Abstract

We present closed and simple expressions of the spatial and angular Goos–Hänchen and Imbert–Fedorov shifts in terms of the second-order irradiance moments of a beam. Our results are applicable to a general totally polarized partially coherent beam. One of the main advantages of this formalism is that it can be applied directly from the knowledge of the cross-spectral density function and the polarization state without using any modal beam expansion. The obtained expressions allow understanding of the relationship between the global spatial characteristics of the incident beam and the experimented shifts in the reflected beam. Cosine-Gaussian Schell-model beams with rectangular symmetry are used to exemplify results.

© 2018 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref]
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2016 (4)

M. P. Araujo, S. De Leo, and G. G. Maia, “Closed-form expression for the Goos-Hänchen lateral displacement,” Phys. Rev. A 93, 023801 (2016).
[Crossref]

O. J. Santana, S. A. Carvalho, S. De Leo, and L. E. de Araujo, “Weak measurement of the composite Goos-Hänchen shift in the critical region,” Opt. Lett. 41, 3884–3887 (2016).
[Crossref]

X. Zhou and X. Ling, “Enhanced photonic spin Hall effect due to surface plasmon resonance,” IEEE Photon. J. 8, 4801108 (2016).
[Crossref]

Y.-L. C. Ziauddin, S. Qamar, and R.-K. Lee, “Goos-Hänchen shift of partially coherent light fields in epsilon-near-zero metamaterials,” Sci. Rep. 6, 26504 (2016).
[Crossref]

2015 (1)

M. Ornigotti and A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts for astigmatic Gaussian beams,” J. Opt. 17, 065608 (2015).
[Crossref]

2014 (1)

2013 (4)

L. G. Wang, S. Y. Zhu, and M. S. Zubairy, “Goos-Hänchen shifts of partially coherent light fields,” Phys. Rev. Lett. 111, 223901 (2013).
[Crossref]

K. Y. Bliokh and A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts: an overview,” J. Opt. 15, 014001 (2013).
[Crossref]

F. Töppel, M. Ornigotti, and A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts from a quantum-mechanical perspective,” New J. Phys. 15, 113059 (2013).
[Crossref]

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

2012 (8)

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

M. R. Dennis and J. B. Götte, “The analogy between optical beam shifts and quantum weak measurements,” New J. Phys. 14, 073013 (2012).
[Crossref]

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

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbsen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109, 013901 (2012).
[Crossref]

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85, 043809 (2012).
[Crossref]

A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts: a novel perspective,” New J. Phys. 14, 013058 (2012).
[Crossref]

M. Merano, G. Umbriaco, and G. Mistura, “Observation of nonspecular effects for Gaussian Schell-model light beams,” Phys. Rev. A 86, 033842 (2012).
[Crossref]

W. Löffler, A. Aiello, and J. P. Woerdman, “Spatial coherence and optical beam shifts,” Phys. Rev. Lett. 109, 213901 (2012).
[Crossref]

2011 (4)

2010 (1)

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82, 023817 (2010).
[Crossref]

2009 (3)

2008 (3)

L. Q. Wang, L. G. Wang, and S. Y. Zhu, “The influence of spatial coherence on the Goos-Hänchen shift at total internal reflection,” J. Phys. B 41, 055401 (2008).

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

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319, 787–790 (2008).
[Crossref]

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, 066609 (2007).
[Crossref]

M. Merano, A. Aiello, G. W. ’t Hooft, M. P. von Exter, E. R. Eliel, and J. P. Woerdman, “Observation of Goos-Hänchen shifts in metallic reflection,” Opt. Express 15, 15928–15934 (2007).
[Crossref]

P. T. Leung, C. W. Chen, and H. P. Chiang, “Large negative Goos-Hänchen shift at metal surfaces,” Opt. Commun. 276, 206–208 (2007).
[Crossref]

2006 (3)

2004 (1)

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372–374 (2004).
[Crossref]

1995 (1)

1993 (1)

R. Martínez-Herrero, P. M. Mejías, and H. Weber, “On the different definitions of laser beam moments,” Opt. Quantum Electron. 25, 423–428 (1993).
[Crossref]

