Abstract

The spatial (ΔGH) and the angular (ΘGH) Goos-Hänchen (GH) shifts for an Airy beam impinging upon a weakly absorbing medium coated with the monolayer graphene are theoretically investigated. The influence of the GH shift on the incident angle, the incident wavelength, the Fermi energy, and the decay factors of Airy beams is discussed. A significant magnification of ΔGH, which reaches its maximum of about three orders of wavelengths, is predicted. Our findings may provide a feasible tool to obtain a huge ΔGH in experiments.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2020 (8)

W. Zhen and D. Deng, “Goos-Hänchen and Imbert-Fedorov shifts in temporally dispersive attenuative materials,” J. Phys. D: Appl. Phys. 53(25), 255104 (2020).
[Crossref]

W. Zhen and D. Deng, “Goos-Hänchen shift for elegant Hermite-Gauss light beams impinging on dielectric surfaces coated with a monolayer of graphene,” Appl. Phys. B 126(3), 35 (2020).
[Crossref]

M. Gao and D. Deng, “Spatial Goos-Hänchen and Imbert-Fedorov shifts of rotational 2-D finite energy Airy beams,” Opt. Express 28(7), 10531–10541 (2020).
[Crossref]

W. Kong, Y. Sun, and Y Lu, “Enhanced Goos-Hänchen shift of graphene coated on one-dimensional photonic crystal,” Results Phys. 17, 103107 (2020).
[Crossref]

S. Chen, X. Ling, W. Shu, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Phys. Rev. Appl. 13(1), 014057 (2020).
[Crossref]

D. Xu, S. He, J. Zhou, S. Chen, S. Wen, and H. Luo, “Goos-Hänchen effect enabled optical differential operation and image edge detection,” Appl. Phys. Lett. 116(21), 211103 (2020).
[Crossref]

W. Zhen and D. Deng, “Giant Goos-Hänchen shift of a reflected spin wave from the ultrathin interface separating two antiferromagnetically coupled ferromagnets,” Opt. Commun. 474, 126067 (2020).
[Crossref]

A. Nieminen, A. Marini, and M. Ornigotti, “Goos-Hänchen and Imbert-Fedorov shifts for epsilon-near-zero materials,” J. Opt. 22(3), 035601 (2020).
[Crossref]

2019 (4)

C. Zhai and S. Zhang, “Goos-Hänchen shift of an Airy beam reflected in an epsilon-near-zero metamaterial,” Optik 184, 234–240 (2019).
[Crossref]

X. Zhou, S. Liu, Y. Ding, L. Min, and Z. Luo, “Precise control of positive and negative Goos-Hänchen shifts in graphene,” Carbon 149, 604–608 (2019).
[Crossref]

X. Guo, X. Liu, W. Zhu, M. Gao, W. Long, J. Yu, H. Zheng, H. Guan, Y. Luo, H. Lu, J. Zhang, and Z. Chen, “Surface plasmon resonance enhanced Goos-Hänchen and Imbert-Fedorov shifts of Laguerre-Gaussian beams,” Opt. Commun. 445, 5–9 (2019).
[Crossref]

F. Wu, J. Wu, Z. Guo, H. Jiang, Y. Sun, Y. Li, J. Ren, and H. Chen, “Giant Enhancement of the Goos-Hänchen Shift Assisted by Quasibound States in the Continuum,” Phys. Rev. Appl. 12(1), 014028 (2019).
[Crossref]

2018 (4)

2017 (6)

J. Wen, J. Zhang, L.-G. Wang, and S.-Y. Zhu, “Goos-Hänchen shifts in an epsilon-near-zero slab,” J. Opt. Soc. Am. B 34(11), 2310–2316 (2017).
[Crossref]

S. Chen, C. Mi, L. Cai, M. Liu, H. Luo, and S. Wen, “Observation of the Goos-Hänchen shift in graphene via weak measurements,” Appl. Phys. Lett. 110(3), 031105 (2017).
[Crossref]

W. Wu, S. Chen, C. Mi, W. Zhang, H. Luo, and S. Wen, “Giant quantized Goos-Hänchen effect on the surface of graphene in the quantum Hall regime,” Phys. Rev. A 96(4), 043814 (2017).
[Crossref]

