Abstract

Using Yasumoto and Oishi’s energy flux method, we evaluated the Goos–Hänchen (GH) and Imbert–Fedorov (IF) shifts of beam incident from the ordinary dielectric upon the topological insulator (TI) with totally internal reflection. Comparing with the case of two ordinary isotropic dielectrics, it is found that the topological parameter Θ of TI can affect two shifts. More important, IF shift appears even for a linear polarized TE or TM beam and achieves the maximum with elliptical polarization, which completely originates from the TI’s intrinsic magnetoelectric coupling effect. This observation provides an optical experimental approach to determine the topological parameters Θ and provide a new way to control the GH shift and IF shift.

© 2013 Optical Society of America

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2013 (1)

G. Xu, J. Sun, T. Zang, H. Mao, and T. Pan, “Imbert-Fedorov shifts of a Gaussian beam reflected from anisotropic topological insulators,” Opt. Commun. 287, 154–161 (2013).
[CrossRef]

2011 (4)

G. Xu, T. Zang, H. Mao, and T. Pan, “Transverse shifts of a reflected light beam from the air-chiral interface,” Phys. Rev. A 83, 053828 (2011).
[CrossRef]

N. Hermosa, A. M. Nugrowati, A. Aiello, and J. P. Woerdman, “Spin Hall effect of light in metallic reflection,” Opt. Lett. 36, 3200–3202 (2011).
[CrossRef]

Y. Y. Huang, W. T. Dong, L. Gao, and C. W. Qiu, “Large positive and negative lateral shifts near pseudo-Brewster dip on reflection from a chiral metamaterial slab,” Opt. Express 19, 1310–1323 (2011).
[CrossRef]

X.-L. Qi and S.-C. Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys. 83, 1057–1110 (2011).
[CrossRef]

2010 (4)

M. Z. Hasan and C. L. Kane, “Colloquium: topological insulators,” Rev. Mod. Phys. 82, 3045–3067 (2010).
[CrossRef]

J. E. Moore, “The birth of topological insulators,” Nature 464, 194–198 (2010).
[CrossRef]

T. Sato, K. Segawa, H. Guo, K. Sugawara, S. Souma, T. Takahashi, and Y. Ando, “Direct evidence for the Dirac-cone topological surface states in the ternary chalcogenide TlBiSe2,” Phys. Rev. Lett. 105, 136802 (2010).
[CrossRef]

W.-K. Tse and A. H. MacDonald, “Giant magneto-optical Kerr effect and universal Faraday effect in thin-film topological insulators,” Phys. Rev. Lett. 105, 057401 (2010).
[CrossRef]

2009 (3)

M.-C. Chang and M.-F. Yang, “Optical signature of topological insulators,” Phys. Rev. B 80, 113304 (2009).
[CrossRef]

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator Bi2Te3,” Science 325, 178–181 (2009).
[CrossRef]

Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5, 398–402 (2009).
[CrossRef]

2008 (3)

X.-L. Qi, T. L. Hughes, and S.-C. Zhang, “Topological field theory of time-reversal invariant insulators,” Phys. Rev. B 78, 195424 (2008).
[CrossRef]

D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “A topological Dirac insulator in a quantum spin Hall phase,” Nature 452, 970–974 (2008).
[CrossRef]

A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos–Hänchen and Imbert–Fedorov shifts,” Opt. Lett. 33, 1437–1439 (2008).
[CrossRef]

2007 (2)

L. Fu, C. L. Kane, and E. J. Mele, “Topological insulators in three dimensions,” Phys. Rev. Lett. 98, 106803 (2007).
[CrossRef]

J. E. Moore and L. Balents, “Topological invariants of time-reversal-invariant band structures,” Phys. Rev. B 75, 121306(2007).
[CrossRef]

2006 (1)

Y. Miyagawa, T. Yamamoto, H. Masuda, M. Abe, H. Takahashi, and H. Takara, “Over-10000-channel 2.5 GHz-spaced ultra-dense WDM light source,” Electron. Lett. 42, 655–657 (2006).
[CrossRef]

2005 (1)

Y. N. Obukhov and F. W. Hehl, “Measuring a piecewise constant axion field in classical electrodynamics,” Phys. Lett. A 341, 357–365 (2005).
[CrossRef]

