Abstract

The ability to control the light-matter interaction in the deep subwavelength regime has fascinating consequences for material sciences and a range of photonics technologies. The statistical properties of emerging fields strongly depend on both the source of radiation and specific characteristics of the material system. Here we consider the coherence properties in the proximity of surfaces illuminated by strongly randomized optical fields and demonstrate that the spatial extent of near-field correlations depends on the density of defects in two-dimensional crystalline lattices. We also show that this effect can be used as an efficient elastic scattering method to characterize the density of defects in two-dimensional crystalline materials. Systematic experiments demonstrate the relationship between the spatial coherence length of scattered light and a characteristic length associated with structural disorder in graphene. The fact that one single layer of atoms can modify properties of electromagnetic radiation could lead to new means of controlling light at subwavelength scales and has implications for the emerging field of two-dimensional materials.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Near-field to far-field characterization of speckle patterns generated by disordered nanomaterials

Valentina Parigi, Elodie Perros, Guillaume Binard, Céline Bourdillon, Agnès Maître, Rémi Carminati, Valentina Krachmalnicoff, and Yannick De Wilde
Opt. Express 24(7) 7019-7027 (2016)

First- and second-order statistics of optical near fields

Adela Apostol and Aristide Dogariu
Opt. Lett. 29(3) 235-237 (2004)

Light spectra in the near field of random media

A. Apostol and A. Dogariu
Opt. Lett. 29(9) 920-922 (2004)

References

  • View by:
  • |
  • |
  • |

  1. W. H. Carter and E. Wolf, “Coherence properties of Lambertian and non-Lambertian sources,” J. Opt. Soc. Am. 65, 1067–1071 (1975).
    [Crossref]
  2. A. Dogariu and R. Carminati, “Electromagnetic field correlations in three-dimensional speckles,” Phys. Rep. 559, 1–29 (2015).
    [Crossref]
  3. A. Apostol and A. Dogariu, “Spatial correlations in the near field of random media,” Phys. Rev. Lett. 91, 093901 (2003).
    [Crossref]
  4. C. Henkel, K. Joulain, R. Carminati, and J.-J. Greffet, “Spatial coherence of thermal near fields,” Opt. Commun. 186, 57–67 (2000).
    [Crossref]
  5. H. Roychowdhury and E. Wolf, “Effects of spatial coherence on near-field spectra,” Opt. Lett. 28, 170–172 (2003).
    [Crossref]
  6. R. Carminati, “Subwavelength spatial correlations in near-field speckle patterns,” Phys. Rev. A 81, 053804 (2010).
    [Crossref]
  7. A. Apostol and A. Dogariu, “Coherence properties near interfaces of random media,” Phys. Rev. E 67, 055601 (2003).
    [Crossref]
  8. V. Parigi, E. Perros, G. Binard, C. Bourdillon, A. Maître, R. Carminati, V. Krachmalnicoff, and Y. D. Wilde, “Near-field to far-field characterization of speckle patterns generated by disordered nanomaterials,” Opt. Express 24, 7019–7027 (2016).
    [Crossref]
  9. R. R. Naraghi, S. Sukhov, and A. Dogariu, “Disorder fingerprint: intensity distributions in the near field of random media,” Phys. Rev. B 94, 174205 (2016).
    [Crossref]
  10. F. Banhart, J. Kotakoski, and A. V. Krasheninnikov, “Structural defects in graphene,” ACS Nano 5, 26–41 (2011).
    [Crossref]
  11. O. V. Yazyev and Y. P. Chen, “Polycrystalline graphene and other two-dimensional materials,” Nat. Nanotechnol. 9, 755–767 (2014).
    [Crossref]
  12. L. Vicarelli, S. J. Heerema, C. Dekker, and H. W. Zandbergen, “Controlling defects in graphene for optimizing the electrical properties of graphene nanodevices,” ACS Nano 9, 3428–3435 (2015).
    [Crossref]
  13. W. Zhao, Y. Wang, Z. Wu, W. Wang, K. Bi, Z. Liang, J. Yang, Y. Chen, Z. Xu, and Z. Ni, “Defect-engineered heat transport in graphene: a route to high efficient thermal rectification,” Sci. Rep. 5, 11962 (2015).
    [Crossref]
  14. T. V. Alencar, M. G. Silva, L. M. Malard, and A. M. de Paula, “Defect-induced supercollision cooling of photoexcited carriers in graphene,” Nano Lett. 14, 5621–5624 (2014).
    [Crossref]
  15. Z.-J. Wang, G. Weinberg, Q. Zhang, T. Lunkenbein, A. Klein-Hoffmann, M. Kurnatowska, M. Plodinec, Q. Li, L. Chi, R. Schloegl, and M.-G. Willinger, “Direct observation of graphene growth and associated copper substrate dynamics by in situ scanning electron microscopy,” ACS Nano 9, 1506–1519 (2015).
    [Crossref]
  16. A. W. Robertson and J. H. Warner, “Atomic resolution imaging of graphene by transmission electron microscopy,” Nanoscale 5, 4079–4093 (2013).
    [Crossref]
  17. G. López-Polín, C. Gómez-Navarro, V. Parente, F. Guinea, M. I. Katsnelson, F. Pérez-Murano, and J. Gómez-Herrero, “Increasing the elastic modulus of graphene by controlled defect creation,” Nat. Phys. 11, 26–31 (2015).
    [Crossref]
  18. J. C. Koepke, J. D. Wood, D. Estrada, Z.-Y. Ong, K. T. He, E. Pop, and J. W. Lyding, “Atomic-scale evidence for potential barriers and strong carrier scattering at graphene grain boundaries: a scanning tunneling microscopy study,” ACS Nano 7, 75–86 (2013).
    [Crossref]
  19. R. Beams, L. G. Cançado, and L. Novotny, “Raman characterization of defects and dopants in graphene,” J. Phys. Condens. Matter 27, 83002 (2015).
    [Crossref]
  20. A. C. Ferrari and D. M. Basko, “Raman spectroscopy as a versatile tool for studying the properties of graphene,” Nat. Nanotechnol. 8, 235–246 (2013).
    [Crossref]
  21. L. G. Cançado, A. Jorio, E. H. M. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
    [Crossref]
  22. M. M. Lucchese, F. Stavale, E. H. M. Ferreira, C. Vilani, M. V. O. Moutinho, R. B. Capaz, C. A. Achete, and A. Jorio, “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon 48, 1592–1597 (2010).
    [Crossref]
  23. J. Ribeiro-Soares, M. E. Oliveros, C. Garin, M. V. David, L. G. P. Martins, C. A. Almeida, E. H. Martins-Ferreira, K. Takai, T. Enoki, R. Magalhães-Paniago, A. Malachias, A. Jorio, B. S. Archanjo, C. A. Achete, and L. G. Cançado, “Structural analysis of polycrystalline graphene systems by Raman spectroscopy,” Carbon 95, 646–652 (2015).
    [Crossref]
  24. A. Eckmann, A. Felten, A. Mishchenko, L. Britnell, R. Krupke, K. S. Novoselov, and C. Casiraghi, “Probing the nature of defects in graphene by Raman spectroscopy,” Nano Lett. 12, 3925–3930 (2012).
    [Crossref]
  25. Y. Huang, E. Sutter, N. N. Shi, J. Zheng, T. Yang, D. Englund, H.-J. Gao, and P. Sutter, “Reliable exfoliation of large-area high-quality flakes of graphene and other two-dimensional materials,” ACS Nano 9, 10612–10620 (2015).
    [Crossref]
  26. M. C. Prado, D. Jariwala, T. J. Marks, and M. C. Hersam, “Optimization of graphene dry etching conditions via combined microscopic and spectroscopic analysis,” Appl. Phys. Lett. 102, 193111 (2013).
    [Crossref]
  27. C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
    [Crossref]
  28. R. Beams, L. G. Cançado, and L. Novotny, “Low temperature Raman study of the electron coherence length near graphene edges,” Nano Lett. 11, 1177–1181 (2011).
    [Crossref]

