Abstract

We present the first calculation of the Goos-Hänchen shifts in the context of the nonlinear generation of fields. We specifically concentrate on shifts of second harmonic generated at metallic surfaces. At metallic surfaces the second harmonic primarily arises from discontinuities of the field at surfaces which not only result in large harmonic generation but also in significant Goos-Hänchen shifts of the generated second harmonic. Our results can be extended to other shifts like angular shifts and Fedorov-Imbert shifts.

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  1. F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. (Berlin)436(7-8), 333–346 (1947).
    [CrossRef]
  2. K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. (Berlin)437(1-2), 87–102 (1948).
    [CrossRef]
  3. B. R. Horowitz and T. Tamir, “Lateral displacement of a light beam at a dielectric interface,” J. Opt. Soc. Am.61(5), 586 (1971).
    [CrossRef]
  4. W. J. Wild and C. L. Giles, “Goos-Hänchen shifts from absorbing media,” Phys. Rev. A25(4), 2099–2101 (1982).
    [CrossRef]
  5. H. G. L. Schwefel, W. Köhler, Z. H. Lu, J. Fan, and L. J. Wang, “Direct experimental observation of the single reflection optical Goos-Hänchen shift,” Opt. Lett.33(8), 794–796 (2008).
    [CrossRef] [PubMed]
  6. M. Merano, A. Aiello, G. W. ’t Hooft, M. P. van Exter, E. R. Eliel, and J. P. Woerdman, “Observation of Goos-Hänchen shifts in metallic reflection,” Opt. Express15(24), 15928–15934 (2007).
    [CrossRef] [PubMed]
  7. C. Bonnet, D. Chauvat, O. Emile, F. Bretenaker, A. Le Floch, and L. Dutriaux, “Measurement of positive and negative Goos-Hänchen effects for metallic gratings near Wood anomalies,” Opt. Lett.26(10), 666–668 (2001).
    [CrossRef] [PubMed]
  8. M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics3(6), 337–340 (2009).
    [CrossRef]
  9. J. He, J. Yi, and S. He, “Giant negative Goos-Hänchen shifts for a photonic crystal with a negative effective index,” Opt. Express14(7), 3024–3029 (2006).
    [CrossRef] [PubMed]
  10. F. I. Fedorov, “K teorii polnovo otrazenija,” Dokl. Akad. Nauk. SSR105, 465 (1955).
  11. C. Imbert, “Calculation and experimental proof of the transverse shift Induced by total internal reflection of a circularly polarized light beam,” Phys. Rev. D Part. Fields5(4), 787–796 (1972).
    [CrossRef]
  12. O. de Beauregard and C. Imbert, “Quantized longitudinal and transverse shifts associated with total internal reflection,” Phys. Rev. D Part. Fields7(12), 3555–3563 (1973).
    [CrossRef]
  13. Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett.101(4), 043903 (2008).
    [CrossRef] [PubMed]
  14. O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science319(5864), 787–790 (2008).
    [CrossRef] [PubMed]
  15. N. Hermosa, A. M. Nugrowati, A. Aiello, and J. P. Woerdman, “Spin Hall effect of light in metallic reflection,” Opt. Lett.36(16), 3200–3202 (2011).
    [CrossRef] [PubMed]
  16. D. Haefner, S. Sukhov, and A. Dogariu, “Spin Hall effect of light in spherical geometry,” Phys. Rev. Lett.102(12), 123903 (2009).
    [CrossRef] [PubMed]
  17. L. Allen, S. M. Barnett, and M. J. Padgett, eds., Optical Angular Momentum (Taylor & Francis, 2003).
  18. A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon.3(2), 161 (2011).
    [CrossRef]
  19. A. Dogariu and C. Schwartz, “Conservation of angular momentum of light in single scattering,” Opt. Express14(18), 8425–8433 (2006).
    [CrossRef] [PubMed]
  20. N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev.128(2), 606–622 (1962).
    [CrossRef]
  21. S. S. Jha, “Theory of optical harmonic generation at a metal surface,” Phys. Rev.140(6A), A2020–A2030 (1965).
    [CrossRef]
  22. N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev.174(3), 813–822 (1968).
    [CrossRef]
  23. P. Guyot-Sionnest, W. Chen, and Y. R. Shen, “General considerations on optical second-harmonic generation from surfaces and interfaces,” Phys. Rev. B Condens. Matter33(12), 8254–8263 (1986).
    [CrossRef] [PubMed]
  24. C. F. Li, “Unified theory for Goos-Haenchen and Imbert-Fedorov effects,” Phys. Rev. A76(1), 013811 (2007).
    [CrossRef]
  25. G. S. Agarwal and S. S. Jha, “Surface-enhanced second-harmonic generation at a metallic grating,” Phys. Rev. B26(2), 482–496 (1982).
    [CrossRef]
  26. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
    [CrossRef]
  27. J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B Condens. Matter35(3), 1129–1141 (1987).
    [CrossRef] [PubMed]
  28. W. L. Schaich and B. S. Mendoza, “simple model of second-harmonic generation,” Phys. Rev. B Condens. Matter45(24), 14279–14292 (1992).
    [CrossRef] [PubMed]
  29. B. S. Mendoza and W. L. Mochán, “Exactly solvable model of surface second-harmonic generation,” Phys. Rev. B Condens. Matter53(8), 4999–5006 (1996).
    [CrossRef] [PubMed]
  30. X. Yin and L. Hesselink, “Goos-Hänchen shift surface plasmon resonance sensor,” Appl. Phys. Lett.89(26), 261108 (2006).
    [CrossRef]
  31. M. Kumari and S. Dutta Gupta, “Positive and negative Giant Goos--Hänchen shift in a Near-symmetric layered medium for illumination from opposite ends,” Opt. Commun.285(5), 617–620 (2012).
    [CrossRef]