2004 (1)

2000 (1)

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos–Hänchen effect,” Phys. Rev. E 62, 7330–7339 (2000).
[CrossRef]

1988 (1)

1987 (1)

F. Wilczek, “Two applications of axion electrodynamics,” Phys. Rev. Lett. 58, 1799–1802 (1987).
[CrossRef]

1986 (1)

1983 (1)

K. Yasumoto and Y. Oishi, “A new evaluation of the Goos–Hänchen shift and associated time delay,” J. Appl. Phys. 54, 2170–2176 (1983).
[CrossRef]

1972 (1)

C. Imbert, “Calculation and experimental proof of the transverse shift induced by total internal reflection of a circularly polarized beam,” Phys. Rev. D 5, 787–796 (1972).
[CrossRef]

1964 (1)

1955 (1)

F. I. Fedorov, “Theory of total reflection,” Dokl. Akad. Nauk. SSSR 105, 465–468 (1955).

1948 (1)

K. V. Artmann, “Berechung der Seitenversetzung des total-reflektierten Strahles,” Ann. Phys. 437, 87–102 (1948).
[CrossRef]

1947 (1)

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436, 333–346 (1947).
[CrossRef]

1941 (1)

Abe, M.

Y. Miyagawa, T. Yamamoto, H. Masuda, M. Abe, H. Takahashi, and H. Takara, “Over-10000-channel 2.5 GHz-spaced ultra-dense WDM light source,” Electron. Lett. 42, 655–657 (2006).
[CrossRef]

Aiello, A.

Analytis, J. G.

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator Bi2Te3,” Science 325, 178–181 (2009).
[CrossRef]

Ando, Y.

T. Sato, K. Segawa, H. Guo, K. Sugawara, S. Souma, T. Takahashi, and Y. Ando, “Direct evidence for the Dirac-cone topological surface states in the ternary chalcogenide TlBiSe2,” Phys. Rev. Lett. 105, 136802 (2010).
[CrossRef]

Artmann, K. V.

K. V. Artmann, “Berechung der Seitenversetzung des total-reflektierten Strahles,” Ann. Phys. 437, 87–102 (1948).
[CrossRef]

Balents, L.

J. E. Moore and L. Balents, “Topological invariants of time-reversal-invariant band structures,” Phys. Rev. B 75, 121306(2007).
[CrossRef]

Bansil, A.

Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5, 398–402 (2009).
[CrossRef]

Cava, R. J.

Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5, 398–402 (2009).
[CrossRef]

D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “A topological Dirac insulator in a quantum spin Hall phase,” Nature 452, 970–974 (2008).
[CrossRef]

Chang, M.-C.

M.-C. Chang and M.-F. Yang, “Optical signature of topological insulators,” Phys. Rev. B 80, 113304 (2009).
[CrossRef]

Chen, Y. L.

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator Bi2Te3,” Science 325, 178–181 (2009).
[CrossRef]

Cheng, F. C.

Chu, J.-H.

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator Bi2Te3,” Science 325, 178–181 (2009).
[CrossRef]

Dai, X.

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator Bi2Te3,” Science 325, 178–181 (2009).
[CrossRef]

Dong, W. T.

Fang, Z.

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator Bi2Te3,” Science 325, 178–181 (2009).
[CrossRef]

Fedorov, F. I.

F. I. Fedorov, “Theory of total reflection,” Dokl. Akad. Nauk. SSSR 105, 465–468 (1955).

Fisher, I. R.

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator Bi2Te3,” Science 325, 178–181 (2009).
[CrossRef]

Fu, L.

L. Fu, C. L. Kane, and E. J. Mele, “Topological insulators in three dimensions,” Phys. Rev. Lett. 98, 106803 (2007).
[CrossRef]

Gao, L.

Gilles, H.

Girard, S.

Goos, F.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436, 333–346 (1947).
[CrossRef]

Grauer, D.

Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5, 398–402 (2009).
[CrossRef]

Guo, H.

