Abstract

We introduce spinning-disc Picometrology which is designed to measure complex refractive index of ultra-thin and size-limited sample deposited on a solid surface. Picometrology is applied to measure the refractive index of graphene on thermal oxide on silicon. The refractive index varies from ñg=2.4-1.0i at 532 nm to ñg=3.0-1.4i at 633 nm at room temperature. The dispersion is five times stronger than bulk graphite (2.67- 1.34i to 2.73-1.42i from 532 nm to 633 nm).

© 2008 Optical Society of America

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  1. K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, "Two-dimensional atomic crystals," Proc. Natl. Acad. Sci. USA 102, 10451-10453 (2005).
    [CrossRef] [PubMed]
  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]
  3. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, "Two-dimensional gas of massless Dirac fermions in graphene," Nature 438, 197-200 (2005).
    [CrossRef] [PubMed]
  4. Y. B. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, "Experimental observation of the quantum Hall effect and Berry's phase in graphene," Nature 438, 201-204 (2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2008 (2)

F. Wang, Y. B. Zhang, C. S. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, "Gate-variable optical transitions in graphene," Science 320, 206-209 (2008).
[CrossRef] [PubMed]

C. Lee, X. D. Wei, J. W. Kysar, and J. Hone, "Measurement of the elastic properties and intrinsic strength of monolayer graphene," Science 321, 385-388 (2008).
[CrossRef] [PubMed]

2007 (3)

Z. H. Ni, H. M. Wang, J. Kasim, H. M. Fan, T. Yu, Y. H. Wu, Y. P. Feng, and Z. X. Shen, "Graphene thickness determination using reflection and contrast spectroscopy," Nano Lett. 7, 2758-2763 (2007).
[CrossRef] [PubMed]

I. Jung, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, S. Watcharotone, M. Hausner, and R. S. Ruoff, "Simple approach for high-contrast optical imaging and characterization of graphene-based sheets," Nano Lett. 7, 3569-3575 (2007).
[CrossRef]

X. F. Wang, M. Zhao, and D. D. Nolte, "Common-path interferometric detection of protein monolayer on the BioCD," Appl. Opt. 46, 7836-7849 (2007).
[CrossRef] [PubMed]

2006 (1)

A. Calogeracos, "Relativistic quantum mechanics - Paradox in a pencil," Nature Phys. 2, 579-580 (2006).
[CrossRef]

2005 (3)

K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. 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, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, "Two-dimensional gas of massless Dirac fermions in graphene," Nature 438, 197-200 (2005).
[CrossRef] [PubMed]

Y. B. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, "Experimental observation of the quantum Hall effect and Berry's phase in graphene," Nature 438, 201-204 (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]

2003 (1)

J. Li, H. T. Ng, A. Cassell, W. Fan, H. Chen, Q. Ye, J. Koehne, J. Han, and M. Meyyappan, "Carbon nanotube nanoelectrode array for ultrasensitive DNA detection," Nano Lett. 3, 597-602 (2003).
[CrossRef]

1999 (1)

A. B. Djurisic and E. H. Li, "Optical properties of graphite," J. Appl. Phys. 85, 7404-7410 (1999).
[CrossRef]

1996 (1)

P. Hoyer, "Formation of a titanium dioxide nanotube array," Langmuir 12, 1411-1413 (1996).
[CrossRef]

Booth, T. J.

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

Calogeracos, A.

A. Calogeracos, "Relativistic quantum mechanics - Paradox in a pencil," Nature Phys. 2, 579-580 (2006).
[CrossRef]

Cassell, A.

J. Li, H. T. Ng, A. Cassell, W. Fan, H. Chen, Q. Ye, J. Koehne, J. Han, and M. Meyyappan, "Carbon nanotube nanoelectrode array for ultrasensitive DNA detection," Nano Lett. 3, 597-602 (2003).
[CrossRef]

Chen, H.

J. Li, H. T. Ng, A. Cassell, W. Fan, H. Chen, Q. Ye, J. Koehne, J. Han, and M. Meyyappan, "Carbon nanotube nanoelectrode array for ultrasensitive DNA detection," Nano Lett. 3, 597-602 (2003).
[CrossRef]

Crommie, M.

F. Wang, Y. B. Zhang, C. S. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, "Gate-variable optical transitions in graphene," Science 320, 206-209 (2008).
[CrossRef] [PubMed]

Dikin, D. A.

