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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 21 — Oct. 21, 2013
  • pp: 24736–24741
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Fabry-Perot enhanced Faraday rotation in graphene

Nicolas Ubrig, Iris Crassee, Julien Levallois, Ievgeniia O. Nedoliuk, Felix Fromm, Michl Kaiser, Thomas Seyller, and Alexey B. Kuzmenko  »View Author Affiliations


Optics Express, Vol. 21, Issue 21, pp. 24736-24741 (2013)
http://dx.doi.org/10.1364/OE.21.024736


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Abstract

We demonstrate that giant Faraday rotation in graphene in the terahertz range due to the cyclotron resonance is further increased by constructive Fabry-Perot interference in the supporting substrate. Simultaneously, an enhanced total transmission is achieved, making this effect doubly advantageous for graphene-based magneto-optical applications. As an example, we present far-infrared spectra of epitaxial multilayer graphene grown on the C-face of 6H-SiC, where the interference fringes are spectrally resolved and a Faraday rotation up to 0.15 radians (9°) is attained. Further, we discuss and compare other ways to increase the Faraday rotation using the principle of an optical cavity.

© 2013 OSA

1. Introduction

Graphitic materials, such as carbon nanotubes and graphene, find numerous applications in various fields of optics [1

1. L. Ren, C. L. Pint, L. G. Booshehri, W. D. Rice, X. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon nanotube terahertz polarizer,” Nano Lett. 9, 2610–2613 (2009). [CrossRef] [PubMed]

4

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

]. The giant terahertz Faraday rotation in graphene [5

5. I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. v. d. Marel, and A. B. Kuzmenko, “Giant faraday rotation in single- and multilayer graphene,” Nature Physics 7, 48–51 (2011). [CrossRef]

10

10. R. Shimano, G. Yumoto, J. Y. Yoo, R. Matsunaga, S. Tanabe, H. Hibino, T. Morimoto, and H. Aoki, “Quantum faraday and kerr rotations in graphene,” Nat. Comm. 4, 1841 (2013). [CrossRef]

] suggests that this novel material can be useful in applied magneto-optics. The exceptionally strong Faraday effect, combined with a high doping tunability, which is a hallmark of graphene, may potentially lead to a new class of ultrafast tunable magneto-optical modulators and isolators [5

5. I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. v. d. Marel, and A. B. Kuzmenko, “Giant faraday rotation in single- and multilayer graphene,” Nature Physics 7, 48–51 (2011). [CrossRef]

,8

8. H. Da and G. Liang, “Enhanced faraday rotation in magnetophotonic crystal infiltrated with graphene,” Appl. Phys. Lett. 98, 261915–261915–3 (2011). [CrossRef]

,11

11. H. Da and C.-W. Qiu, “Graphene-based photonic crystal to steer giant faraday rotation,” Appl. Phys. Lett. 100, 241106–241106–4 (2012). [CrossRef]

,12

12. Y. Zhou, X. L. Xu, H. Fan, Z. Ren, J. Bai, and L. Wang, “Tunable magnetoplasmons for efficient terahertz modulator and isolator by gated monolayer graphene,” Phys. Chem. Chem. Phys. (2013). [CrossRef]

]. Apart from practical importance, the magneto-optical phenomena are helpful to study the charge carrier dynamics in these systems [5

5. I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. v. d. Marel, and A. B. Kuzmenko, “Giant faraday rotation in single- and multilayer graphene,” Nature Physics 7, 48–51 (2011). [CrossRef]

, 13

13. I. Crassee, J. Levallois, D. van der Marel, A. L. Walter, T. Seyller, and A. B. Kuzmenko, “Multicomponent magneto-optical conductivity of multilayer graphene on SiC,” Phys. Rev. B 84, 035103 (2011). [CrossRef]

, 14

14. J. Levallois, M. Tran, and A. B. Kuzmenko, “Decrypting the cyclotron effect in graphite using kerr rotation spectroscopy,” Solid State Commun. 152, 1294–1300 (2012). [CrossRef]

].