T. Sato, K. Segawa, H. Guo, K. Sugawara, S. Souma, T. Takahashi, and Y. Ando, “Direct evidence for the Dirac-cone topological surface states in the ternary chalcogenide TlBiSe2,” Phys. Rev. Lett. 105, 136802 (2010).
[CrossRef]

Hänchen, H.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436, 333–346 (1947).
[CrossRef]

Hasan, M. Z.

M. Z. Hasan and C. L. Kane, “Colloquium: topological insulators,” Rev. Mod. Phys. 82, 3045–3067 (2010).
[CrossRef]

Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5, 398–402 (2009).
[CrossRef]

D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “A topological Dirac insulator in a quantum spin Hall phase,” Nature 452, 970–974 (2008).
[CrossRef]

Hehl, F. W.

Y. N. Obukhov and F. W. Hehl, “Measuring a piecewise constant axion field in classical electrodynamics,” Phys. Lett. A 341, 357–365 (2005).
[CrossRef]

Hermosa, N.

Hor, Y. S.

Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5, 398–402 (2009).
[CrossRef]

D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “A topological Dirac insulator in a quantum spin Hall phase,” Nature 452, 970–974 (2008).
[CrossRef]

Hsieh, D.

Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5, 398–402 (2009).
[CrossRef]

D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “A topological Dirac insulator in a quantum spin Hall phase,” Nature 452, 970–974 (2008).
[CrossRef]

Huang, Y. Y.

Hughes, T. L.

X.-L. Qi, T. L. Hughes, and S.-C. Zhang, “Topological field theory of time-reversal invariant insulators,” Phys. Rev. B 78, 195424 (2008).
[CrossRef]

Hussain, Z.

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator Bi2Te3,” Science 325, 178–181 (2009).
[CrossRef]

Imbert, C.

C. Imbert, “Calculation and experimental proof of the transverse shift induced by total internal reflection of a circularly polarized beam,” Phys. Rev. D 5, 787–796 (1972).
[CrossRef]

Jones, R. C.

Kane, C. L.

M. Z. Hasan and C. L. Kane, “Colloquium: topological insulators,” Rev. Mod. Phys. 82, 3045–3067 (2010).
[CrossRef]

L. Fu, C. L. Kane, and E. J. Mele, “Topological insulators in three dimensions,” Phys. Rev. Lett. 98, 106803 (2007).
[CrossRef]

Kwok, C. W.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos–Hänchen effect,” Phys. Rev. E 62, 7330–7339 (2000).
[CrossRef]

Lai, H. M.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos–Hänchen effect,” Phys. Rev. E 62, 7330–7339 (2000).
[CrossRef]

H. M. Lai, F. C. Cheng, and W. K. Tang, “Goos–Hänchen effect around and off the critical angle,” J. Opt. Soc. Am. A 3, 550–557 (1986).
[CrossRef]

Lin, H.

Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5, 398–402 (2009).
[CrossRef]

Liu, Z. K.

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator Bi2Te3,” Science 325, 178–181 (2009).
[CrossRef]

Loo, Y. W.

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos–Hänchen effect,” Phys. Rev. E 62, 7330–7339 (2000).
[CrossRef]

Lu, D. H.

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator Bi2Te3,” Science 325, 178–181 (2009).
[CrossRef]

MacDonald, A. H.

W.-K. Tse and A. H. MacDonald, “Giant magneto-optical Kerr effect and universal Faraday effect in thin-film topological insulators,” Phys. Rev. Lett. 105, 057401 (2010).
[CrossRef]

Mao, H.

G. Xu, J. Sun, T. Zang, H. Mao, and T. Pan, “Imbert-Fedorov shifts of a Gaussian beam reflected from anisotropic topological insulators,” Opt. Commun. 287, 154–161 (2013).
[CrossRef]

G. Xu, T. Zang, H. Mao, and T. Pan, “Transverse shifts of a reflected light beam from the air-chiral interface,” Phys. Rev. A 83, 053828 (2011).
[CrossRef]

Masuda, H.

Y. Miyagawa, T. Yamamoto, H. Masuda, M. Abe, H. Takahashi, and H. Takara, “Over-10000-channel 2.5 GHz-spaced ultra-dense WDM light source,” Electron. Lett. 42, 655–657 (2006).
[CrossRef]

Mele, E. J.

