Abstract

I propose an expression for the electromagnetic wave impedance of a two-dimensional atomic crystal, and I deduce the Fresnel coefficients in terms of this quantity. It is widely known that a two-dimensional crystal can absorb light, if its conductivity is different from zero. It is less emphasized that they can also store a certain amount of electromagnetic energy. The concept of impedance is useful to quantify this point.

© 2015 Optical Society of America

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Corrections

22 January 2016: Corrections were made to the body text.


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References

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  1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
    [Crossref] [PubMed]
  2. K. Novoselov, D. Jiang, F. Schedin, T. Booth, V. Khotkevich, S. Morozov, and A. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. USA 102, 10451–10453 (2005).
    [Crossref] [PubMed]
  3. 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]
  4. K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically Thin MoS2: A New Direct-Gap Semiconductor,” Phys. Rev. Lett. 105, 136805 (2010).
    [Crossref]
  5. R. V. Gorbachev, I. Riaz, R. R. Nair, R. Jalil, L. Britnell, B. D. Belle, E. W. Hill, K. S. Novoselov, K. Watanabe, T. Taniguchi, A. K. Geim, and P. Blake, “Hunting for monolayer boron nitride: Optical and raman signatures,” Small 7, 465–468 (2011).
    [Crossref] [PubMed]
  6. 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 (2008).
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    [Crossref]
  9. M. M. Benameur, B. Radisavljevic, J. S. Héron, S. Sahoo, H. Berger, and A. Kis, “Visibility of dichalcogenide nanolayers,” Nanotechnology 22, 125706 (2011).
    [Crossref] [PubMed]
  10. D. Golla, K. Chattrakun, K. Watanabe, T. Taniguchi, B. J. LeRoy, and A. Sandhu, “Optical thickness determination of hexagonal boron nitride flakes,” Appl. Phys. Lett. 102, 161906 (2013).
    [Crossref]
  11. I. Jung, J.-S. Rhyee, J. Y. Son, R. S. Ruoff, and K.-Y. Rhee, “Colors of graphene and graphene-oxide multilayers on various substrates,” Nanotechnology 23, 025708 (2012).
    [Crossref]
  12. K. Peters, A. Tittel, N. Gayer, A. Graf, V. Paulava, U. Wurstbauer, and W. Hansen, “Enhancing the visibility of graphene on GaAs,” Appl. Phys. Lett. 99, 191912 (2011).
    [Crossref]
  13. M. Dorn, P. Lange, A. Chekushin, N. Severin, and J. P. Rabe, “High contrast optical detection of single graphenes on optically transparent substrates,” J. Appl. Phys. 108, 106101 (2010).
    [Crossref]
  14. H. Zhang, Y. Ma, Y. Wan, X. Rong, Z. Xie, W. Wang, and L. Dai, “Measuring the Refractive Index of Highly Crystalline Monolayer MoS2 with High Confidence,” Sci. Rep. 5, 8440 (2015).
    [Crossref] [PubMed]
  15. X. Wang, M. Zhao, and D. D. Nolte, “Optical contrast and clarity of graphene on an arbitrary substrate,” Appl. Phys. Lett. 95, 081102 (2009).
    [Crossref]
  16. A. Castellanos-Gomez, N. Agrait, and G. Rubio-Bollinger, “Optical identification of atomically thin dichalcogenide crystals,” Appl. Phys. Lett. 96, 213116 (2010).
    [Crossref]
  17. V. G. Kravets, A. N. Grigorenko, R. R. Nair, P. Blake, S. Anissimova, K. S. Novoselov, and A. K. Geim, “Spectroscopic ellipsometry of graphene and an exciton-shifted van Hove peak in absorption,” Phys. Rev. B 81, 155413 (2010).
    [Crossref]
  18. Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. M. Hill, A. M. van der Zande, D. A. Chenet, E.-M. Shih, J. Hone, and T. F. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90, 205422 (2014).
    [Crossref]
  19. F. J. Nelson, V. K. Kamineni, T. Zhang, E. S. Comfort, J. U. Lee, and A. C. Diebold, “Optical properties of large-area polycrystalline chemical vapor deposited graphene by spectroscopic ellipsometry,” Appl. Phys. Lett. 97, 253110 (2010).
    [Crossref]
  20. U. Wurstbauer, C. Roeling, U. Wurstbauer, W. Wegscheider, M. Vaupel, P. H. Thiesen, and D. Weiss, “Imaging ellipsometry of graphene,” Appl. Phys. Lett 97, 231901 (2010).
    [Crossref]
  21. A. Matkovic, M. Chhikara, M. Milicevic, U. Ralevic, B. Vasic, D. Jovanovic, M. R. Belic, G. Bratina, and R. S. Gajic, “Influence of a gold substrate on the optical properties of graphene,” J. Appl. Phys. 117, 015305 (2015).
    [Crossref]
  22. J. W. Weber, V. E. Calado, and M. C. M. van de Sanden, “Optical constants of graphene measured by spectroscopic ellipsometry,” Appl. Phys. Lett. 97, 091904 (2010).
    [Crossref]
  23. M. Vaupel, A. Dutschke, U. Wurstbauer, F. Hitzel, and A. Pasupathy, “Topography, complex refractive index, and conductivity of graphene layers measured by correlation of optical interference contrast, atomic force, and back scattered electron microscopy,” J. Appl. Phys. 114, 183107 (2013).
    [Crossref]
  24. Q. Ye, J. Wang, Z. Liu, Z.-C. Deng, X.-T. Kong, F. Xing, X.-D. Chen, W.-Y. Zhou, C.-P. Zhang, and J.-G. Tian, “Polarization-dependent optical absorption of graphene under total internal reflection,” Appl. Phys. Lett. 102, 021912 (2013).
    [Crossref]
  25. R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Enery Transmission and Radiation(Wiley, 1960).
  26. R. M. Fano, L. J. Chu, and R. B. Adler, Electromagnetic Fields Energy and Forces (Wiley, 1960), pp. 320–324.

2015 (2)

H. Zhang, Y. Ma, Y. Wan, X. Rong, Z. Xie, W. Wang, and L. Dai, “Measuring the Refractive Index of Highly Crystalline Monolayer MoS2 with High Confidence,” Sci. Rep. 5, 8440 (2015).
[Crossref] [PubMed]

A. Matkovic, M. Chhikara, M. Milicevic, U. Ralevic, B. Vasic, D. Jovanovic, M. R. Belic, G. Bratina, and R. S. Gajic, “Influence of a gold substrate on the optical properties of graphene,” J. Appl. Phys. 117, 015305 (2015).
[Crossref]

2014 (1)

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. M. Hill, A. M. van der Zande, D. A. Chenet, E.-M. Shih, J. Hone, and T. F. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90, 205422 (2014).
[Crossref]

2013 (3)

D. Golla, K. Chattrakun, K. Watanabe, T. Taniguchi, B. J. LeRoy, and A. Sandhu, “Optical thickness determination of hexagonal boron nitride flakes,” Appl. Phys. Lett. 102, 161906 (2013).
[Crossref]

M. Vaupel, A. Dutschke, U. Wurstbauer, F. Hitzel, and A. Pasupathy, “Topography, complex refractive index, and conductivity of graphene layers measured by correlation of optical interference contrast, atomic force, and back scattered electron microscopy,” J. Appl. Phys. 114, 183107 (2013).
[Crossref]

