Abstract

We theoretically investigate the plasmonic Talbot effect in monolayer graphene sheet arrays (MGSAs) when surface plasmon polaritons (SPPs) between graphene experience weak coupling. The Talbot effect occurs only when the incident field has a pattern with a few selected periods. The Talbot distance is found to decrease exponentially with the decreasing period of the MGSA and can be as small as 1/20 of the incident wavelength. In addition, the Talbot distance can be further reduced by increasing the chemical potential of graphene or operating at longer wavelengths.

© 2014 Optical Society of America

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2013 (1)

Y. Sun, Z. Zheng, J. Cheng, J. Liu, J. Liu, and S. Li, Appl. Phys. Lett. 103, 241116 (2013).
[CrossRef]

2012 (3)

A. N. Grigorenko, M. Polini, and K. S. Novoselov, Nat. Photonics 6, 749 (2012).
[CrossRef]

C. H. Gan, Appl. Phys. Lett. 101, 111609 (2012).
[CrossRef]

B. Wang, X. Zhang, F. J. García-Vidal, X. C. Yuan, and J. H. Teng, Phys. Rev. Lett. 109, 073901 (2012).
[CrossRef]

2011 (2)

A. Vakil and N. Engheta, Science 332, 1291 (2011).
[CrossRef]

P. Y. Chen and A. Alù, ACS Nano 5, 5855 (2011).
[CrossRef]

2010 (2)

2009 (2)

P. Maddaloni, M. Paturzo, P. Ferraro, P. Malara, P. De Natale, M. Gioffrè, G. Coppola, and M. Iodice, Appl. Phys. Lett. 94, 121105 (2009).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef]

2008 (1)

G. W. Hanson, J. Appl. Phys. 104, 084314 (2008).
[CrossRef]

2007 (1)

2005 (1)

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef]

2002 (1)

G. Spagnolo, D. Ambrosini, and D. Paoletti, J. Opt. A 4, S376 (2002).
[CrossRef]

1989 (2)

1988 (1)

1836 (1)

H. F. Talbot, Philos. Mag. 9(56), 401 (1836).
[CrossRef]

Alù, A.

P. Y. Chen and A. Alù, ACS Nano 5, 5855 (2011).
[CrossRef]

Ambrosini, D.

G. Spagnolo, D. Ambrosini, and D. Paoletti, J. Opt. A 4, S376 (2002).
[CrossRef]

Bhattacharya, J.

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef]

Chen, P. Y.

P. Y. Chen and A. Alù, ACS Nano 5, 5855 (2011).
[CrossRef]

Cheng, J.

Y. Sun, Z. Zheng, J. Cheng, J. Liu, J. Liu, and S. Li, Appl. Phys. Lett. 103, 241116 (2013).
[CrossRef]

Christodoulides, D. N.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef]

Christodoulides, N.

Coppola, G.

P. Maddaloni, M. Paturzo, P. Ferraro, P. Malara, P. De Natale, M. Gioffrè, G. Coppola, and M. Iodice, Appl. Phys. Lett. 94, 121105 (2009).
[CrossRef]

De Natale, P.

P. Maddaloni, M. Paturzo, P. Ferraro, P. Malara, P. De Natale, M. Gioffrè, G. Coppola, and M. Iodice, Appl. Phys. Lett. 94, 121105 (2009).
[CrossRef]

Dennis, M. R.

Engheta, N.

A. Vakil and N. Engheta, Science 332, 1291 (2011).
[CrossRef]

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef]

Ferraro, P.

P. Maddaloni, M. Paturzo, P. Ferraro, P. Malara, P. De Natale, M. Gioffrè, G. Coppola, and M. Iodice, Appl. Phys. Lett. 94, 121105 (2009).
[CrossRef]

Gan, C. H.

C. H. Gan, Appl. Phys. Lett. 101, 111609 (2012).
[CrossRef]

García de Abajo, F. J.