1992 (2)

J. Serna, P. M. Mejías, and R. Martínez-Herrero, “Rotation of partially coherent beams propagating through free space,” Opt. Quantum Electron. 24, S873–S880 (1992).
[Crossref]

R. Martínez-Herrero and P. M. Mejías, “Expansion of the cross-spectral density function of general fields and its application to beam characterization,” Opt. Commun. 94, 197–202 (1992).
[Crossref]

1991 (1)

1989 (1)

1986 (1)

1984 (1)

R. Martínez-Herrero and P. M. Mejías, “Radiometric definitions for partially coherent sources,” J. Opt. Soc. Am. 1, 556–558 (1984).
[Crossref]

1979 (1)

R. Martínez-Herrero, “Expansion of complex degree of coherence,” Il Nuovo Cimento B 54, 205–210 (1979).

1975 (1)

1972 (1)

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

1971 (1)

1964 (1)

1955 (1)

F. I. Fedorov, “K teorii polnogo otrazheniya,” Dokl. Akad. Nauk SSSR 105, 465–468 (1955).

1948 (1)

K. Artmann, “Calculation of the lateral shift of totally reflected beams,” 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]

’t Hooft, G. W.

Agarwal, G. S.

Aiello, A.

M. Ornigotti and A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts for astigmatic Gaussian beams,” J. Opt. 17, 065608 (2015).
[Crossref]

K. Y. Bliokh and A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts: an overview,” J. Opt. 15, 014001 (2013).
[Crossref]

F. Töppel, M. Ornigotti, and A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts from a quantum-mechanical perspective,” New J. Phys. 15, 113059 (2013).
[Crossref]

A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts: a novel perspective,” New J. Phys. 14, 013058 (2012).
[Crossref]

W. Löffler, A. Aiello, and J. P. Woerdman, “Spatial coherence and optical beam shifts,” Phys. Rev. Lett. 109, 213901 (2012).
[Crossref]

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

A. Aiello and J. P. Woerdman, “Role of spatial coherence in Goos-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. 36, 3151–3153 (2011).
[Crossref]

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82, 023817 (2010).
[Crossref]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics 3, 337–340 (2009).
[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]

M. Merano, A. Aiello, G. W. ’t Hooft, M. P. von Exter, E. R. Eliel, and J. P. Woerdman, “Observation of Goos-Hänchen shifts in metallic reflection,” Opt. Express 15, 15928–15934 (2007).
[Crossref]

Alonso, M. A.

Araujo, M. P.

M. P. Araujo, S. De Leo, and G. G. Maia, “Closed-form expression for the Goos-Hänchen lateral displacement,” Phys. Rev. A 93, 023801 (2016).
[Crossref]

Artmann, K.

K. Artmann, “Calculation of the lateral shift of totally reflected beams,” Ann. Phys. 437, 87–102 (1948).
[Crossref]

Bliokh, K. Y.

K. Y. Bliokh and A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts: an overview,” J. Opt. 15, 014001 (2013).
[Crossref]

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbsen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109, 013901 (2012).
[Crossref]

K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, “Goos-Hänchen and Imbert-Fedorov shifts of polarized vortex beams,” Opt. Lett. 34, 389–391 (2009).
[Crossref]

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, 066609 (2007).
[Crossref]

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, 073903 (2006).
[Crossref]

Bliokh, Y. P.

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, 066609 (2007).
[Crossref]

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, 073903 (2006).
[Crossref]

Cai, Y.

Carvalho, S. A.

Chen, C. W.

P. T. Leung, C. W. Chen, and H. P. Chiang, “Large negative Goos-Hänchen shift at metal surfaces,” Opt. Commun. 276, 206–208 (2007).
[Crossref]

Chiang, H. P.

P. T. Leung, C. W. Chen, and H. P. Chiang, “Large negative Goos-Hänchen shift at metal surfaces,” Opt. Commun. 276, 206–208 (2007).
[Crossref]

de Araujo, L. E.

De Leo, S.