Even though the observed Faraday angles of a few degrees at fields of only a few Tesla [5

5. I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. v. d. Marel, and A. B. Kuzmenko, “Giant faraday rotation in single- and multilayer graphene,” Nature Physics 7, 48–51 (2011). [CrossRef]

] are exceptionally large for a single atomic layer, the use of this effect in practical devices will certainly be facilitated by increasing the rotations even more, while reducing the required magnetic field. Modifying the properties of graphene itself, for example, increasing the number of magneto-optically active layers, enhancing the mobility of charge carriers and fabrication of plasmonic nanostructures, is obviously one of the avenues for this improvement. However, the electromagnetic properties of the environment surrounding a magneto-optical layer, also play an important role. In particular, it is known that small Faraday rotation can be boosted by placing magneto-optically active samples inside a Fabry-Perot cavity. The rotation angle is enhanced after multiple internal beam passages [15

15. R. Rosenberg, C. B. Rubinstein, and D. R. Herriott, “Resonant optical faraday rotator,” Applied Optics 3, 1079–1083 (1964). [CrossRef]

]. This principle was used to build magneto-optical devices [16

16. J. Stone, R. Jopson, L. Stulz, and S. Licht, “Enhancement of faraday rotation in a fibre fabry-perot cavity,” Electronics Letters 26, 849–851 (1990). [CrossRef]

], to increase the sensitivity of magnetic field sensors [17

17. R. Wagreich and C. Davis, “Magnetic field detection enhancement in an external cavity fiber fabry-perot sensor,” Journal of Lightwave Technology 14, 2246–2249 (1996). [CrossRef]

] or to measure ultrasmall Verdet constants [18

18. D. Jacob, M. Vallet, F. Bretenaker, A. Le Floch, and R. Le Naour, “Small faraday rotation measurement with a Fabry–Pérot cavity,” Appl. Phys. Lett. 66, 3546–3548 (1995). [CrossRef]

]. In the context of graphene, the idea was recently studied theoretically in [6

6. A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. Castro Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84, 235410 (2011). [CrossRef]

], Ferreira et al.

2. Experimental details

Our sample is multilayer epitaxial graphene grown on the C-face [19

19. C. Berger, Z. Song, T. Li, X. Li, A. Y. Ogbazghi, R. Feng, Z. Dai, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics,” J. Phys. Chem. B 108, 19912–19916 (2004). [CrossRef]

] of 6H-SiC by annealing silicon carbide in an Ar atmosphere for 90 minutes at 1650 ° C. Before the growth, the substrate was hydrogen-etched at 1600° C for 15 minutes. The total number of graphene layers was about 20, as determined by X-ray photoelectron spectroscopy and confirmed by infrared absorption in the near-infrared range. However, only one or two layers closest to the SiC are highly doped (n-type) [20

20. C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. d. Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312, 1191–1196 (2006). [CrossRef] [PubMed]

] and therefore responsible for the classical cyclotron resonance, which dominates the magneto-optical response in the range of energies and magnetic fields [13

13. I. Crassee, J. Levallois, D. van der Marel, A. L. Walter, T. Seyller, and A. B. Kuzmenko, “Multicomponent magneto-optical conductivity of multilayer graphene on SiC,” Phys. Rev. B 84, 035103 (2011). [CrossRef]

] considered in this paper. The remaining layers, which are quasineutral, only contribute to the overall absorption at low frequencies [13

13. I. Crassee, J. Levallois, D. van der Marel, A. L. Walter, T. Seyller, and A. B. Kuzmenko, “Multicomponent magneto-optical conductivity of multilayer graphene on SiC,” Phys. Rev. B 84, 035103 (2011). [CrossRef]

, 21

21. M. L. Sadowski, G. Martinez, M. Potemski, C. Berger, and W. A. de Heer, “Landau level spectroscopy of ultrathin graphite layers,” Phys. Rev. Lett. 97, 266405 (2006). [CrossRef]

