Abstract

We investigate the Bloch mode conversion of surface plasmon polaritons in a periodic array of graphene pairs with each consisting of two separated parallel graphene sheets. The employment of graphene pair as a unit cell in the array yields two Bloch modes belonging to different bands. By periodically modulating the permittivity of dielectrics between graphene along the propagation direction, the interband transitions occur and the modes will alternatively couple to each other, similar to traditional Rabi oscillations in quantum systems. The indirect Rabi oscillations can also be observed through introducing transverse modulation momentum. The period of Rabi oscillations can be optimized by taking advantage of the flexible tunability of graphene. The study suggests that the structure have applications in optical switches and mode converters operating on deep-subwavelength scale.

© 2015 Optical Society of America

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References

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    [Crossref]

2015 (5)

2014 (2)

2013 (3)

2012 (7)

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[Crossref] [PubMed]

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

C. H. Gan, “Analysis of surface plasmon excitation at terahertz frequencies with highly doped graphene sheets via attenuated total reflection,” Appl. Phys. Lett. 101(11), 111609 (2012).
[Crossref]

A. Y. Nikitin, F. Guinea, and L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101(15), 151119 (2012).
[Crossref]

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100(13), 131111 (2012).
[Crossref]

K. V. Sreekanth, S. Zeng, J. Shang, K. T. Yong, and T. Yu, “Excitation of surface electromagnetic waves in a graphene-based Bragg grating,” Sci. Rep. 2, 737 (2012).
[Crossref] [PubMed]

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[Crossref]

2011 (4)

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, “Generation of optical vortices in layered helical waveguides,” Phys. Rev. A 83(6), 063820 (2011).
[Crossref]

2010 (1)

N. M. R. Peres, “Colloquium: the transport properties of graphene: an introduction,” Rev. Mod. Phys. 82(3), 2673–2700 (2010).
[Crossref]

2009 (3)

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102(12), 123905 (2009).
[Crossref] [PubMed]

K. Schuh, J. Seebeck, M. Lorke, and F. Jahnke, “Rabi oscillations in semiconductor quantum dots revisited: influence of LO-phonon collisions,” Appl. Phys. Lett. 94(20), 201108 (2009).
[Crossref]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009).
[Crossref]

2008 (1)

2007 (3)

V. S. Shchesnovich and S. Chávez-Cerda, “Bragg-resonance-induced Rabi oscillations in photonic lattices,” Opt. Lett. 32(13), 1920–1922 (2007).
[Crossref] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Resonant mode oscillations in modulated waveguiding structures,” Phys. Rev. Lett. 99(23), 233903 (2007).
[Crossref] [PubMed]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[Crossref] [PubMed]

2000 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

1999 (1)

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, M. J. Holland, J. E. Williams, C. E. Wieman, and E. A. Cornell, “Watching a superfluid untwist itself: recurrence of Rabi oscillations in a Bose-Einstein condensate,” Phys. Rev. Lett. 83(17), 3358–3361 (1999).
[Crossref]

1987 (1)

V. Gericke, P. Hertel, E. Krätzig, J. P. Nisius, and R. Sommerfeldt, “Light-induced refractive index changes in LiNbO3: Ti waveguides,” Appl. Phys. B 44(3), 155–162 (1987).
[Crossref]

1936 (1)

I. I. Rabi, “On the process of space quantization,” Phys. Rev. 49(4), 324–328 (1936).
[Crossref]

Aceves, A. B.

Ahn, J.

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

Alexeyev, C. N.

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, “Generation of optical vortices in layered helical waveguides,” Phys. Rev. A 83(6), 063820 (2011).
[Crossref]

Alù, A.

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

Anderson, B. P.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, M. J. Holland, J. E. Williams, C. E. Wieman, and E. A. Cornell, “Watching a superfluid untwist itself: recurrence of Rabi oscillations in a Bose-Einstein condensate,” Phys. Rev. Lett. 83(17), 3358–3361 (1999).
[Crossref]

Andryieuski, A.

Auditore, A.

Bartal, G.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[Crossref] [PubMed]

Biancalana, F.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

Chang, D. E.

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Chávez-Cerda, S.

Chen, P. Y.

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

Chen, X.

Cheng, J.