O. J. Santana, S. A. Carvalho, S. De Leo, and L. E. de Araujo, “Weak measurement of the composite Goos-Hänchen shift in the critical region,” Opt. Lett. 41, 3884–3887 (2016).
[Crossref]

M. P. Araujo, S. De Leo, and G. G. Maia, “Closed-form expression for the Goos-Hänchen lateral displacement,” Phys. Rev. A 93, 023801 (2016).
[Crossref]

Dennis, M. R.

M. R. Dennis and J. B. Götte, “The analogy between optical beam shifts and quantum weak measurements,” New J. Phys. 14, 073013 (2012).
[Crossref]

Ebbsen, T. W.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbsen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109, 013901 (2012).
[Crossref]

Eliel, E. R.

Fang, N.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372–374 (2004).
[Crossref]

Fedorov, F. I.

F. I. Fedorov, “K teorii polnogo otrazheniya,” Dokl. Akad. Nauk SSSR 105, 465–468 (1955).

Feng, X.

Gang, Q.

Genet, C.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbsen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109, 013901 (2012).
[Crossref]

Goos, F.

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

Gori, F.

Gorodetski, Y.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbsen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109, 013901 (2012).
[Crossref]

Götte, J. B.

M. R. Dennis and J. B. Götte, “The analogy between optical beam shifts and quantum weak measurements,” New J. Phys. 14, 073013 (2012).
[Crossref]

Hänchen, H.

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

Hasman, E.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbsen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109, 013901 (2012).
[Crossref]

Hermosa, N.

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82, 023817 (2010).
[Crossref]

Hesselink, L.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372–374 (2004).
[Crossref]

Horowitz, B.

Hosten, O.

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319, 787–790 (2008).
[Crossref]

Imbert, C.

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

Jayaswal, G.

Kivshar, Y. S.

Kleiner, V.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbsen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109, 013901 (2012).
[Crossref]

Korotkova, O.

Kwiat, P.

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319, 787–790 (2008).
[Crossref]

Lee, R.-K.

Y.-L. C. Ziauddin, S. Qamar, and R.-K. Lee, “Goos-Hänchen shift of partially coherent light fields in epsilon-near-zero metamaterials,” Sci. Rep. 6, 26504 (2016).
[Crossref]

Leung, P. T.

P. T. Leung, C. W. Chen, and H. P. Chiang, “Large negative Goos-Hänchen shift at metal surfaces,” Opt. Commun. 276, 206–208 (2007).
[Crossref]

Li, Y.

Liang, C.

Ling, X.

X. Zhou and X. Ling, “Enhanced photonic spin Hall effect due to surface plasmon resonance,” IEEE Photon. J. 8, 4801108 (2016).
[Crossref]

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

Liu, X.

Liu, Z.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372–374 (2004).
[Crossref]

Löffler, W.

W. Löffler, A. Aiello, and J. P. Woerdman, “Spatial coherence and optical beam shifts,” Phys. Rev. Lett. 109, 213901 (2012).
[Crossref]

Luo, H.

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85, 043809 (2012).
[Crossref]

Luoa, H.

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

Maia, G. G.

M. P. Araujo, S. De Leo, and G. G. Maia, “Closed-form expression for the Goos-Hänchen lateral displacement,” Phys. Rev. A 93, 023801 (2016).
[Crossref]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Martínez-Herrero, R.

R. Martínez-Herrero, P. M. Mejías, and F. Gori, “Genuine cross-spectral densities and pseudo-modal expansions,” Opt. Lett. 34, 1399–1401 (2009).
[Crossref]

R. Martínez-Herrero and P. M. Mejías, “On the spatial orientation of the transverse irradiance profile of partially coherent beams,” Opt. Express 14, 3294–3303 (2006).
[Crossref]

R. Martínez-Herrero and P. M. Mejías, “On the control of the spatial orientation of the transverse profile of a light beam,” Opt. Express 14, 1086–1093 (2006).
[Crossref]

P. M. Mejías and R. Martínez-Herrero, “Time-resolved spatial parametric characterization of pulsed light beams,” Opt. Lett. 20, 660–662 (1995).
[Crossref]