I. Jung, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, S. Watcharotone, M. Hausner, and R. S. Ruoff, "Simple approach for high-contrast optical imaging and characterization of graphene-based sheets," Nano Lett. 7, 3569-3575 (2007).
[CrossRef]

Djurisic, A. B.

A. B. Djurisic and E. H. Li, "Optical properties of graphite," J. Appl. Phys. 85, 7404-7410 (1999).
[CrossRef]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, "Two-dimensional gas of massless Dirac fermions in graphene," Nature 438, 197-200 (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]

Fan, H. M.

Z. H. Ni, H. M. Wang, J. Kasim, H. M. Fan, T. Yu, Y. H. Wu, Y. P. Feng, and Z. X. Shen, "Graphene thickness determination using reflection and contrast spectroscopy," Nano Lett. 7, 2758-2763 (2007).
[CrossRef] [PubMed]

Fan, W.

J. Li, H. T. Ng, A. Cassell, W. Fan, H. Chen, Q. Ye, J. Koehne, J. Han, and M. Meyyappan, "Carbon nanotube nanoelectrode array for ultrasensitive DNA detection," Nano Lett. 3, 597-602 (2003).
[CrossRef]

Feng, Y. P.

Z. H. Ni, H. M. Wang, J. Kasim, H. M. Fan, T. Yu, Y. H. Wu, Y. P. Feng, and Z. X. Shen, "Graphene thickness determination using reflection and contrast spectroscopy," Nano Lett. 7, 2758-2763 (2007).
[CrossRef] [PubMed]

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, "Two-dimensional gas of massless Dirac fermions in graphene," Nature 438, 197-200 (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]

Geim, A. K.

K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. 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, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, "Two-dimensional gas of massless Dirac fermions in graphene," Nature 438, 197-200 (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]

Girit, C.

F. Wang, Y. B. Zhang, C. S. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, "Gate-variable optical transitions in graphene," Science 320, 206-209 (2008).
[CrossRef] [PubMed]

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, "Two-dimensional gas of massless Dirac fermions in graphene," Nature 438, 197-200 (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]

Han, J.

J. Li, H. T. Ng, A. Cassell, W. Fan, H. Chen, Q. Ye, J. Koehne, J. Han, and M. Meyyappan, "Carbon nanotube nanoelectrode array for ultrasensitive DNA detection," Nano Lett. 3, 597-602 (2003).
[CrossRef]

Hausner, M.

I. Jung, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, S. Watcharotone, M. Hausner, and R. S. Ruoff, "Simple approach for high-contrast optical imaging and characterization of graphene-based sheets," Nano Lett. 7, 3569-3575 (2007).
[CrossRef]

Hone, J.

C. Lee, X. D. Wei, J. W. Kysar, and J. Hone, "Measurement of the elastic properties and intrinsic strength of monolayer graphene," Science 321, 385-388 (2008).
[CrossRef] [PubMed]

Hoyer, P.

P. Hoyer, "Formation of a titanium dioxide nanotube array," Langmuir 12, 1411-1413 (1996).
[CrossRef]

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, "Two-dimensional gas of massless Dirac fermions in graphene," Nature 438, 197-200 (2005).
[CrossRef] [PubMed]

K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. 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]

Jung, I.

I. Jung, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, S. Watcharotone, M. Hausner, and R. S. Ruoff, "Simple approach for high-contrast optical imaging and characterization of graphene-based sheets," Nano Lett. 7, 3569-3575 (2007).
[CrossRef]

Kasim, J.

Z. H. Ni, H. M. Wang, J. Kasim, H. M. Fan, T. Yu, Y. H. Wu, Y. P. Feng, and Z. X. Shen, "Graphene thickness determination using reflection and contrast spectroscopy," Nano Lett. 7, 2758-2763 (2007).
[CrossRef] [PubMed]

Katsnelson, M. I.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, "Two-dimensional gas of massless Dirac fermions in graphene," Nature 438, 197-200 (2005).
[CrossRef] [PubMed]

Khotkevich, V. V.

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

Kim, P.

Y. B. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, "Experimental observation of the quantum Hall effect and Berry's phase in graphene," Nature 438, 201-204 (2005).
[CrossRef] [PubMed]

Koehne, J.

J. Li, H. T. Ng, A. Cassell, W. Fan, H. Chen, Q. Ye, J. Koehne, J. Han, and M. Meyyappan, "Carbon nanotube nanoelectrode array for ultrasensitive DNA detection," Nano Lett. 3, 597-602 (2003).
[CrossRef]

Kysar, J. W.