2012

M. Kumari and S. Dutta Gupta, “Positive and negative Giant Goos--Hänchen shift in a Near-symmetric layered medium for illumination from opposite ends,” Opt. Commun.285(5), 617–620 (2012).
[CrossRef]

2011

2009

D. Haefner, S. Sukhov, and A. Dogariu, “Spin Hall effect of light in spherical geometry,” Phys. Rev. Lett.102(12), 123903 (2009).
[CrossRef] [PubMed]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics3(6), 337–340 (2009).
[CrossRef]

2008

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett.101(4), 043903 (2008).
[CrossRef] [PubMed]

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science319(5864), 787–790 (2008).
[CrossRef] [PubMed]

H. G. L. Schwefel, W. Köhler, Z. H. Lu, J. Fan, and L. J. Wang, “Direct experimental observation of the single reflection optical Goos-Hänchen shift,” Opt. Lett.33(8), 794–796 (2008).
[CrossRef] [PubMed]

2007

2006

2001

1996

B. S. Mendoza and W. L. Mochán, “Exactly solvable model of surface second-harmonic generation,” Phys. Rev. B Condens. Matter53(8), 4999–5006 (1996).
[CrossRef] [PubMed]

1992

W. L. Schaich and B. S. Mendoza, “simple model of second-harmonic generation,” Phys. Rev. B Condens. Matter45(24), 14279–14292 (1992).
[CrossRef] [PubMed]

1987

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B Condens. Matter35(3), 1129–1141 (1987).
[CrossRef] [PubMed]

1986

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, “General considerations on optical second-harmonic generation from surfaces and interfaces,” Phys. Rev. B Condens. Matter33(12), 8254–8263 (1986).
[CrossRef] [PubMed]

1982

W. J. Wild and C. L. Giles, “Goos-Hänchen shifts from absorbing media,” Phys. Rev. A25(4), 2099–2101 (1982).
[CrossRef]

G. S. Agarwal and S. S. Jha, “Surface-enhanced second-harmonic generation at a metallic grating,” Phys. Rev. B26(2), 482–496 (1982).
[CrossRef]