García-Vidal, F. J.

B. Wang, X. Zhang, F. J. García-Vidal, X. C. Yuan, and J. H. Teng, Phys. Rev. Lett. 109, 073901 (2012).
[CrossRef]

Gioffrè, M.

P. Maddaloni, M. Paturzo, P. Ferraro, P. Malara, P. De Natale, M. Gioffrè, G. Coppola, and M. Iodice, Appl. Phys. Lett. 94, 121105 (2009).
[CrossRef]

Grigorenko, A. N.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, Nat. Photonics 6, 749 (2012).
[CrossRef]

Hanson, G. W.

G. W. Hanson, J. Appl. Phys. 104, 084314 (2008).
[CrossRef]

Harzendorf, T.

Iodice, M.

P. Maddaloni, M. Paturzo, P. Ferraro, P. Malara, P. De Natale, M. Gioffrè, G. Coppola, and M. Iodice, Appl. Phys. Lett. 94, 121105 (2009).
[CrossRef]

Iwanow, R.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef]

Joseph, R. I.

Li, S.

Y. Sun, Z. Zheng, J. Cheng, J. Liu, J. Liu, and S. Li, Appl. Phys. Lett. 103, 241116 (2013).
[CrossRef]

Liu, J.

Y. Sun, Z. Zheng, J. Cheng, J. Liu, J. Liu, and S. Li, Appl. Phys. Lett. 103, 241116 (2013).
[CrossRef]

Y. Sun, Z. Zheng, J. Cheng, J. Liu, J. Liu, and S. Li, Appl. Phys. Lett. 103, 241116 (2013).
[CrossRef]

Liu, L.

Liu, S. T.

Maddaloni, P.

P. Maddaloni, M. Paturzo, P. Ferraro, P. Malara, P. De Natale, M. Gioffrè, G. Coppola, and M. Iodice, Appl. Phys. Lett. 94, 121105 (2009).
[CrossRef]

Malara, P.

P. Maddaloni, M. Paturzo, P. Ferraro, P. Malara, P. De Natale, M. Gioffrè, G. Coppola, and M. Iodice, Appl. Phys. Lett. 94, 121105 (2009).
[CrossRef]

May-Arrioja, D. A.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef]

Novoselov, K. S.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, Nat. Photonics 6, 749 (2012).
[CrossRef]

Paoletti, D.

G. Spagnolo, D. Ambrosini, and D. Paoletti, J. Opt. A 4, S376 (2002).
[CrossRef]

Paturzo, M.

P. Maddaloni, M. Paturzo, P. Ferraro, P. Malara, P. De Natale, M. Gioffrè, G. Coppola, and M. Iodice, Appl. Phys. Lett. 94, 121105 (2009).
[CrossRef]

Polini, M.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, Nat. Photonics 6, 749 (2012).
[CrossRef]

Song, Y. L.

Spagnolo, G.

G. Spagnolo, D. Ambrosini, and D. Paoletti, J. Opt. A 4, S376 (2002).
[CrossRef]

Stegeman, G. I.

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef]

Stuerzebecher, L.

Sun, Y.

Y. Sun, Z. Zheng, J. Cheng, J. Liu, J. Liu, and S. Li, Appl. Phys. Lett. 103, 241116 (2013).
[CrossRef]

Talbot, H. F.

H. F. Talbot, Philos. Mag. 9(56), 401 (1836).
[CrossRef]

Teng, J. H.

B. Wang, X. Zhang, F. J. García-Vidal, X. C. Yuan, and J. H. Teng, Phys. Rev. Lett. 109, 073901 (2012).
[CrossRef]

Vakil, A.

A. Vakil and N. Engheta, Science 332, 1291 (2011).
[CrossRef]

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef]

Voelkel, R.

Vogler, U.

Wang, B.

B. Wang, X. Zhang, F. J. García-Vidal, X. C. Yuan, and J. H. Teng, Phys. Rev. Lett. 109, 073901 (2012).
[CrossRef]

Wang, Y. K.