Q. Ye, J. Wang, Z. Liu, Z.-C. Deng, X.-T. Kong, F. Xing, X.-D. Chen, W.-Y. Zhou, C.-P. Zhang, and J.-G. Tian, “Polarization-dependent optical absorption of graphene under total internal reflection,” Appl. Phys. Lett. 102, 021912 (2013).
[Crossref]

2012 (1)

I. Jung, J.-S. Rhyee, J. Y. Son, R. S. Ruoff, and K.-Y. Rhee, “Colors of graphene and graphene-oxide multilayers on various substrates,” Nanotechnology 23, 025708 (2012).
[Crossref]

2011 (3)

K. Peters, A. Tittel, N. Gayer, A. Graf, V. Paulava, U. Wurstbauer, and W. Hansen, “Enhancing the visibility of graphene on GaAs,” Appl. Phys. Lett. 99, 191912 (2011).
[Crossref]

R. V. Gorbachev, I. Riaz, R. R. Nair, R. Jalil, L. Britnell, B. D. Belle, E. W. Hill, K. S. Novoselov, K. Watanabe, T. Taniguchi, A. K. Geim, and P. Blake, “Hunting for monolayer boron nitride: Optical and raman signatures,” Small 7, 465–468 (2011).
[Crossref] [PubMed]

M. M. Benameur, B. Radisavljevic, J. S. Héron, S. Sahoo, H. Berger, and A. Kis, “Visibility of dichalcogenide nanolayers,” Nanotechnology 22, 125706 (2011).
[Crossref] [PubMed]

2010 (7)

J. W. Weber, V. E. Calado, and M. C. M. van de Sanden, “Optical constants of graphene measured by spectroscopic ellipsometry,” Appl. Phys. Lett. 97, 091904 (2010).
[Crossref]

F. J. Nelson, V. K. Kamineni, T. Zhang, E. S. Comfort, J. U. Lee, and A. C. Diebold, “Optical properties of large-area polycrystalline chemical vapor deposited graphene by spectroscopic ellipsometry,” Appl. Phys. Lett. 97, 253110 (2010).
[Crossref]

U. Wurstbauer, C. Roeling, U. Wurstbauer, W. Wegscheider, M. Vaupel, P. H. Thiesen, and D. Weiss, “Imaging ellipsometry of graphene,” Appl. Phys. Lett 97, 231901 (2010).
[Crossref]

A. Castellanos-Gomez, N. Agrait, and G. Rubio-Bollinger, “Optical identification of atomically thin dichalcogenide crystals,” Appl. Phys. Lett. 96, 213116 (2010).
[Crossref]

V. G. Kravets, A. N. Grigorenko, R. R. Nair, P. Blake, S. Anissimova, K. S. Novoselov, and A. K. Geim, “Spectroscopic ellipsometry of graphene and an exciton-shifted van Hove peak in absorption,” Phys. Rev. B 81, 155413 (2010).
[Crossref]

M. Dorn, P. Lange, A. Chekushin, N. Severin, and J. P. Rabe, “High contrast optical detection of single graphenes on optically transparent substrates,” J. Appl. Phys. 108, 106101 (2010).
[Crossref]

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically Thin MoS2: A New Direct-Gap Semiconductor,” Phys. Rev. Lett. 105, 136805 (2010).
[Crossref]

2009 (1)

X. Wang, M. Zhao, and D. D. Nolte, “Optical contrast and clarity of graphene on an arbitrary substrate,” Appl. Phys. Lett. 95, 081102 (2009).
[Crossref]

2008 (1)

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 (2008).
[Crossref] [PubMed]

2007 (1)

P. Blake, E. W. Hill, A. H. CastroNeto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91, 063124 (2007).
[Crossref]

2005 (1)

K. Novoselov, D. Jiang, F. Schedin, T. Booth, V. Khotkevich, S. Morozov, and A. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. USA 102, 10451–10453 (2005).
[Crossref] [PubMed]

2004 (1)

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

2002 (1)

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]

Adler, R. B.

R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Enery Transmission and Radiation(Wiley, 1960).

R. M. Fano, L. J. Chu, and R. B. Adler, Electromagnetic Fields Energy and Forces (Wiley, 1960), pp. 320–324.

Agrait, N.

A. Castellanos-Gomez, N. Agrait, and G. Rubio-Bollinger, “Optical identification of atomically thin dichalcogenide crystals,” Appl. Phys. Lett. 96, 213116 (2010).
[Crossref]

Ando, T.

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]

Anissimova, S.

V. G. Kravets, A. N. Grigorenko, R. R. Nair, P. Blake, S. Anissimova, K. S. Novoselov, and A. K. Geim, “Spectroscopic ellipsometry of graphene and an exciton-shifted van Hove peak in absorption,” Phys. Rev. B 81, 155413 (2010).
[Crossref]

Belic, M. R.

A. Matkovic, M. Chhikara, M. Milicevic, U. Ralevic, B. Vasic, D. Jovanovic, M. R. Belic, G. Bratina, and R. S. Gajic, “Influence of a gold substrate on the optical properties of graphene,” J. Appl. Phys. 117, 015305 (2015).
[Crossref]

Belle, B. D.

R. V. Gorbachev, I. Riaz, R. R. Nair, R. Jalil, L. Britnell, B. D. Belle, E. W. Hill, K. S. Novoselov, K. Watanabe, T. Taniguchi, A. K. Geim, and P. Blake, “Hunting for monolayer boron nitride: Optical and raman signatures,” Small 7, 465–468 (2011).
[Crossref] [PubMed]

Benameur, M. M.

M. M. Benameur, B. Radisavljevic, J. S. Héron, S. Sahoo, H. Berger, and A. Kis, “Visibility of dichalcogenide nanolayers,” Nanotechnology 22, 125706 (2011).
[Crossref] [PubMed]

Berger, H.

M. M. Benameur, B. Radisavljevic, J. S. Héron, S. Sahoo, H. Berger, and A. Kis, “Visibility of dichalcogenide nanolayers,” Nanotechnology 22, 125706 (2011).
[Crossref] [PubMed]

Blake, P.

R. V. Gorbachev, I. Riaz, R. R. Nair, R. Jalil, L. Britnell, B. D. Belle, E. W. Hill, K. S. Novoselov, K. Watanabe, T. Taniguchi, A. K. Geim, and P. Blake, “Hunting for monolayer boron nitride: Optical and raman signatures,” Small 7, 465–468 (2011).
[Crossref] [PubMed]

V. G. Kravets, A. N. Grigorenko, R. R. Nair, P. Blake, S. Anissimova, K. S. Novoselov, and A. K. Geim, “Spectroscopic ellipsometry of graphene and an exciton-shifted van Hove peak in absorption,” Phys. Rev. B 81, 155413 (2010).
[Crossref]

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 (2008).
[Crossref] [PubMed]

P. Blake, E. W. Hill, A. H. CastroNeto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91, 063124 (2007).
[Crossref]

Booth, T.

K. Novoselov, D. Jiang, F. Schedin, T. Booth, V. Khotkevich, S. Morozov, and A. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. USA 102, 10451–10453 (2005).
[Crossref] [PubMed]

Booth, T. J.