Y. Sun, Z. Zheng, J. Cheng, J. Liu, J. Liu, and S. Li, “The un-symmetric hybridization of graphene surface plasmons incorporating graphene sheets and nano-ribbons,” Appl. Phys. Lett. 103(24), 241116 (2013).
[Crossref]

Christodoulides, D. N.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102(12), 123905 (2009).
[Crossref] [PubMed]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express 16(14), 10309–10314 (2008).
[Crossref] [PubMed]

Conti, C.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

Cornell, E. A.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, M. J. Holland, J. E. Williams, C. E. Wieman, and E. A. Cornell, “Watching a superfluid untwist itself: recurrence of Rabi oscillations in a Bose-Einstein condensate,” Phys. Rev. Lett. 83(17), 3358–3361 (1999).
[Crossref]

de Angelis, C.

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

Engheta, N.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

Fadeyeva, T. A.

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, “Generation of optical vortices in layered helical waveguides,” Phys. Rev. A 83(6), 063820 (2011).
[Crossref]

Fan, S.

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009).
[Crossref]

Fan, Y.

Gan, C. H.

C. H. Gan, “Analysis of surface plasmon excitation at terahertz frequencies with highly doped graphene sheets via attenuated total reflection,” Appl. Phys. Lett. 101(11), 111609 (2012).
[Crossref]

García de Abajo, F. J.

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

García-Vidal, F. J.

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[Crossref] [PubMed]

Genov, D. A.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[Crossref] [PubMed]

Gericke, V.

V. Gericke, P. Hertel, E. Krätzig, J. P. Nisius, and R. Sommerfeldt, “Light-induced refractive index changes in LiNbO3: Ti waveguides,” Appl. Phys. B 44(3), 155–162 (1987).
[Crossref]

Grigorenko, A. N.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[Crossref]

Guinea, F.

A. Y. Nikitin, F. Guinea, and L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101(15), 151119 (2012).
[Crossref]

Haljan, P. C.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, M. J. Holland, J. E. Williams, C. E. Wieman, and E. A. Cornell, “Watching a superfluid untwist itself: recurrence of Rabi oscillations in a Bose-Einstein condensate,” Phys. Rev. Lett. 83(17), 3358–3361 (1999).
[Crossref]

Hall, D. S.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, M. J. Holland, J. E. Williams, C. E. Wieman, and E. A. Cornell, “Watching a superfluid untwist itself: recurrence of Rabi oscillations in a Bose-Einstein condensate,” Phys. Rev. Lett. 83(17), 3358–3361 (1999).
[Crossref]

Hertel, P.

V. Gericke, P. Hertel, E. Krätzig, J. P. Nisius, and R. Sommerfeldt, “Light-induced refractive index changes in LiNbO3: Ti waveguides,” Appl. Phys. B 44(3), 155–162 (1987).
[Crossref]

Holland, M. J.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, M. J. Holland, J. E. Williams, C. E. Wieman, and E. A. Cornell, “Watching a superfluid untwist itself: recurrence of Rabi oscillations in a Bose-Einstein condensate,” Phys. Rev. Lett. 83(17), 3358–3361 (1999).
[Crossref]

Hu, H.

H. Hu, K. Wang, H. Long, W. Liu, B. Wang, and P. Lu, “Precise determination of the crystallographic orientations in single ZnS nanowires by second-harmonic generation microscopy,” Nano Lett. 15(5), 3351–3357 (2015).
[Crossref] [PubMed]

Huang, H.

Jahnke, F.

K. Schuh, J. Seebeck, M. Lorke, and F. Jahnke, “Rabi oscillations in semiconductor quantum dots revisited: influence of LO-phonon collisions,” Appl. Phys. Lett. 94(20), 201108 (2009).
[Crossref]

Kang, M. S.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

Kartashov, Y. V.

X. Zhang, F. Ye, Y. V. Kartashov, and X. Chen, “Rabi oscillations and stimulated mode conversion on the subwavelength scale,” Opt. Express 23(5), 6731–6737 (2015).
[Crossref] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Resonant mode oscillations in modulated waveguiding structures,” Phys. Rev. Lett. 99(23), 233903 (2007).
[Crossref] [PubMed]

Ke, S.

Kim, H.

Kip, D.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102(12), 123905 (2009).
[Crossref] [PubMed]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express 16(14), 10309–10314 (2008).
[Crossref] [PubMed]

Koppens, F. H. L.

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Krätzig, E.

V. Gericke, P. Hertel, E. Krätzig, J. P. Nisius, and R. Sommerfeldt, “Light-induced refractive index changes in LiNbO3: Ti waveguides,” Appl. Phys. B 44(3), 155–162 (1987).
[Crossref]

Lapin, B. P.