Wang, Y. X.

Yang, K.

Yu, Z.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef]

Yuan, X. C.

B. Wang, X. Zhang, F. J. García-Vidal, X. C. Yuan, and J. H. Teng, Phys. Rev. Lett. 109, 073901 (2012).
[CrossRef]

Zeitner, U. D.

Zhang, X.

B. Wang, X. Zhang, F. J. García-Vidal, X. C. Yuan, and J. H. Teng, Phys. Rev. Lett. 109, 073901 (2012).
[CrossRef]

Zhang, X. R.

Zheludev, N. I.

Zheng, Z.

Y. Sun, Z. Zheng, J. Cheng, J. Liu, J. Liu, and S. Li, Appl. Phys. Lett. 103, 241116 (2013).
[CrossRef]

Zhou, K. Y.

ACS Nano (1)

P. Y. Chen and A. Alù, ACS Nano 5, 5855 (2011).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

P. Maddaloni, M. Paturzo, P. Ferraro, P. Malara, P. De Natale, M. Gioffrè, G. Coppola, and M. Iodice, Appl. Phys. Lett. 94, 121105 (2009).
[CrossRef]

C. H. Gan, Appl. Phys. Lett. 101, 111609 (2012).
[CrossRef]

Y. Sun, Z. Zheng, J. Cheng, J. Liu, J. Liu, and S. Li, Appl. Phys. Lett. 103, 241116 (2013).
[CrossRef]

J. Appl. Phys. (1)

G. W. Hanson, J. Appl. Phys. 104, 084314 (2008).
[CrossRef]

J. Opt. A (1)

G. Spagnolo, D. Ambrosini, and D. Paoletti, J. Opt. A 4, S376 (2002).
[CrossRef]

Nat. Photonics (1)

A. N. Grigorenko, M. Polini, and K. S. Novoselov, Nat. Photonics 6, 749 (2012).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Philos. Mag. (1)

H. F. Talbot, Philos. Mag. 9(56), 401 (1836).
[CrossRef]

Phys. Rev. Lett. (3)

R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 95, 053902 (2005).
[CrossRef]

B. Wang, X. Zhang, F. J. García-Vidal, X. C. Yuan, and J. H. Teng, Phys. Rev. Lett. 109, 073901 (2012).
[CrossRef]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
[CrossRef]

Science (1)

A. Vakil and N. Engheta, Science 332, 1291 (2011).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Diffraction relation of SPPs in the MGSA as d=60nm and 80 nm. The solid curves denote the rigorous data obtained by Eq. (1), while the dashed ones are approximated data. The inset shows the schematic diagram of the MGSA.

Fig. 2.
Fig. 2.

Distributions of magnetic field intensity (|Hy|2) in the MGSA. (a)–(c) Intensity distributions as the patterns of incident field are given by (a) {1,0,1,0,}, (b) {1,0,0,1,0,0,}, and (c) {1,0,1,0,}. The period is fixed at d=80nm. (d) and (e) The intensity distributions as (d) d=60nm, (e) d=70nm, and (f) d=90nm. The incident conditions are the same with (a).

Fig. 3.
Fig. 3.

Normalized Talbot distance [ln(kSPzT)] versus the period of the MGSA for different embedding materials. The incident field pattern has a period of N=2. The solid curves and circles represent the analytical and numerical results, respectively.

Fig. 4.
Fig. 4.

Dependence of the Talbot distance of SPPs on μc and λ for embedding materials of (a) air and (b) KCl as d=80nm. The blank areas represent the meaningless regions with respect to zT.

Equations (4)

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

cos(ϕ)=cosh(κd)κξ2sinh(κd),
kz=βe+βo2+βeβo2cos(kxd)
idandz=Cg(an1+an+1),
zT=π2|Cg|π4ξexp(2d/ξ).

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