Abstract

In this paper, we theoretically propose for the first time that graphene monolayer can be used to manipulate the Cosine-Gauss beams (CGBs). We show that both the transverse oscillation period and propagation length of a CGB can be dynamically manipulated by utilizing the tunability of the graphene’s chemical potential. The graphene-based planar plasmonic waveguide provides a good platform to investigate the propagation properties of CGBs, which is potentially compatible to the microelectronic technology.

© 2017 Optical Society of America

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References

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2017 (2)

R. Li, M. Imran, X. Lin, H. Wang, Z. Xu, and H. Chen, “Hybrid Airy plasmons with Dynamically Steerable Trajectories,” Nanoscale 9(4), 1449–1456 (2017).
[Crossref] [PubMed]

R. Li, B. Zheng, X. Lin, R. Hao, S. Lin, W. Yin, E. Li, and H. Chen, “Design of Ultracompact Graphene-Based Superscatterers,” IEEE J. Sel. Top. Quantum Electron. 23(1), 4600208 (2017).
[Crossref]

2016 (1)

R. Li, X. Lin, S. Lin, X. Zhang, E. Li, and H. Chen, “Graphene induced mode bifurcation at low input power,” Carbon 98, 463–467 (2016).
[Crossref]

2015 (5)

M. Ghorbanzadeh, M. K. Moravvej-Farshi, and S. Darbari, “Designing a plasmonic optophoresis system for trapping and simultaneous sorting/counting of micro- and nano- particles,” J. Lightwave Technol. 33(16), 3453–3460 (2015).
[Crossref]

R. J. Li, X. Lin, S. S. Lin, X. Liu, and H. S. Chen, “Tunable deep-subwavelength superscattering using graphene monolayers,” Opt. Lett. 40(8), 1651–1654 (2015).
[Crossref] [PubMed]

R. Li, X. Lin, S. Lin, X. Liu, and H. Chen, “Atomically thin spherical shell-shaped superscatterers based on a Bohr model,” Nanotechnology 26(50), 505201 (2015).
[Crossref] [PubMed]

E. Gazzola, G. Ruffato, and F. Romanato, “Propagation of grating-coupled surface plasmon polaritons and cosine–Gauss beam generation,” J. Opt. Soc. Am. B 32(8), 1564–1569 (2015).
[Crossref]

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
[Crossref] [PubMed]

2014 (8)

2013 (4)

2012 (3)

C. J. Regan, L. G. de Peralta, and A. A. Bernussi, “Two-dimensional Bessel-like surface plasmon-polariton beams,” J. Appl. Phys. 112(10), 103107 (2012).
[Crossref]

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Fornel, and F. Capasso, “Cosine-Gauss plasmon beam: a localized long-range nondiffracting surface wave,” Phys. Rev. Lett. 109(9), 093904 (2012).
[Crossref] [PubMed]

L. J. Guo, C. J. Min, G. H. Yuan, C. L. Zhang, J. G. Wang, Z. Shen, and X. C. Yuan, “Optically stitched arbitrary fan-sectors with selective polarization states for dynamic manipulation of surface plasmon polaritons,” Opt. Express 20(22), 24748–24753 (2012).
[Crossref] [PubMed]

2011 (4)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (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]

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011).
[Crossref]

2010 (4)

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
[Crossref] [PubMed]

A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35(12), 2082–2084 (2010).
[Crossref] [PubMed]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

K. Baumann, T. Stöferle, N. Moll, G. Raino, R. Mahrt, T. Wahlbrink, J. Bolten, and U. Scherf, “Design and optical characterization of photonic crystal lasers with organic gain material,” J. Opt. 12(6), 065003 (2010).
[Crossref]

2009 (1)

Y. J. Yu, Y. Zhao, S. Ryu, L. E. Brus, K. S. Kim, and P. Kim, “Tuning the graphene work function by electric field effect,” Nano Lett. 9(10), 3430–3434 (2009).
[Crossref] [PubMed]