L. Fu, C. L. Kane, and E. J. Mele, “Topological insulators in three dimensions,” Phys. Rev. Lett. 98, 106803 (2007).
[CrossRef]

Miyagawa, Y.

Y. Miyagawa, T. Yamamoto, H. Masuda, M. Abe, H. Takahashi, and H. Takara, “Over-10000-channel 2.5 GHz-spaced ultra-dense WDM light source,” Electron. Lett. 42, 655–657 (2006).
[CrossRef]

Mo, S.-K.

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator Bi2Te3,” Science 325, 178–181 (2009).
[CrossRef]

Moore, J. E.

J. E. Moore, “The birth of topological insulators,” Nature 464, 194–198 (2010).
[CrossRef]

J. E. Moore and L. Balents, “Topological invariants of time-reversal-invariant band structures,” Phys. Rev. B 75, 121306(2007).
[CrossRef]

Nugrowati, A. M.

Obukhov, Y. N.

Y. N. Obukhov and F. W. Hehl, “Measuring a piecewise constant axion field in classical electrodynamics,” Phys. Lett. A 341, 357–365 (2005).
[CrossRef]

Oishi, Y.

K. Yasumoto and Y. Oishi, “A new evaluation of the Goos–Hänchen shift and associated time delay,” J. Appl. Phys. 54, 2170–2176 (1983).
[CrossRef]

Pal, A.

Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5, 398–402 (2009).
[CrossRef]

Pan, T.

G. Xu, J. Sun, T. Zang, H. Mao, and T. Pan, “Imbert-Fedorov shifts of a Gaussian beam reflected from anisotropic topological insulators,” Opt. Commun. 287, 154–161 (2013).
[CrossRef]

G. Xu, T. Zang, H. Mao, and T. Pan, “Transverse shifts of a reflected light beam from the air-chiral interface,” Phys. Rev. A 83, 053828 (2011).
[CrossRef]

Pillon, F.

Qi, X. L.

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator Bi2Te3,” Science 325, 178–181 (2009).
[CrossRef]

Qi, X.-L.

X.-L. Qi and S.-C. Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys. 83, 1057–1110 (2011).
[CrossRef]

X.-L. Qi, T. L. Hughes, and S.-C. Zhang, “Topological field theory of time-reversal invariant insulators,” Phys. Rev. B 78, 195424 (2008).
[CrossRef]

Qian, D.

Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5, 398–402 (2009).
[CrossRef]

D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “A topological Dirac insulator in a quantum spin Hall phase,” Nature 452, 970–974 (2008).
[CrossRef]

Qiu, C. W.

Renard, R. H.

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T. Sato, K. Segawa, H. Guo, K. Sugawara, S. Souma, T. Takahashi, and Y. Ando, “Direct evidence for the Dirac-cone topological surface states in the ternary chalcogenide TlBiSe2,” Phys. Rev. Lett. 105, 136802 (2010).
[CrossRef]

Segawa, K.

T. Sato, K. Segawa, H. Guo, K. Sugawara, S. Souma, T. Takahashi, and Y. Ando, “Direct evidence for the Dirac-cone topological surface states in the ternary chalcogenide TlBiSe2,” Phys. Rev. Lett. 105, 136802 (2010).
[CrossRef]

Seshadri, S. R.

Shen, Z.-X.

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator Bi2Te3,” Science 325, 178–181 (2009).
[CrossRef]

Souma, S.

T. Sato, K. Segawa, H. Guo, K. Sugawara, S. Souma, T. Takahashi, and Y. Ando, “Direct evidence for the Dirac-cone topological surface states in the ternary chalcogenide TlBiSe2,” Phys. Rev. Lett. 105, 136802 (2010).
[CrossRef]

Sugawara, K.

T. Sato, K. Segawa, H. Guo, K. Sugawara, S. Souma, T. Takahashi, and Y. Ando, “Direct evidence for the Dirac-cone topological surface states in the ternary chalcogenide TlBiSe2,” Phys. Rev. Lett. 105, 136802 (2010).
[CrossRef]

Sun, J.