C. Lee, X. D. Wei, J. W. Kysar, and J. Hone, "Measurement of the elastic properties and intrinsic strength of monolayer graphene," Science 321, 385-388 (2008).
[CrossRef] [PubMed]

Lee, C.

C. Lee, X. D. Wei, J. W. Kysar, and J. Hone, "Measurement of the elastic properties and intrinsic strength of monolayer graphene," Science 321, 385-388 (2008).
[CrossRef] [PubMed]

Li, E. H.

A. B. Djurisic and E. H. Li, "Optical properties of graphite," J. Appl. Phys. 85, 7404-7410 (1999).
[CrossRef]

Li, J.

J. Li, H. T. Ng, A. Cassell, W. Fan, H. Chen, Q. Ye, J. Koehne, J. Han, and M. Meyyappan, "Carbon nanotube nanoelectrode array for ultrasensitive DNA detection," Nano Lett. 3, 597-602 (2003).
[CrossRef]

Meyyappan, M.

J. Li, H. T. Ng, A. Cassell, W. Fan, H. Chen, Q. Ye, J. Koehne, J. Han, and M. Meyyappan, "Carbon nanotube nanoelectrode array for ultrasensitive DNA detection," Nano Lett. 3, 597-602 (2003).
[CrossRef]

Morozov, S. V.

K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. 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, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, "Two-dimensional gas of massless Dirac fermions in graphene," Nature 438, 197-200 (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]

Ng, H. T.

J. Li, H. T. Ng, A. Cassell, W. Fan, H. Chen, Q. Ye, J. Koehne, J. Han, and M. Meyyappan, "Carbon nanotube nanoelectrode array for ultrasensitive DNA detection," Nano Lett. 3, 597-602 (2003).
[CrossRef]

Ni, Z. H.

Z. H. Ni, H. M. Wang, J. Kasim, H. M. Fan, T. Yu, Y. H. Wu, Y. P. Feng, and Z. X. Shen, "Graphene thickness determination using reflection and contrast spectroscopy," Nano Lett. 7, 2758-2763 (2007).
[CrossRef] [PubMed]

Nolte, D. D.

Novoselov, K. S.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, "Two-dimensional gas of massless Dirac fermions in graphene," Nature 438, 197-200 (2005).
[CrossRef] [PubMed]

K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. 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]

Pelton, M.

I. Jung, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, S. Watcharotone, M. Hausner, and R. S. Ruoff, "Simple approach for high-contrast optical imaging and characterization of graphene-based sheets," Nano Lett. 7, 3569-3575 (2007).
[CrossRef]

Piner, R.

I. Jung, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, S. Watcharotone, M. Hausner, and R. S. Ruoff, "Simple approach for high-contrast optical imaging and characterization of graphene-based sheets," Nano Lett. 7, 3569-3575 (2007).
[CrossRef]

Ruoff, R. S.

I. Jung, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, S. Watcharotone, M. Hausner, and R. S. Ruoff, "Simple approach for high-contrast optical imaging and characterization of graphene-based sheets," Nano Lett. 7, 3569-3575 (2007).
[CrossRef]

Schedin, F.

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

Shen, Y. R.

F. Wang, Y. B. Zhang, C. S. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, "Gate-variable optical transitions in graphene," Science 320, 206-209 (2008).
[CrossRef] [PubMed]

Shen, Z. X.

Z. H. Ni, H. M. Wang, J. Kasim, H. M. Fan, T. Yu, Y. H. Wu, Y. P. Feng, and Z. X. Shen, "Graphene thickness determination using reflection and contrast spectroscopy," Nano Lett. 7, 2758-2763 (2007).
[CrossRef] [PubMed]

Stankovich, S.

I. Jung, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, S. Watcharotone, M. Hausner, and R. S. Ruoff, "Simple approach for high-contrast optical imaging and characterization of graphene-based sheets," Nano Lett. 7, 3569-3575 (2007).
[CrossRef]

Stormer, H. L.

Y. B. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, "Experimental observation of the quantum Hall effect and Berry's phase in graphene," Nature 438, 201-204 (2005).
[CrossRef] [PubMed]

Tan, Y. W.

Y. B. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, "Experimental observation of the quantum Hall effect and Berry's phase in graphene," Nature 438, 201-204 (2005).
[CrossRef] [PubMed]

Tian, C. S.