2008 (3)

G. W. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008).
[Crossref]

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[Crossref]

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

2007 (1)

C. Casiraghi, A. Hartschuh, E. Lidorikis, H. Qian, H. Harutyunyan, T. Gokus, K. S. Novoselov, and A. C. Ferrari, “Rayleigh imaging of graphene and graphene layers,” Nano Lett. 7(9), 2711–2717 (2007).
[Crossref] [PubMed]

2005 (1)

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

1987 (1)

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss Beams,” Opt. Commun. 64(6), 491–495 (1987).
[Crossref]

Alonso-González, P.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
[Crossref] [PubMed]

Alù, A.

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

Arie, A.

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Baumann, K.

K. Baumann, T. Stöferle, N. Moll, G. Raino, R. Mahrt, T. Wahlbrink, J. Bolten, and U. Scherf, “Design and optical characterization of photonic crystal lasers with organic gain material,” J. Opt. 12(6), 065003 (2010).
[Crossref]

Baumgartl, J.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[Crossref]

Bernussi, A. A.

C. J. Regan, L. G. de Peralta, and A. A. Bernussi, “Two-dimensional Bessel-like surface plasmon-polariton beams,” J. Appl. Phys. 112(10), 103107 (2012).
[Crossref]

Blanchard, R.

Bolten, J.

K. Baumann, T. Stöferle, N. Moll, G. Raino, R. Mahrt, T. Wahlbrink, J. Bolten, and U. Scherf, “Design and optical characterization of photonic crystal lasers with organic gain material,” J. Opt. 12(6), 065003 (2010).
[Crossref]

Brus, L. E.

Y. J. Yu, Y. Zhao, S. Ryu, L. E. Brus, K. S. Kim, and P. Kim, “Tuning the graphene work function by electric field effect,” Nano Lett. 9(10), 3430–3434 (2009).
[Crossref] [PubMed]

Capasso, F.

P. Genevet, J. Dellinger, R. Blanchard, A. She, M. Petit, B. Cluzel, M. A. Kats, F. de Fornel, and F. Capasso, “Generation of two-dimensional plasmonic bottle beams,” Opt. Express 21(8), 10295–10300 (2013).
[Crossref] [PubMed]

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Fornel, and F. Capasso, “Cosine-Gauss plasmon beam: a localized long-range nondiffracting surface wave,” Phys. Rev. Lett. 109(9), 093904 (2012).
[Crossref] [PubMed]

Carrega, M.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2015).
[Crossref] [PubMed]

Casiraghi, C.

C. Casiraghi, A. Hartschuh, E. Lidorikis, H. Qian, H. Harutyunyan, T. Gokus, K. S. Novoselov, and A. C. Ferrari, “Rayleigh imaging of graphene and graphene layers,” Nano Lett. 7(9), 2711–2717 (2007).
[Crossref] [PubMed]

Chen, H.

R. Li, M. Imran, X. Lin, H. Wang, Z. Xu, and H. Chen, “Hybrid Airy plasmons with Dynamically Steerable Trajectories,” Nanoscale 9(4), 1449–1456 (2017).
[Crossref] [PubMed]

R. Li, B. Zheng, X. Lin, R. Hao, S. Lin, W. Yin, E. Li, and H. Chen, “Design of Ultracompact Graphene-Based Superscatterers,” IEEE J. Sel. Top. Quantum Electron. 23(1), 4600208 (2017).
[Crossref]

R. Li, X. Lin, S. Lin, X. Zhang, E. Li, and H. Chen, “Graphene induced mode bifurcation at low input power,” Carbon 98, 463–467 (2016).
[Crossref]

R. Li, X. Lin, S. Lin, X. Liu, and H. Chen, “Atomically thin spherical shell-shaped superscatterers based on a Bohr model,” Nanotechnology 26(50), 505201 (2015).
[Crossref] [PubMed]

Chen, H. S.