G. Xu, J. Sun, T. Zang, H. Mao, and T. Pan, “Imbert-Fedorov shifts of a Gaussian beam reflected from anisotropic topological insulators,” Opt. Commun. 287, 154–161 (2013).
[CrossRef]

Takahashi, H.

Y. Miyagawa, T. Yamamoto, H. Masuda, M. Abe, H. Takahashi, and H. Takara, “Over-10000-channel 2.5 GHz-spaced ultra-dense WDM light source,” Electron. Lett. 42, 655–657 (2006).
[CrossRef]

Takahashi, T.

T. Sato, K. Segawa, H. Guo, K. Sugawara, S. Souma, T. Takahashi, and Y. Ando, “Direct evidence for the Dirac-cone topological surface states in the ternary chalcogenide TlBiSe2,” Phys. Rev. Lett. 105, 136802 (2010).
[CrossRef]

Takara, H.

Y. Miyagawa, T. Yamamoto, H. Masuda, M. Abe, H. Takahashi, and H. Takara, “Over-10000-channel 2.5 GHz-spaced ultra-dense WDM light source,” Electron. Lett. 42, 655–657 (2006).
[CrossRef]

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Tse, W.-K.

W.-K. Tse and A. H. MacDonald, “Giant magneto-optical Kerr effect and universal Faraday effect in thin-film topological insulators,” Phys. Rev. Lett. 105, 057401 (2010).
[CrossRef]

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F. Wilczek, “Two applications of axion electrodynamics,” Phys. Rev. Lett. 58, 1799–1802 (1987).
[CrossRef]

Woerdman, J. P.

Wray, L.

Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5, 398–402 (2009).
[CrossRef]

D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “A topological Dirac insulator in a quantum spin Hall phase,” Nature 452, 970–974 (2008).
[CrossRef]

Xia, Y.

Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5, 398–402 (2009).
[CrossRef]

D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “A topological Dirac insulator in a quantum spin Hall phase,” Nature 452, 970–974 (2008).
[CrossRef]

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H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos–Hänchen effect,” Phys. Rev. E 62, 7330–7339 (2000).
[CrossRef]

Xu, G.

G. Xu, J. Sun, T. Zang, H. Mao, and T. Pan, “Imbert-Fedorov shifts of a Gaussian beam reflected from anisotropic topological insulators,” Opt. Commun. 287, 154–161 (2013).
[CrossRef]

G. Xu, T. Zang, H. Mao, and T. Pan, “Transverse shifts of a reflected light beam from the air-chiral interface,” Phys. Rev. A 83, 053828 (2011).
[CrossRef]

Yamamoto, T.

Y. Miyagawa, T. Yamamoto, H. Masuda, M. Abe, H. Takahashi, and H. Takara, “Over-10000-channel 2.5 GHz-spaced ultra-dense WDM light source,” Electron. Lett. 42, 655–657 (2006).
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M.-C. Chang and M.-F. Yang, “Optical signature of topological insulators,” Phys. Rev. B 80, 113304 (2009).
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K. Yasumoto and Y. Oishi, “A new evaluation of the Goos–Hänchen shift and associated time delay,” J. Appl. Phys. 54, 2170–2176 (1983).
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G. Xu, J. Sun, T. Zang, H. Mao, and T. Pan, “Imbert-Fedorov shifts of a Gaussian beam reflected from anisotropic topological insulators,” Opt. Commun. 287, 154–161 (2013).
[CrossRef]

G. Xu, T. Zang, H. Mao, and T. Pan, “Transverse shifts of a reflected light beam from the air-chiral interface,” Phys. Rev. A 83, 053828 (2011).
[CrossRef]

Zhang, H. J.

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator Bi2Te3,” Science 325, 178–181 (2009).
[CrossRef]

Zhang, S. C.

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator Bi2Te3,” Science 325, 178–181 (2009).
[CrossRef]

Zhang, S.-C.