F. Wang, Y. B. Zhang, C. S. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, "Gate-variable optical transitions in graphene," Science 320, 206-209 (2008).
[CrossRef] [PubMed]

Wang, F.

F. Wang, Y. B. Zhang, C. S. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, "Gate-variable optical transitions in graphene," Science 320, 206-209 (2008).
[CrossRef] [PubMed]

Wang, H. M.

Z. H. Ni, H. M. Wang, J. Kasim, H. M. Fan, T. Yu, Y. H. Wu, Y. P. Feng, and Z. X. Shen, "Graphene thickness determination using reflection and contrast spectroscopy," Nano Lett. 7, 2758-2763 (2007).
[CrossRef] [PubMed]

Wang, X. F.

Watcharotone, S.

I. Jung, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, S. Watcharotone, M. Hausner, and R. S. Ruoff, "Simple approach for high-contrast optical imaging and characterization of graphene-based sheets," Nano Lett. 7, 3569-3575 (2007).
[CrossRef]

Wei, X. D.

C. Lee, X. D. Wei, J. W. Kysar, and J. Hone, "Measurement of the elastic properties and intrinsic strength of monolayer graphene," Science 321, 385-388 (2008).
[CrossRef] [PubMed]

Wu, Y. H.

Z. H. Ni, H. M. Wang, J. Kasim, H. M. Fan, T. Yu, Y. H. Wu, Y. P. Feng, and Z. X. Shen, "Graphene thickness determination using reflection and contrast spectroscopy," Nano Lett. 7, 2758-2763 (2007).
[CrossRef] [PubMed]

Ye, Q.

J. Li, H. T. Ng, A. Cassell, W. Fan, H. Chen, Q. Ye, J. Koehne, J. Han, and M. Meyyappan, "Carbon nanotube nanoelectrode array for ultrasensitive DNA detection," Nano Lett. 3, 597-602 (2003).
[CrossRef]

Yu, T.

Z. H. Ni, H. M. Wang, J. Kasim, H. M. Fan, T. Yu, Y. H. Wu, Y. P. Feng, and Z. X. Shen, "Graphene thickness determination using reflection and contrast spectroscopy," Nano Lett. 7, 2758-2763 (2007).
[CrossRef] [PubMed]

Zettl, A.

F. Wang, Y. B. Zhang, C. S. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, "Gate-variable optical transitions in graphene," Science 320, 206-209 (2008).
[CrossRef] [PubMed]

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]

Zhang, Y. B.

F. Wang, Y. B. Zhang, C. S. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, "Gate-variable optical transitions in graphene," Science 320, 206-209 (2008).
[CrossRef] [PubMed]

Y. B. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, "Experimental observation of the quantum Hall effect and Berry's phase in graphene," Nature 438, 201-204 (2005).
[CrossRef] [PubMed]

Zhao, M.

Appl. Opt. (1)

J. Appl. Phys. (1)

A. B. Djurisic and E. H. Li, "Optical properties of graphite," J. Appl. Phys. 85, 7404-7410 (1999).
[CrossRef]

Langmuir (1)

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[CrossRef]

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J. Li, H. T. Ng, A. Cassell, W. Fan, H. Chen, Q. Ye, J. Koehne, J. Han, and M. Meyyappan, "Carbon nanotube nanoelectrode array for ultrasensitive DNA detection," Nano Lett. 3, 597-602 (2003).
[CrossRef]

Z. H. Ni, H. M. Wang, J. Kasim, H. M. Fan, T. Yu, Y. H. Wu, Y. P. Feng, and Z. X. Shen, "Graphene thickness determination using reflection and contrast spectroscopy," Nano Lett. 7, 2758-2763 (2007).
[CrossRef] [PubMed]

I. Jung, M. Pelton, R. Piner, D. A. Dikin, S. Stankovich, S. Watcharotone, M. Hausner, and R. S. Ruoff, "Simple approach for high-contrast optical imaging and characterization of graphene-based sheets," Nano Lett. 7, 3569-3575 (2007).
[CrossRef]

Nature (2)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, "Two-dimensional gas of massless Dirac fermions in graphene," Nature 438, 197-200 (2005).
[CrossRef] [PubMed]

Y. B. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, "Experimental observation of the quantum Hall effect and Berry's phase in graphene," Nature 438, 201-204 (2005).
[CrossRef] [PubMed]

Nature Phys. (1)

A. Calogeracos, "Relativistic quantum mechanics - Paradox in a pencil," Nature Phys. 2, 579-580 (2006).
[CrossRef]

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

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

Science (3)

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]

C. Lee, X. D. Wei, J. W. Kysar, and J. Hone, "Measurement of the elastic properties and intrinsic strength of monolayer graphene," Science 321, 385-388 (2008).
[CrossRef] [PubMed]

F. Wang, Y. B. Zhang, C. S. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, "Gate-variable optical transitions in graphene," Science 320, 206-209 (2008).
[CrossRef] [PubMed]

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B. T. Kelly, Physics of Graphite (Applied Science, London, 1981).

