizer absorbs the s-polarized wave and let p-polarized wave pass, so it is “p-polarized pass” and vice versa. All of the extinction ratios are higher than 36 dB, which means excellent polarization performance of the graphene polarizer. The change of the extinction ratios at different wavelength seems not regular, because the number of graphene layers are not continuous but integers, so the most appropriate thickness to gain the largest extinction ratio may be missed. 4. Conclusions In summary, we studied the polarization-dependent optical absorption property of graphene in visible wavelength domain further by the multilayer matrix method. Numerical simulation reveals that under TIR, graphene polarizer of the three-layer Kretschmann configuration theoretically shows extraordinary extinction ratio in a broadband wavelength range
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L. Ding et al. / Optik 137 (2017) 59–64
from 450 nm to 750 nm, indicating that graphene layers can totally absorb s- or p-polarized wave of visible light, as long as the number of graphene layers and the incident angle are set appropriately, and the exact numbers of them are easy to determine. It provides a new way, besides chemical doping and electrical gating, to modulate the absorption selectivity of graphene for s-or p-polarized wave, thus transforming unpolarized incident light into polarized light. Acknowledgment This work was supported by the National Natural Science Foundation of China (Grant No. 61575150 and No. 61377092). References [1] A.K. Geim, Graphene: status and prospects, Science 324 (2009) 1530–1534. [2] Z. Yanwu, M. Shanthi, C. Weiwei, L. Xuesong, S.J. Won, J.R. Potts, R.S. Ruoff, Graphene and graphene oxide: synthesis, properties, and applications, Adv. Mater. 22 (2010) 5226. [3] A.K. Geim, K.S. Novoselov, The rise of graphene, Nat. Mater. 6 (2007) 183–191. [4] F.H. Koppens, D.E. Chang, F.J. Garcia de Abajo, Graphene plasmonics: a platform for strong light-matter interactions, Nano Lett. 11 (2011) 3370–3377. [5] 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 (2011) 630–634. [6] A.N. Grigorenko, M. Polini, K.S. Novoselov, Graphene plasmonics, Nat. Photonics 6 (2012) 749–758. [7] T. Low, P. Avouris, Graphene plasmonics for terahertz to mid-infrared applications, ACS Nano 8 (2014) 1086–1101. [8] 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 (2012) 330–334. [9] Q. Bao, K.P. Loh, Graphene photonics, plasmonics, and broadband optoelectronic devices, ACS Nano 6 (2012) 3677–3694. [10] A. Vakil, N. Engheta, Transformation optics using graphene, Science 332 (2011) 1291–1294. [11] 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 (2011) 411–415. [12] N.M.R. Peres, The electronic properties of graphene and its bilayer, Vacuum 83 (2009) 1248–1252. [13] R.R. Nair, P. Blake, A.N. Grigorenko, K.S. Novoselov, T.J. Booth, T. Stauber, N.M. Peres, A.K. Geim, Fine structure constant defines visual transparency of graphene, Science 320 (2008) 1308. [14] Q. Ye, J. Wang, Z. Liu, Z.-C. Deng, X.-T. Kong, F. Xing, X.-D. Chen, W.-Y. Zhou, C.-P. Zhang, J.-G. Tian, Polarization-dependent optical absorption of graphene under total internal reflection, Appl. Phys. Lett. 102 (2013) 021912. [15] P. Wang, Z.-B. Liu, X.-D. Chen, F. Xing, W.-S. Jiang, B. Dong, W. Xin, J.-G. Tian, Accurate layers determination of graphene on transparent substrate based on polarization-sensitive absorption effect, Appl. Phys. Lett. 103 (2013) 181902. [16] A.K. Sharma, B.D. Gupta, On the performance of different bimetallic combinations in surface plasmon resonance based fiber optic sensors, J. Appl. Phys. 101 (2007) 093111. [17] H. Moayyed, I.T. Leite, L. Coelho, J.L. Santos, D. Viegas, Analysis of phase interrogated SPR fiber optic sensors with bimetallic layers, IEEE Sens. J. 14 (2014) 3662–3668. [18] E. Kretschmann, H. Raether, Notizen: radiative decay of non radiative surface plasmons excited by light, Zeitschrift für Naturforschung A (1968) 2135. [19] P. Yeh, M. Hendry, Optical Waves in Layered Media, Elsevier, 1987. [20] M. Bruna, S. Borini, Optical constants of graphene layers in the visible range, Appl. Phys. Lett. 94 (2009) 031901.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Original research article
Controlling polarization-dependent optical absorption of graphene through its thickness Liyun Ding a , Chuang Xu a , Zhilin Xia b,∗ , Bing Xu a , Jun Huang a a b
National Engineering Laboratory for Fiber Optic Sensing Technology, Wuhan University of Technology, Wuhan, 430070, China School of Materials Science and Engineering, Wuhan University of Technology, Wuhan, 430070, China
a r t i c l e
i n f o
Article history: Received 23 September 2016 Received in revised form 14 February 2017 Accepted 14 February 2017 Keywords: Graphene Polarization-dependent absorption Polarizer
a b s t r a c t Graphene, a promising material with unique electric and photonic properties, has been reported to show polarization-dependent optical absorption in the visible spectral range. Here, we study further on it and demonstrate that this polarization-dependent optical absorption is highly related with the thickness of graphene, i.e., the number of graphene layers. Numerical simulation result shows the extinction ratio of the three-layer graphene polarizer, which is switchable to be s-polarized pass or p-polarized pass, is remarkably high, indicating a great potential in many applications such as broadband polarizer and optical sensor. © 2017 Elsevier GmbH. All rights reserved.