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, “Generation of optical vortices in layered helical waveguides,” Phys. Rev. A 83(6), 063820 (2011).
[Crossref]

Lavrinenko, A. V.

Lee, H. G.

Lee, H. W.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

Li, S.

Y. Sun, Z. Zheng, J. Cheng, J. Liu, J. Liu, and S. Li, “The un-symmetric hybridization of graphene surface plasmons incorporating graphene sheets and nano-ribbons,” Appl. Phys. Lett. 103(24), 241116 (2013).
[Crossref]

Liu, J.

Y. Sun, Z. Zheng, J. Cheng, J. Liu, J. Liu, and S. Li, “The un-symmetric hybridization of graphene surface plasmons incorporating graphene sheets and nano-ribbons,” Appl. Phys. Lett. 103(24), 241116 (2013).
[Crossref]

Y. Sun, Z. Zheng, J. Cheng, J. Liu, J. Liu, and S. Li, “The un-symmetric hybridization of graphene surface plasmons incorporating graphene sheets and nano-ribbons,” Appl. Phys. Lett. 103(24), 241116 (2013).
[Crossref]

Liu, W.

H. Hu, K. Wang, H. Long, W. Liu, B. Wang, and P. Lu, “Precise determination of the crystallographic orientations in single ZnS nanowires by second-harmonic generation microscopy,” Nano Lett. 15(5), 3351–3357 (2015).
[Crossref] [PubMed]

Liu, Y.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[Crossref] [PubMed]

Locatelli, A.

Long, H.

Lorke, M.

K. Schuh, J. Seebeck, M. Lorke, and F. Jahnke, “Rabi oscillations in semiconductor quantum dots revisited: influence of LO-phonon collisions,” Appl. Phys. Lett. 94(20), 201108 (2009).
[Crossref]

Lu, P.

Makris, K. G.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102(12), 123905 (2009).
[Crossref] [PubMed]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express 16(14), 10309–10314 (2008).
[Crossref] [PubMed]

Martin-Moreno, L.

A. Y. Nikitin, F. Guinea, and L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101(15), 151119 (2012).
[Crossref]

Matthews, M. R.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, M. J. Holland, J. E. Williams, C. E. Wieman, and E. A. Cornell, “Watching a superfluid untwist itself: recurrence of Rabi oscillations in a Bose-Einstein condensate,” Phys. Rev. Lett. 83(17), 3358–3361 (1999).
[Crossref]

Morandotti, R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

Nikitin, A. Y.

A. Y. Nikitin, F. Guinea, and L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101(15), 151119 (2012).
[Crossref]

Nisius, J. P.

V. Gericke, P. Hertel, E. Krätzig, J. P. Nisius, and R. Sommerfeldt, “Light-induced refractive index changes in LiNbO3: Ti waveguides,” Appl. Phys. B 44(3), 155–162 (1987).
[Crossref]

Novoselov, K. S.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[Crossref]

Peleg, O.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102(12), 123905 (2009).
[Crossref] [PubMed]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express 16(14), 10309–10314 (2008).
[Crossref] [PubMed]

Peres, N. M. R.

N. M. R. Peres, “Colloquium: the transport properties of graphene: an introduction,” Rev. Mod. Phys. 82(3), 2673–2700 (2010).
[Crossref]

Polini, M.

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[Crossref]

Qin, C.

Rabi, I. I.

I. I. Rabi, “On the process of space quantization,” Phys. Rev. 49(4), 324–328 (1936).
[Crossref]

Russell, P. St. J.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

Rüter, C. E.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102(12), 123905 (2009).
[Crossref] [PubMed]

Schuh, K.

K. Schuh, J. Seebeck, M. Lorke, and F. Jahnke, “Rabi oscillations in semiconductor quantum dots revisited: influence of LO-phonon collisions,” Appl. Phys. Lett. 94(20), 201108 (2009).
[Crossref]

Seebeck, J.

K. Schuh, J. Seebeck, M. Lorke, and F. Jahnke, “Rabi oscillations in semiconductor quantum dots revisited: influence of LO-phonon collisions,” Appl. Phys. Lett. 94(20), 201108 (2009).
[Crossref]

Segev, M.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102(12), 123905 (2009).
[Crossref] [PubMed]

K. G. Makris, D. N. Christodoulides, O. Peleg, M. Segev, and D. Kip, “Optical transitions and Rabi oscillations in waveguide arrays,” Opt. Express 16(14), 10309–10314 (2008).
[Crossref] [PubMed]

Shandarova, K.