2016 (2)

2015 (8)

A. Dogariu and R. Carminati, “Electromagnetic field correlations in three-dimensional speckles,” Phys. Rep. 559, 1–29 (2015).
[Crossref]

L. Vicarelli, S. J. Heerema, C. Dekker, and H. W. Zandbergen, “Controlling defects in graphene for optimizing the electrical properties of graphene nanodevices,” ACS Nano 9, 3428–3435 (2015).
[Crossref]

W. Zhao, Y. Wang, Z. Wu, W. Wang, K. Bi, Z. Liang, J. Yang, Y. Chen, Z. Xu, and Z. Ni, “Defect-engineered heat transport in graphene: a route to high efficient thermal rectification,” Sci. Rep. 5, 11962 (2015).
[Crossref]

Z.-J. Wang, G. Weinberg, Q. Zhang, T. Lunkenbein, A. Klein-Hoffmann, M. Kurnatowska, M. Plodinec, Q. Li, L. Chi, R. Schloegl, and M.-G. Willinger, “Direct observation of graphene growth and associated copper substrate dynamics by in situ scanning electron microscopy,” ACS Nano 9, 1506–1519 (2015).
[Crossref]

G. López-Polín, C. Gómez-Navarro, V. Parente, F. Guinea, M. I. Katsnelson, F. Pérez-Murano, and J. Gómez-Herrero, “Increasing the elastic modulus of graphene by controlled defect creation,” Nat. Phys. 11, 26–31 (2015).
[Crossref]

R. Beams, L. G. Cançado, and L. Novotny, “Raman characterization of defects and dopants in graphene,” J. Phys. Condens. Matter 27, 83002 (2015).
[Crossref]

J. Ribeiro-Soares, M. E. Oliveros, C. Garin, M. V. David, L. G. P. Martins, C. A. Almeida, E. H. Martins-Ferreira, K. Takai, T. Enoki, R. Magalhães-Paniago, A. Malachias, A. Jorio, B. S. Archanjo, C. A. Achete, and L. G. Cançado, “Structural analysis of polycrystalline graphene systems by Raman spectroscopy,” Carbon 95, 646–652 (2015).
[Crossref]

Y. Huang, E. Sutter, N. N. Shi, J. Zheng, T. Yang, D. Englund, H.-J. Gao, and P. Sutter, “Reliable exfoliation of large-area high-quality flakes of graphene and other two-dimensional materials,” ACS Nano 9, 10612–10620 (2015).
[Crossref]

2014 (2)

T. V. Alencar, M. G. Silva, L. M. Malard, and A. M. de Paula, “Defect-induced supercollision cooling of photoexcited carriers in graphene,” Nano Lett. 14, 5621–5624 (2014).
[Crossref]

O. V. Yazyev and Y. P. Chen, “Polycrystalline graphene and other two-dimensional materials,” Nat. Nanotechnol. 9, 755–767 (2014).
[Crossref]

2013 (4)

J. C. Koepke, J. D. Wood, D. Estrada, Z.-Y. Ong, K. T. He, E. Pop, and J. W. Lyding, “Atomic-scale evidence for potential barriers and strong carrier scattering at graphene grain boundaries: a scanning tunneling microscopy study,” ACS Nano 7, 75–86 (2013).
[Crossref]

A. W. Robertson and J. H. Warner, “Atomic resolution imaging of graphene by transmission electron microscopy,” Nanoscale 5, 4079–4093 (2013).
[Crossref]

M. C. Prado, D. Jariwala, T. J. Marks, and M. C. Hersam, “Optimization of graphene dry etching conditions via combined microscopic and spectroscopic analysis,” Appl. Phys. Lett. 102, 193111 (2013).
[Crossref]

A. C. Ferrari and D. M. Basko, “Raman spectroscopy as a versatile tool for studying the properties of graphene,” Nat. Nanotechnol. 8, 235–246 (2013).
[Crossref]

2012 (1)

A. Eckmann, A. Felten, A. Mishchenko, L. Britnell, R. Krupke, K. S. Novoselov, and C. Casiraghi, “Probing the nature of defects in graphene by Raman spectroscopy,” Nano Lett. 12, 3925–3930 (2012).
[Crossref]

2011 (3)

L. G. Cançado, A. Jorio, E. H. M. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

F. Banhart, J. Kotakoski, and A. V. Krasheninnikov, “Structural defects in graphene,” ACS Nano 5, 26–41 (2011).
[Crossref]

R. Beams, L. G. Cançado, and L. Novotny, “Low temperature Raman study of the electron coherence length near graphene edges,” Nano Lett. 11, 1177–1181 (2011).
[Crossref]

2010 (2)

R. Carminati, “Subwavelength spatial correlations in near-field speckle patterns,” Phys. Rev. A 81, 053804 (2010).
[Crossref]

M. M. Lucchese, F. Stavale, E. H. M. Ferreira, C. Vilani, M. V. O. Moutinho, R. B. Capaz, C. A. Achete, and A. Jorio, “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon 48, 1592–1597 (2010).
[Crossref]

2009 (1)

C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
[Crossref]

2003 (3)

A. Apostol and A. Dogariu, “Coherence properties near interfaces of random media,” Phys. Rev. E 67, 055601 (2003).
[Crossref]

H. Roychowdhury and E. Wolf, “Effects of spatial coherence on near-field spectra,” Opt. Lett. 28, 170–172 (2003).
[Crossref]

A. Apostol and A. Dogariu, “Spatial correlations in the near field of random media,” Phys. Rev. Lett. 91, 093901 (2003).
[Crossref]

2000 (1)

C. Henkel, K. Joulain, R. Carminati, and J.-J. Greffet, “Spatial coherence of thermal near fields,” Opt. Commun. 186, 57–67 (2000).
[Crossref]

1975 (1)

Achete, C. A.

J. Ribeiro-Soares, M. E. Oliveros, C. Garin, M. V. David, L. G. P. Martins, C. A. Almeida, E. H. Martins-Ferreira, K. Takai, T. Enoki, R. Magalhães-Paniago, A. Malachias, A. Jorio, B. S. Archanjo, C. A. Achete, and L. G. Cançado, “Structural analysis of polycrystalline graphene systems by Raman spectroscopy,” Carbon 95, 646–652 (2015).
[Crossref]

L. G. Cançado, A. Jorio, E. H. M. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

M. M. Lucchese, F. Stavale, E. H. M. Ferreira, C. Vilani, M. V. O. Moutinho, R. B. Capaz, C. A. Achete, and A. Jorio, “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon 48, 1592–1597 (2010).
[Crossref]

Alencar, T. V.

T. V. Alencar, M. G. Silva, L. M. Malard, and A. M. de Paula, “Defect-induced supercollision cooling of photoexcited carriers in graphene,” Nano Lett. 14, 5621–5624 (2014).
[Crossref]

Almeida, C. A.