1. Introduction Graphene, a two-dimensional form of carbon, has unique mechanical, electric, magnetic and thermal properties with a multitude of exciting applications [1–3]. It is a rising star in optics and photonics, and studies on interaction between electromagnetic wave and graphene mainly concentrate on graphene plasmonics, corresponding to the wavelength range from infrared to terahertz [4–8]. Photons in this wavelength domain can be readily coupled to surface plasmons in graphene [9], exciting a surface plasmon polariton (SPP) wave with many appealing properties such as extreme confinement, tunability via electrical gating or chemical doping, and low losses [4]. Unlike noble metals such as Au and Ag, graphene supports a tunable SPP wave, because of its complex dynamic conductivity [10]. That makes graphene an attractive alternative to traditional noble metal as plasmonic material. Bao et al. [11] have demonstrated a graphene TE (s-polarized)-pass polarizer with an extinction ratio up to 27 dB in the telecommunications band, and if graphene’s chemical potential is modulated relatively high (|| > ω/2) by electrical gating or chemical doping, making the interband conductivity imaginary and the intraband contribution dominant, the TE-pass polarizer can be switched to a TM (p-polarized) -pass polarizer. As for researches on graphene in the visible region, optical conductivity of graphene is a universal constant equal to e2 / 2h, from which one can infer that graphene’s optical transmittance is also universal and given by T = (1 + ˛/2)-2 ≈ 1 − ˛ ≈ 97.7%, where ˛ = e2 /(4ε0 c) ≈ 1/137 is the fine structure constant [12], and this result was experimentally confirmed [13]. However, reports on polarization-dependent absorption of graphene in the visible domain are very few. Recently, a research group of Nankai University has demonstrated, theoretically and experimentally, that graphene exhibited strong polarizationdependent optical absorption (for s-polarized wave) under total internal reflection (TIR) in the visible spectral range [14,15].
∗ Corresponding author. E-mail address: [email protected] (Z. Xia). http://dx.doi.org/10.1016/j.ijleo.2017.02.048 0030-4026/© 2017 Elsevier GmbH. All rights reserved.
60
L. Ding et al. / Optik 137 (2017) 59–64
Fig. 1. Diagram of the Kretschmann configuration for simulation.
Fig. 2. Principle of the multilayer matrix method.
In this letter, we study the polarization-dependent optical absorption of graphene under TIR in the visible spectral range further, using multilayer matrix method [16,17], and numerically reveal that graphene’s selective absorption of s-polarized wave or p-polarized wave can be controlled through its thickness. We then propose a switchable graphene polarizer and calculate the extinction ratios for different polarization directions (s- and p-polarized) in the visible wavelength domain. 2. Theory We adopted a traditional Kretschmann configuration [18] (Fig. 1), which is generally used in surface plasmon resonance (SPR) measurements, to carry out our numerical simulation process. The three-layer configuration consists of a prism, graphene, and air with refractive index of n1 , nG and n2 , respectively. The matrix method for a multilayer optical system based on boundary conditions for electromagnetic field [19] is used to calculate the reflectance of the incident light with different polarization directions. The principle of the multilayer matrix method is shown in Fig. 2. Suppose that the incident light is s-polarized, then E1 , H1 , E2 , H2 are linked by certain numerical relationship in a matrix form:
E1 H1
=
A
B
C
D
E2 H2
⎡
=⎣
⎤
cos ıG −iG sin ıG
−
i E2 sin ıG G ⎦ , H2 cos ı
(1)
G
where Ek and Hk (k = 1, 2), are the electric and magnetic fields at the kth boundary, respectively, with ıG , G given by: ıG =
2 nG h cos t1
G =
ε0 nG cos t1 0
(2)
(3)
where h, are the thickness of graphene and the wavelength of the incident light in vacuum, respectively and ε0 and 0 are the dielectric constant and permeability of vacuum, respectively. then one can derive the coefficient of reflection: rs =
A1 + B1 2 − C − D2 A1 + B1 2 + C + D2
(4)
L. Ding et al. / Optik 137 (2017) 59–64
61
Fig. 3. Reflectance spectra with N changes in low(a)/high(b) number range.