]. The thickness of the substrate was reduced to d = 80 μm by polishing in order to increase the period of the Fabry-Perot oscillations (about 20 cm−1 in the THz range). We measured magneto-transmission T(ω, B) with unpolarized light and the Faraday rotation θF (ω, B) by a two-polarizer technique between 15 and 700 cm−1 with the help of a Fourier transform spectrometer coupled to a split-coil superconducting magnet [5

5. I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. v. d. Marel, and A. B. Kuzmenko, “Giant faraday rotation in single- and multilayer graphene,” Nature Physics 7, 48–51 (2011). [CrossRef]

]. A mercury light source, silicon beamsplitter and liquid-helium cooled Si bolometer were used. The spectral resolution (1 cm−1 for the transmission and 2 cm−1 for the Faraday rotation) was sufficient to fully resolve the interference fringes. The spectra at 5 Kelvin and 7 Tesla are plotted in Fig. 1. At lower fields the data show a qualitatively similar behavior. The energy of the cyclotron resonance (marked by the dashed line) can be identified as a broad minimum in (oscillation-averaged) transmission and a reduced amplitude of the fringes. The (oscillation-averaged) Faraday angle changes sign in this region. The negative value at low frequencies indicates that the layer responsible for the resonance is n-doped.

Fig. 1 Transmission (black squares, left axis) and Faraday rotation (red circles, right axis) spectra at 7 Tesla and 5 Kelvin. Note that the Faraday rotation scale is inverted. The horizontal line corresponds to zero Faraday rotation, the vertical line indicates the cyclotron frequency.

3. Discussion

An important observation is that the maxima of the transmission and the absolute value of the Faraday rotation virtually coincide, except close to the cyclotron resonance, ωc. It means that a constructive interference between internally reflected beams is favorable for both quantities. We note also that at some frequencies the Faraday angle reaches 9°, which is 50 percent higher than the value reported earlier [5

5. I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. v. d. Marel, and A. B. Kuzmenko, “Giant faraday rotation in single- and multilayer graphene,” Nature Physics 7, 48–51 (2011). [CrossRef]

].

In order to explain this finding, we model the experimental spectra by treating all graphene layers as a thin film with the total conductivity σ+ (σ) for the right- (left-) circular polarized light:
σ±(ω)=2Dπiωωc+iγ+σb
(1)
represented by a sum of the cyclotron resonance, described by a Drude weight D, a cyclotron frequency ωc and a scattering rate γ, and a constant background σb, approximating the absorption in other layers [13

13. I. Crassee, J. Levallois, D. van der Marel, A. L. Walter, T. Seyller, and A. B. Kuzmenko, “Multicomponent magneto-optical conductivity of multilayer graphene on SiC,” Phys. Rev. B 84, 035103 (2011). [CrossRef]

,22

22. I. Crassee, To be published.

]. This quasi-classical approach is valid in our case since the condition ω, ωc < 2EF is satisfied [6

6. A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. Castro Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84, 235410 (2011). [CrossRef]

, 23

23. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “On the universal ac optical background in graphene,” New Journal of Physics 11, 095013 (2009). [CrossRef]

]. The transmission and the Faraday rotation are given by:
T=|t|2+|t+|22,θF=12arg(tt+)
(2)
where t± are the complex transmission coefficients for the two circular polarizations. Taking into account multiple internal reflections in the substrate, for which the refractive index n ≈ 3.1 and zero absorption were assumed in the spectral range of interest we get [24

24. O. S. Heavens, Thin film physics (Methuen, 1970).

]:
t±=4nτs[(n+1)2(n1)2τs2+Z0σ±(n+1+(n1)τs2)]1,
(3)
where τs = exp(iωdn/c) is the phase factor acquired by light in the substrate and Z0 is the impedance of vacuum.