R. Martínez-Herrero, P. M. Mejías, and H. Weber, “On the different definitions of laser beam moments,” Opt. Quantum Electron. 25, 423–428 (1993).
[Crossref]

J. Serna, P. M. Mejías, and R. Martínez-Herrero, “Rotation of partially coherent beams propagating through free space,” Opt. Quantum Electron. 24, S873–S880 (1992).
[Crossref]

R. Martínez-Herrero and P. M. Mejías, “Expansion of the cross-spectral density function of general fields and its application to beam characterization,” Opt. Commun. 94, 197–202 (1992).
[Crossref]

J. Serna, R. Martínez-Herrero, and P. Mejías, “Parametric characterization of general partially coherent beams propagating through ABCD optical systems,” J. Opt. Soc. Am. A 8, 1094–1098 (1991).
[Crossref]

R. Martínez-Herrero and P. M. Mejías, “Radiometric definitions for partially coherent sources,” J. Opt. Soc. Am. 1, 556–558 (1984).
[Crossref]

R. Martínez-Herrero, “Expansion of complex degree of coherence,” Il Nuovo Cimento B 54, 205–210 (1979).

Mejías, P.

Mejías, P. M.

R. Martínez-Herrero, P. M. Mejías, and F. Gori, “Genuine cross-spectral densities and pseudo-modal expansions,” Opt. Lett. 34, 1399–1401 (2009).
[Crossref]

R. Martínez-Herrero and P. M. Mejías, “On the control of the spatial orientation of the transverse profile of a light beam,” Opt. Express 14, 1086–1093 (2006).
[Crossref]

R. Martínez-Herrero and P. M. Mejías, “On the spatial orientation of the transverse irradiance profile of partially coherent beams,” Opt. Express 14, 3294–3303 (2006).
[Crossref]

P. M. Mejías and R. Martínez-Herrero, “Time-resolved spatial parametric characterization of pulsed light beams,” Opt. Lett. 20, 660–662 (1995).
[Crossref]

R. Martínez-Herrero, P. M. Mejías, and H. Weber, “On the different definitions of laser beam moments,” Opt. Quantum Electron. 25, 423–428 (1993).
[Crossref]

J. Serna, P. M. Mejías, and R. Martínez-Herrero, “Rotation of partially coherent beams propagating through free space,” Opt. Quantum Electron. 24, S873–S880 (1992).
[Crossref]

R. Martínez-Herrero and P. M. Mejías, “Expansion of the cross-spectral density function of general fields and its application to beam characterization,” Opt. Commun. 94, 197–202 (1992).
[Crossref]

R. Martínez-Herrero and P. M. Mejías, “Radiometric definitions for partially coherent sources,” J. Opt. Soc. Am. 1, 556–558 (1984).
[Crossref]

Merano, M.

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

M. Merano, G. Umbriaco, and G. Mistura, “Observation of nonspecular effects for Gaussian Schell-model light beams,” Phys. Rev. A 86, 033842 (2012).
[Crossref]

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82, 023817 (2010).
[Crossref]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics 3, 337–340 (2009).
[Crossref]

M. Merano, A. Aiello, G. W. ’t Hooft, M. P. von Exter, E. R. Eliel, and J. P. Woerdman, “Observation of Goos-Hänchen shifts in metallic reflection,” Opt. Express 15, 15928–15934 (2007).
[Crossref]

Mistura, G.

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

M. Merano, G. Umbriaco, and G. Mistura, “Observation of nonspecular effects for Gaussian Schell-model light beams,” Phys. Rev. A 86, 033842 (2012).
[Crossref]

Ornigotti, M.

M. Ornigotti and A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts for astigmatic Gaussian beams,” J. Opt. 17, 065608 (2015).
[Crossref]

F. Töppel, M. Ornigotti, and A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts from a quantum-mechanical perspective,” New J. Phys. 15, 113059 (2013).
[Crossref]

Prajapati, C.

Qamar, S.

Y.-L. C. Ziauddin, S. Qamar, and R.-K. Lee, “Goos-Hänchen shift of partially coherent light fields in epsilon-near-zero metamaterials,” Sci. Rep. 6, 26504 (2016).
[Crossref]

Qin, Y.