J. Ribeiro-Soares, M. E. Oliveros, C. Garin, M. V. David, L. G. P. Martins, C. A. Almeida, E. H. Martins-Ferreira, K. Takai, T. Enoki, R. Magalhães-Paniago, A. Malachias, A. Jorio, B. S. Archanjo, C. A. Achete, and L. G. Cançado, “Structural analysis of polycrystalline graphene systems by Raman spectroscopy,” Carbon 95, 646–652 (2015).
[Crossref]

Apostol, A.

A. Apostol and A. Dogariu, “Spatial correlations in the near field of random media,” Phys. Rev. Lett. 91, 093901 (2003).
[Crossref]

A. Apostol and A. Dogariu, “Coherence properties near interfaces of random media,” Phys. Rev. E 67, 055601 (2003).
[Crossref]

Archanjo, B. S.

J. Ribeiro-Soares, M. E. Oliveros, C. Garin, M. V. David, L. G. P. Martins, C. A. Almeida, E. H. Martins-Ferreira, K. Takai, T. Enoki, R. Magalhães-Paniago, A. Malachias, A. Jorio, B. S. Archanjo, C. A. Achete, and L. G. Cançado, “Structural analysis of polycrystalline graphene systems by Raman spectroscopy,” Carbon 95, 646–652 (2015).
[Crossref]

Banhart, F.

F. Banhart, J. Kotakoski, and A. V. Krasheninnikov, “Structural defects in graphene,” ACS Nano 5, 26–41 (2011).
[Crossref]

Basko, D. M.

A. C. Ferrari and D. M. Basko, “Raman spectroscopy as a versatile tool for studying the properties of graphene,” Nat. Nanotechnol. 8, 235–246 (2013).
[Crossref]

C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
[Crossref]

Beams, R.

R. Beams, L. G. Cançado, and L. Novotny, “Raman characterization of defects and dopants in graphene,” J. Phys. Condens. Matter 27, 83002 (2015).
[Crossref]

R. Beams, L. G. Cançado, and L. Novotny, “Low temperature Raman study of the electron coherence length near graphene edges,” Nano Lett. 11, 1177–1181 (2011).
[Crossref]

Bi, K.

W. Zhao, Y. Wang, Z. Wu, W. Wang, K. Bi, Z. Liang, J. Yang, Y. Chen, Z. Xu, and Z. Ni, “Defect-engineered heat transport in graphene: a route to high efficient thermal rectification,” Sci. Rep. 5, 11962 (2015).
[Crossref]

Binard, G.

Bourdillon, C.

Britnell, L.

A. Eckmann, A. Felten, A. Mishchenko, L. Britnell, R. Krupke, K. S. Novoselov, and C. Casiraghi, “Probing the nature of defects in graphene by Raman spectroscopy,” Nano Lett. 12, 3925–3930 (2012).
[Crossref]

Cançado, L. G.

J. Ribeiro-Soares, M. E. Oliveros, C. Garin, M. V. David, L. G. P. Martins, C. A. Almeida, E. H. Martins-Ferreira, K. Takai, T. Enoki, R. Magalhães-Paniago, A. Malachias, A. Jorio, B. S. Archanjo, C. A. Achete, and L. G. Cançado, “Structural analysis of polycrystalline graphene systems by Raman spectroscopy,” Carbon 95, 646–652 (2015).
[Crossref]

R. Beams, L. G. Cançado, and L. Novotny, “Raman characterization of defects and dopants in graphene,” J. Phys. Condens. Matter 27, 83002 (2015).
[Crossref]

L. G. Cançado, A. Jorio, E. H. M. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

R. Beams, L. G. Cançado, and L. Novotny, “Low temperature Raman study of the electron coherence length near graphene edges,” Nano Lett. 11, 1177–1181 (2011).
[Crossref]

Capaz, R. B.

L. G. Cançado, A. Jorio, E. H. M. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

M. M. Lucchese, F. Stavale, E. H. M. Ferreira, C. Vilani, M. V. O. Moutinho, R. B. Capaz, C. A. Achete, and A. Jorio, “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon 48, 1592–1597 (2010).
[Crossref]

Carminati, R.

V. Parigi, E. Perros, G. Binard, C. Bourdillon, A. Maître, R. Carminati, V. Krachmalnicoff, and Y. D. Wilde, “Near-field to far-field characterization of speckle patterns generated by disordered nanomaterials,” Opt. Express 24, 7019–7027 (2016).
[Crossref]

A. Dogariu and R. Carminati, “Electromagnetic field correlations in three-dimensional speckles,” Phys. Rep. 559, 1–29 (2015).
[Crossref]

R. Carminati, “Subwavelength spatial correlations in near-field speckle patterns,” Phys. Rev. A 81, 053804 (2010).
[Crossref]

C. Henkel, K. Joulain, R. Carminati, and J.-J. Greffet, “Spatial coherence of thermal near fields,” Opt. Commun. 186, 57–67 (2000).
[Crossref]

Carter, W. H.

Casiraghi, C.

A. Eckmann, A. Felten, A. Mishchenko, L. Britnell, R. Krupke, K. S. Novoselov, and C. Casiraghi, “Probing the nature of defects in graphene by Raman spectroscopy,” Nano Lett. 12, 3925–3930 (2012).
[Crossref]

C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
[Crossref]

Chen, Y.

W. Zhao, Y. Wang, Z. Wu, W. Wang, K. Bi, Z. Liang, J. Yang, Y. Chen, Z. Xu, and Z. Ni, “Defect-engineered heat transport in graphene: a route to high efficient thermal rectification,” Sci. Rep. 5, 11962 (2015).
[Crossref]

Chen, Y. P.

O. V. Yazyev and Y. P. Chen, “Polycrystalline graphene and other two-dimensional materials,” Nat. Nanotechnol. 9, 755–767 (2014).
[Crossref]

Chi, L.

Z.-J. Wang, G. Weinberg, Q. Zhang, T. Lunkenbein, A. Klein-Hoffmann, M. Kurnatowska, M. Plodinec, Q. Li, L. Chi, R. Schloegl, and M.-G. Willinger, “Direct observation of graphene growth and associated copper substrate dynamics by in situ scanning electron microscopy,” ACS Nano 9, 1506–1519 (2015).
[Crossref]

David, M. V.

J. Ribeiro-Soares, M. E. Oliveros, C. Garin, M. V. David, L. G. P. Martins, C. A. Almeida, E. H. Martins-Ferreira, K. Takai, T. Enoki, R. Magalhães-Paniago, A. Malachias, A. Jorio, B. S. Archanjo, C. A. Achete, and L. G. Cançado, “Structural analysis of polycrystalline graphene systems by Raman spectroscopy,” Carbon 95, 646–652 (2015).
[Crossref]

de Paula, A. M.

T. V. Alencar, M. G. Silva, L. M. Malard, and A. M. de Paula, “Defect-induced supercollision cooling of photoexcited carriers in graphene,” Nano Lett. 14, 5621–5624 (2014).
[Crossref]

Dekker, C.

L. Vicarelli, S. J. Heerema, C. Dekker, and H. W. Zandbergen, “Controlling defects in graphene for optimizing the electrical properties of graphene nanodevices,” ACS Nano 9, 3428–3435 (2015).
[Crossref]

Dogariu, A.