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 (2008).
[Crossref] [PubMed]

P. Blake, E. W. Hill, A. H. CastroNeto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91, 063124 (2007).
[Crossref]

Bratina, G.

A. Matkovic, M. Chhikara, M. Milicevic, U. Ralevic, B. Vasic, D. Jovanovic, M. R. Belic, G. Bratina, and R. S. Gajic, “Influence of a gold substrate on the optical properties of graphene,” J. Appl. Phys. 117, 015305 (2015).
[Crossref]

Britnell, L.

R. V. Gorbachev, I. Riaz, R. R. Nair, R. Jalil, L. Britnell, B. D. Belle, E. W. Hill, K. S. Novoselov, K. Watanabe, T. Taniguchi, A. K. Geim, and P. Blake, “Hunting for monolayer boron nitride: Optical and raman signatures,” Small 7, 465–468 (2011).
[Crossref] [PubMed]

Calado, V. E.

J. W. Weber, V. E. Calado, and M. C. M. van de Sanden, “Optical constants of graphene measured by spectroscopic ellipsometry,” Appl. Phys. Lett. 97, 091904 (2010).
[Crossref]

Castellanos-Gomez, A.

A. Castellanos-Gomez, N. Agrait, and G. Rubio-Bollinger, “Optical identification of atomically thin dichalcogenide crystals,” Appl. Phys. Lett. 96, 213116 (2010).
[Crossref]

CastroNeto, A. H.

P. Blake, E. W. Hill, A. H. CastroNeto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91, 063124 (2007).
[Crossref]

Chattrakun, K.

D. Golla, K. Chattrakun, K. Watanabe, T. Taniguchi, B. J. LeRoy, and A. Sandhu, “Optical thickness determination of hexagonal boron nitride flakes,” Appl. Phys. Lett. 102, 161906 (2013).
[Crossref]

Chekushin, A.

M. Dorn, P. Lange, A. Chekushin, N. Severin, and J. P. Rabe, “High contrast optical detection of single graphenes on optically transparent substrates,” J. Appl. Phys. 108, 106101 (2010).
[Crossref]

Chen, X.-D.

Q. Ye, J. Wang, Z. Liu, Z.-C. Deng, X.-T. Kong, F. Xing, X.-D. Chen, W.-Y. Zhou, C.-P. Zhang, and J.-G. Tian, “Polarization-dependent optical absorption of graphene under total internal reflection,” Appl. Phys. Lett. 102, 021912 (2013).
[Crossref]

Chenet, D. A.

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. M. Hill, A. M. van der Zande, D. A. Chenet, E.-M. Shih, J. Hone, and T. F. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90, 205422 (2014).
[Crossref]

Chernikov, A.

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. M. Hill, A. M. van der Zande, D. A. Chenet, E.-M. Shih, J. Hone, and T. F. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90, 205422 (2014).
[Crossref]

Chhikara, M.

A. Matkovic, M. Chhikara, M. Milicevic, U. Ralevic, B. Vasic, D. Jovanovic, M. R. Belic, G. Bratina, and R. S. Gajic, “Influence of a gold substrate on the optical properties of graphene,” J. Appl. Phys. 117, 015305 (2015).
[Crossref]

Chu, L. J.

R. M. Fano, L. J. Chu, and R. B. Adler, Electromagnetic Fields Energy and Forces (Wiley, 1960), pp. 320–324.

R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Enery Transmission and Radiation(Wiley, 1960).

Comfort, E. S.

F. J. Nelson, V. K. Kamineni, T. Zhang, E. S. Comfort, J. U. Lee, and A. C. Diebold, “Optical properties of large-area polycrystalline chemical vapor deposited graphene by spectroscopic ellipsometry,” Appl. Phys. Lett. 97, 253110 (2010).
[Crossref]

Dai, L.

H. Zhang, Y. Ma, Y. Wan, X. Rong, Z. Xie, W. Wang, and L. Dai, “Measuring the Refractive Index of Highly Crystalline Monolayer MoS2 with High Confidence,” Sci. Rep. 5, 8440 (2015).
[Crossref] [PubMed]

Deng, Z.-C.

Q. Ye, J. Wang, Z. Liu, Z.-C. Deng, X.-T. Kong, F. Xing, X.-D. Chen, W.-Y. Zhou, C.-P. Zhang, and J.-G. Tian, “Polarization-dependent optical absorption of graphene under total internal reflection,” Appl. Phys. Lett. 102, 021912 (2013).
[Crossref]

Diebold, A. C.

F. J. Nelson, V. K. Kamineni, T. Zhang, E. S. Comfort, J. U. Lee, and A. C. Diebold, “Optical properties of large-area polycrystalline chemical vapor deposited graphene by spectroscopic ellipsometry,” Appl. Phys. Lett. 97, 253110 (2010).
[Crossref]

Dorn, M.

M. Dorn, P. Lange, A. Chekushin, N. Severin, and J. P. Rabe, “High contrast optical detection of single graphenes on optically transparent substrates,” J. Appl. Phys. 108, 106101 (2010).
[Crossref]

Dubonos, S. V.

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

Dutschke, A.

M. Vaupel, A. Dutschke, U. Wurstbauer, F. Hitzel, and A. Pasupathy, “Topography, complex refractive index, and conductivity of graphene layers measured by correlation of optical interference contrast, atomic force, and back scattered electron microscopy,” J. Appl. Phys. 114, 183107 (2013).
[Crossref]

Fano, R. M.

R. M. Fano, L. J. Chu, and R. B. Adler, Electromagnetic Fields Energy and Forces (Wiley, 1960), pp. 320–324.

R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Enery Transmission and Radiation(Wiley, 1960).

Firsov, A. A.

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

Gajic, R. S.

A. Matkovic, M. Chhikara, M. Milicevic, U. Ralevic, B. Vasic, D. Jovanovic, M. R. Belic, G. Bratina, and R. S. Gajic, “Influence of a gold substrate on the optical properties of graphene,” J. Appl. Phys. 117, 015305 (2015).
[Crossref]

Gayer, N.

K. Peters, A. Tittel, N. Gayer, A. Graf, V. Paulava, U. Wurstbauer, and W. Hansen, “Enhancing the visibility of graphene on GaAs,” Appl. Phys. Lett. 99, 191912 (2011).
[Crossref]

Geim, A.

K. Novoselov, D. Jiang, F. Schedin, T. Booth, V. Khotkevich, S. Morozov, and A. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. USA 102, 10451–10453 (2005).
[Crossref] [PubMed]

Geim, A. K.

R. V. Gorbachev, I. Riaz, R. R. Nair, R. Jalil, L. Britnell, B. D. Belle, E. W. Hill, K. S. Novoselov, K. Watanabe, T. Taniguchi, A. K. Geim, and P. Blake, “Hunting for monolayer boron nitride: Optical and raman signatures,” Small 7, 465–468 (2011).
[Crossref] [PubMed]

V. G. Kravets, A. N. Grigorenko, R. R. Nair, P. Blake, S. Anissimova, K. S. Novoselov, and A. K. Geim, “Spectroscopic ellipsometry of graphene and an exciton-shifted van Hove peak in absorption,” Phys. Rev. B 81, 155413 (2010).
[Crossref]

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 (2008).
[Crossref] [PubMed]

P. Blake, E. W. Hill, A. H. CastroNeto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91, 063124 (2007).
[Crossref]

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

Golla, D.