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102(12), 123905 (2009).
[Crossref] [PubMed]

Shang, J.

K. V. Sreekanth, S. Zeng, J. Shang, K. T. Yong, and T. Yu, “Excitation of surface electromagnetic waves in a graphene-based Bragg grating,” Sci. Rep. 2, 737 (2012).
[Crossref] [PubMed]

Shchesnovich, V. S.

Silberberg, Y.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

Sommerfeldt, R.

V. Gericke, P. Hertel, E. Krätzig, J. P. Nisius, and R. Sommerfeldt, “Light-induced refractive index changes in LiNbO3: Ti waveguides,” Appl. Phys. B 44(3), 155–162 (1987).
[Crossref]

Sreekanth, K. V.

K. V. Sreekanth, S. Zeng, J. Shang, K. T. Yong, and T. Yu, “Excitation of surface electromagnetic waves in a graphene-based Bragg grating,” Sci. Rep. 2, 737 (2012).
[Crossref] [PubMed]

Sun, Y.

Y. Sun, Z. Zheng, J. Cheng, J. Liu, J. Liu, and S. Li, “The un-symmetric hybridization of graphene surface plasmons incorporating graphene sheets and nano-ribbons,” Appl. Phys. Lett. 103(24), 241116 (2013).
[Crossref]

Teng, J.

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[Crossref] [PubMed]

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100(13), 131111 (2012).
[Crossref]

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Resonant mode oscillations in modulated waveguiding structures,” Phys. Rev. Lett. 99(23), 233903 (2007).
[Crossref] [PubMed]

Vakil, A.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Resonant mode oscillations in modulated waveguiding structures,” Phys. Rev. Lett. 99(23), 233903 (2007).
[Crossref] [PubMed]

Wang, B.

H. Hu, K. Wang, H. Long, W. Liu, B. Wang, and P. Lu, “Precise determination of the crystallographic orientations in single ZnS nanowires by second-harmonic generation microscopy,” Nano Lett. 15(5), 3351–3357 (2015).
[Crossref] [PubMed]

C. Qin, B. Wang, H. Long, K. Wang, and P. Lu, “Bloch mode engineering in graphene modulated periodic waveguides and cavities,” J. Opt. Soc. Am. B 32(8), 1748–1753 (2015).
[Crossref]

S. Ke, B. Wang, H. Huang, H. Long, K. Wang, and P. Lu, “Plasmonic absorption enhancement in periodic cross-shaped graphene arrays,” Opt. Express 23(7), 8888–8900 (2015).
[Crossref] [PubMed]

C. Qin, B. Wang, H. Huang, H. Long, K. Wang, and P. Lu, “Low-loss plasmonic supermodes in graphene multilayers,” Opt. Express 22(21), 25324–25332 (2014).
[Crossref] [PubMed]

Y. Fan, B. Wang, K. Wang, H. Long, and P. Lu, “Talbot effect in weakly coupled monolayer graphene sheet arrays,” Opt. Lett. 39(12), 3371–3373 (2014).
[Crossref] [PubMed]

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[Crossref] [PubMed]

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100(13), 131111 (2012).
[Crossref]

Wang, K.

Weiss, T.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

Wieman, C. E.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, M. J. Holland, J. E. Williams, C. E. Wieman, and E. A. Cornell, “Watching a superfluid untwist itself: recurrence of Rabi oscillations in a Bose-Einstein condensate,” Phys. Rev. Lett. 83(17), 3358–3361 (1999).
[Crossref]

Williams, J. E.

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, M. J. Holland, J. E. Williams, C. E. Wieman, and E. A. Cornell, “Watching a superfluid untwist itself: recurrence of Rabi oscillations in a Bose-Einstein condensate,” Phys. Rev. Lett. 83(17), 3358–3361 (1999).
[Crossref]

Wong, G. K. L.

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

Yavorsky, M. A.

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, “Generation of optical vortices in layered helical waveguides,” Phys. Rev. A 83(6), 063820 (2011).
[Crossref]

Ye, F.

Yong, K. T.

K. V. Sreekanth, S. Zeng, J. Shang, K. T. Yong, and T. Yu, “Excitation of surface electromagnetic waves in a graphene-based Bragg grating,” Sci. Rep. 2, 737 (2012).
[Crossref] [PubMed]

Yu, T.