R. R. Naraghi, S. Sukhov, and A. Dogariu, “Disorder fingerprint: intensity distributions in the near field of random media,” Phys. Rev. B 94, 174205 (2016).
[Crossref]

A. Dogariu and R. Carminati, “Electromagnetic field correlations in three-dimensional speckles,” Phys. Rep. 559, 1–29 (2015).
[Crossref]

A. Apostol and A. Dogariu, “Spatial correlations in the near field of random media,” Phys. Rev. Lett. 91, 093901 (2003).
[Crossref]

A. Apostol and A. Dogariu, “Coherence properties near interfaces of random media,” Phys. Rev. E 67, 055601 (2003).
[Crossref]

Eckmann, A.

A. Eckmann, A. Felten, A. Mishchenko, L. Britnell, R. Krupke, K. S. Novoselov, and C. Casiraghi, “Probing the nature of defects in graphene by Raman spectroscopy,” Nano Lett. 12, 3925–3930 (2012).
[Crossref]

Englund, D.

Y. Huang, E. Sutter, N. N. Shi, J. Zheng, T. Yang, D. Englund, H.-J. Gao, and P. Sutter, “Reliable exfoliation of large-area high-quality flakes of graphene and other two-dimensional materials,” ACS Nano 9, 10612–10620 (2015).
[Crossref]

Enoki, T.

J. Ribeiro-Soares, M. E. Oliveros, C. Garin, M. V. David, L. G. P. Martins, C. A. Almeida, E. H. Martins-Ferreira, K. Takai, T. Enoki, R. Magalhães-Paniago, A. Malachias, A. Jorio, B. S. Archanjo, C. A. Achete, and L. G. Cançado, “Structural analysis of polycrystalline graphene systems by Raman spectroscopy,” Carbon 95, 646–652 (2015).
[Crossref]

Estrada, D.

J. C. Koepke, J. D. Wood, D. Estrada, Z.-Y. Ong, K. T. He, E. Pop, and J. W. Lyding, “Atomic-scale evidence for potential barriers and strong carrier scattering at graphene grain boundaries: a scanning tunneling microscopy study,” ACS Nano 7, 75–86 (2013).
[Crossref]

Fasoli, A.

C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
[Crossref]

Felten, A.

A. Eckmann, A. Felten, A. Mishchenko, L. Britnell, R. Krupke, K. S. Novoselov, and C. Casiraghi, “Probing the nature of defects in graphene by Raman spectroscopy,” Nano Lett. 12, 3925–3930 (2012).
[Crossref]

Ferrari, A. C.

A. C. Ferrari and D. M. Basko, “Raman spectroscopy as a versatile tool for studying the properties of graphene,” Nat. Nanotechnol. 8, 235–246 (2013).
[Crossref]

L. G. Cançado, A. Jorio, E. H. M. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
[Crossref]

Ferreira, E. H. M.

L. G. Cançado, A. Jorio, E. H. M. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

M. M. Lucchese, F. Stavale, E. H. M. Ferreira, C. Vilani, M. V. O. Moutinho, R. B. Capaz, C. A. Achete, and A. Jorio, “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon 48, 1592–1597 (2010).
[Crossref]

Gao, H.-J.

Y. Huang, E. Sutter, N. N. Shi, J. Zheng, T. Yang, D. Englund, H.-J. Gao, and P. Sutter, “Reliable exfoliation of large-area high-quality flakes of graphene and other two-dimensional materials,” ACS Nano 9, 10612–10620 (2015).
[Crossref]

Garin, C.

J. Ribeiro-Soares, M. E. Oliveros, C. Garin, M. V. David, L. G. P. Martins, C. A. Almeida, E. H. Martins-Ferreira, K. Takai, T. Enoki, R. Magalhães-Paniago, A. Malachias, A. Jorio, B. S. Archanjo, C. A. Achete, and L. G. Cançado, “Structural analysis of polycrystalline graphene systems by Raman spectroscopy,” Carbon 95, 646–652 (2015).
[Crossref]

Georgi, C.

C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
[Crossref]

Gómez-Herrero, J.

G. López-Polín, C. Gómez-Navarro, V. Parente, F. Guinea, M. I. Katsnelson, F. Pérez-Murano, and J. Gómez-Herrero, “Increasing the elastic modulus of graphene by controlled defect creation,” Nat. Phys. 11, 26–31 (2015).
[Crossref]

Gómez-Navarro, C.

G. López-Polín, C. Gómez-Navarro, V. Parente, F. Guinea, M. I. Katsnelson, F. Pérez-Murano, and J. Gómez-Herrero, “Increasing the elastic modulus of graphene by controlled defect creation,” Nat. Phys. 11, 26–31 (2015).
[Crossref]

Greffet, J.-J.

C. Henkel, K. Joulain, R. Carminati, and J.-J. Greffet, “Spatial coherence of thermal near fields,” Opt. Commun. 186, 57–67 (2000).
[Crossref]

Guinea, F.

G. López-Polín, C. Gómez-Navarro, V. Parente, F. Guinea, M. I. Katsnelson, F. Pérez-Murano, and J. Gómez-Herrero, “Increasing the elastic modulus of graphene by controlled defect creation,” Nat. Phys. 11, 26–31 (2015).
[Crossref]

Hartschuh, A.

C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
[Crossref]

He, K. T.

J. C. Koepke, J. D. Wood, D. Estrada, Z.-Y. Ong, K. T. He, E. Pop, and J. W. Lyding, “Atomic-scale evidence for potential barriers and strong carrier scattering at graphene grain boundaries: a scanning tunneling microscopy study,” ACS Nano 7, 75–86 (2013).
[Crossref]

Heerema, S. J.

L. Vicarelli, S. J. Heerema, C. Dekker, and H. W. Zandbergen, “Controlling defects in graphene for optimizing the electrical properties of graphene nanodevices,” ACS Nano 9, 3428–3435 (2015).
[Crossref]

Henkel, C.

C. Henkel, K. Joulain, R. Carminati, and J.-J. Greffet, “Spatial coherence of thermal near fields,” Opt. Commun. 186, 57–67 (2000).
[Crossref]

Hersam, M. C.

M. C. Prado, D. Jariwala, T. J. Marks, and M. C. Hersam, “Optimization of graphene dry etching conditions via combined microscopic and spectroscopic analysis,” Appl. Phys. Lett. 102, 193111 (2013).
[Crossref]

Huang, Y.

Y. Huang, E. Sutter, N. N. Shi, J. Zheng, T. Yang, D. Englund, H.-J. Gao, and P. Sutter, “Reliable exfoliation of large-area high-quality flakes of graphene and other two-dimensional materials,” ACS Nano 9, 10612–10620 (2015).
[Crossref]

Jariwala, D.

M. C. Prado, D. Jariwala, T. J. Marks, and M. C. Hersam, “Optimization of graphene dry etching conditions via combined microscopic and spectroscopic analysis,” Appl. Phys. Lett. 102, 193111 (2013).
[Crossref]

Jorio, A.

J. Ribeiro-Soares, M. E. Oliveros, C. Garin, M. V. David, L. G. P. Martins, C. A. Almeida, E. H. Martins-Ferreira, K. Takai, T. Enoki, R. Magalhães-Paniago, A. Malachias, A. Jorio, B. S. Archanjo, C. A. Achete, and L. G. Cançado, “Structural analysis of polycrystalline graphene systems by Raman spectroscopy,” Carbon 95, 646–652 (2015).
[Crossref]

L. G. Cançado, A. Jorio, E. H. M. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

M. M. Lucchese, F. Stavale, E. H. M. Ferreira, C. Vilani, M. V. O. Moutinho, R. B. Capaz, C. A. Achete, and A. Jorio, “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon 48, 1592–1597 (2010).
[Crossref]

Joulain, K.