A. Farmani, M. Miri, and M. H. Sheikhi, “Tunable resonant Goos-Hänchen and Imbert-Fedorov shifts in total reflection of terahertz beams from graphene plasmonic metasurfaces,” J. Opt. Soc. Am. B 34(6), 1097–1106 (2017).
[Crossref]

C. Mi, S. Chen, W. Wu, W. Zhang, X. Zhou, X. Ling, W. Shu, H. Luo, and S. Wen, “Precise identification of graphene layers at the air-prism interface via a pseudo-Brewster angle,” Opt. Lett. 42(20), 4135–4138 (2017).
[Crossref]

X. Ling, X. Zhou, K. Huang, Y. Liu, C.-W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
[Crossref]

2016 (4)

2015 (2)

2014 (3)

2013 (5)

M. Ornigotti and A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts for bounded wavepackets of light,” J. Opt. 15(1), 014004 (2013).
[Crossref]

P. Rose, F. Diebel, M. Boguslawski, and C. Denz, “Airy beam induced optical routing,” Appl. Phys. Lett. 102(10), 101101 (2013).
[Crossref]

Y. Zhang, M. R. Belic, Z. Wu, H. Zheng, K. Lu, Y. Li, and Y. Zhang, “Soliton pair generation in the interactions of Airy and nonlinear accelerating beams,” Opt. Lett. 38(22), 4585–4588 (2013).
[Crossref]

G. Jayaswal, G. Mistura, and M. Merano, “Weak measurement of the Goos-Hänchen shift,” Opt. Lett. 38(8), 1232–1234 (2013).
[Crossref]

T. Zhan, X. Shi, Y. Dai, X. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys.: Condens. Matter 25(21), 215301 (2013).
[Crossref]

2012 (6)

C. Prajapati and D. Ranganathan, “Goos-Hanchen and Imbert-Fedorov shifts for Hermite-Gauss beams,” J. Opt. Soc. Am. A 29(7), 1377–1382 (2012).
[Crossref]

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3(1), 780 (2012).
[Crossref]

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
[Crossref]

Z. Xiao, H. Luo, and S. Wen, “Goos-Hänchen and Imbert-Fedorov shifts of vortex beams at air-left-handed-material interfaces,” Phys. Rev. A 85(5), 053822 (2012).
[Crossref]

X. Zhou, H. Luo, and S. Wen, “Identifying graphene layers via spin Hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (2012).
[Crossref]

I. V. Soboleva, V. V. Moskalenko, and A. A. Fedyanin, “Giant Goos-Hänchen Effect and Fano Resonance at Photonic Crystal Surfaces,” Phys. Rev. Lett. 108(12), 123901 (2012).
[Crossref]

2011 (6)

A. Aiello and J. P. Woerdman, “Goos-Hänchen and Imbert-Fedorov shifts of a nondiffracting Bessel beam,” Opt. Lett. 36(4), 543–545 (2011).
[Crossref]

Q. Bao, H. Zhang, B. Wang, Z. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

D. Golla and S. D. Gupta, “Goos-Hänchen shift for higher-order Hermite-Gaussian beams,” Pramana 76(4), 603–612 (2011).
[Crossref]

Z. Zheng, B.-F. Zhang, H. Chen, J. Ding, and H.-T. Wang, “Optical trapping with focused Airy beams,” Appl. Opt. 50(1), 43–49 (2011).
[Crossref]

J.-X. Li, X.-L. Fan, W.-P. Zang, and J.-G. Tian, “Vacuum electron acceleration driven by two crossed Airy beams,” Opt. Lett. 36(5), 648–650 (2011).
[Crossref]

F. H. L. Koppens, D. E. Chang, and F. J. Garcĺa de Abajo, “Graphene plasmonics: A platform for strong lightmatter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref]

2010 (2)

J.-X. Li, W.-P. Zang, and J.-G. Tian, “Vacuum laser-driven acceleration by Airy beams,” Opt. Express 18(7), 7300–7306 (2010).
[Crossref]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref]

2009 (4)

A. K. Geim, “Graphene: Status and Prospects,” Science 324(5934), 1530–1534 (2009).
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A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
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K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, “Goos-Hänchen and Imbert-Fedorov shifts of polarized vortex beams,” Opt. Lett. 34(3), 389–391 (2009).
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2008 (7)