K. V. Sreekanth, S. Zeng, J. Shang, K. T. Yong, and T. Yu, “Excitation of surface electromagnetic waves in a graphene-based Bragg grating,” Sci. Rep. 2, 737 (2012).
[Crossref] [PubMed]

Yu, Z.

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009).
[Crossref]

Yuan, X.

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100(13), 131111 (2012).
[Crossref]

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[Crossref] [PubMed]

Zeng, S.

K. V. Sreekanth, S. Zeng, J. Shang, K. T. Yong, and T. Yu, “Excitation of surface electromagnetic waves in a graphene-based Bragg grating,” Sci. Rep. 2, 737 (2012).
[Crossref] [PubMed]

Zhang, X.

X. Zhang, F. Ye, Y. V. Kartashov, and X. Chen, “Rabi oscillations and stimulated mode conversion on the subwavelength scale,” Opt. Express 23(5), 6731–6737 (2015).
[Crossref] [PubMed]

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[Crossref] [PubMed]

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100(13), 131111 (2012).
[Crossref]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[Crossref] [PubMed]

Zheng, Z.

Y. Sun, Z. Zheng, J. Cheng, J. Liu, J. Liu, and S. Li, “The un-symmetric hybridization of graphene surface plasmons incorporating graphene sheets and nano-ribbons,” Appl. Phys. Lett. 103(24), 241116 (2013).
[Crossref]

ACS Nano (1)

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

Appl. Phys. B (1)

V. Gericke, P. Hertel, E. Krätzig, J. P. Nisius, and R. Sommerfeldt, “Light-induced refractive index changes in LiNbO3: Ti waveguides,” Appl. Phys. B 44(3), 155–162 (1987).
[Crossref]

Appl. Phys. Lett. (5)

A. Y. Nikitin, F. Guinea, and L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101(15), 151119 (2012).
[Crossref]

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett. 100(13), 131111 (2012).
[Crossref]

C. H. Gan, “Analysis of surface plasmon excitation at terahertz frequencies with highly doped graphene sheets via attenuated total reflection,” Appl. Phys. Lett. 101(11), 111609 (2012).
[Crossref]

Y. Sun, Z. Zheng, J. Cheng, J. Liu, J. Liu, and S. Li, “The un-symmetric hybridization of graphene surface plasmons incorporating graphene sheets and nano-ribbons,” Appl. Phys. Lett. 103(24), 241116 (2013).
[Crossref]

K. Schuh, J. Seebeck, M. Lorke, and F. Jahnke, “Rabi oscillations in semiconductor quantum dots revisited: influence of LO-phonon collisions,” Appl. Phys. Lett. 94(20), 201108 (2009).
[Crossref]

J. Opt. Soc. Am. B (1)

Nano Lett. (2)

H. Hu, K. Wang, H. Long, W. Liu, B. Wang, and P. Lu, “Precise determination of the crystallographic orientations in single ZnS nanowires by second-harmonic generation microscopy,” Nano Lett. 15(5), 3351–3357 (2015).
[Crossref] [PubMed]

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Nat. Photonics (2)

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012).
[Crossref]

Z. Yu and S. Fan, “Complete optical isolation created by indirect interband photonic transitions,” Nat. Photonics 3(2), 91–94 (2009).
[Crossref]

Opt. Express (5)

Opt. Lett. (4)

Phys. Rev. (1)

I. I. Rabi, “On the process of space quantization,” Phys. Rev. 49(4), 324–328 (1936).
[Crossref]

Phys. Rev. A (1)

C. N. Alexeyev, T. A. Fadeyeva, B. P. Lapin, and M. A. Yavorsky, “Generation of optical vortices in layered helical waveguides,” Phys. Rev. A 83(6), 063820 (2011).
[Crossref]

Phys. Rev. Lett. (6)

M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, M. J. Holland, J. E. Williams, C. E. Wieman, and E. A. Cornell, “Watching a superfluid untwist itself: recurrence of Rabi oscillations in a Bose-Einstein condensate,” Phys. Rev. Lett. 83(17), 3358–3361 (1999).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Resonant mode oscillations in modulated waveguiding structures,” Phys. Rev. Lett. 99(23), 233903 (2007).
[Crossref] [PubMed]

K. Shandarova, C. E. Rüter, D. Kip, K. G. Makris, D. N. Christodoulides, O. Peleg, and M. Segev, “Experimental observation of Rabi oscillations in photonic lattices,” Phys. Rev. Lett. 102(12), 123905 (2009).
[Crossref] [PubMed]