Ranganathan, D.

Renard, R. H.

Santana, O. J.

Serna, J.

J. Serna, P. M. Mejías, and R. Martínez-Herrero, “Rotation of partially coherent beams propagating through free space,” Opt. Quantum Electron. 24, S873–S880 (1992).
[Crossref]

J. Serna, R. Martínez-Herrero, and P. Mejías, “Parametric characterization of general partially coherent beams propagating through ABCD optical systems,” J. Opt. Soc. Am. A 8, 1094–1098 (1991).
[Crossref]

Shadrivov, I. V.

Shitrit, N.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbsen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109, 013901 (2012).
[Crossref]

Simon, R.

Stein, B.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbsen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109, 013901 (2012).
[Crossref]

Tamir, T.

Töppel, F.

F. Töppel, M. Ornigotti, and A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts from a quantum-mechanical perspective,” New J. Phys. 15, 113059 (2013).
[Crossref]

Umbriaco, G.

M. Merano, G. Umbriaco, and G. Mistura, “Observation of nonspecular effects for Gaussian Schell-model light beams,” Phys. Rev. A 86, 033842 (2012).
[Crossref]

van Exter, M. P.

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics 3, 337–340 (2009).
[Crossref]

von Exter, M. P.

Wang, F.

Wang, L. G.

L. G. Wang, S. Y. Zhu, and M. S. Zubairy, “Goos-Hänchen shifts of partially coherent light fields,” Phys. Rev. Lett. 111, 223901 (2013).
[Crossref]

L. Q. Wang, L. G. Wang, and S. Y. Zhu, “The influence of spatial coherence on the Goos-Hänchen shift at total internal reflection,” J. Phys. B 41, 055401 (2008).

Wang, L. Q.

L. Q. Wang, L. G. Wang, and S. Y. Zhu, “The influence of spatial coherence on the Goos-Hänchen shift at total internal reflection,” J. Phys. B 41, 055401 (2008).

Weber, H.

R. Martínez-Herrero, P. M. Mejías, and H. Weber, “On the different definitions of laser beam moments,” Opt. Quantum Electron. 25, 423–428 (1993).
[Crossref]

Wen, S.

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85, 043809 (2012).
[Crossref]

Wenb, S.

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

Woerdman, J. P.

W. Löffler, A. Aiello, and J. P. Woerdman, “Spatial coherence and optical beam shifts,” Phys. Rev. Lett. 109, 213901 (2012).
[Crossref]

A. Aiello and J. P. Woerdman, “Role of spatial coherence in Goos-Hänchen and Imbert-Fedorov shifts,” Opt. Lett. 36, 3151–3153 (2011).
[Crossref]

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

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82, 023817 (2010).
[Crossref]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics 3, 337–340 (2009).
[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]

M. Merano, A. Aiello, G. W. ’t Hooft, M. P. von Exter, E. R. Eliel, and J. P. Woerdman, “Observation of Goos-Hänchen shifts in metallic reflection,” Opt. Express 15, 15928–15934 (2007).
[Crossref]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Xiao, Y. F.

Xiao, Z.

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85, 043809 (2012).
[Crossref]

Yin, X.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372–374 (2004).
[Crossref]

Yong, H.

Zhang, X.

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372–374 (2004).
[Crossref]

Zhou, X.

X. Zhou and X. Ling, “Enhanced photonic spin Hall effect due to surface plasmon resonance,” IEEE Photon. J. 8, 4801108 (2016).
[Crossref]

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

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85, 043809 (2012).
[Crossref]

Zhu, S. Y.

L. G. Wang, S. Y. Zhu, and M. S. Zubairy, “Goos-Hänchen shifts of partially coherent light fields,” Phys. Rev. Lett. 111, 223901 (2013).
[Crossref]

L. Q. Wang, L. G. Wang, and S. Y. Zhu, “The influence of spatial coherence on the Goos-Hänchen shift at total internal reflection,” J. Phys. B 41, 055401 (2008).