D. Golla, K. Chattrakun, K. Watanabe, T. Taniguchi, B. J. LeRoy, and A. Sandhu, “Optical thickness determination of hexagonal boron nitride flakes,” Appl. Phys. Lett. 102, 161906 (2013).
[Crossref]

Gorbachev, R. V.

R. V. Gorbachev, I. Riaz, R. R. Nair, R. Jalil, L. Britnell, B. D. Belle, E. W. Hill, K. S. Novoselov, K. Watanabe, T. Taniguchi, A. K. Geim, and P. Blake, “Hunting for monolayer boron nitride: Optical and raman signatures,” Small 7, 465–468 (2011).
[Crossref] [PubMed]

Graf, A.

K. Peters, A. Tittel, N. Gayer, A. Graf, V. Paulava, U. Wurstbauer, and W. Hansen, “Enhancing the visibility of graphene on GaAs,” Appl. Phys. Lett. 99, 191912 (2011).
[Crossref]

Grigorenko, A. N.

V. G. Kravets, A. N. Grigorenko, R. R. Nair, P. Blake, S. Anissimova, K. S. Novoselov, and A. K. Geim, “Spectroscopic ellipsometry of graphene and an exciton-shifted van Hove peak in absorption,” Phys. Rev. B 81, 155413 (2010).
[Crossref]

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 (2008).
[Crossref] [PubMed]

Grigorieva, I. V.

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

Hansen, W.

K. Peters, A. Tittel, N. Gayer, A. Graf, V. Paulava, U. Wurstbauer, and W. Hansen, “Enhancing the visibility of graphene on GaAs,” Appl. Phys. Lett. 99, 191912 (2011).
[Crossref]

Heinz, T. F.

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. M. Hill, A. M. van der Zande, D. A. Chenet, E.-M. Shih, J. Hone, and T. F. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90, 205422 (2014).
[Crossref]

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically Thin MoS2: A New Direct-Gap Semiconductor,” Phys. Rev. Lett. 105, 136805 (2010).
[Crossref]

Héron, J. S.

M. M. Benameur, B. Radisavljevic, J. S. Héron, S. Sahoo, H. Berger, and A. Kis, “Visibility of dichalcogenide nanolayers,” Nanotechnology 22, 125706 (2011).
[Crossref] [PubMed]

Hill, E. W.

R. V. Gorbachev, I. Riaz, R. R. Nair, R. Jalil, L. Britnell, B. D. Belle, E. W. Hill, K. S. Novoselov, K. Watanabe, T. Taniguchi, A. K. Geim, and P. Blake, “Hunting for monolayer boron nitride: Optical and raman signatures,” Small 7, 465–468 (2011).
[Crossref] [PubMed]

P. Blake, E. W. Hill, A. H. CastroNeto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91, 063124 (2007).
[Crossref]

Hill, H. M.

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. M. Hill, A. M. van der Zande, D. A. Chenet, E.-M. Shih, J. Hone, and T. F. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90, 205422 (2014).
[Crossref]

Hitzel, F.

M. Vaupel, A. Dutschke, U. Wurstbauer, F. Hitzel, and A. Pasupathy, “Topography, complex refractive index, and conductivity of graphene layers measured by correlation of optical interference contrast, atomic force, and back scattered electron microscopy,” J. Appl. Phys. 114, 183107 (2013).
[Crossref]

Hone, J.

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. M. Hill, A. M. van der Zande, D. A. Chenet, E.-M. Shih, J. Hone, and T. F. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90, 205422 (2014).
[Crossref]

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically Thin MoS2: A New Direct-Gap Semiconductor,” Phys. Rev. Lett. 105, 136805 (2010).
[Crossref]

Jalil, R.

R. V. Gorbachev, I. Riaz, R. R. Nair, R. Jalil, L. Britnell, B. D. Belle, E. W. Hill, K. S. Novoselov, K. Watanabe, T. Taniguchi, A. K. Geim, and P. Blake, “Hunting for monolayer boron nitride: Optical and raman signatures,” Small 7, 465–468 (2011).
[Crossref] [PubMed]

Jiang, D.

P. Blake, E. W. Hill, A. H. CastroNeto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91, 063124 (2007).
[Crossref]

K. Novoselov, D. Jiang, F. Schedin, T. Booth, V. Khotkevich, S. Morozov, and A. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. USA 102, 10451–10453 (2005).
[Crossref] [PubMed]

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

Jovanovic, D.

A. Matkovic, M. Chhikara, M. Milicevic, U. Ralevic, B. Vasic, D. Jovanovic, M. R. Belic, G. Bratina, and R. S. Gajic, “Influence of a gold substrate on the optical properties of graphene,” J. Appl. Phys. 117, 015305 (2015).
[Crossref]

Jung, I.

I. Jung, J.-S. Rhyee, J. Y. Son, R. S. Ruoff, and K.-Y. Rhee, “Colors of graphene and graphene-oxide multilayers on various substrates,” Nanotechnology 23, 025708 (2012).
[Crossref]

Kamineni, V. K.

F. J. Nelson, V. K. Kamineni, T. Zhang, E. S. Comfort, J. U. Lee, and A. C. Diebold, “Optical properties of large-area polycrystalline chemical vapor deposited graphene by spectroscopic ellipsometry,” Appl. Phys. Lett. 97, 253110 (2010).
[Crossref]

Khotkevich, V.

K. Novoselov, D. Jiang, F. Schedin, T. Booth, V. Khotkevich, S. Morozov, and A. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. USA 102, 10451–10453 (2005).
[Crossref] [PubMed]

Kis, A.

M. M. Benameur, B. Radisavljevic, J. S. Héron, S. Sahoo, H. Berger, and A. Kis, “Visibility of dichalcogenide nanolayers,” Nanotechnology 22, 125706 (2011).
[Crossref] [PubMed]

Kong, X.-T.

Q. Ye, J. Wang, Z. Liu, Z.-C. Deng, X.-T. Kong, F. Xing, X.-D. Chen, W.-Y. Zhou, C.-P. Zhang, and J.-G. Tian, “Polarization-dependent optical absorption of graphene under total internal reflection,” Appl. Phys. Lett. 102, 021912 (2013).
[Crossref]

Kravets, V. G.

V. G. Kravets, A. N. Grigorenko, R. R. Nair, P. Blake, S. Anissimova, K. S. Novoselov, and A. K. Geim, “Spectroscopic ellipsometry of graphene and an exciton-shifted van Hove peak in absorption,” Phys. Rev. B 81, 155413 (2010).
[Crossref]

Lange, P.

M. Dorn, P. Lange, A. Chekushin, N. Severin, and J. P. Rabe, “High contrast optical detection of single graphenes on optically transparent substrates,” J. Appl. Phys. 108, 106101 (2010).
[Crossref]

Lee, C.

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically Thin MoS2: A New Direct-Gap Semiconductor,” Phys. Rev. Lett. 105, 136805 (2010).
[Crossref]

Lee, J. U.