1973

O. de Beauregard and C. Imbert, “Quantized longitudinal and transverse shifts associated with total internal reflection,” Phys. Rev. D Part. Fields7(12), 3555–3563 (1973).
[CrossRef]

1972

C. Imbert, “Calculation and experimental proof of the transverse shift Induced by total internal reflection of a circularly polarized light beam,” Phys. Rev. D Part. Fields5(4), 787–796 (1972).
[CrossRef]

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

1971

1968

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev.174(3), 813–822 (1968).
[CrossRef]

1965

S. S. Jha, “Theory of optical harmonic generation at a metal surface,” Phys. Rev.140(6A), A2020–A2030 (1965).
[CrossRef]

1962

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev.128(2), 606–622 (1962).
[CrossRef]

1955

F. I. Fedorov, “K teorii polnovo otrazenija,” Dokl. Akad. Nauk. SSR105, 465 (1955).

1948

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. (Berlin)437(1-2), 87–102 (1948).
[CrossRef]

1947

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. (Berlin)436(7-8), 333–346 (1947).
[CrossRef]

’t Hooft, G. W.

Agarwal, G. S.

G. S. Agarwal and S. S. Jha, “Surface-enhanced second-harmonic generation at a metallic grating,” Phys. Rev. B26(2), 482–496 (1982).
[CrossRef]

Aiello, A.

Artmann, K.

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. (Berlin)437(1-2), 87–102 (1948).
[CrossRef]

Bloembergen, N.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev.174(3), 813–822 (1968).
[CrossRef]

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev.128(2), 606–622 (1962).
[CrossRef]

Bonnet, C.

Bretenaker, F.

Chang, R. K.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev.174(3), 813–822 (1968).
[CrossRef]

Chauvat, D.

Chen, W.

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, “General considerations on optical second-harmonic generation from surfaces and interfaces,” Phys. Rev. B Condens. Matter33(12), 8254–8263 (1986).
[CrossRef] [PubMed]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

de Beauregard, O.

O. de Beauregard and C. Imbert, “Quantized longitudinal and transverse shifts associated with total internal reflection,” Phys. Rev. D Part. Fields7(12), 3555–3563 (1973).
[CrossRef]

Dogariu, A.

D. Haefner, S. Sukhov, and A. Dogariu, “Spin Hall effect of light in spherical geometry,” Phys. Rev. Lett.102(12), 123903 (2009).
[CrossRef] [PubMed]

A. Dogariu and C. Schwartz, “Conservation of angular momentum of light in single scattering,” Opt. Express14(18), 8425–8433 (2006).
[CrossRef] [PubMed]

Dutriaux, L.

Dutta Gupta, S.

M. Kumari and S. Dutta Gupta, “Positive and negative Giant Goos--Hänchen shift in a Near-symmetric layered medium for illumination from opposite ends,” Opt. Commun.285(5), 617–620 (2012).
[CrossRef]

Eliel, E. R.

Emile, O.

Fan, J.

Fedorov, F. I.

F. I. Fedorov, “K teorii polnovo otrazenija,” Dokl. Akad. Nauk. SSR105, 465 (1955).

Giles, C. L.

W. J. Wild and C. L. Giles, “Goos-Hänchen shifts from absorbing media,” Phys. Rev. A25(4), 2099–2101 (1982).
[CrossRef]

Goos, F.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. (Berlin)436(7-8), 333–346 (1947).
[CrossRef]

Gorodetski, Y.

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett.101(4), 043903 (2008).
[CrossRef] [PubMed]

Guyot-Sionnest, P.

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, “General considerations on optical second-harmonic generation from surfaces and interfaces,” Phys. Rev. B Condens. Matter33(12), 8254–8263 (1986).
[CrossRef] [PubMed]

Haefner, D.

D. Haefner, S. Sukhov, and A. Dogariu, “Spin Hall effect of light in spherical geometry,” Phys. Rev. Lett.102(12), 123903 (2009).
[CrossRef] [PubMed]

Hänchen, H.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. (Berlin)436(7-8), 333–346 (1947).
[CrossRef]

Hasman, E.