The following parameter values were found to fit the data at 7 Tesla in the best way: ωc = 156 cm−1, γ =56 cm−1, D/σ0 = 3620 cm−1, σb0 = 23, where σ0 = e2/4 is the universal conductivity of monolayer graphene [25

25. T. Ando, Y. Zheng, and H. Suzuura, “Dynamical conductivity and zero-mode anomaly in honeycomb lattices,” J. Phys. Soc. Jpn. 71, 1318–1324 (2002). [CrossRef]

]. We estimate the Fermi energy EF = 0.24 eV from the Drude weight extracted from the fit through the relation D = 2σ0EF/h̄. The theoretical curves are shown in Fig. 2(a). One can see that this simple model reproduces the data accurately, including the coincidence of maxima of the Faraday rotation and transmission.

Fig. 2 Simulation of the magneto-optical transmission and Faraday rotation of graphene on and in SiC for three different configurations. Note that the Faraday rotation scale is inverted. (a) Graphene covers one side of SiC, (b) graphene covers both sides of SiC, (c) graphene is in the middle of SiC slab, (d) graphene is in the middle of a SiC slab covered by metallic layers on both sides.

The physical meaning of this result becomes obvious in the following. The constructive interference occurs at frequencies, where τs = ±1. In this case, Eq. (3) reduces to
tconstr,±=τs(1+Z0σ±2)1,
(4)
which is equal, apart from the prefactor τs, to the transmission of free standing graphene with the same optical conductivity [26

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

, 27

27. A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100, 117401 (2008). [CrossRef] [PubMed]

]. It thus appears that the effect of the constructive Fabry-Perot interference is to exactly compensate the screening effect of the substrate. If monochromatic light is used (such as a terahertz laser), it would be desirable in magneto-optical applications to adjust the substrate thickness in order to achieve this condition.

We first consider the case where both sides of the substrate are covered with graphene. Although this cannot be done by growing graphene on two sides one can simply press two identical samples together. Equation (3) is now modified as follows:
t±=4nτs.[(n+1)2(n1)2τs2+2Z0σ±(n+1+(n1)τs)2+Z02σ±2(1τs2)]1.
(5)
For the constructive interference we obtain tconstr,± = τs (1 + Z0σ±)−1, which is the same result as Eq. (4), except for the factor 2 in the graphene conductivity term, due to the presence of two graphene layers. The computed spectra are plotted in Fig. 2(b). The Faraday rotation now reaches 15°. The transmission is lowered but remains at a reasonable level.

Next, we consider the graphene film to be in the middle of a SiC plate, which can, in principle, be achieved by pressing a substrate with graphene against a bare substrate with the same thickness. This case is described by the equation:
t±=4nτs[(n+1)2(n1)2τs2+Z0σ±2n(n+1+(n1)τs)2]1.
(6)
The computed spectra are plotted in Fig. 2(c). Now the cases τs = +1 and −1 are fundamentally different. In the first case the result for free-standing graphene (Eq. (4)) is again recovered. Indeed, the same transmission and rotation as in Fig. 2(a) are observed for these frequencies. However, if τs = −1 then t± =τs(1+Z0σ±/2n2)−1, which means that the effective conductivity of graphene is reduced by a factor of n2 ≈ 10 as compared to Eq. (4). Although this case is beneficial for the overall transmission, the Faraday rotation is so small that this case is not of practical interest for magneto-optical applications. Thus, the configuration with graphene in the middle is not more advantageous for the enhancement of the Faraday rotation than the original one.

One should note that the magneto-optically inactive graphene layers in the present sample, modeled with the term σb, only reduce the transmission without improving the rotation. In monolayer graphene grown on the Si-face [28

28. K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater. 8, 203–207 (2009). [CrossRef] [PubMed]

, 29

29. C. Riedl, C. Coletti, T. Iwasaki, A. A. Zakharov, and U. Starke, “Quasi-free-standing epitaxial graphene on SiC obtained by hydrogen intercalation,” Phys. Rev. Lett. 103, 246804 (2009). [CrossRef]

], such layers are absent and the transmission is expected to be higher than in the data presented here, with a similar value of the Faraday rotation.