X.-L. Qi and S.-C. Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys. 83, 1057–1110 (2011).
[CrossRef]

X.-L. Qi, T. L. Hughes, and S.-C. Zhang, “Topological field theory of time-reversal invariant insulators,” Phys. Rev. B 78, 195424 (2008).
[CrossRef]

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[CrossRef]

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Appl. Opt. (1)

Dokl. Akad. Nauk. SSSR (1)

F. I. Fedorov, “Theory of total reflection,” Dokl. Akad. Nauk. SSSR 105, 465–468 (1955).

Electron. Lett. (1)

Y. Miyagawa, T. Yamamoto, H. Masuda, M. Abe, H. Takahashi, and H. Takara, “Over-10000-channel 2.5 GHz-spaced ultra-dense WDM light source,” Electron. Lett. 42, 655–657 (2006).
[CrossRef]

J. Appl. Phys. (1)

K. Yasumoto and Y. Oishi, “A new evaluation of the Goos–Hänchen shift and associated time delay,” J. Appl. Phys. 54, 2170–2176 (1983).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Nat. Phys. (1)

Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5, 398–402 (2009).
[CrossRef]

Nature (2)

D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “A topological Dirac insulator in a quantum spin Hall phase,” Nature 452, 970–974 (2008).
[CrossRef]

J. E. Moore, “The birth of topological insulators,” Nature 464, 194–198 (2010).
[CrossRef]

Opt. Commun. (1)

G. Xu, J. Sun, T. Zang, H. Mao, and T. Pan, “Imbert-Fedorov shifts of a Gaussian beam reflected from anisotropic topological insulators,” Opt. Commun. 287, 154–161 (2013).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Lett. A (1)

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[CrossRef]

Phys. Rev. A (1)

G. Xu, T. Zang, H. Mao, and T. Pan, “Transverse shifts of a reflected light beam from the air-chiral interface,” Phys. Rev. A 83, 053828 (2011).
[CrossRef]

Phys. Rev. B (3)

X.-L. Qi, T. L. Hughes, and S.-C. Zhang, “Topological field theory of time-reversal invariant insulators,” Phys. Rev. B 78, 195424 (2008).
[CrossRef]

M.-C. Chang and M.-F. Yang, “Optical signature of topological insulators,” Phys. Rev. B 80, 113304 (2009).
[CrossRef]

J. E. Moore and L. Balents, “Topological invariants of time-reversal-invariant band structures,” Phys. Rev. B 75, 121306(2007).
[CrossRef]

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C. Imbert, “Calculation and experimental proof of the transverse shift induced by total internal reflection of a circularly polarized beam,” Phys. Rev. D 5, 787–796 (1972).
[CrossRef]

Phys. Rev. E (1)

H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern in the Goos–Hänchen effect,” Phys. Rev. E 62, 7330–7339 (2000).
[CrossRef]

Phys. Rev. Lett. (4)

W.-K. Tse and A. H. MacDonald, “Giant magneto-optical Kerr effect and universal Faraday effect in thin-film topological insulators,” Phys. Rev. Lett. 105, 057401 (2010).
[CrossRef]

L. Fu, C. L. Kane, and E. J. Mele, “Topological insulators in three dimensions,” Phys. Rev. Lett. 98, 106803 (2007).
[CrossRef]

F. Wilczek, “Two applications of axion electrodynamics,” Phys. Rev. Lett. 58, 1799–1802 (1987).
[CrossRef]

T. Sato, K. Segawa, H. Guo, K. Sugawara, S. Souma, T. Takahashi, and Y. Ando, “Direct evidence for the Dirac-cone topological surface states in the ternary chalcogenide TlBiSe2,” Phys. Rev. Lett. 105, 136802 (2010).
[CrossRef]

Rev. Mod. Phys. (2)

X.-L. Qi and S.-C. Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys. 83, 1057–1110 (2011).
[CrossRef]

M. Z. Hasan and C. L. Kane, “Colloquium: topological insulators,” Rev. Mod. Phys. 82, 3045–3067 (2010).
[CrossRef]

Science (1)

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator Bi2Te3,” Science 325, 178–181 (2009).
[CrossRef]

Other (1)

R. Roy, “Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect,” http://arxiv.org/pdf/cond-mat/0607531.pdf .

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Figures (5)

Fig. 1.
Fig. 1.

Schematic diagram of total internal reflection at the plane interface between an ordinary dielectric (medium 1) and TI (medium 2).

Fig. 2.
Fig. 2.