F. J. Nelson, V. K. Kamineni, T. Zhang, E. S. Comfort, J. U. Lee, and A. C. Diebold, “Optical properties of large-area polycrystalline chemical vapor deposited graphene by spectroscopic ellipsometry,” Appl. Phys. Lett. 97, 253110 (2010).
[Crossref]

LeRoy, B. J.

D. Golla, K. Chattrakun, K. Watanabe, T. Taniguchi, B. J. LeRoy, and A. Sandhu, “Optical thickness determination of hexagonal boron nitride flakes,” Appl. Phys. Lett. 102, 161906 (2013).
[Crossref]

Li, Y.

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. M. Hill, A. M. van der Zande, D. A. Chenet, E.-M. Shih, J. Hone, and T. F. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90, 205422 (2014).
[Crossref]

Liu, Z.

Q. Ye, J. Wang, Z. Liu, Z.-C. Deng, X.-T. Kong, F. Xing, X.-D. Chen, W.-Y. Zhou, C.-P. Zhang, and J.-G. Tian, “Polarization-dependent optical absorption of graphene under total internal reflection,” Appl. Phys. Lett. 102, 021912 (2013).
[Crossref]

Ma, Y.

H. Zhang, Y. Ma, Y. Wan, X. Rong, Z. Xie, W. Wang, and L. Dai, “Measuring the Refractive Index of Highly Crystalline Monolayer MoS2 with High Confidence,” Sci. Rep. 5, 8440 (2015).
[Crossref] [PubMed]

Mak, K. F.

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically Thin MoS2: A New Direct-Gap Semiconductor,” Phys. Rev. Lett. 105, 136805 (2010).
[Crossref]

Matkovic, A.

A. Matkovic, M. Chhikara, M. Milicevic, U. Ralevic, B. Vasic, D. Jovanovic, M. R. Belic, G. Bratina, and R. S. Gajic, “Influence of a gold substrate on the optical properties of graphene,” J. Appl. Phys. 117, 015305 (2015).
[Crossref]

Merano, M.

M. Merano, “The Fresnel coefficients of a two-dimensional atomic crystal,” submitted to Phys. Rev. A; arXiv:1509.04136 (2015).

Milicevic, M.

A. Matkovic, M. Chhikara, M. Milicevic, U. Ralevic, B. Vasic, D. Jovanovic, M. R. Belic, G. Bratina, and R. S. Gajic, “Influence of a gold substrate on the optical properties of graphene,” J. Appl. Phys. 117, 015305 (2015).
[Crossref]

Morozov, S.

K. Novoselov, D. Jiang, F. Schedin, T. Booth, V. Khotkevich, S. Morozov, and A. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. USA 102, 10451–10453 (2005).
[Crossref] [PubMed]

Morozov, S. V.

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

Nair, R. R.

R. V. Gorbachev, I. Riaz, R. R. Nair, R. Jalil, L. Britnell, B. D. Belle, E. W. Hill, K. S. Novoselov, K. Watanabe, T. Taniguchi, A. K. Geim, and P. Blake, “Hunting for monolayer boron nitride: Optical and raman signatures,” Small 7, 465–468 (2011).
[Crossref] [PubMed]

V. G. Kravets, A. N. Grigorenko, R. R. Nair, P. Blake, S. Anissimova, K. S. Novoselov, and A. K. Geim, “Spectroscopic ellipsometry of graphene and an exciton-shifted van Hove peak in absorption,” Phys. Rev. B 81, 155413 (2010).
[Crossref]

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 (2008).
[Crossref] [PubMed]

Nelson, F. J.

F. J. Nelson, V. K. Kamineni, T. Zhang, E. S. Comfort, J. U. Lee, and A. C. Diebold, “Optical properties of large-area polycrystalline chemical vapor deposited graphene by spectroscopic ellipsometry,” Appl. Phys. Lett. 97, 253110 (2010).
[Crossref]

Nolte, D. D.

X. Wang, M. Zhao, and D. D. Nolte, “Optical contrast and clarity of graphene on an arbitrary substrate,” Appl. Phys. Lett. 95, 081102 (2009).
[Crossref]

Novoselov, K.

K. Novoselov, D. Jiang, F. Schedin, T. Booth, V. Khotkevich, S. Morozov, and A. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. USA 102, 10451–10453 (2005).
[Crossref] [PubMed]

Novoselov, K. S.

R. V. Gorbachev, I. Riaz, R. R. Nair, R. Jalil, L. Britnell, B. D. Belle, E. W. Hill, K. S. Novoselov, K. Watanabe, T. Taniguchi, A. K. Geim, and P. Blake, “Hunting for monolayer boron nitride: Optical and raman signatures,” Small 7, 465–468 (2011).
[Crossref] [PubMed]

V. G. Kravets, A. N. Grigorenko, R. R. Nair, P. Blake, S. Anissimova, K. S. Novoselov, and A. K. Geim, “Spectroscopic ellipsometry of graphene and an exciton-shifted van Hove peak in absorption,” Phys. Rev. B 81, 155413 (2010).
[Crossref]

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 (2008).
[Crossref] [PubMed]

P. Blake, E. W. Hill, A. H. CastroNeto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91, 063124 (2007).
[Crossref]

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

Pasupathy, A.

M. Vaupel, A. Dutschke, U. Wurstbauer, F. Hitzel, and A. Pasupathy, “Topography, complex refractive index, and conductivity of graphene layers measured by correlation of optical interference contrast, atomic force, and back scattered electron microscopy,” J. Appl. Phys. 114, 183107 (2013).
[Crossref]

Paulava, V.

K. Peters, A. Tittel, N. Gayer, A. Graf, V. Paulava, U. Wurstbauer, and W. Hansen, “Enhancing the visibility of graphene on GaAs,” Appl. Phys. Lett. 99, 191912 (2011).
[Crossref]

Peres, N. M. R.

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 (2008).
[Crossref] [PubMed]

Peters, K.

K. Peters, A. Tittel, N. Gayer, A. Graf, V. Paulava, U. Wurstbauer, and W. Hansen, “Enhancing the visibility of graphene on GaAs,” Appl. Phys. Lett. 99, 191912 (2011).
[Crossref]

Rabe, J. P.

M. Dorn, P. Lange, A. Chekushin, N. Severin, and J. P. Rabe, “High contrast optical detection of single graphenes on optically transparent substrates,” J. Appl. Phys. 108, 106101 (2010).
[Crossref]

Radisavljevic, B.

M. M. Benameur, B. Radisavljevic, J. S. Héron, S. Sahoo, H. Berger, and A. Kis, “Visibility of dichalcogenide nanolayers,” Nanotechnology 22, 125706 (2011).
[Crossref] [PubMed]

Ralevic, U.

A. Matkovic, M. Chhikara, M. Milicevic, U. Ralevic, B. Vasic, D. Jovanovic, M. R. Belic, G. Bratina, and R. S. Gajic, “Influence of a gold substrate on the optical properties of graphene,” J. Appl. Phys. 117, 015305 (2015).
[Crossref]

Rhee, K.-Y.

I. Jung, J.-S. Rhyee, J. Y. Son, R. S. Ruoff, and K.-Y. Rhee, “Colors of graphene and graphene-oxide multilayers on various substrates,” Nanotechnology 23, 025708 (2012).
[Crossref]

Rhyee, J.-S.