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett.101(4), 043903 (2008).
[CrossRef] [PubMed]

He, J.

He, S.

Hermosa, N.

Hesselink, L.

X. Yin and L. Hesselink, “Goos-Hänchen shift surface plasmon resonance sensor,” Appl. Phys. Lett.89(26), 261108 (2006).
[CrossRef]

Horowitz, B. R.

Hosten, O.

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science319(5864), 787–790 (2008).
[CrossRef] [PubMed]

Imbert, C.

O. de Beauregard and C. Imbert, “Quantized longitudinal and transverse shifts associated with total internal reflection,” Phys. Rev. D Part. Fields7(12), 3555–3563 (1973).
[CrossRef]

C. Imbert, “Calculation and experimental proof of the transverse shift Induced by total internal reflection of a circularly polarized light beam,” Phys. Rev. D Part. Fields5(4), 787–796 (1972).
[CrossRef]

Jha, S. S.

G. S. Agarwal and S. S. Jha, “Surface-enhanced second-harmonic generation at a metallic grating,” Phys. Rev. B26(2), 482–496 (1982).
[CrossRef]

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev.174(3), 813–822 (1968).
[CrossRef]

S. S. Jha, “Theory of optical harmonic generation at a metal surface,” Phys. Rev.140(6A), A2020–A2030 (1965).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Kleiner, V.

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett.101(4), 043903 (2008).
[CrossRef] [PubMed]

Köhler, W.

Kumari, M.

M. Kumari and S. Dutta Gupta, “Positive and negative Giant Goos--Hänchen shift in a Near-symmetric layered medium for illumination from opposite ends,” Opt. Commun.285(5), 617–620 (2012).
[CrossRef]

Kwiat, P.

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science319(5864), 787–790 (2008).
[CrossRef] [PubMed]

Le Floch, A.

Lee, C. H.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev.174(3), 813–822 (1968).
[CrossRef]

Li, C. F.

C. F. Li, “Unified theory for Goos-Haenchen and Imbert-Fedorov effects,” Phys. Rev. A76(1), 013811 (2007).
[CrossRef]

Lu, Z. H.

Mendoza, B. S.

B. S. Mendoza and W. L. Mochán, “Exactly solvable model of surface second-harmonic generation,” Phys. Rev. B Condens. Matter53(8), 4999–5006 (1996).
[CrossRef] [PubMed]

W. L. Schaich and B. S. Mendoza, “simple model of second-harmonic generation,” Phys. Rev. B Condens. Matter45(24), 14279–14292 (1992).
[CrossRef] [PubMed]

Merano, M.

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics3(6), 337–340 (2009).
[CrossRef]

M. Merano, A. Aiello, G. W. ’t Hooft, M. P. van Exter, E. R. Eliel, and J. P. Woerdman, “Observation of Goos-Hänchen shifts in metallic reflection,” Opt. Express15(24), 15928–15934 (2007).
[CrossRef] [PubMed]

Mochán, W. L.

B. S. Mendoza and W. L. Mochán, “Exactly solvable model of surface second-harmonic generation,” Phys. Rev. B Condens. Matter53(8), 4999–5006 (1996).
[CrossRef] [PubMed]

Moss, D. J.

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B Condens. Matter35(3), 1129–1141 (1987).
[CrossRef] [PubMed]

Niv, A.

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett.101(4), 043903 (2008).
[CrossRef] [PubMed]

Nugrowati, A. M.

Padgett, M. J.

Pershan, P. S.

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev.128(2), 606–622 (1962).
[CrossRef]

Schaich, W. L.

W. L. Schaich and B. S. Mendoza, “simple model of second-harmonic generation,” Phys. Rev. B Condens. Matter45(24), 14279–14292 (1992).
[CrossRef] [PubMed]

Schwartz, C.

Schwefel, H. G. L.

Shen, Y. R.

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, “General considerations on optical second-harmonic generation from surfaces and interfaces,” Phys. Rev. B Condens. Matter33(12), 8254–8263 (1986).
[CrossRef] [PubMed]

Sipe, J. E.