A. Matthews and Y. Kivshar, “Tunable Goos-Hänchen shift for self-collimated beams in two-dimensional photonic crystals,” Phys. Lett. A 372(17), 3098–3101 (2008).
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A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. 33(13), 1437–1439 (2008).
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2007 (3)

K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E 75(6), 066609 (2007).
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G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99(21), 213901 (2007).
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2006 (2)

K. Y. Bliokh and Y. P. Bliokh, Conservation of Angular Momentum, “Transverse Shift, and Spin Hall Effect in Reflection and Refraction of an Electromagnetic Wave Packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
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J. He, J. Yi, and S. He, “Giant negative Goos-Hänchen shifts for a photonic crystal with a negative effective index,” Opt. Express 14(7), 3024–3029 (2006).
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2005 (2)

L.-G. Wang, H. Chen, and S.-Y. Zhu, “Large negative Goos-Hänchen shift from a weakly absorbing dielectric slab,” Opt. Lett. 30(21), 2936–2938 (2005).
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2004 (2)

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2002 (1)

1998 (1)

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1995 (1)

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1988 (1)

R. F. Gragg, “The total reflection of a compact wave group: long-range trasmission in a waveguide,” Am. J. Phys. 56(12), 1092–1094 (1988).
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1979 (1)

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1955 (1)

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D. Golla and S. D. Gupta, “Goos-Hänchen shift for higher-order Hermite-Gaussian beams,” Pramana 76(4), 603–612 (2011).
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He, S.

D. Xu, S. He, J. Zhou, S. Chen, S. Wen, and H. Luo, “Goos-Hänchen effect enabled optical differential operation and image edge detection,” Appl. Phys. Lett. 116(21), 211103 (2020).
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Figures (6)

Fig. 1.
Fig. 1. Schematic plot of the GH shift at the graphene-coated surface between air ($z<0$) and a semi-infinite weakly absorbing medium ($z>0$). The single graphene layer (characterized by its optical conductivity $\sigma$) is located on the interface at $z = 0$. $\varepsilon _{1}=1$ and $\varepsilon _{2}=\varepsilon _{2r}+\varepsilon _{2i}i$ represent the relative permittivity of air and the absorbing medium, respectively.
Fig. 2.
Fig. 2. The GHS ($\Delta _{\mathrm {GH}}$) as a function of the incident angle $\theta$ for (a) Gaussian beam without graphene (solid line), Gaussian beam with the monolayer graphene (dashed line), Airy beam without graphene (dotted line), and (b) Airy beam with the monolayer graphene. Here, $\varepsilon _2=2+0.02i$, $\lambda =850$ nm, $E_f=0.5$ eV, and $\alpha =\beta =0.1$.
Fig. 3.
Fig. 3. The GHS ($\Delta _{\mathrm {GH}}$) with the monolayer graphene in dependence on the incident angle $\theta$, with different incident wavelengths: $\lambda =325$ nm (solid line), $\lambda =488$ nm (dashed line), $\lambda =633$ nm (dotted line), and $\lambda =850$ nm (dash-dotted line) for two cases of (a) Gaussian beams and (b) Airy beams. Here, $\varepsilon _2=2+0.02i$, $E_f=0.5$ eV, and $\alpha =\beta =0.1$.
Fig. 4.
Fig. 4. (a) GHS ($\Delta _{\mathrm {GH}}$) as a function of the incident angle $\theta$ and the Fermi energy $E_f$ for Airy beams with the monolayer graphene. (b) The real part (solid line) and imaginary part (dashed line) of the conductivity $\sigma$ of graphene as the function of $E_f$. Here, $\varepsilon _2=2+0.02i$, $\lambda =850$ nm, and $\alpha =\beta =0.1$.
Fig. 5.
Fig. 5. The GHS ($\Delta _{\mathrm {GH}}$) as a function of the incident angle $\theta$ and the decay factor $\alpha$ $(\beta =\alpha )$ of Airy beams (a) without graphene and (b) with the monolayer graphene ($E_f=0.3$ eV). Here, $\varepsilon _2=2+0.02i$, and $\lambda =850$ nm.
Fig. 6.
Fig. 6. The GHA ($\Theta _{\mathrm {GH}}$) as a function of the incident angle $\theta$ for (a) Gaussian beam without graphene (solid line), Gaussian beam with the monolayer graphene (dashed line), Airy beam without graphene (dotted line), and (b) Airy beam with the monolayer graphene. Here, $w_0=1$ mm, $\varepsilon _2=2+0.02i$, $\lambda =1550$ nm, $E_f=0.3$ eV, and $\alpha =\beta =0.1$.