I. Jung, J.-S. Rhyee, J. Y. Son, R. S. Ruoff, and K.-Y. Rhee, “Colors of graphene and graphene-oxide multilayers on various substrates,” Nanotechnology 23, 025708 (2012).
[Crossref]

Riaz, I.

R. V. Gorbachev, I. Riaz, R. R. Nair, R. Jalil, L. Britnell, B. D. Belle, E. W. Hill, K. S. Novoselov, K. Watanabe, T. Taniguchi, A. K. Geim, and P. Blake, “Hunting for monolayer boron nitride: Optical and raman signatures,” Small 7, 465–468 (2011).
[Crossref] [PubMed]

Rigosi, A.

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. M. Hill, A. M. van der Zande, D. A. Chenet, E.-M. Shih, J. Hone, and T. F. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90, 205422 (2014).
[Crossref]

Roeling, C.

U. Wurstbauer, C. Roeling, U. Wurstbauer, W. Wegscheider, M. Vaupel, P. H. Thiesen, and D. Weiss, “Imaging ellipsometry of graphene,” Appl. Phys. Lett 97, 231901 (2010).
[Crossref]

Rong, X.

H. Zhang, Y. Ma, Y. Wan, X. Rong, Z. Xie, W. Wang, and L. Dai, “Measuring the Refractive Index of Highly Crystalline Monolayer MoS2 with High Confidence,” Sci. Rep. 5, 8440 (2015).
[Crossref] [PubMed]

Rubio-Bollinger, G.

A. Castellanos-Gomez, N. Agrait, and G. Rubio-Bollinger, “Optical identification of atomically thin dichalcogenide crystals,” Appl. Phys. Lett. 96, 213116 (2010).
[Crossref]

Ruoff, R. S.

I. Jung, J.-S. Rhyee, J. Y. Son, R. S. Ruoff, and K.-Y. Rhee, “Colors of graphene and graphene-oxide multilayers on various substrates,” Nanotechnology 23, 025708 (2012).
[Crossref]

Sahoo, S.

M. M. Benameur, B. Radisavljevic, J. S. Héron, S. Sahoo, H. Berger, and A. Kis, “Visibility of dichalcogenide nanolayers,” Nanotechnology 22, 125706 (2011).
[Crossref] [PubMed]

Sandhu, A.

D. Golla, K. Chattrakun, K. Watanabe, T. Taniguchi, B. J. LeRoy, and A. Sandhu, “Optical thickness determination of hexagonal boron nitride flakes,” Appl. Phys. Lett. 102, 161906 (2013).
[Crossref]

Schedin, F.

K. Novoselov, D. Jiang, F. Schedin, T. Booth, V. Khotkevich, S. Morozov, and A. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. USA 102, 10451–10453 (2005).
[Crossref] [PubMed]

Severin, N.

M. Dorn, P. Lange, A. Chekushin, N. Severin, and J. P. Rabe, “High contrast optical detection of single graphenes on optically transparent substrates,” J. Appl. Phys. 108, 106101 (2010).
[Crossref]

Shan, J.

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically Thin MoS2: A New Direct-Gap Semiconductor,” Phys. Rev. Lett. 105, 136805 (2010).
[Crossref]

Shih, E.-M.

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. M. Hill, A. M. van der Zande, D. A. Chenet, E.-M. Shih, J. Hone, and T. F. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90, 205422 (2014).
[Crossref]

Son, J. Y.

I. Jung, J.-S. Rhyee, J. Y. Son, R. S. Ruoff, and K.-Y. Rhee, “Colors of graphene and graphene-oxide multilayers on various substrates,” Nanotechnology 23, 025708 (2012).
[Crossref]

Stauber, T.

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 (2008).
[Crossref] [PubMed]

Suzuura, H.

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]

Taniguchi, T.

D. Golla, K. Chattrakun, K. Watanabe, T. Taniguchi, B. J. LeRoy, and A. Sandhu, “Optical thickness determination of hexagonal boron nitride flakes,” Appl. Phys. Lett. 102, 161906 (2013).
[Crossref]

R. V. Gorbachev, I. Riaz, R. R. Nair, R. Jalil, L. Britnell, B. D. Belle, E. W. Hill, K. S. Novoselov, K. Watanabe, T. Taniguchi, A. K. Geim, and P. Blake, “Hunting for monolayer boron nitride: Optical and raman signatures,” Small 7, 465–468 (2011).
[Crossref] [PubMed]

Thiesen, P. H.

U. Wurstbauer, C. Roeling, U. Wurstbauer, W. Wegscheider, M. Vaupel, P. H. Thiesen, and D. Weiss, “Imaging ellipsometry of graphene,” Appl. Phys. Lett 97, 231901 (2010).
[Crossref]

Tian, J.-G.

Q. Ye, J. Wang, Z. Liu, Z.-C. Deng, X.-T. Kong, F. Xing, X.-D. Chen, W.-Y. Zhou, C.-P. Zhang, and J.-G. Tian, “Polarization-dependent optical absorption of graphene under total internal reflection,” Appl. Phys. Lett. 102, 021912 (2013).
[Crossref]

Tittel, A.

K. Peters, A. Tittel, N. Gayer, A. Graf, V. Paulava, U. Wurstbauer, and W. Hansen, “Enhancing the visibility of graphene on GaAs,” Appl. Phys. Lett. 99, 191912 (2011).
[Crossref]

van de Sanden, M. C. M.

J. W. Weber, V. E. Calado, and M. C. M. van de Sanden, “Optical constants of graphene measured by spectroscopic ellipsometry,” Appl. Phys. Lett. 97, 091904 (2010).
[Crossref]

van der Zande, A. M.

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. M. Hill, A. M. van der Zande, D. A. Chenet, E.-M. Shih, J. Hone, and T. F. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90, 205422 (2014).
[Crossref]

Vasic, B.

A. Matkovic, M. Chhikara, M. Milicevic, U. Ralevic, B. Vasic, D. Jovanovic, M. R. Belic, G. Bratina, and R. S. Gajic, “Influence of a gold substrate on the optical properties of graphene,” J. Appl. Phys. 117, 015305 (2015).
[Crossref]

Vaupel, M.

M. Vaupel, A. Dutschke, U. Wurstbauer, F. Hitzel, and A. Pasupathy, “Topography, complex refractive index, and conductivity of graphene layers measured by correlation of optical interference contrast, atomic force, and back scattered electron microscopy,” J. Appl. Phys. 114, 183107 (2013).
[Crossref]

U. Wurstbauer, C. Roeling, U. Wurstbauer, W. Wegscheider, M. Vaupel, P. H. Thiesen, and D. Weiss, “Imaging ellipsometry of graphene,” Appl. Phys. Lett 97, 231901 (2010).
[Crossref]

Wan, Y.

H. Zhang, Y. Ma, Y. Wan, X. Rong, Z. Xie, W. Wang, and L. Dai, “Measuring the Refractive Index of Highly Crystalline Monolayer MoS2 with High Confidence,” Sci. Rep. 5, 8440 (2015).
[Crossref] [PubMed]

Wang, J.

Q. Ye, J. Wang, Z. Liu, Z.-C. Deng, X.-T. Kong, F. Xing, X.-D. Chen, W.-Y. Zhou, C.-P. Zhang, and J.-G. Tian, “Polarization-dependent optical absorption of graphene under total internal reflection,” Appl. Phys. Lett. 102, 021912 (2013).
[Crossref]

Wang, W.