M. S. Dresselhaus, G. Dresselhaus, and P. C. Eklund, Science of Fullerenes and Carbon Nanotubes (Academic Press, San Diego, 1996).

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Figures (6)

Fig. 1.
Fig. 1.

Principles of Picometrology. A graphene layer modifies the reflection coefficient r̃ of a substrate into r̃′ according to Eq. (3). By measuring both the amplitude change and phase change of r̃, the complex ñg can be calculated. (a) A focused Gaussian beam scans across a graphene sample. The reflected light forms a Fraunhoffer diffraction pattern in the far field or Fourier plane. (b) When the spot scans across the edge of the graphene, the center of the diffraction pattern is shifted from the original position due to the phase difference between r̃ and r̃′. When the spot is on the graphene, the reflected intensity drops due to the amplitude difference between r̃ and r̃′. By combining the center shift and intensity drop of the diffraction pattern, the full change of r̃ is calculated. (c) A split detector is used to monitor the intensity drop and center shift simultaneously. The output I and PC signals are directly related with ñg by Eq. (6).

Fig. 2.
Fig. 2.

The optical layout of the Picometrology system.

Fig. 3.
Fig. 3.

Two graphene samples scanned under 532 nm wavelength. The substrates for two graphene monolayer samples are silicon wafers grown with 310 nm and 285 nm SiO2 respectively. The normalized amplitudes of I and PC signals are calculated and listed in Table 1. Using Eq.6, ñg was calculated to be 2.37-0.97i and 2.37 -1.07i for sample 1 and 2.

Fig. 4.
Fig. 4.

Two graphene samples scanned under 633 nm wavelength. The normalized amplitudes of I and PC signals are calculated and listed in Table 1. Using Eq. 6, ñg was calculated to be 2.95-1.32i and 2.98 -1.44i for samples 1 and 2.

Fig. 5.
Fig. 5.

Complex refractive indexes of graphene monolayer, bilayer (based on the results of sample 2) and bulk graphite (ordinary refractive index).

Fig. 6.
Fig. 6.

Calculation method for the full PC signal

Tables (1)

Tables Icon

Table 1. The conditions of and results for refractive index measurement of graphene

Equations (8)

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r ˜ = ( e i δ g e i δ g ) r ˜ g + r ˜ ( e i δ g r ˜ g 2 e i δ g ) ( e i δ g r ˜ g 2 e i δ g ) + r ˜ ( e i δ g e i δ g ) r ˜ g e 2 i δ g n ˜ g
r ˜ = r ˜ + [ ( r ˜ g r ˜ ) ( 1 r ˜ r ˜ g ) ( 1 r ˜ g 2 ) + r ˜ n ˜ g ] 4 π i n ˜ g d λ
r ˜ = r ˜ + ( 1 + r ˜ ) 2 ( 1 n ˜ g 2 ) π i λ d
i I ( x ) = Im [ ( n ˜ g 2 1 ) ( 1 + r ˜ ) 2 r ˜ ] 2 π d λ g 2 ( x ) s ( x )
i PC ( x ) = Re [ ( n ˜ g 2 1 ) ( 1 + r ˜ ) 2 r ˜ ] 2 π d λ ( D ( x ) × g ( x ) ) s ( x )
A [ i I ( x ) ] = Im [ ( n ˜ g 2 1 ) ( 1 + r ˜ ) 2 r ˜ ] 2 π d λ A [ g 2 ( x ) s ( x ) ]
A [ i PC ( x ) ] = Re [ ( n ˜ g 2 1 ) ( 1 + r ˜ ) 2 r ˜ ] 2 π d λ A [ ( D ( x ) × g ( x ) ) s ( x ) ]
( n ˜ g 2 1 ) ( 1 + r ˜ ) 2 r ˜ 2 π d λ = 3.565 A [ i PC ( x ) ] + A [ i I ( x ) ] i

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