where
1 =
2 =
ε0 n1 cos i1 0
(5)
ε0 n2 cos t2 0
(6)
finally, we get the reflectance: Rs = |rs |2
(7)
As for p-polarized light, we can also get the reflectance by replacing the transfer matrix and parameters with
A
B
C
D
1 =
⎡
=⎣
cos ıG −
−iG sin ıG
i sin ıG G
⎤ ⎦
0 cos i1 /n1 , G = ε0
0 cos t1 /nG , 2 = ε0
and Rp = |rp |2 where rp =
D 1 D1
(8)
cos ıG
0 cos t2 /n2 , ε0
(9) (10)
+ C1 2 + C1 2
− B + B
− A2 + A2
.
(11)
3. Results and discussions The structure parameters of the three-layer configuration are set as follows: n1 = 1.5, nG = 3 + i**5.446(m−1 )/3 [20], n2 = 1, =600 m, and the thickness of graphene, h = N × 0.34 nm, where 0.34 nm is the thickness of a single layer of graphene and N is the number of graphene layers, from 0 to 150. The reflectance spectra with N changes in low/high number range are shown in Fig. 3(a) and (b), respectively. When N = 0, i.e., there is no graphene layer between prism and air, the reflectance
62
L. Ding et al. / Optik 137 (2017) 59–64
Fig. 4. Extinction ratio of the graphene polarizer with different graphene layers number around 35(a)/123(b).
curves of p-polarized wave and s-polarized wave are typical examples of TIR, that the reflectance, Rp and Rs are both equal to 1 as the incident angle is greater than the critical angle. However, as N increases, Rs becomes smaller than Rp under TIR. Since the absorbance of graphene is given by 1-R-T, where T, the transmittance is 0 under TIR, graphene has greater absorption for s-polarized wave than for p-polarized wave. What’s more, it’s possible for Rs to approach zero as long as the incident angle is around 57.76◦ and N is around 35, while Rp still holds a relatively high value. In contrast, if N becomes much larger (larger than 53 at least according to our simulation), then Rp curves lies below Rs curves at the large incident angle region, indicating that graphene has greater absorption for p-polarized wave than for s-polarized wave. Similarly, if N is around 123, Rp can approach zero at the incident angle around 78.5◦ , while Rs still holds a relatively high value, and this switchable absorption for p- and s-polarized wave of graphene makes it possible to design a polarizer based on this three-layer configuration to selectively let s- or p-polarized wave pass. Although the configuration we adopted is generally used for SPR, the polarization-dependent optical absorption of graphene is not based on SPR, because according to the refractive index of graphene, the real part of its relative dielectric constant is positive, which doesn’t satisfy the prerequisite of SPR, e.g. εr εm < 0, where εr , εm are the relative dielectric constants of materials on whose boundary SPR happens. We think the optical absorption of graphene can be attributed to the light energy loss in graphene due to its imaginary part of refractive index. To evaluate the potential extinction ability of the graphene polarizer based on this three-layer configuration, we calculated extinction ratios for different layers of graphene. Fig. 4(a) and (b) depicts the extinction ratios of the graphene polarizer with different graphene layers number around 35 and 123, respectively. Obviously, graphene of 35 layers shows the most intense absorption for s-polarized wave at 57.75◦ , with an extinction ratio (−10 × lg(Rs /Rp )) of 37.48 dB, and graphene of 123 layers shows the most intense absorption for p-polarized wave at 78.51◦ , with an extinction ratio (−10 × lg(Rp /Rs )) of 47.06 dB. That is to say, we can get highly polarized light of either polarization direction(s-polarized or p-polarized) just by changing the number of graphene layers and the incident angle, which provides a new approach besides chemical doping and electrical gating, to fabricate a switchable graphene polarizer. In addition, we investigated the polarization-dependent optical absorption of this configuration in a broadband wavelength range from 450 nm to 750 nm, in which the refractive index of graphene extracted from [20] is valid. To realize a total absorption of s- or p-polarized wave of different wavelength, appropriate number of graphene layers(N) and incident angle() are necessary, as shown in Fig. 5(a) and (b). As the wavelength of incident light increases, the number of graphene layers(N) should increase and the incident angle() should decrease appropriately to gain total absorption, or high extinc-
L. Ding et al. / Optik 137 (2017) 59–64
63
Fig. 5. N and for incident light from 450 nm to 750 nm to totally absorb s- (a) and p-polarized wave (b).