H. Zhang, Y. Ma, Y. Wan, X. Rong, Z. Xie, W. Wang, and L. Dai, “Measuring the Refractive Index of Highly Crystalline Monolayer MoS2 with High Confidence,” Sci. Rep. 5, 8440 (2015).
[Crossref] [PubMed]

Wang, X.

X. Wang, M. Zhao, and D. D. Nolte, “Optical contrast and clarity of graphene on an arbitrary substrate,” Appl. Phys. Lett. 95, 081102 (2009).
[Crossref]

Watanabe, K.

D. Golla, K. Chattrakun, K. Watanabe, T. Taniguchi, B. J. LeRoy, and A. Sandhu, “Optical thickness determination of hexagonal boron nitride flakes,” Appl. Phys. Lett. 102, 161906 (2013).
[Crossref]

R. V. Gorbachev, I. Riaz, R. R. Nair, R. Jalil, L. Britnell, B. D. Belle, E. W. Hill, K. S. Novoselov, K. Watanabe, T. Taniguchi, A. K. Geim, and P. Blake, “Hunting for monolayer boron nitride: Optical and raman signatures,” Small 7, 465–468 (2011).
[Crossref] [PubMed]

Weber, J. W.

J. W. Weber, V. E. Calado, and M. C. M. van de Sanden, “Optical constants of graphene measured by spectroscopic ellipsometry,” Appl. Phys. Lett. 97, 091904 (2010).
[Crossref]

Wegscheider, W.

U. Wurstbauer, C. Roeling, U. Wurstbauer, W. Wegscheider, M. Vaupel, P. H. Thiesen, and D. Weiss, “Imaging ellipsometry of graphene,” Appl. Phys. Lett 97, 231901 (2010).
[Crossref]

Weiss, D.

U. Wurstbauer, C. Roeling, U. Wurstbauer, W. Wegscheider, M. Vaupel, P. H. Thiesen, and D. Weiss, “Imaging ellipsometry of graphene,” Appl. Phys. Lett 97, 231901 (2010).
[Crossref]

Wurstbauer, U.

M. Vaupel, A. Dutschke, U. Wurstbauer, F. Hitzel, and A. Pasupathy, “Topography, complex refractive index, and conductivity of graphene layers measured by correlation of optical interference contrast, atomic force, and back scattered electron microscopy,” J. Appl. Phys. 114, 183107 (2013).
[Crossref]

K. Peters, A. Tittel, N. Gayer, A. Graf, V. Paulava, U. Wurstbauer, and W. Hansen, “Enhancing the visibility of graphene on GaAs,” Appl. Phys. Lett. 99, 191912 (2011).
[Crossref]

U. Wurstbauer, C. Roeling, U. Wurstbauer, W. Wegscheider, M. Vaupel, P. H. Thiesen, and D. Weiss, “Imaging ellipsometry of graphene,” Appl. Phys. Lett 97, 231901 (2010).
[Crossref]

U. Wurstbauer, C. Roeling, U. Wurstbauer, W. Wegscheider, M. Vaupel, P. H. Thiesen, and D. Weiss, “Imaging ellipsometry of graphene,” Appl. Phys. Lett 97, 231901 (2010).
[Crossref]

Xie, Z.

H. Zhang, Y. Ma, Y. Wan, X. Rong, Z. Xie, W. Wang, and L. Dai, “Measuring the Refractive Index of Highly Crystalline Monolayer MoS2 with High Confidence,” Sci. Rep. 5, 8440 (2015).
[Crossref] [PubMed]

Xing, F.

Q. Ye, J. Wang, Z. Liu, Z.-C. Deng, X.-T. Kong, F. Xing, X.-D. Chen, W.-Y. Zhou, C.-P. Zhang, and J.-G. Tian, “Polarization-dependent optical absorption of graphene under total internal reflection,” Appl. Phys. Lett. 102, 021912 (2013).
[Crossref]

Yang, R.

P. Blake, E. W. Hill, A. H. CastroNeto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91, 063124 (2007).
[Crossref]

Ye, Q.

Q. Ye, J. Wang, Z. Liu, Z.-C. Deng, X.-T. Kong, F. Xing, X.-D. Chen, W.-Y. Zhou, C.-P. Zhang, and J.-G. Tian, “Polarization-dependent optical absorption of graphene under total internal reflection,” Appl. Phys. Lett. 102, 021912 (2013).
[Crossref]

Zhang, C.-P.

Q. Ye, J. Wang, Z. Liu, Z.-C. Deng, X.-T. Kong, F. Xing, X.-D. Chen, W.-Y. Zhou, C.-P. Zhang, and J.-G. Tian, “Polarization-dependent optical absorption of graphene under total internal reflection,” Appl. Phys. Lett. 102, 021912 (2013).
[Crossref]

Zhang, H.

H. Zhang, Y. Ma, Y. Wan, X. Rong, Z. Xie, W. Wang, and L. Dai, “Measuring the Refractive Index of Highly Crystalline Monolayer MoS2 with High Confidence,” Sci. Rep. 5, 8440 (2015).
[Crossref] [PubMed]

Zhang, T.

F. J. Nelson, V. K. Kamineni, T. Zhang, E. S. Comfort, J. U. Lee, and A. C. Diebold, “Optical properties of large-area polycrystalline chemical vapor deposited graphene by spectroscopic ellipsometry,” Appl. Phys. Lett. 97, 253110 (2010).
[Crossref]

Zhang, X.

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. M. Hill, A. M. van der Zande, D. A. Chenet, E.-M. Shih, J. Hone, and T. F. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90, 205422 (2014).
[Crossref]

Zhang, Y.

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

Zhao, M.

X. Wang, M. Zhao, and D. D. Nolte, “Optical contrast and clarity of graphene on an arbitrary substrate,” Appl. Phys. Lett. 95, 081102 (2009).
[Crossref]

Zheng, Y.

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]

Zhou, W.-Y.

Q. Ye, J. Wang, Z. Liu, Z.-C. Deng, X.-T. Kong, F. Xing, X.-D. Chen, W.-Y. Zhou, C.-P. Zhang, and J.-G. Tian, “Polarization-dependent optical absorption of graphene under total internal reflection,” Appl. Phys. Lett. 102, 021912 (2013).
[Crossref]

Appl. Phys. Lett (1)

U. Wurstbauer, C. Roeling, U. Wurstbauer, W. Wegscheider, M. Vaupel, P. H. Thiesen, and D. Weiss, “Imaging ellipsometry of graphene,” Appl. Phys. Lett 97, 231901 (2010).
[Crossref]

Appl. Phys. Lett. (8)

J. W. Weber, V. E. Calado, and M. C. M. van de Sanden, “Optical constants of graphene measured by spectroscopic ellipsometry,” Appl. Phys. Lett. 97, 091904 (2010).
[Crossref]

Q. Ye, J. Wang, Z. Liu, Z.-C. Deng, X.-T. Kong, F. Xing, X.-D. Chen, W.-Y. Zhou, C.-P. Zhang, and J.-G. Tian, “Polarization-dependent optical absorption of graphene under total internal reflection,” Appl. Phys. Lett. 102, 021912 (2013).
[Crossref]