Projections of the incident and reflected beams and evanescent refracted wave in xoz plane (a) and xoy plane (b). lGH, lIF denote the GH shift and IF shift, respectively.

Fig. 3.
Fig. 3.

Variances with the incident angle at linear polarizations incidence of (a) lGH and (b) lIF (unit is wavelength in vacuum). The vertical line in (a) represents the location θc=71.6°. The inset in (a) shows D=lGH|Θ=πlGH|Θ=0 of TE (black dash) and TM (red dash). The inset in (b) shows the incident angle is dependent on the value of imaginary part for product q and p* with linear polarizations.

Fig. 4.
Fig. 4.

Transverse shift with respect to the angle of γ (a) and incident angle θ1 (b). The olive line and orange line correspond to δ=+π/2 and δ=π/2 elliptical polarizations. Noting that the maximum of lIFe is at angle γ=56° and γ=34° in (a), as θ1=72°.

Fig. 5.
Fig. 5.

As circle-polarization (with δ=π/2) incidence, dependence of the lIF on the incident angle with Θ2=π, 3π, 5π. Other parameters are the same as those in Fig. 3(b).

Equations (15)

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D=ε0ε2E+αΘ2πBH=1μ0μ2BαΘ2πE(forx<0),
Ei=(aeiδb)ei(k1xx+k1zz)=(cosγeiδsinγ)ei(k1xx+k1zz),
Er=(mn)ei(k1xx+k1zz)=1Δ(ε1μ1ε2μ2(αε0cΘ2π)2+ε1ε2μ1μ2(cosθ1cosθ2cosθ2cosθ1)2ε1μ1αε0cΘ2π2ε1μ1αε0cΘ2πε1μ1+ε2μ2+(αε0cΘ2π)2+ε1ε2μ1μ2(cosθ1cosθ2cosθ2cosθ1))(aeiδb)ei(k1xx+k1zz),
Et=(pq)ei(k2xx+k2zz)=2Δε1μ1(ε1μ1+ε2μ2cosθ1cosθ2αε0cΘ2παε0cΘ2πcosθ1cosθ2ε1μ1cosθ1cosθ2+ε2μ2)(aeiδb)ei(k2xx+k2zz),
Δ=ε1μ1+ε2μ2+(αε0cΘ2π)2+ε1ε2μ1μ2(cosθ1cosθ2+cosθ2cosθ1).
lGH=(Pzt+Pzir)/Sxr,
Szt=12Re[Et×Ht*]z=12ε2μ2e2κk2x(|q|2+|p|2)sinθ2Pzt=0+Sztdx=14κk2ε2μ2(|q|2+|p|2)sinθ1Pzir=12Re[Ei×Hr*+Er×Hi*]z=tanθ12k1ε1μ1Im(am+beiδ)Sxr=12Re[Er×Hr*]x=12ε1μ1(|a|2+|b|2)cosθ1,
lGH=(Pzt+Pzir)/Sxr=tanθ12[1κk2μ1μ2(|q|2+|p|2)2cosθ1k1Im(am+beiδn)]/(a2+b2).
lIF=Pyt/Sxr=tanθ1k2μ1μ2Im(qp*)/(a2+b2).
mTE=1Δ[ε1ε2(αε0c)2+ε1ε2(cosθ1cosθ2cosθ2cosθ1)]nTE=2Δαε0cε1pTE=2Δ(ε1+ε1ε2cosθ1cosθ2)qTE=2Δε1αε0ccosθ1cosθ2,
lGHTE=tanθ1{2ε1κk21|Δ|2[ε1+ε2(cosθ1κ)2+(αε0c)2(cosθ1κ)2]Im(mTE)cosθ1k1},
lIFTE=αε0cΘ2π4ε1|Δ|2ε1κk2sinθ1.
lGHTM=tanθ1{2ε1κk21|Δ|2[ε2+ε1(cosθ1κ)2+(αε0c)2]Im(nTM)cosθ1k1},
lIFTM=αε0cΘ2π4ε1|Δ|2ε1κk2sinθ1.
lIFe=4ε1ε1tanθ1|Δ|2k2[αε0ccosθ1κ(cos2γsin2γ)[1+(cosθ1κ)2]ε2sinγcosγ],

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