Abstract

We discover deep-subwavelength, low-loss, and diffraction-free surface plasmon polariton (SPP) beam routing effects in aperiodic graphene sheet arrays (a-GSAs). The a-GSAs are constructed by varying either the interlayer spaces between graphene or the individual graphene chemical potentials. The SPP beams can be accelerated or decelerated in the a-GSAs, resulting in beam routing in different paths. The wave fronts of the beams are always parallel to the propagation direction, allowing the generation of transverse radiation pressure. All of these behaviors of SPPs are demonstrated by fully vectorial simulation and Hamilton optics analysis.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
    [CrossRef]
  2. T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
    [CrossRef]
  3. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
    [CrossRef]
  4. L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, Phys. Rev. Lett. 103, 033902 (2009).
    [CrossRef]
  5. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
    [CrossRef]
  6. X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
    [CrossRef]
  7. B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, Phys. Rev. Lett. 109, 073901 (2012).
    [CrossRef]
  8. F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, Nano Lett. 11, 3370 (2011).
    [CrossRef]
  9. B. Wang, X. Zhang, X. Yuan, and J. Teng, Appl. Phys. Lett. 100, 131111 (2012).
    [CrossRef]
  10. Y. Fan, B. Wang, K. Wang, H. Long, and P. Lu, Opt. Lett. 39, 3371 (2014).
    [CrossRef]
  11. B. Wang, X. Zhang, K. P. Loh, and J. Teng, J. Appl. Phys. 115, 213102 (2014).
    [CrossRef]
  12. D. W. Prather, S. Shi, D. M. Pustai, C. Chen, S. Venkataraman, A. Sharkawy, G. J. Schneider, and J. Murakowski, Opt. Lett. 29, 50 (2004).
    [CrossRef]
  13. P. Rose, F. Diebel, M. Boguslawski, and C. Denz, Appl. Phys. Lett. 102, 101101 (2013).
    [CrossRef]
  14. G. W. Hanson, J. Appl. Phys. 103, 064302 (2008).
    [CrossRef]
  15. A. Vakil and N. Engheta, Science 332, 1291 (2011).
    [CrossRef]
  16. G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
    [CrossRef]
  17. J. Nemirovsky, M. C. Rechtsman, and M. Segev, Opt. Express 20, 8907 (2012).
    [CrossRef]
  18. H. A. Buchdahl, An Introduction to Hamiltonian Optics (Dover, 1970).
  19. E. Verhagen, R. D. Waele, L. Kuipers, and A. Polman, Phys. Rev. Lett. 105, 223901 (2010).
    [CrossRef]
  20. P. Y. Chen and A. Alù, ACS Nano 5, 5855 (2011).
    [CrossRef]

2014

B. Wang, X. Zhang, K. P. Loh, and J. Teng, J. Appl. Phys. 115, 213102 (2014).
[CrossRef]

Y. Fan, B. Wang, K. Wang, H. Long, and P. Lu, Opt. Lett. 39, 3371 (2014).
[CrossRef]

2013

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, Appl. Phys. Lett. 102, 101101 (2013).
[CrossRef]

2012

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

B. Wang, X. Zhang, X. Yuan, and J. Teng, Appl. Phys. Lett. 100, 131111 (2012).
[CrossRef]

J. Nemirovsky, M. C. Rechtsman, and M. Segev, Opt. Express 20, 8907 (2012).
[CrossRef]

2011

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, Nano Lett. 11, 3370 (2011).
[CrossRef]

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

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

2010

E. Verhagen, R. D. Waele, L. Kuipers, and A. Polman, Phys. Rev. Lett. 105, 223901 (2010).
[CrossRef]

2009

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

2008

G. W. Hanson, J. Appl. Phys. 103, 064302 (2008).
[CrossRef]

2007

2006

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef]

2004

2003

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef]

2002

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

2000

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef]

1988

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef]

Alù, A.

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

Boguslawski, M.

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, Appl. Phys. Lett. 102, 101101 (2013).
[CrossRef]

Bräuer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Buchdahl, H. A.

H. A. Buchdahl, An Introduction to Hamiltonian Optics (Dover, 1970).

Catrysse, P. B.

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

Chan, C. T.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef]

Chang, D. E.

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, Nano Lett. 11, 3370 (2011).
[CrossRef]

Chen, C.

Chen, P. Y.

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

Christodoulides, D. N.

Denz, C.

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, Appl. Phys. Lett. 102, 101101 (2013).
[CrossRef]

Diebel, F.

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, Appl. Phys. Lett. 102, 101101 (2013).
[CrossRef]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef]

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]

Fan, X.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef]

Fan, Y.

García de Abajo, F. J.

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, Nano Lett. 11, 3370 (2011).
[CrossRef]

García-Vidal, F. J.

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

Hanson, G. W.

G. W. Hanson, J. Appl. Phys. 103, 064302 (2008).
[CrossRef]

Joseph, R. I.

Koppens, F. H. L.

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, Nano Lett. 11, 3370 (2011).
[CrossRef]

Kuipers, L.

E. Verhagen, R. D. Waele, L. Kuipers, and A. Polman, Phys. Rev. Lett. 105, 223901 (2010).
[CrossRef]

Lederer, F.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Lee, J. C. W.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef]

Loh, K. P.

B. Wang, X. Zhang, K. P. Loh, and J. Teng, J. Appl. Phys. 115, 213102 (2014).
[CrossRef]

Long, H.