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B Condens. Matter35(3), 1129–1141 (1987).
[CrossRef] [PubMed]

Sukhov, S.

D. Haefner, S. Sukhov, and A. Dogariu, “Spin Hall effect of light in spherical geometry,” Phys. Rev. Lett.102(12), 123903 (2009).
[CrossRef] [PubMed]

Tamir, T.

van Driel, H. M.

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B Condens. Matter35(3), 1129–1141 (1987).
[CrossRef] [PubMed]

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. Photonics3(6), 337–340 (2009).
[CrossRef]

M. Merano, A. Aiello, G. W. ’t Hooft, M. P. van Exter, E. R. Eliel, and J. P. Woerdman, “Observation of Goos-Hänchen shifts in metallic reflection,” Opt. Express15(24), 15928–15934 (2007).
[CrossRef] [PubMed]

Wang, L. J.

Wild, W. J.

W. J. Wild and C. L. Giles, “Goos-Hänchen shifts from absorbing media,” Phys. Rev. A25(4), 2099–2101 (1982).
[CrossRef]

Woerdman, J. P.

Yao, A. M.

Yi, J.

Yin, X.

X. Yin and L. Hesselink, “Goos-Hänchen shift surface plasmon resonance sensor,” Appl. Phys. Lett.89(26), 261108 (2006).
[CrossRef]

Adv. Opt. Photon.

Ann. Phys. (Berlin)

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. (Berlin)436(7-8), 333–346 (1947).
[CrossRef]

K. Artmann, “Berechnung der Seitenversetzung des totalreflektierten Strahles,” Ann. Phys. (Berlin)437(1-2), 87–102 (1948).
[CrossRef]

Appl. Phys. Lett.

X. Yin and L. Hesselink, “Goos-Hänchen shift surface plasmon resonance sensor,” Appl. Phys. Lett.89(26), 261108 (2006).
[CrossRef]

Dokl. Akad. Nauk. SSR

F. I. Fedorov, “K teorii polnovo otrazenija,” Dokl. Akad. Nauk. SSR105, 465 (1955).

J. Opt. Soc. Am.

Nat. Photonics

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics3(6), 337–340 (2009).
[CrossRef]

Opt. Commun.

M. Kumari and S. Dutta Gupta, “Positive and negative Giant Goos--Hänchen shift in a Near-symmetric layered medium for illumination from opposite ends,” Opt. Commun.285(5), 617–620 (2012).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev.

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev.128(2), 606–622 (1962).
[CrossRef]

S. S. Jha, “Theory of optical harmonic generation at a metal surface,” Phys. Rev.140(6A), A2020–A2030 (1965).
[CrossRef]

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion symmetry,” Phys. Rev.174(3), 813–822 (1968).
[CrossRef]

Phys. Rev. A

C. F. Li, “Unified theory for Goos-Haenchen and Imbert-Fedorov effects,” Phys. Rev. A76(1), 013811 (2007).
[CrossRef]

W. J. Wild and C. L. Giles, “Goos-Hänchen shifts from absorbing media,” Phys. Rev. A25(4), 2099–2101 (1982).
[CrossRef]

Phys. Rev. B

G. S. Agarwal and S. S. Jha, “Surface-enhanced second-harmonic generation at a metallic grating,” Phys. Rev. B26(2), 482–496 (1982).
[CrossRef]

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Phys. Rev. B Condens. Matter

J. E. Sipe, D. J. Moss, and H. M. van Driel, “Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals,” Phys. Rev. B Condens. Matter35(3), 1129–1141 (1987).
[CrossRef] [PubMed]

W. L. Schaich and B. S. Mendoza, “simple model of second-harmonic generation,” Phys. Rev. B Condens. Matter45(24), 14279–14292 (1992).
[CrossRef] [PubMed]

B. S. Mendoza and W. L. Mochán, “Exactly solvable model of surface second-harmonic generation,” Phys. Rev. B Condens. Matter53(8), 4999–5006 (1996).
[CrossRef] [PubMed]