Equations (25)

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E μ ( r μ ) = 1 2 π E ~ μ ( k μ ) e i ( k μ r μ ) d k x μ d k y μ ,
E I ( k 1 r I ) = k 1 2 2 π E ~ I ( U , V ; θ ) e i ( U X ^ I + V Y ^ I + W Z ^ I ) d U d V ,
E R ( k 1 r R ) = k 1 2 2 π E ~ R ( U , V ; θ ) e i ( U X ^ R + V Y ^ R + W Z ^ R ) d U d V ,
E ~ μ ( U , V ; θ ) = λ p , s e ^ λ ( k μ ) α λ ( U , V ; θ ) A ~ μ ( U , V ; θ ) ,
e ^ p ( k μ ) = e ^ s ( k μ ) × k μ | e ^ s ( k μ ) × k μ | ,
e ^ s ( k μ ) = z ^ × k μ | z ^ × k μ | .
r λ ( U , V ; θ ) r λ + U r λ + 1 2 U 2 r λ + 1 2 V 2 r λ ,
A ~ ( U , V ) = w 0 2 2 π e x p ( α 3 + β 3 3 ) e x p ( α U 2 + β V 2 ϑ 2 ) e x p [ i ( U 3 + V 3 3 ϑ 3 α 2 U + β 2 V ϑ ) ] ,
X ¯ = X ¯ R X ¯ I ,
X ¯ R = I m [ E ~ R U E ~ R ] d U d V | E ~ R | 2 d U d V ( Z R + Z I ) U W | E ~ R | 2 d U d V | E ~ R | 2 d U d V ,
X ¯ I = I m [ E ~ I U E ~ I ] d U d V | E ~ I | 2 d U d V Z I U W | E ~ I | 2 d U d V | E ~ I | 2 d U d V .
Δ G H = I m [ E ~ R U E ~ R ] d U d V k 1 | E ~ R | 2 d U d V + I m [ E ~ I V E ~ I ] d U d V k 1 | E ~ I | 2 d U d V ,
Θ G H = X ¯ R / Z R = U W | E ~ R | 2 d U d V | E ~ R | 2 d U d V .
Δ G H A i r y = 1 Λ ( Δ G H g + ϑ 8 α 2 k 1 λ p , s ω λ 1 ) ,
Θ G H A i r y = 1 4 α Λ Θ G H g ,
H 1 y = ( a 1 e k 1 z z + b 1 e k 1 z z ) e k 1 x x ( z < 0 ) ,
H 2 y = ( a 2 e k 2 z z + b 2 e k 2 z z ) e k 2 x x ( z > 0 ) ,
k 1 x = k 2 x .
D p ( 1 2 ) = 1 2 [ 1 + η p + ξ p 1 η p ξ p 1 η p + ξ p 1 + η p ξ p ] ,
D s ( 1 2 ) = 1 2 [ 1 + η s + ξ s 1 η s + ξ s 1 η s ξ s 1 + η s ξ s ] ,
P ( 0 ) = [ 1 0 0 1 ] .
P ( 0 ) = M p , s = D p , s ( 1 2 ) P ( 0 ) = D p , s ( 1 2 ) .
r p = M p , 21 M p , 11 = ε 2 / k 2 z ε 1 / k 1 z + σ / ( ε 0 ω ) ε 2 / k 2 z + ε 1 / k 1 z + σ / ( ε 0 ω ) ,
r s = M s , 21 M s , 11 = k 1 z k 2 z k 1 σ / ( ε 0 c ) k 1 z + k 2 z + k 1 σ / ( ε 0 c ) .
σ ( ω , E f ) = e 2 E f π 2 i ω + i τ 1 + e 2 4 2 [ H ( ω 2 E f ) + i π ln | ω 2 E f ω + 2 E f | ] ,