Acknowledgments

We acknowledge Daniel Chablaix, Michaël Tran and Mehdi Brandt for technical assistance. This work was supported by the SNSF through project 140710 and via the NCCR “Materials with Novel Electronic Properties - MaNEP”. We acknowledge support by the EC under Graphene Flagship (contract no. CNECT-ICT-604391).

References and links

1.

L. Ren, C. L. Pint, L. G. Booshehri, W. D. Rice, X. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon nanotube terahertz polarizer,” Nano Lett. 9, 2610–2613 (2009). [CrossRef] [PubMed]

2.

J. Yan, M.-H. Kim, J. A. Elle, A. B. Sushkov, G. S. Jenkins, H. M. Milchberg, M. S. Fuhrer, and H. D. Drew, “Dual-gated bilayer graphene hot-electron bolometer,” Nat. Nanotechnol. 7, 472–478 (2012). [CrossRef] [PubMed]

3.

N. M. Gabor, J. C. W. Song, Q. Ma, N. L. Nair, T. Taychatanapat, K. Watanabe, T. Taniguchi, L. S. Levitov, and P. Jarillo-Herrero, “Hot Carrier–Assisted intrinsic photoresponse in graphene,” Science 334, 648–652 (2011). [CrossRef] [PubMed]

4.

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

5.

I. Crassee, J. Levallois, A. L. Walter, M. Ostler, A. Bostwick, E. Rotenberg, T. Seyller, D. v. d. Marel, and A. B. Kuzmenko, “Giant faraday rotation in single- and multilayer graphene,” Nature Physics 7, 48–51 (2011). [CrossRef]

6.

A. Ferreira, J. Viana-Gomes, Y. V. Bludov, V. Pereira, N. M. R. Peres, and A. H. Castro Neto, “Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids,” Phys. Rev. B 84, 235410 (2011). [CrossRef]

7.

I. Fialkovsky and D. V. Vassilevich, “Faraday rotation in graphene,” The European Physical Journal B 85, 1–10 (2012). [CrossRef]

8.

H. Da and G. Liang, “Enhanced faraday rotation in magnetophotonic crystal infiltrated with graphene,” Appl. Phys. Lett. 98, 261915–261915–3 (2011). [CrossRef]

9.

A. Fallahi and J. Perruisseau-Carrier, “Manipulation of giant faraday rotation in graphene metasurfaces,” Appl. Phys. Lett. 101, 231605–231605–4 (2012). [CrossRef]

10.

R. Shimano, G. Yumoto, J. Y. Yoo, R. Matsunaga, S. Tanabe, H. Hibino, T. Morimoto, and H. Aoki, “Quantum faraday and kerr rotations in graphene,” Nat. Comm. 4, 1841 (2013). [CrossRef]

11.

H. Da and C.-W. Qiu, “Graphene-based photonic crystal to steer giant faraday rotation,” Appl. Phys. Lett. 100, 241106–241106–4 (2012). [CrossRef]

12.

Y. Zhou, X. L. Xu, H. Fan, Z. Ren, J. Bai, and L. Wang, “Tunable magnetoplasmons for efficient terahertz modulator and isolator by gated monolayer graphene,” Phys. Chem. Chem. Phys. (2013). [CrossRef]

13.

I. Crassee, J. Levallois, D. van der Marel, A. L. Walter, T. Seyller, and A. B. Kuzmenko, “Multicomponent magneto-optical conductivity of multilayer graphene on SiC,” Phys. Rev. B 84, 035103 (2011). [CrossRef]

14.

J. Levallois, M. Tran, and A. B. Kuzmenko, “Decrypting the cyclotron effect in graphite using kerr rotation spectroscopy,” Solid State Commun. 152, 1294–1300 (2012). [CrossRef]

15.

R. Rosenberg, C. B. Rubinstein, and D. R. Herriott, “Resonant optical faraday rotator,” Applied Optics 3, 1079–1083 (1964). [CrossRef]

16.