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, “General considerations on optical second-harmonic generation from surfaces and interfaces,” Phys. Rev. B Condens. Matter33(12), 8254–8263 (1986).
[CrossRef] [PubMed]

Phys. Rev. D Part. Fields

C. Imbert, “Calculation and experimental proof of the transverse shift Induced by total internal reflection of a circularly polarized light beam,” Phys. Rev. D Part. Fields5(4), 787–796 (1972).
[CrossRef]

O. de Beauregard and C. Imbert, “Quantized longitudinal and transverse shifts associated with total internal reflection,” Phys. Rev. D Part. Fields7(12), 3555–3563 (1973).
[CrossRef]

Phys. Rev. Lett.

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett.101(4), 043903 (2008).
[CrossRef] [PubMed]

D. Haefner, S. Sukhov, and A. Dogariu, “Spin Hall effect of light in spherical geometry,” Phys. Rev. Lett.102(12), 123903 (2009).
[CrossRef] [PubMed]

Science

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science319(5864), 787–790 (2008).
[CrossRef] [PubMed]

Other

L. Allen, S. M. Barnett, and M. J. Padgett, eds., Optical Angular Momentum (Taylor & Francis, 2003).

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Figures (3)

Fig. 1
Fig. 1

Shown is the geometry of the problem involving reflection of a light beam off the surface of a metal with the quantities of interest. We consider a beam propagating in the x-z plane, without loss of generality, i.e. the central value of ky = 0.

Fig. 2
Fig. 2

The GH Shift D = <x>cos(θ) of the fundamental beam of wavelength 826 nm in reflection. Red corresponds to an input polarization normal to the xz plane, and black corresponds to polarization parallel to the xz plane. For collimated beams of light, these correspond to s and p polarization. Solid lines correspond to those predicted by Artmann’s formula. Dashed line is y = 0 to guide eye.

Fig. 3
Fig. 3

Predicted GH shift D = <x>cos(θ) for the reflected fundamental (1600nm) and second harmonic light (800 nm) which is generated at the metal surface. Also shown is the shift for fundamental 800nm. The data points are obtained by numerically integrating Eq. (16). Inset shows the zoomed part between 60 and 90 degrees.

Equations (15)

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E I = d k x d k y exp(ik·r ) I ( k x , k y )
k x 2 + k y 2 + k z 2 = ( ω/c ) 2 ε
E I | z=0 = d k x d k y exp(i k x x+i k y y ) I ( k x , k y )
E R (ρ)= d k x d k y exp(iκ·ρ ) R ( k x , k y )
E T (ρ)= d k x d k y exp(iκ·ρ ) T ( k x , k y )
ρ = dx dy[ E * R (ρ) E R (ρ)ρ ] dx dy[ E * R (ρ) E R (ρ) ] = d k x d k y α [ * Rα ( k x , k y ) κ Rα ( k x , k y ) ] dx dy[ * R ( k x , k y ) R ( k x , k y ) ] ;α=s,p
x =i d k x d k y [ Rs * d d k x Rs + Rp * d d k x Rp ] dx dy[ | Rs | 2 + | Rp | 2 ]
P NL (r,2ω)=γ[ E 2 (r,ω)]+βE(r,ω)·E(r,ω)
F R (r)= d k x d k y exp(i Q R ·r ) R ( k x , k y )
F T (r)= d k x d k y exp(iQ·r ) T ( k x , k y )
Rs = 1 κ(Λ Λ R ) z[ Λ(κ×A)+(κ×(z×B) ]
Rp = Q R κ( Λ Q R 2 Λ R Q 2 ) [ Λκ(z×B)+ Q 2 (κA) ]
A= 8πγi ε(2ω) ( T · T )κ
B= 16πi ω 2 β c 2 ( ε(ω)1 ) Tz ( z× T )
x = i 2 d k x d k y [ Rs * d d k x Rs + Rp * d d k x Rp ] dx dy[ | Rs | 2 + | Rp | 2 ]

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