C. Henkel, K. Joulain, R. Carminati, and J.-J. Greffet, “Spatial coherence of thermal near fields,” Opt. Commun. 186, 57–67 (2000).
[Crossref]

Katsnelson, M. I.

G. López-Polín, C. Gómez-Navarro, V. Parente, F. Guinea, M. I. Katsnelson, F. Pérez-Murano, and J. Gómez-Herrero, “Increasing the elastic modulus of graphene by controlled defect creation,” Nat. Phys. 11, 26–31 (2015).
[Crossref]

Klein-Hoffmann, A.

Z.-J. Wang, G. Weinberg, Q. Zhang, T. Lunkenbein, A. Klein-Hoffmann, M. Kurnatowska, M. Plodinec, Q. Li, L. Chi, R. Schloegl, and M.-G. Willinger, “Direct observation of graphene growth and associated copper substrate dynamics by in situ scanning electron microscopy,” ACS Nano 9, 1506–1519 (2015).
[Crossref]

Koepke, J. C.

J. C. Koepke, J. D. Wood, D. Estrada, Z.-Y. Ong, K. T. He, E. Pop, and J. W. Lyding, “Atomic-scale evidence for potential barriers and strong carrier scattering at graphene grain boundaries: a scanning tunneling microscopy study,” ACS Nano 7, 75–86 (2013).
[Crossref]

Kotakoski, J.

F. Banhart, J. Kotakoski, and A. V. Krasheninnikov, “Structural defects in graphene,” ACS Nano 5, 26–41 (2011).
[Crossref]

Krachmalnicoff, V.

Krasheninnikov, A. V.

F. Banhart, J. Kotakoski, and A. V. Krasheninnikov, “Structural defects in graphene,” ACS Nano 5, 26–41 (2011).
[Crossref]

Krupke, R.

A. Eckmann, A. Felten, A. Mishchenko, L. Britnell, R. Krupke, K. S. Novoselov, and C. Casiraghi, “Probing the nature of defects in graphene by Raman spectroscopy,” Nano Lett. 12, 3925–3930 (2012).
[Crossref]

Kulmala, T. S.

L. G. Cançado, A. Jorio, E. H. M. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

Kurnatowska, M.

Z.-J. Wang, G. Weinberg, Q. Zhang, T. Lunkenbein, A. Klein-Hoffmann, M. Kurnatowska, M. Plodinec, Q. Li, L. Chi, R. Schloegl, and M.-G. Willinger, “Direct observation of graphene growth and associated copper substrate dynamics by in situ scanning electron microscopy,” ACS Nano 9, 1506–1519 (2015).
[Crossref]

Li, Q.

Z.-J. Wang, G. Weinberg, Q. Zhang, T. Lunkenbein, A. Klein-Hoffmann, M. Kurnatowska, M. Plodinec, Q. Li, L. Chi, R. Schloegl, and M.-G. Willinger, “Direct observation of graphene growth and associated copper substrate dynamics by in situ scanning electron microscopy,” ACS Nano 9, 1506–1519 (2015).
[Crossref]

Liang, Z.

W. Zhao, Y. Wang, Z. Wu, W. Wang, K. Bi, Z. Liang, J. Yang, Y. Chen, Z. Xu, and Z. Ni, “Defect-engineered heat transport in graphene: a route to high efficient thermal rectification,” Sci. Rep. 5, 11962 (2015).
[Crossref]

Lombardo, A.

L. G. Cançado, A. Jorio, E. H. M. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

López-Polín, G.

G. López-Polín, C. Gómez-Navarro, V. Parente, F. Guinea, M. I. Katsnelson, F. Pérez-Murano, and J. Gómez-Herrero, “Increasing the elastic modulus of graphene by controlled defect creation,” Nat. Phys. 11, 26–31 (2015).
[Crossref]

Lucchese, M. M.

M. M. Lucchese, F. Stavale, E. H. M. Ferreira, C. Vilani, M. V. O. Moutinho, R. B. Capaz, C. A. Achete, and A. Jorio, “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon 48, 1592–1597 (2010).
[Crossref]

Lunkenbein, T.

Z.-J. Wang, G. Weinberg, Q. Zhang, T. Lunkenbein, A. Klein-Hoffmann, M. Kurnatowska, M. Plodinec, Q. Li, L. Chi, R. Schloegl, and M.-G. Willinger, “Direct observation of graphene growth and associated copper substrate dynamics by in situ scanning electron microscopy,” ACS Nano 9, 1506–1519 (2015).
[Crossref]

Lyding, J. W.

J. C. Koepke, J. D. Wood, D. Estrada, Z.-Y. Ong, K. T. He, E. Pop, and J. W. Lyding, “Atomic-scale evidence for potential barriers and strong carrier scattering at graphene grain boundaries: a scanning tunneling microscopy study,” ACS Nano 7, 75–86 (2013).
[Crossref]

Magalhães-Paniago, R.

J. Ribeiro-Soares, M. E. Oliveros, C. Garin, M. V. David, L. G. P. Martins, C. A. Almeida, E. H. Martins-Ferreira, K. Takai, T. Enoki, R. Magalhães-Paniago, A. Malachias, A. Jorio, B. S. Archanjo, C. A. Achete, and L. G. Cançado, “Structural analysis of polycrystalline graphene systems by Raman spectroscopy,” Carbon 95, 646–652 (2015).
[Crossref]

Maître, A.

Malachias, A.

J. Ribeiro-Soares, M. E. Oliveros, C. Garin, M. V. David, L. G. P. Martins, C. A. Almeida, E. H. Martins-Ferreira, K. Takai, T. Enoki, R. Magalhães-Paniago, A. Malachias, A. Jorio, B. S. Archanjo, C. A. Achete, and L. G. Cançado, “Structural analysis of polycrystalline graphene systems by Raman spectroscopy,” Carbon 95, 646–652 (2015).
[Crossref]

Malard, L. M.

T. V. Alencar, M. G. Silva, L. M. Malard, and A. M. de Paula, “Defect-induced supercollision cooling of photoexcited carriers in graphene,” Nano Lett. 14, 5621–5624 (2014).
[Crossref]

Marks, T. J.

M. C. Prado, D. Jariwala, T. J. Marks, and M. C. Hersam, “Optimization of graphene dry etching conditions via combined microscopic and spectroscopic analysis,” Appl. Phys. Lett. 102, 193111 (2013).
[Crossref]

Martins, L. G. P.

J. Ribeiro-Soares, M. E. Oliveros, C. Garin, M. V. David, L. G. P. Martins, C. A. Almeida, E. H. Martins-Ferreira, K. Takai, T. Enoki, R. Magalhães-Paniago, A. Malachias, A. Jorio, B. S. Archanjo, C. A. Achete, and L. G. Cançado, “Structural analysis of polycrystalline graphene systems by Raman spectroscopy,” Carbon 95, 646–652 (2015).
[Crossref]

Martins-Ferreira, E. H.

J. Ribeiro-Soares, M. E. Oliveros, C. Garin, M. V. David, L. G. P. Martins, C. A. Almeida, E. H. Martins-Ferreira, K. Takai, T. Enoki, R. Magalhães-Paniago, A. Malachias, A. Jorio, B. S. Archanjo, C. A. Achete, and L. G. Cançado, “Structural analysis of polycrystalline graphene systems by Raman spectroscopy,” Carbon 95, 646–652 (2015).
[Crossref]

Mishchenko, A.