Ziauddin, Y.-L. C.

Y.-L. C. Ziauddin, S. Qamar, and R.-K. Lee, “Goos-Hänchen shift of partially coherent light fields in epsilon-near-zero metamaterials,” Sci. Rep. 6, 26504 (2016).
[Crossref]

Zubairy, M. S.

L. G. Wang, S. Y. Zhu, and M. S. Zubairy, “Goos-Hänchen shifts of partially coherent light fields,” Phys. Rev. Lett. 111, 223901 (2013).
[Crossref]

Adv. Opt. Photon. (1)

Ann. Phys. (2)

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

K. Artmann, “Calculation of the lateral shift of totally reflected beams,” Ann. Phys. 437, 87–102 (1948).
[Crossref]

Appl. Phys. Lett. (2)

X. Yin, L. Hesselink, Z. Liu, N. Fang, and X. Zhang, “Large positive and negative lateral optical beam displacements due to surface plasmon resonance,” Appl. Phys. Lett. 85, 372–374 (2004).
[Crossref]

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

Dokl. Akad. Nauk SSSR (1)

F. I. Fedorov, “K teorii polnogo otrazheniya,” Dokl. Akad. Nauk SSSR 105, 465–468 (1955).

IEEE Photon. J. (1)

X. Zhou and X. Ling, “Enhanced photonic spin Hall effect due to surface plasmon resonance,” IEEE Photon. J. 8, 4801108 (2016).
[Crossref]

Il Nuovo Cimento B (1)

R. Martínez-Herrero, “Expansion of complex degree of coherence,” Il Nuovo Cimento B 54, 205–210 (1979).

J. Opt. (2)

M. Ornigotti and A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts for astigmatic Gaussian beams,” J. Opt. 17, 065608 (2015).
[Crossref]

K. Y. Bliokh and A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts: an overview,” J. Opt. 15, 014001 (2013).
[Crossref]

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (4)

J. Phys. B (1)

L. Q. Wang, L. G. Wang, and S. Y. Zhu, “The influence of spatial coherence on the Goos-Hänchen shift at total internal reflection,” J. Phys. B 41, 055401 (2008).

Nat. Photonics (1)

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics 3, 337–340 (2009).
[Crossref]

New J. Phys. (3)

M. R. Dennis and J. B. Götte, “The analogy between optical beam shifts and quantum weak measurements,” New J. Phys. 14, 073013 (2012).
[Crossref]

F. Töppel, M. Ornigotti, and A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts from a quantum-mechanical perspective,” New J. Phys. 15, 113059 (2013).
[Crossref]

A. Aiello, “Goos-Hänchen and Imbert-Fedorov shifts: a novel perspective,” New J. Phys. 14, 013058 (2012).
[Crossref]

Opt. Commun. (2)

P. T. Leung, C. W. Chen, and H. P. Chiang, “Large negative Goos-Hänchen shift at metal surfaces,” Opt. Commun. 276, 206–208 (2007).
[Crossref]

R. Martínez-Herrero and P. M. Mejías, “Expansion of the cross-spectral density function of general fields and its application to beam characterization,” Opt. Commun. 94, 197–202 (1992).
[Crossref]

Opt. Express (4)

Opt. Lett. (9)

Opt. Quantum Electron. (2)

J. Serna, P. M. Mejías, and R. Martínez-Herrero, “Rotation of partially coherent beams propagating through free space,” Opt. Quantum Electron. 24, S873–S880 (1992).
[Crossref]

R. Martínez-Herrero, P. M. Mejías, and H. Weber, “On the different definitions of laser beam moments,” Opt. Quantum Electron. 25, 423–428 (1993).
[Crossref]

Phys. Rev. A (4)

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82, 023817 (2010).
[Crossref]

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin Hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85, 043809 (2012).
[Crossref]

M. Merano, G. Umbriaco, and G. Mistura, “Observation of nonspecular effects for Gaussian Schell-model light beams,” Phys. Rev. A 86, 033842 (2012).
[Crossref]