J. Stone, R. Jopson, L. Stulz, and S. Licht, “Enhancement of faraday rotation in a fibre fabry-perot cavity,” Electronics Letters 26, 849–851 (1990). [CrossRef]

17.

R. Wagreich and C. Davis, “Magnetic field detection enhancement in an external cavity fiber fabry-perot sensor,” Journal of Lightwave Technology 14, 2246–2249 (1996). [CrossRef]

18.

D. Jacob, M. Vallet, F. Bretenaker, A. Le Floch, and R. Le Naour, “Small faraday rotation measurement with a Fabry–Pérot cavity,” Appl. Phys. Lett. 66, 3546–3548 (1995). [CrossRef]

19.

C. Berger, Z. Song, T. Li, X. Li, A. Y. Ogbazghi, R. Feng, Z. Dai, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics,” J. Phys. Chem. B 108, 19912–19916 (2004). [CrossRef]

20.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. d. Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312, 1191–1196 (2006). [CrossRef] [PubMed]

21.

M. L. Sadowski, G. Martinez, M. Potemski, C. Berger, and W. A. de Heer, “Landau level spectroscopy of ultrathin graphite layers,” Phys. Rev. Lett. 97, 266405 (2006). [CrossRef]

22.

I. Crassee, To be published.

23.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “On the universal ac optical background in graphene,” New Journal of Physics 11, 095013 (2009). [CrossRef]

24.

O. S. Heavens, Thin film physics (Methuen, 1970).

25.

T. Ando, Y. Zheng, and H. Suzuura, “Dynamical conductivity and zero-mode anomaly in honeycomb lattices,” J. Phys. Soc. Jpn. 71, 1318–1324 (2002). [CrossRef]

26.

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

27.

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100, 117401 (2008). [CrossRef] [PubMed]

28.

K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D. Waldmann, H. B. Weber, and T. Seyller, “Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide,” Nat. Mater. 8, 203–207 (2009). [CrossRef] [PubMed]

29.

C. Riedl, C. Coletti, T. Iwasaki, A. A. Zakharov, and U. Starke, “Quasi-free-standing epitaxial graphene on SiC obtained by hydrogen intercalation,” Phys. Rev. Lett. 103, 246804 (2009). [CrossRef]

30.

T. Morimoto, Y. Hatsugai, and H. Aoki, “Cyclotron radiation and emission in graphene — a possibility of landau-level laser,” Journal of Physics: Conference Series 150, 022059 (2009). [CrossRef]

OCIS Codes
(230.2240) Optical devices : Faraday effect
(300.6270) Spectroscopy : Spectroscopy, far infrared

ToC Category:
Spectroscopy

History
Original Manuscript: April 19, 2013
Revised Manuscript: September 18, 2013
Manuscript Accepted: September 29, 2013
Published: October 9, 2013

Citation
Nicolas Ubrig, Iris Crassee, Julien Levallois, Ievgeniia O. Nedoliuk, Felix Fromm, Michl Kaiser, Thomas Seyller, and Alexey B. Kuzmenko, "Fabry-Perot enhanced Faraday rotation in graphene," Opt. Express 21, 24736-24741 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-21-24736


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References

  1. L. Ren, C. L. Pint, L. G. Booshehri, W. D. Rice, X. Wang, D. J. Hilton, K. Takeya, I. Kawayama, M. Tonouchi, R. H. Hauge, and J. Kono, “Carbon nanotube terahertz polarizer,” Nano Lett.9, 2610–2613 (2009). [CrossRef] [PubMed]
  2. J. Yan, M.-H. Kim, J. A. Elle, A. B. Sushkov, G. S. Jenkins, H. M. Milchberg, M. S. Fuhrer, and H. D. Drew, “Dual-gated bilayer graphene hot-electron bolometer,” Nat. Nanotechnol.7, 472–478 (2012). [CrossRef] [PubMed]
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