Chen, L.

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, Y. G.

Chen, Y. H.

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

Christodoulides, D. N.

A. E. Minovich, A. E. Klein, D. N. Neshev, T. Pertsch, Y. S. Kivshar, and D. N. Christodoulides, “Airy plasmons: nondiffracting optical surface waves,” Laser Photonics Rev. 8(2), 221–232 (2014).
[Crossref]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy-Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

A. Salandrino and D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35(12), 2082–2084 (2010).
[Crossref] [PubMed]

Cluzel, B.

P. Genevet, J. Dellinger, R. Blanchard, A. She, M. Petit, B. Cluzel, M. A. Kats, F. de Fornel, and F. Capasso, “Generation of two-dimensional plasmonic bottle beams,” Opt. Express 21(8), 10295–10300 (2013).
[Crossref] [PubMed]

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Fornel, and F. Capasso, “Cosine-Gauss plasmon beam: a localized long-range nondiffracting surface wave,” Phys. Rev. Lett. 109(9), 093904 (2012).
[Crossref] [PubMed]

Crommie, M.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Dai, H. T.

Y. Yang, H. T. Dai, B. F. Zhu, and X. W. Sun, “Dynamic control of the Airy plasmons in a graphene platform,” IEEE Photonics J. 6(4), 4801207 (2014).
[Crossref]

Darbari, S.

de Fornel, F.

P. Genevet, J. Dellinger, R. Blanchard, A. She, M. Petit, B. Cluzel, M. A. Kats, F. de Fornel, and F. Capasso, “Generation of two-dimensional plasmonic bottle beams,” Opt. Express 21(8), 10295–10300 (2013).
[Crossref] [PubMed]

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Fornel, and F. Capasso, “Cosine-Gauss plasmon beam: a localized long-range nondiffracting surface wave,” Phys. Rev. Lett. 109(9), 093904 (2012).
[Crossref] [PubMed]

de Peralta, L. G.

C. J. Regan, L. G. de Peralta, and A. A. Bernussi, “Two-dimensional Bessel-like surface plasmon-polariton beams,” J. Appl. Phys. 112(10), 103107 (2012).
[Crossref]

Dean, C. R.

C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
[Crossref] [PubMed]

Dellinger, J.

P. Genevet, J. Dellinger, R. Blanchard, A. She, M. Petit, B. Cluzel, M. A. Kats, F. de Fornel, and F. Capasso, “Generation of two-dimensional plasmonic bottle beams,” Opt. Express 21(8), 10295–10300 (2013).
[Crossref] [PubMed]

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Fornel, and F. Capasso, “Cosine-Gauss plasmon beam: a localized long-range nondiffracting surface wave,” Phys. Rev. Lett. 109(9), 093904 (2012).
[Crossref] [PubMed]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Dholakia, K.

J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics 2(11), 675–678 (2008).
[Crossref]

Dong, X.

Du, C.

Du, L.

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Engheta, N.

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

Epstein, I.

Ferrari, A. C.

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C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L. Shepard, and J. Hone, “Boron nitride substrates for high-quality graphene electronics,” Nat. Nanotechnol. 5(10), 722–726 (2010).
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Figures (7)