M. P. Araujo, S. De Leo, and G. G. Maia, “Closed-form expression for the Goos-Hänchen lateral displacement,” Phys. Rev. A 93, 023801 (2016).
[Crossref]

Phys. Rev. D (1)

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

Phys. Rev. E (1)

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, 066609 (2007).
[Crossref]

Phys. Rev. Lett. (4)

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbsen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109, 013901 (2012).
[Crossref]

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, 073903 (2006).
[Crossref]

W. Löffler, A. Aiello, and J. P. Woerdman, “Spatial coherence and optical beam shifts,” Phys. Rev. Lett. 109, 213901 (2012).
[Crossref]

L. G. Wang, S. Y. Zhu, and M. S. Zubairy, “Goos-Hänchen shifts of partially coherent light fields,” Phys. Rev. Lett. 111, 223901 (2013).
[Crossref]

Sci. Rep. (1)

Y.-L. C. Ziauddin, S. Qamar, and R.-K. Lee, “Goos-Hänchen shift of partially coherent light fields in epsilon-near-zero metamaterials,” Sci. Rep. 6, 26504 (2016).
[Crossref]

Science (1)

O. Hosten and P. Kwiat, “Observation of the spin hall effect of light via weak measurements,” Science 319, 787–790 (2008).
[Crossref]

Other (1)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

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Figures (5)

Fig. 1.
Fig. 1. Optical reflection in a planar interface. Two Cartesian frames, respectively, attached to the incident and reflected beam are considered, namely, (xI,yI,zI) and (xR,yR,zR).
Fig. 2.
Fig. 2. Angular GH shift with respect to βx=δx2/σ02. The incident mean angle θ0 is fixed to 70°.
Fig. 3.
Fig. 3. Angular IF shift with respect to βy=δy2/σ02. The incident mean angle θ0 is fixed to 70°.
Fig. 4.
Fig. 4. Angular GH shift with respect to the incident mean angle θ0. In this plot, βy is fixed to 1.
Fig. 5.
Fig. 5. Angular IF shift with respect to the incident mean angle θ0. In this plot, βy is fixed to 1.

Equations (49)