A. Eckmann, A. Felten, A. Mishchenko, L. Britnell, R. Krupke, K. S. Novoselov, and C. Casiraghi, “Probing the nature of defects in graphene by Raman spectroscopy,” Nano Lett. 12, 3925–3930 (2012).
[Crossref]

Moutinho, M. V. O.

L. G. Cançado, A. Jorio, E. H. M. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

M. M. Lucchese, F. Stavale, E. H. M. Ferreira, C. Vilani, M. V. O. Moutinho, R. B. Capaz, C. A. Achete, and A. Jorio, “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon 48, 1592–1597 (2010).
[Crossref]

Naraghi, R. R.

R. R. Naraghi, S. Sukhov, and A. Dogariu, “Disorder fingerprint: intensity distributions in the near field of random media,” Phys. Rev. B 94, 174205 (2016).
[Crossref]

Ni, Z.

W. Zhao, Y. Wang, Z. Wu, W. Wang, K. Bi, Z. Liang, J. Yang, Y. Chen, Z. Xu, and Z. Ni, “Defect-engineered heat transport in graphene: a route to high efficient thermal rectification,” Sci. Rep. 5, 11962 (2015).
[Crossref]

Novoselov, K. S.

A. Eckmann, A. Felten, A. Mishchenko, L. Britnell, R. Krupke, K. S. Novoselov, and C. Casiraghi, “Probing the nature of defects in graphene by Raman spectroscopy,” Nano Lett. 12, 3925–3930 (2012).
[Crossref]

C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
[Crossref]

Novotny, L.

R. Beams, L. G. Cançado, and L. Novotny, “Raman characterization of defects and dopants in graphene,” J. Phys. Condens. Matter 27, 83002 (2015).
[Crossref]

R. Beams, L. G. Cançado, and L. Novotny, “Low temperature Raman study of the electron coherence length near graphene edges,” Nano Lett. 11, 1177–1181 (2011).
[Crossref]

Oliveros, M. E.

J. Ribeiro-Soares, M. E. Oliveros, C. Garin, M. V. David, L. G. P. Martins, C. A. Almeida, E. H. Martins-Ferreira, K. Takai, T. Enoki, R. Magalhães-Paniago, A. Malachias, A. Jorio, B. S. Archanjo, C. A. Achete, and L. G. Cançado, “Structural analysis of polycrystalline graphene systems by Raman spectroscopy,” Carbon 95, 646–652 (2015).
[Crossref]

Ong, Z.-Y.

J. C. Koepke, J. D. Wood, D. Estrada, Z.-Y. Ong, K. T. He, E. Pop, and J. W. Lyding, “Atomic-scale evidence for potential barriers and strong carrier scattering at graphene grain boundaries: a scanning tunneling microscopy study,” ACS Nano 7, 75–86 (2013).
[Crossref]

Parente, V.

G. López-Polín, C. Gómez-Navarro, V. Parente, F. Guinea, M. I. Katsnelson, F. Pérez-Murano, and J. Gómez-Herrero, “Increasing the elastic modulus of graphene by controlled defect creation,” Nat. Phys. 11, 26–31 (2015).
[Crossref]

Parigi, V.

Pérez-Murano, F.

G. López-Polín, C. Gómez-Navarro, V. Parente, F. Guinea, M. I. Katsnelson, F. Pérez-Murano, and J. Gómez-Herrero, “Increasing the elastic modulus of graphene by controlled defect creation,” Nat. Phys. 11, 26–31 (2015).
[Crossref]

Perros, E.

Piscanec, S.

C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
[Crossref]

Plodinec, M.

Z.-J. Wang, G. Weinberg, Q. Zhang, T. Lunkenbein, A. Klein-Hoffmann, M. Kurnatowska, M. Plodinec, Q. Li, L. Chi, R. Schloegl, and M.-G. Willinger, “Direct observation of graphene growth and associated copper substrate dynamics by in situ scanning electron microscopy,” ACS Nano 9, 1506–1519 (2015).
[Crossref]

Pop, E.

J. C. Koepke, J. D. Wood, D. Estrada, Z.-Y. Ong, K. T. He, E. Pop, and J. W. Lyding, “Atomic-scale evidence for potential barriers and strong carrier scattering at graphene grain boundaries: a scanning tunneling microscopy study,” ACS Nano 7, 75–86 (2013).
[Crossref]

Prado, M. C.

M. C. Prado, D. Jariwala, T. J. Marks, and M. C. Hersam, “Optimization of graphene dry etching conditions via combined microscopic and spectroscopic analysis,” Appl. Phys. Lett. 102, 193111 (2013).
[Crossref]

Qian, H.

C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
[Crossref]

Ribeiro-Soares, J.

J. Ribeiro-Soares, M. E. Oliveros, C. Garin, M. V. David, L. G. P. Martins, C. A. Almeida, E. H. Martins-Ferreira, K. Takai, T. Enoki, R. Magalhães-Paniago, A. Malachias, A. Jorio, B. S. Archanjo, C. A. Achete, and L. G. Cançado, “Structural analysis of polycrystalline graphene systems by Raman spectroscopy,” Carbon 95, 646–652 (2015).
[Crossref]

Robertson, A. W.

A. W. Robertson and J. H. Warner, “Atomic resolution imaging of graphene by transmission electron microscopy,” Nanoscale 5, 4079–4093 (2013).
[Crossref]

Roychowdhury, H.

Schloegl, R.

Z.-J. Wang, G. Weinberg, Q. Zhang, T. Lunkenbein, A. Klein-Hoffmann, M. Kurnatowska, M. Plodinec, Q. Li, L. Chi, R. Schloegl, and M.-G. Willinger, “Direct observation of graphene growth and associated copper substrate dynamics by in situ scanning electron microscopy,” ACS Nano 9, 1506–1519 (2015).
[Crossref]

Shi, N. N.

Y. Huang, E. Sutter, N. N. Shi, J. Zheng, T. Yang, D. Englund, H.-J. Gao, and P. Sutter, “Reliable exfoliation of large-area high-quality flakes of graphene and other two-dimensional materials,” ACS Nano 9, 10612–10620 (2015).
[Crossref]

Silva, M. G.

T. V. Alencar, M. G. Silva, L. M. Malard, and A. M. de Paula, “Defect-induced supercollision cooling of photoexcited carriers in graphene,” Nano Lett. 14, 5621–5624 (2014).
[Crossref]

Stavale, F.

L. G. Cançado, A. Jorio, E. H. M. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

M. M. Lucchese, F. Stavale, E. H. M. Ferreira, C. Vilani, M. V. O. Moutinho, R. B. Capaz, C. A. Achete, and A. Jorio, “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon 48, 1592–1597 (2010).
[Crossref]

Sukhov, S.

R. R. Naraghi, S. Sukhov, and A. Dogariu, “Disorder fingerprint: intensity distributions in the near field of random media,” Phys. Rev. B 94, 174205 (2016).
[Crossref]

Sutter, E.

Y. Huang, E. Sutter, N. N. Shi, J. Zheng, T. Yang, D. Englund, H.-J. Gao, and P. Sutter, “Reliable exfoliation of large-area high-quality flakes of graphene and other two-dimensional materials,” ACS Nano 9, 10612–10620 (2015).
[Crossref]

Sutter, P.