Fig. 1
Fig. 1 Schematic of the plasmonic waveguide structure, where a graphene monolayer is placed on the x-y plane and sandwiched by the dielectric 1 and dielectric 2.
Fig. 2
Fig. 2 The dependences between the chemical potential and (a) the real part of the surface conductivity of graphene, (b) the imaginary part of the surface conductivity of graphene, (c) the real part of the wave vector k sp , (d) the imaginary part of the wave vector k sp , (e) the real part of the wave vector k y and (f) the imaginary part of the wave vector k x , respectively. The parameters are f=10THz, τ=0.5ps, T=300K, θ= 1 , ε 1 =1 and ε 2 =1.5.
Fig. 3
Fig. 3 (a) The distributions of for a CGB on three y-z cut planes with x=0μm, x=5μmand x=12μm, respectively, and on x-y cut planes along the propagation direction with z = 0 and on x-z plane with y = 0. The distributions at the y-z plane with x=0μm and x=12μmare shown in (b) and (c), respectively. The distributions at the x-z plane with y = 0 and the x-y plane with z = 0 are shown in (d) and (e), respectively. The other parameters are f=10THz, τ=0.5ps, T=300K, θ= 1 , w 0 =200μm, μ c =0.4eV, ε 1 =1and ε 1 =1.5.
Fig. 4
Fig. 4 The electric filed intensity distribution | E z | 2 of a CGB at the x-y plane with z = 0 for different chemical potentials (a) μ c =0.1eV, (b) μ c =0.2eV, (c) μ c =0.3eV and (d) μ c =0.4eV. The other parameters are f=10THz, τ=0.5ps, T=300K, w 0 =200μm, θ= 1 , ε 1 =1 and ε 2 =1.5.
Fig. 5
Fig. 5 The dependences between the frequency and (a) the real part of the wave vector k y , (b) the imaginary part of the wave vector k x , (c) the propagation length L CGB and (d) the oscillation period T CGB of a CGB, respectively. The electric filed intensity distribution | E z | 2 of a CGB at the x-y plane with z = 0 for different frequency (e) f=9THz, (f) f=10THz, The parameters are τ=0.5ps, T=300K, θ= 1 , w 0 =200μm, μ c =0.3eV, ε 1 =1 and ε 2 =1.5.
Fig. 6
Fig. 6 The dependences between the angleθ and (a) the real part of the wave vector k y , (b) the imaginary part of the wave vector k x , (c) the propagation length L CGB and (d) the oscillation period T CGB of a CGB, respectively. The electric filed intensity distribution | E z | 2 of a CGB at the x-y plane with z = 0 for different angle (e) θ= 1 and (f) θ= 2 . The parameters are f=10THz, τ=0.5ps, T=300K, w 0 =200μm, μ c =0.3eV, ε 1 =1and ε 2 =1.5.
Fig. 7
Fig. 7 The dependences between the refractive index difference Δn and (a) the real part of the wave vector k sp , (b) the imaginary part of the wave vector k sp , (c) the propagation length L CGB and (d) the oscillation period T CGB of a CGB, respectively. The electric filed intensity distribution | E z | 2 of a CGB at the x-y plane with z = 0 for different refractive index difference (e) Δn=0and (f) Δn=1, respectively. The parameters are f=10THz, τ=0.5ps, T=300K, w 0 =200μm, θ= 1 , μ c =0.3eVand ε 1 =1.

Equations (9)

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σ g = σ intra (ω,T,τ, μ c )+ σ inter (ω,T,τ, μ c ),
σ intra (ω,T,τ, μ c )= i e 2 k B T π 2 ( ω+i τ 1 ) [ μ c k B T +2ln( exp( μ c k B T )+1 ) ]
σ inter (ω,T,τ, μ c )= i e 2 4π ln( 2| μ c |( ω+i τ 1 ) 2| μ c |+( ω+i τ 1 ) )
2 E z ( x,y,z )+ ε d k 0 2 E z ( x,y,z )=0,
E z (x,y,z)={ Aexp( i k x x )cos( k y y )exp( αz ), z>0 Aexp( i k x x )cos( k y y )exp( αz ), z<0 ,
k y = k sp sinθ
k sp 2 = k x 2 + k y 2 = α 2 + ε d k 0 2
k 2 ε 2 + k 1 ε 1 + i σ g η 0 k 2 k 1 k 0 ε 2 ε 1 =0
E z (x,y,z)={ Aexp( i k x x )cos( k y y )exp( y 2 w 0 2 )exp( αz ), z>0 Aexp( i k x x )cos( k y y )exp( y 2 w 0 2 )exp( αz ), z<0

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