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

h(r,η,z)=W(r+s2,rs2)exp(ikη·s)ds,
xmynupvq(z)=1Ixmynupvqh(r,η,z)dsdr,
u2=(2W(r1,r2)x1x2)r1=r2=rdxdyk2W(r,r)dxdy,v2=(2W(r1,r2)y1y2)r1=r2=rdxdyk2W(r,r)dxdy,xu=x(W(r1,r2)x2W(r1,r2)x1)r1=r2=rdxdy2kiW(r,r)dxdy,xv=x(W(r1,r2)y2W(r1,r2)y1)r1=r2=rdxdy2kiW(r,r)dxdy,yu=y(W(r1,r2)x2W(r1,r2)x1)r1=r2=rdxdy2kiW(r,r)dxdy,yv=y(W(r1,r2)y2W(r1,r2)y1)r1=r2=rdxdy2kiW(r,r)dxdy.
E(rI,zI)=E0f(rI,zI),
ER(rR,zR)=(a1r1f(xR+x1,yRy1,zR),a2r2f(xR+x2,yRy2,zR)).
xj=ik(lnrjθ)θ=θ0,j=1,2,
y1=ia2a1k(1+r2r1)cotθ0,
y2=ia1a2k(1+r1r2)cotθ0.
IR(rR,zR)=j=12|ajrj|2|f(xR+xj,yRyj,zR)|2.
ΔGH=xR(0),ΘGH=xR(zR)zR,
ΔIF=yR(0),ΘIF=yR(zR)zR.
W^I(r1I,r2I,zI)=E0E0W(r1I,r2I,zI),
W(r1I,r2I,zI)=L*(r1I,σ,zI)L(r2I,σ,zI)dσ,
W^I(r1I,r2I,zI)=V(r1I,σ,zI)V(r2I,σ,zI)dσ,
V(rI,σ,zI)=(a1,a2)L(rI,σ,zI).
V(rR,σ,zR)=(a1r1L(xR+x1,yRy1,σ,zR),a2r2L(xR+x2,yRy2,σ,zR)),
IR(rR)=j=12|ajrj|2|L(xR+xj,yRyj,σ,zR)|2dσ.
|L(xR+xj,yRyj,σ,zR)|2|L(xR,yR,σ,zR)|22Re(xj)Re(L*LxR)+2Im(xj)Im(L*LxR)+2Im(yj)Im(L*LyR)2Re(yj)Re(L*LyR).
R(zR)=j=12wj(Δj+2kM^(zR)Θj),
wj=|ajrj|2j=12|ajrj|2,
M^(zR)=(xu(zR)xv(zR)yu(zR)yv(zR)).
M^(zR)=M^(0)+zRΩ^,
Ω^=(u2uvuvv2).
ΔGH=j=12wj(Re(xj)+2kxu(0)Im(xj)+2kxv(0)Im(yj)),
ΘGH=2kj=12wj(u2(0)Im(xj)+uv(0)Im(yj)),
ΔIF=j=12wj(Re(yj)+2kyu(0)Im(xj)+2kyv(0)Im(yj)),
ΘIF=2kj=12wj(uv(0)Im(xj)+v2(0)Im(yj)).
Rx=x2xu,
Ry=y2yv.
ΔGH=j=12wjRe(xj),
ΔIF=j=12wjRe(yj).
ΘGH=2ku2j=12wjIm(xj),
ΘIF=2kv2j=12wjIm(yj).
W(x1,y1,x2,y2)=Fx(x1,x2)Fy(y1,y2),
Fx(x1,x2)=exp(x12+x224σ02)exp((x2x1)22δx2)×cos(2πm(x2x1)δx),
Fy(y1,y2)=exp(y12+y224σ02)exp((y2y1)22δy2)×cos(2πm(y2y1)δy),
u2=14  k2σ02(1+4σ02(1+2πm2δx2)),
v2=14  k2σ02(1+4σ02(1+2πm2δy2)).
ΘGH=12kσ02(1+4σ02(1+2πm2δx2))j=12wjIm(xj),
ΘIF=12kσ02(1+4σ02(1+2πm2δy2))j=12wjIm(yj).
ΘGH=ΘGH0+4πm2kδx2RGH,
ΘIF=ΘIF0+4πm2kδy2RIF.
ΘGHΘGH0ΘIFΘIF0=δy2δx2RGHRIF.
xR(|L(xR+xj,yRyj,σ,zR)|2dσ)dxRdyR=xR(|L(xR,yR,σ,zR)|2dσ)dxRdyR2Re(xj)xR(Re(L*LxR)dσ)dxRdyR+2Im(xj)xR(Im(L*LxR)dσ)dxRdyR+2Im(yj)xR(Im(L*LyR)dσ)dxRdyR2Re(yj)xR(Re(L*LyR)dσ)dxRdyR.
Im(L*LxR)dσ=12i(W(r1R,r2R)x2RW(r1R,r2R)x1R)r1R=r2R=rR,Im(L*LyR)dσ=12i(W(r1R,r2R)y2RW(r1R,r2R)y1R)r1R=r2R=rR.
xRRe(L*LxR)dxRdyR=12|L(xR,yR,σ,zR)|2dxRdyR,xRRe(L*LyR)dxRdyR=0.
xR(|L(xR+xj,yRyj,σ,zR)|2dσ)dxRdyR=xRW(r1R,r2R,zR)dxRdyR+Re(xj)W(r1R,r2R,zR)dxRdyRiIm(xj)xR(W(r1R,r2R)x2RW(r1R,r2R)x1R)r1=r2=rRdxRdyRiIm(yj)xR(W(r1R,r2R)y2RW(r1R,r2R)y1R)r1=r2=rRdxRdyR.
xR(zR)=xRIR(rR)dxRdyRIR(rR)dxRdyR=j=12wj(Re(xj)+2kxu(zR)Im(xj)+2kxv(zR)Im(yj)),
yR(zR)=yRIR(rR)dxRdyRIR(rR)dxRdyR=j=12wj(Re(yj)+2kyu(zR)Im(xj)+2kyv(zR)Im(yj)).

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