Lu, P.

Morandotti, R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef]

Murakowski, J.

Nemirovsky, J.

Pertsch, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Peschel, U.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Polman, A.

E. Verhagen, R. D. Waele, L. Kuipers, and A. Polman, Phys. Rev. Lett. 105, 223901 (2010).
[CrossRef]

Prather, D. W.

Pustai, D. M.

Rechtsman, M. C.

Rose, P.

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, Appl. Phys. Lett. 102, 101101 (2013).
[CrossRef]

Schneider, G. J.

Segev, M.

Sharkawy, A.

Shi, S.

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef]

Siviloglou, G. A.

Teng, J.

B. Wang, X. Zhang, K. P. Loh, and J. Teng, J. Appl. Phys. 115, 213102 (2014).
[CrossRef]

B. Wang, X. Zhang, X. Yuan, and J. Teng, Appl. Phys. Lett. 100, 131111 (2012).
[CrossRef]

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

Vakil, A.

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

Venkataraman, S.

Verhagen, E.

E. Verhagen, R. D. Waele, L. Kuipers, and A. Polman, Phys. Rev. Lett. 105, 223901 (2010).
[CrossRef]

Verslegers, L.

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

Waele, R. D.

E. Verhagen, R. D. Waele, L. Kuipers, and A. Polman, Phys. Rev. Lett. 105, 223901 (2010).
[CrossRef]

Wang, B.

Y. Fan, B. Wang, K. Wang, H. Long, and P. Lu, Opt. Lett. 39, 3371 (2014).
[CrossRef]

B. Wang, X. Zhang, K. P. Loh, and J. Teng, J. Appl. Phys. 115, 213102 (2014).
[CrossRef]

B. Wang, X. Zhang, X. Yuan, and J. Teng, Appl. Phys. Lett. 100, 131111 (2012).
[CrossRef]

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

Wang, G. P.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef]

Wang, K.

Yu, Z.

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

Yuan, X.

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

B. Wang, X. Zhang, X. Yuan, and J. Teng, Appl. Phys. Lett. 100, 131111 (2012).
[CrossRef]

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

Zhang, X.

B. Wang, X. Zhang, K. P. Loh, and J. Teng, J. Appl. Phys. 115, 213102 (2014).
[CrossRef]

B. Wang, X. Zhang, X. Yuan, and J. Teng, Appl. Phys. Lett. 100, 131111 (2012).
[CrossRef]

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

ACS Nano

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

Appl. Phys. Lett.

B. Wang, X. Zhang, X. Yuan, and J. Teng, Appl. Phys. Lett. 100, 131111 (2012).
[CrossRef]

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, Appl. Phys. Lett. 102, 101101 (2013).
[CrossRef]

J. Appl. Phys.

G. W. Hanson, J. Appl. Phys. 103, 064302 (2008).
[CrossRef]

B. Wang, X. Zhang, K. P. Loh, and J. Teng, J. Appl. Phys. 115, 213102 (2014).
[CrossRef]

Nano Lett.

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, Nano Lett. 11, 3370 (2011).
[CrossRef]

Nature

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef]

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

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef]

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef]

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

E. Verhagen, R. D. Waele, L. Kuipers, and A. Polman, Phys. Rev. Lett. 105, 223901 (2010).
[CrossRef]

Science

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

Other

H. A. Buchdahl, An Introduction to Hamiltonian Optics (Dover, 1970).

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) Schematic of the a-GSA structure. (b) Wave vector (normalized by k0) of the collective SPPs in the periodic GSA versus the Bloch momentum (ϕ=kxd) in the first Brillouin zone for different periods. The solid and dashed curves refer to the real and imaginary parts of the normalized wave vectors, respectively. The normalized wave vector of SPPs in a single-layer graphene is marked with green arrows on the boundaries of the figure.

Fig. 2.
Fig. 2.

Magnetic field (Hy) distribution of SPPs as the interlayer space of graphene sheets follows d=ξ/(axb+1). (a) Magnetic field distribution of the accelerated beam as a=4 and b=1. (b) Decelerated beam as a=1 and b=2. The insets show the schematics of the incident field (Hy) profiles in the a-GSAs. The incident beam widths are both w0=0.2μm and the local Bloch momentum ϕ=0.1π. The arrows indicate the Poynting vectors. (c) and (d) Propagation routes of SPPs obtained by Hamilton optics. The insets show the dependence of the interlayer space (local period) on the lateral position.

Fig. 3.
Fig. 3.

SPP beam routing in the a-GSA constituted by varying the chemical potential of individual graphene sheets. The interlayer space of graphene is fixed at d=20nm. (a) Intensity of electric field of the accelerated beam as a=4 and b=1. (b) Decelerated beam as a=1 and b=2. The insets show the lateral variation of chemical potential.

Fig. 4.
Fig. 4.

Output position of SPP beams versus graphene distribution density a in the a-GSA for (a) b=2, (b) b=1, (c) b=1, and (d) b=2. The z positions are recorded at x=3μm for accelerated beams (b<0). The x positions are recorded at z=3μm for decelerated beams (b>0). The solid curves correspond to analytical results by using Hamilton optics. The stars and circles refer to the results for the a-GSAs constituted by varying the interlayer space and chemical potential of individual graphene, respectively.

Equations (2)

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

dxdz=α1/2sgn(kx).
z={a1/2b/2+1(xb/2+1x0b/2+1)b2a1/2ln(xx0)b=2.

Metrics