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[Crossref] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

N. M. R. Peres, “Colloquium: the transport properties of graphene: an introduction,” Rev. Mod. Phys. 82(3), 2673–2700 (2010).
[Crossref]

Sci. Rep. (1)

K. V. Sreekanth, S. Zeng, J. Shang, K. T. Yong, and T. Yu, “Excitation of surface electromagnetic waves in a graphene-based Bragg grating,” Sci. Rep. 2, 737 (2012).
[Crossref] [PubMed]

Science (2)

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

G. K. L. Wong, M. S. Kang, H. W. Lee, F. Biancalana, C. Conti, T. Weiss, and P. St. J. Russell, “Excitation of orbital angular momentum resonances in helically twisted photonic crystal fiber,” Science 337(6093), 446–449 (2012).
[Crossref] [PubMed]

Other (3)

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer Verlag, 2007).

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communication (Academic, 2006).

K. Okamoto, Fundamentals and Applications of Optical Waveguides (Academic, 2006).

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic of the GPAs. (b) Real part of the effective index (n eff) of Bloch modes in the GPAs as a funtion of the Bloch momentum, that is, the band structure of the Bloch modes. Solid and dotted curves denote d 1 = 20nm, d 2 = 40nm and d 1 = 20nm, d 2 = 60nm, respectively. (c) Imaginary part of n eff as a function of the Bloch momentum.
Fig. 2
Fig. 2 Normalized transverse magnetic field distributions of the Bloch modes in the GPAs as d 1 = 20nm and d 2 = 60nm. The positions of graphene sheets are denoted by the red dashed lines. (a)-(c) denote the mode profiles of band 1 as φ = 0, π/2, π. (d)-(f) Corresponding mode profiles of band 2 as φ = 0, π/2, π, respectively.
Fig. 3
Fig. 3 The coupling coefficient |M12| as a function of incident Bloch momentum φ1 and momentum difference Δφ = φ2 – φ1. The modulation amplitude is δε = 0.3 as d 1 = 20nm and d 2 = 60nm. In (a) and (b) Δφ = 0, ± π while in (c) and (d) Δφ = ± π/2. In (a) and (c), the transverse modulation is Δε(x) = sin(2πx/d). In (b) and (d), the transverse modulation is Δε(x) = cos(2πx/d).
Fig. 4
Fig. 4 Analytical and simulated magnetic field (Hy ) evolution of Rabi oscillations between the Bloch modes as d 1 = 20nm, d 2 = 60nm, and δε = 0.3. Black dotted lines denote the positions where complete transitions occur. (a) and (b) Analytical and simulated direct interband transtions of Φ1,0 ↔ Φ2,0 as Δε(x) = sin(2πx/d). (c) Bloch mode Φ1,0 as Δε(x) = cos(2πx/d). (d) and (e) Numerical indirect transitions of Φ1,0 ↔ Φ2,π and Φ1,π ↔ Φ2,0 as Δε(x) = sin(2πx/d).
Fig. 5
Fig. 5 The period of Rabi oscillations L c versus different parameters. (a) L c as a function of d 1 and d as φ1 = 0 and Δφ = 0. (b) L c as a function of φ1 and Δφ as d 1 = 20nm and d = 80 nm. In (a) and (b) λ = 10 μm and μc = 0.15 eV. (c) The influence of λ and μc on the period of Rabi oscillations for φ1 = π and Δφ = 0 as d 1 = 20nm and d = 80 nm.

Equations (4)

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

cos ( φ ) = cos h ( κ d ) + ξ sin h ( κ d ) + ξ 2 2 sin h ( κ d 1 ) sin h ( κ d 2 )
Δ ε ( x , z ) = δ ε Δ ε ( x ) cos ( x ϕ d ) cos ( 2 π z Λ z )
{ i d A 1 d z + M 21 2 A 2 exp [ i ( Δ β 21 + 2 π Λ z ) z ] = 0 i d A 2 d z + M 12 2 A 1 exp [ i ( Δ β 12 2 π Λ z ) z ] = 0
M 12 = ω ε 0 d / 2 d / 2 δ ε Δ ε ( x ) c o s ( x ϕ d ) ( E 1 , x E 2 , x + E 1 , z E 2 , z ) d x d / 2 d / 2 ( 2 E 1 , x H 1 , y ) d x d / 2 d / 2 ( 2 E 2 , x H 2 , y ) d x

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