Fig. 6. Extinction ratio at different wavelength in s- and p-polarized pass situation.
tion ratio of either s- or p-polarized wave. Both N and show good linear relationships with the wavelength of incident light, so it’s easy to determine the proper N and for a certain wavelength. The extinction ratios of the graphene polarizer at different wavelength in s- and p-polarized pass situation are shown in Fig. 6. With small graphene layer numbers, the graphene polarizer absorbs the s-polarized wave and let p-polarized wave pass, so it is “p-polarized pass” and vice versa. All of the extinction ratios are higher than 36 dB, which means excellent polarization performance of the graphene polarizer. The change of the extinction ratios at different wavelength seems not regular, because the number of graphene layers are not continuous but integers, so the most appropriate thickness to gain the largest extinction ratio may be missed. 4. Conclusions In summary, we studied the polarization-dependent optical absorption property of graphene in visible wavelength domain further by the multilayer matrix method. Numerical simulation reveals that under TIR, graphene polarizer of the three-layer Kretschmann configuration theoretically shows extraordinary extinction ratio in a broadband wavelength range
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from 450 nm to 750 nm, indicating that graphene layers can totally absorb s- or p-polarized wave of visible light, as long as the number of graphene layers and the incident angle are set appropriately, and the exact numbers of them are easy to determine. It provides a new way, besides chemical doping and electrical gating, to modulate the absorption selectivity of graphene for s-or p-polarized wave, thus transforming unpolarized incident light into polarized light. Acknowledgment This work was supported by the National Natural Science Foundation of China (Grant No. 61575150 and No. 61377092). References [1] A.K. Geim, Graphene: status and prospects, Science 324 (2009) 1530–1534. [2] Z. Yanwu, M. Shanthi, C. Weiwei, L. Xuesong, S.J. Won, J.R. Potts, R.S. Ruoff, Graphene and graphene oxide: synthesis, properties, and applications, Adv. Mater. 22 (2010) 5226. [3] A.K. Geim, K.S. Novoselov, The rise of graphene, Nat. Mater. 6 (2007) 183–191. [4] F.H. Koppens, D.E. Chang, F.J. Garcia de Abajo, Graphene plasmonics: a platform for strong light-matter interactions, Nano Lett. 11 (2011) 3370–3377. [5] 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 (2011) 630–634. [6] A.N. Grigorenko, M. Polini, K.S. Novoselov, Graphene plasmonics, Nat. Photonics 6 (2012) 749–758. [7] T. Low, P. Avouris, Graphene plasmonics for terahertz to mid-infrared applications, ACS Nano 8 (2014) 1086–1101. [8] 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 (2012) 330–334. [9] Q. Bao, K.P. Loh, Graphene photonics, plasmonics, and broadband optoelectronic devices, ACS Nano 6 (2012) 3677–3694. [10] A. Vakil, N. Engheta, Transformation optics using graphene, Science 332 (2011) 1291–1294. [11] 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 (2011) 411–415. [12] N.M.R. Peres, The electronic properties of graphene and its bilayer, Vacuum 83 (2009) 1248–1252. [13] R.R. Nair, P. Blake, A.N. Grigorenko, K.S. Novoselov, T.J. Booth, T. Stauber, N.M. Peres, A.K. Geim, Fine structure constant defines visual transparency of graphene, Science 320 (2008) 1308. [14] Q. Ye, J. Wang, Z. Liu, Z.-C. Deng, X.-T. Kong, F. Xing, X.-D. Chen, W.-Y. Zhou, C.-P. Zhang, J.-G. Tian, Polarization-dependent optical absorption of graphene under total internal reflection, Appl. Phys. Lett. 102 (2013) 021912. [15] P. Wang, Z.-B. Liu, X.-D. Chen, F. Xing, W.-S. Jiang, B. Dong, W. Xin, J.-G. Tian, Accurate layers determination of graphene on transparent substrate based on polarization-sensitive absorption effect, Appl. Phys. Lett. 103 (2013) 181902. [16] A.K. Sharma, B.D. Gupta, On the performance of different bimetallic combinations in surface plasmon resonance based fiber optic sensors, J. Appl. Phys. 101 (2007) 093111. [17] H. Moayyed, I.T. Leite, L. Coelho, J.L. Santos, D. Viegas, Analysis of phase interrogated SPR fiber optic sensors with bimetallic layers, IEEE Sens. J. 14 (2014) 3662–3668. [18] E. Kretschmann, H. Raether, Notizen: radiative decay of non radiative surface plasmons excited by light, Zeitschrift für Naturforschung A (1968) 2135. [19] P. Yeh, M. Hendry, Optical Waves in Layered Media, Elsevier, 1987. [20] M. Bruna, S. Borini, Optical constants of graphene layers in the visible range, Appl. Phys. Lett. 94 (2009) 031901.