Y. Huang, E. Sutter, N. N. Shi, J. Zheng, T. Yang, D. Englund, H.-J. Gao, and P. Sutter, “Reliable exfoliation of large-area high-quality flakes of graphene and other two-dimensional materials,” ACS Nano 9, 10612–10620 (2015).
[Crossref]

Takai, K.

J. Ribeiro-Soares, M. E. Oliveros, C. Garin, M. V. David, L. G. P. Martins, C. A. Almeida, E. H. Martins-Ferreira, K. Takai, T. Enoki, R. Magalhães-Paniago, A. Malachias, A. Jorio, B. S. Archanjo, C. A. Achete, and L. G. Cançado, “Structural analysis of polycrystalline graphene systems by Raman spectroscopy,” Carbon 95, 646–652 (2015).
[Crossref]

Vicarelli, L.

L. Vicarelli, S. J. Heerema, C. Dekker, and H. W. Zandbergen, “Controlling defects in graphene for optimizing the electrical properties of graphene nanodevices,” ACS Nano 9, 3428–3435 (2015).
[Crossref]

Vilani, C.

M. M. Lucchese, F. Stavale, E. H. M. Ferreira, C. Vilani, M. V. O. Moutinho, R. B. Capaz, C. A. Achete, and A. Jorio, “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon 48, 1592–1597 (2010).
[Crossref]

Wang, W.

W. Zhao, Y. Wang, Z. Wu, W. Wang, K. Bi, Z. Liang, J. Yang, Y. Chen, Z. Xu, and Z. Ni, “Defect-engineered heat transport in graphene: a route to high efficient thermal rectification,” Sci. Rep. 5, 11962 (2015).
[Crossref]

Wang, Y.

W. Zhao, Y. Wang, Z. Wu, W. Wang, K. Bi, Z. Liang, J. Yang, Y. Chen, Z. Xu, and Z. Ni, “Defect-engineered heat transport in graphene: a route to high efficient thermal rectification,” Sci. Rep. 5, 11962 (2015).
[Crossref]

Wang, Z.-J.

Z.-J. Wang, G. Weinberg, Q. Zhang, T. Lunkenbein, A. Klein-Hoffmann, M. Kurnatowska, M. Plodinec, Q. Li, L. Chi, R. Schloegl, and M.-G. Willinger, “Direct observation of graphene growth and associated copper substrate dynamics by in situ scanning electron microscopy,” ACS Nano 9, 1506–1519 (2015).
[Crossref]

Warner, J. H.

A. W. Robertson and J. H. Warner, “Atomic resolution imaging of graphene by transmission electron microscopy,” Nanoscale 5, 4079–4093 (2013).
[Crossref]

Weinberg, G.

Z.-J. Wang, G. Weinberg, Q. Zhang, T. Lunkenbein, A. Klein-Hoffmann, M. Kurnatowska, M. Plodinec, Q. Li, L. Chi, R. Schloegl, and M.-G. Willinger, “Direct observation of graphene growth and associated copper substrate dynamics by in situ scanning electron microscopy,” ACS Nano 9, 1506–1519 (2015).
[Crossref]

Wilde, Y. D.

Willinger, M.-G.

Z.-J. Wang, G. Weinberg, Q. Zhang, T. Lunkenbein, A. Klein-Hoffmann, M. Kurnatowska, M. Plodinec, Q. Li, L. Chi, R. Schloegl, and M.-G. Willinger, “Direct observation of graphene growth and associated copper substrate dynamics by in situ scanning electron microscopy,” ACS Nano 9, 1506–1519 (2015).
[Crossref]

Wolf, E.

Wood, J. D.

J. C. Koepke, J. D. Wood, D. Estrada, Z.-Y. Ong, K. T. He, E. Pop, and J. W. Lyding, “Atomic-scale evidence for potential barriers and strong carrier scattering at graphene grain boundaries: a scanning tunneling microscopy study,” ACS Nano 7, 75–86 (2013).
[Crossref]

Wu, Z.

W. Zhao, Y. Wang, Z. Wu, W. Wang, K. Bi, Z. Liang, J. Yang, Y. Chen, Z. Xu, and Z. Ni, “Defect-engineered heat transport in graphene: a route to high efficient thermal rectification,” Sci. Rep. 5, 11962 (2015).
[Crossref]

Xu, Z.

W. Zhao, Y. Wang, Z. Wu, W. Wang, K. Bi, Z. Liang, J. Yang, Y. Chen, Z. Xu, and Z. Ni, “Defect-engineered heat transport in graphene: a route to high efficient thermal rectification,” Sci. Rep. 5, 11962 (2015).
[Crossref]

Yang, J.

W. Zhao, Y. Wang, Z. Wu, W. Wang, K. Bi, Z. Liang, J. Yang, Y. Chen, Z. Xu, and Z. Ni, “Defect-engineered heat transport in graphene: a route to high efficient thermal rectification,” Sci. Rep. 5, 11962 (2015).
[Crossref]

Yang, T.

Y. Huang, E. Sutter, N. N. Shi, J. Zheng, T. Yang, D. Englund, H.-J. Gao, and P. Sutter, “Reliable exfoliation of large-area high-quality flakes of graphene and other two-dimensional materials,” ACS Nano 9, 10612–10620 (2015).
[Crossref]

Yazyev, O. V.

O. V. Yazyev and Y. P. Chen, “Polycrystalline graphene and other two-dimensional materials,” Nat. Nanotechnol. 9, 755–767 (2014).
[Crossref]

Zandbergen, H. W.

L. Vicarelli, S. J. Heerema, C. Dekker, and H. W. Zandbergen, “Controlling defects in graphene for optimizing the electrical properties of graphene nanodevices,” ACS Nano 9, 3428–3435 (2015).
[Crossref]

Zhang, Q.

Z.-J. Wang, G. Weinberg, Q. Zhang, T. Lunkenbein, A. Klein-Hoffmann, M. Kurnatowska, M. Plodinec, Q. Li, L. Chi, R. Schloegl, and M.-G. Willinger, “Direct observation of graphene growth and associated copper substrate dynamics by in situ scanning electron microscopy,” ACS Nano 9, 1506–1519 (2015).
[Crossref]

Zhao, W.

W. Zhao, Y. Wang, Z. Wu, W. Wang, K. Bi, Z. Liang, J. Yang, Y. Chen, Z. Xu, and Z. Ni, “Defect-engineered heat transport in graphene: a route to high efficient thermal rectification,” Sci. Rep. 5, 11962 (2015).
[Crossref]

Zheng, J.