F. J. Nelson, V. K. Kamineni, T. Zhang, E. S. Comfort, J. U. Lee, and A. C. Diebold, “Optical properties of large-area polycrystalline chemical vapor deposited graphene by spectroscopic ellipsometry,” Appl. Phys. Lett. 97, 253110 (2010).
[Crossref]

P. Blake, E. W. Hill, A. H. CastroNeto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, and A. K. Geim, “Making graphene visible,” Appl. Phys. Lett. 91, 063124 (2007).
[Crossref]

D. Golla, K. Chattrakun, K. Watanabe, T. Taniguchi, B. J. LeRoy, and A. Sandhu, “Optical thickness determination of hexagonal boron nitride flakes,” Appl. Phys. Lett. 102, 161906 (2013).
[Crossref]

K. Peters, A. Tittel, N. Gayer, A. Graf, V. Paulava, U. Wurstbauer, and W. Hansen, “Enhancing the visibility of graphene on GaAs,” Appl. Phys. Lett. 99, 191912 (2011).
[Crossref]

X. Wang, M. Zhao, and D. D. Nolte, “Optical contrast and clarity of graphene on an arbitrary substrate,” Appl. Phys. Lett. 95, 081102 (2009).
[Crossref]

A. Castellanos-Gomez, N. Agrait, and G. Rubio-Bollinger, “Optical identification of atomically thin dichalcogenide crystals,” Appl. Phys. Lett. 96, 213116 (2010).
[Crossref]

J. Appl. Phys. (3)

M. Dorn, P. Lange, A. Chekushin, N. Severin, and J. P. Rabe, “High contrast optical detection of single graphenes on optically transparent substrates,” J. Appl. Phys. 108, 106101 (2010).
[Crossref]

M. Vaupel, A. Dutschke, U. Wurstbauer, F. Hitzel, and A. Pasupathy, “Topography, complex refractive index, and conductivity of graphene layers measured by correlation of optical interference contrast, atomic force, and back scattered electron microscopy,” J. Appl. Phys. 114, 183107 (2013).
[Crossref]

A. Matkovic, M. Chhikara, M. Milicevic, U. Ralevic, B. Vasic, D. Jovanovic, M. R. Belic, G. Bratina, and R. S. Gajic, “Influence of a gold substrate on the optical properties of graphene,” J. Appl. Phys. 117, 015305 (2015).
[Crossref]

J. Phys. Soc. Jpn. (1)

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]

Nanotechnology (2)

M. M. Benameur, B. Radisavljevic, J. S. Héron, S. Sahoo, H. Berger, and A. Kis, “Visibility of dichalcogenide nanolayers,” Nanotechnology 22, 125706 (2011).
[Crossref] [PubMed]

I. Jung, J.-S. Rhyee, J. Y. Son, R. S. Ruoff, and K.-Y. Rhee, “Colors of graphene and graphene-oxide multilayers on various substrates,” Nanotechnology 23, 025708 (2012).
[Crossref]

Phys. Rev. B (2)

V. G. Kravets, A. N. Grigorenko, R. R. Nair, P. Blake, S. Anissimova, K. S. Novoselov, and A. K. Geim, “Spectroscopic ellipsometry of graphene and an exciton-shifted van Hove peak in absorption,” Phys. Rev. B 81, 155413 (2010).
[Crossref]

Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. M. Hill, A. M. van der Zande, D. A. Chenet, E.-M. Shih, J. Hone, and T. F. Heinz, “Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS2, MoSe2, WS2, and WSe2,” Phys. Rev. B 90, 205422 (2014).
[Crossref]

Phys. Rev. Lett. (1)

K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, “Atomically Thin MoS2: A New Direct-Gap Semiconductor,” Phys. Rev. Lett. 105, 136805 (2010).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

K. Novoselov, D. Jiang, F. Schedin, T. Booth, V. Khotkevich, S. Morozov, and A. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. USA 102, 10451–10453 (2005).
[Crossref] [PubMed]

Sci. Rep. (1)

H. Zhang, Y. Ma, Y. Wan, X. Rong, Z. Xie, W. Wang, and L. Dai, “Measuring the Refractive Index of Highly Crystalline Monolayer MoS2 with High Confidence,” Sci. Rep. 5, 8440 (2015).
[Crossref] [PubMed]

Science (2)

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

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 (2008).
[Crossref] [PubMed]

Small (1)

R. V. Gorbachev, I. Riaz, R. R. Nair, R. Jalil, L. Britnell, B. D. Belle, E. W. Hill, K. S. Novoselov, K. Watanabe, T. Taniguchi, A. K. Geim, and P. Blake, “Hunting for monolayer boron nitride: Optical and raman signatures,” Small 7, 465–468 (2011).
[Crossref] [PubMed]

Other (3)

M. Merano, “The Fresnel coefficients of a two-dimensional atomic crystal,” submitted to Phys. Rev. A; arXiv:1509.04136 (2015).

R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Enery Transmission and Radiation(Wiley, 1960).

R. M. Fano, L. J. Chu, and R. B. Adler, Electromagnetic Fields Energy and Forces (Wiley, 1960), pp. 320–324.

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Figures (2)

Fig. 1
Fig. 1 Electromagnetic plane wave reflected and transmitted by an interface between two bulk materials separated by an atomically thin 2D crystal. The electric (magnetic) field for s, (p) polarization is shown.
Fig. 2
Fig. 2 Transmission line analogy for the case in Fig. 1. Z1 and Z2 are the wave impedances in the two media; they are different for the s and p polarization (see text). The atomically thin 2D crystal is analogous to a lumped-circuit load.

Equations (7)

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

E x i + E x r = E x t ; E x i + E x r = i ω P x i ω ε 0 χ ; E x i + E x r = j x σ ; H y i H y r = H y t + i ω P x + J x ; E y i E y r = E y t E y i E y r = i ω P y i ω ε 0 χ E y i E y r = j y σ H x i + H x r = H x t + i ω P y + J y
η 1 H i ( r ) = s ^ i ( r ) × E i ( r ) ; η 2 H t = s ^ t × E t
E x i + E x r = E x t ; Y χ ( E x i + E x r ) = i ω P x ; Y σ ( E x i + E x r ) = j x ; E x i + E x r Z 1 s = E x t Z 2 s + i ω P x + J x ; Z 1 p ( H x i H x r ) = Z 2 p H x t Y χ Z 1 p ( H x i H x r ) = i ω P y Y σ Z 1 p ( H x i H x r ) = j y H x i + H x r = H x t + i ω P y + J y
r s = Z s 2 Z s 1 Z s 1 Z s 2 Y Z s 2 + Z s 1 + Z s 1 Z s 2 Y ; r p = Z p 1 Z p 2 + Z p 1 Z p 2 Y Z p 1 + Z p 2 + Z p 1 Z p 2 Y
Π + i Q = 1 2 E x t J * t o t = 1 2 ( Y σ Y χ ) E x t E x t * = 1 2 ( σ i ω ε 0 χ ) | E x t 2 |
Q = ω ε 0 χ | E x t 2 | = ω P x E x t * = ω W e
2 ( Π + i Q ) | J t o t 2 | = σ i ω ε 0 χ | ( σ + i ω ε 0 χ ) 2 | = Z

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