Y. Huang, E. Sutter, N. N. Shi, J. Zheng, T. Yang, D. Englund, H.-J. Gao, and P. Sutter, “Reliable exfoliation of large-area high-quality flakes of graphene and other two-dimensional materials,” ACS Nano 9, 10612–10620 (2015).
[Crossref]

ACS Nano (5)

F. Banhart, J. Kotakoski, and A. V. Krasheninnikov, “Structural defects in graphene,” ACS Nano 5, 26–41 (2011).
[Crossref]

L. Vicarelli, S. J. Heerema, C. Dekker, and H. W. Zandbergen, “Controlling defects in graphene for optimizing the electrical properties of graphene nanodevices,” ACS Nano 9, 3428–3435 (2015).
[Crossref]

Z.-J. Wang, G. Weinberg, Q. Zhang, T. Lunkenbein, A. Klein-Hoffmann, M. Kurnatowska, M. Plodinec, Q. Li, L. Chi, R. Schloegl, and M.-G. Willinger, “Direct observation of graphene growth and associated copper substrate dynamics by in situ scanning electron microscopy,” ACS Nano 9, 1506–1519 (2015).
[Crossref]

J. C. Koepke, J. D. Wood, D. Estrada, Z.-Y. Ong, K. T. He, E. Pop, and J. W. Lyding, “Atomic-scale evidence for potential barriers and strong carrier scattering at graphene grain boundaries: a scanning tunneling microscopy study,” ACS Nano 7, 75–86 (2013).
[Crossref]

Y. Huang, E. Sutter, N. N. Shi, J. Zheng, T. Yang, D. Englund, H.-J. Gao, and P. Sutter, “Reliable exfoliation of large-area high-quality flakes of graphene and other two-dimensional materials,” ACS Nano 9, 10612–10620 (2015).
[Crossref]

Appl. Phys. Lett. (1)

M. C. Prado, D. Jariwala, T. J. Marks, and M. C. Hersam, “Optimization of graphene dry etching conditions via combined microscopic and spectroscopic analysis,” Appl. Phys. Lett. 102, 193111 (2013).
[Crossref]

Carbon (2)

M. M. Lucchese, F. Stavale, E. H. M. Ferreira, C. Vilani, M. V. O. Moutinho, R. B. Capaz, C. A. Achete, and A. Jorio, “Quantifying ion-induced defects and Raman relaxation length in graphene,” Carbon 48, 1592–1597 (2010).
[Crossref]

J. Ribeiro-Soares, M. E. Oliveros, C. Garin, M. V. David, L. G. P. Martins, C. A. Almeida, E. H. Martins-Ferreira, K. Takai, T. Enoki, R. Magalhães-Paniago, A. Malachias, A. Jorio, B. S. Archanjo, C. A. Achete, and L. G. Cançado, “Structural analysis of polycrystalline graphene systems by Raman spectroscopy,” Carbon 95, 646–652 (2015).
[Crossref]

J. Opt. Soc. Am. (1)

J. Phys. Condens. Matter (1)

R. Beams, L. G. Cançado, and L. Novotny, “Raman characterization of defects and dopants in graphene,” J. Phys. Condens. Matter 27, 83002 (2015).
[Crossref]

Nano Lett. (5)

A. Eckmann, A. Felten, A. Mishchenko, L. Britnell, R. Krupke, K. S. Novoselov, and C. Casiraghi, “Probing the nature of defects in graphene by Raman spectroscopy,” Nano Lett. 12, 3925–3930 (2012).
[Crossref]

C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko, and A. C. Ferrari, “Raman spectroscopy of graphene edges,” Nano Lett. 9, 1433–1441 (2009).
[Crossref]

R. Beams, L. G. Cançado, and L. Novotny, “Low temperature Raman study of the electron coherence length near graphene edges,” Nano Lett. 11, 1177–1181 (2011).
[Crossref]

T. V. Alencar, M. G. Silva, L. M. Malard, and A. M. de Paula, “Defect-induced supercollision cooling of photoexcited carriers in graphene,” Nano Lett. 14, 5621–5624 (2014).
[Crossref]

L. G. Cançado, A. Jorio, E. H. M. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11, 3190–3196 (2011).
[Crossref]

Nanoscale (1)

A. W. Robertson and J. H. Warner, “Atomic resolution imaging of graphene by transmission electron microscopy,” Nanoscale 5, 4079–4093 (2013).
[Crossref]

Nat. Nanotechnol. (2)

O. V. Yazyev and Y. P. Chen, “Polycrystalline graphene and other two-dimensional materials,” Nat. Nanotechnol. 9, 755–767 (2014).
[Crossref]

A. C. Ferrari and D. M. Basko, “Raman spectroscopy as a versatile tool for studying the properties of graphene,” Nat. Nanotechnol. 8, 235–246 (2013).
[Crossref]

Nat. Phys. (1)

G. López-Polín, C. Gómez-Navarro, V. Parente, F. Guinea, M. I. Katsnelson, F. Pérez-Murano, and J. Gómez-Herrero, “Increasing the elastic modulus of graphene by controlled defect creation,” Nat. Phys. 11, 26–31 (2015).
[Crossref]

Opt. Commun. (1)

C. Henkel, K. Joulain, R. Carminati, and J.-J. Greffet, “Spatial coherence of thermal near fields,” Opt. Commun. 186, 57–67 (2000).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rep. (1)

A. Dogariu and R. Carminati, “Electromagnetic field correlations in three-dimensional speckles,” Phys. Rep. 559, 1–29 (2015).
[Crossref]

Phys. Rev. A (1)

R. Carminati, “Subwavelength spatial correlations in near-field speckle patterns,” Phys. Rev. A 81, 053804 (2010).
[Crossref]

Phys. Rev. B (1)

R. R. Naraghi, S. Sukhov, and A. Dogariu, “Disorder fingerprint: intensity distributions in the near field of random media,” Phys. Rev. B 94, 174205 (2016).
[Crossref]

Phys. Rev. E (1)

A. Apostol and A. Dogariu, “Coherence properties near interfaces of random media,” Phys. Rev. E 67, 055601 (2003).
[Crossref]

Phys. Rev. Lett. (1)

A. Apostol and A. Dogariu, “Spatial correlations in the near field of random media,” Phys. Rev. Lett. 91, 093901 (2003).
[Crossref]

Sci. Rep. (1)

W. Zhao, Y. Wang, Z. Wu, W. Wang, K. Bi, Z. Liang, J. Yang, Y. Chen, Z. Xu, and Z. Ni, “Defect-engineered heat transport in graphene: a route to high efficient thermal rectification,” Sci. Rep. 5, 11962 (2015).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

(a) Micrograph image of the graphene sample sitting on a cover glass substrate. The green color is a digital filter applied for better visualization of the graphene layer. The dashed line reproduces the contour shape of the monolayer piece, and is slightly displaced from the edges (to the right) for better visualization. (b) Raman analysis of the graphene sample. The bottom spectrum corresponds to freshly produced sample. The single Lorentzian shape of the two-phonon 2D band (at 2680  cm1) is evidence that the sample is a single layer. Additional spectra were obtained after distinct steps of oxygen-plasma etching (the gradually increasing etching time is indicated for each spectrum). The inset depicts the ID/IG ratio as a function of the average distance between adjacent point defects, LD. The solid line is a theoretical curve taken from Refs. [21,22]. The Raman spectra were obtained using a Renishaw inVia Raman spectrometer equipped with a 514.5 nm laser line source. The sample was measured in back scattering with a 50X objective lens (NA 0.75, Leica) used for both illumination and collection. The laser power was kept below 1 mW to avoid sample damage.

Fig. 2.
Fig. 2.

(a) Sketch of experimental setup used to analyze the light spatial coherence in the proximity of the graphene layer. High-resolution intensity maps corresponding to (b) pristine graphene and (c) graphene with defect density of nD=5.54×1012  cm2. Scale bar is 2 μm.

Fig. 3.
Fig. 3.

Average speckle size (δ) as a function of the inverse of the average distance between two point defects (LD). The dotted line represents the exponential decay indicated in the coherence model (see text) and corrected for the measurement PSF. The error bars indicate the uncertainty in evaluating δ with 0.95 confidence.

Fig. 4.
Fig. 4.

Spatial coherence length estimated in a plane situated at 20 nm from the surface of a source of radiation characterized by field-field correlations of extent δ(0). The dotted line indicates an exponential decay.

Metrics