Abstract

Recent studies on surface reflection illustrate how light beams can be laterally shifted from the position predicted by geometrical optics, the so called Goos-Hänchen effect. In antiferromagnets this shifts can be controlled with an external magnetic field. We show that a configuration in which spins cant in response to applied magnetic fields enhance possibilities of field controlled shifts. Moreover, we show that nonreciprocal displacements are possible, for both oblique and normal incidence, due to inherent nonreciprocity of the polariton phase with respect to the propagation direction. In the absence of an external field, reciprocal displacements occur.

© 2014 Optical Society of America

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References

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  1. R. E. Camley, “Nonreciprocal surface modes,” Surf. Sci. Rep. 7, 103–188 (1987).
    [Crossref]
  2. N. S. Almeida and D. L. Mills, “Dynamical response of antiferromagnets in an oblique magnetic field: application to surface magnons,” Phys. Rev. B 37, 3400 (1988).
    [Crossref]
  3. R. L. Stamps, B. L. Johnson, and R. E. Camley, “Nonreciprocal reflection from semi-infinite antiferromagnets,” Phys. Rev. B 43, 3626 (1991).
    [Crossref]
  4. K. Abraha and D. R. Tilley, “Theory of far infrared properties of magnetic surfaces, films and superlattices,” Surf. Sci. Rep. 24, 129 (1996).
    [Crossref]
  5. T. Dumelow and R. E. Camley, “Nonreciprocal reflection of infrared radiation from structures with antiferromagnets and dielectrics,” Phys. Rev. B 54, 12232 (1996).
    [Crossref]
  6. T. Dumelow, R. E. Camley, K. Abraha, and D. R. Tilley, “Nonreciprocal phase behavior in reflection of electromagnetic waves from magnetic materials,” Phys. Rev. B 58, 897 (1998).
    [Crossref]
  7. L. Remer, B. Lüthi, H. Sauer, R. Geick, and R. E. Camley, “Nonreciprocal optical reflection of the uniaxial antiferromagnet MnF2,” Phys. Rev. Lett.. 56, 2752 (1986).
    [Crossref] [PubMed]
  8. D. E. Brown, T. Dumelow, T. J. Parker, K. Abraha, and D. R. Tilley, “Nonreciprocal reflection by magnons in FeF2: a high resolution study,” Phys. Rev. B 49, 12266 (1994).
    [Crossref]
  9. K. Abraha, D. E. Brown, T. Dumelow, T. J. Parker, and D. R. Tilley, “Oblique incidence far-infrared reflectivity study of the uniaxial antiferromagnet FeF2,” Phys. Rev. B 50, 6808 (1994).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  13. F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436(7–8), 33–46 (1947).
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  15. Miri, A. Naqavi, A. Khavasi, K. Mehrany, S. Khorasani, and B. Rashidian, “Geometrical approach in physical understanding of the Goos-Haenchen shift in one- and two-dimensional periodic structures,” Opt. Lett. 332940–2942 (2008).
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    [Crossref]
  18. X. -Q Jiang, Z. W Lu, and X. -D Sun, “Control of direction of Goos-Hänchen shift on reflection from a weakly absorbing medium,” Optik 122, 2140–2142 (2011).
    [Crossref]
  19. B. Zhao and L. Gao, “Temperature-dependent Goos-Hänchen shift on the interface of metal/dielectric composites,” Opt. Express 17, 21433–21441 (2009).
    [Crossref] [PubMed]
  20. D. Gao and L. Gao, “Goos-Hänchen shift of the reflection from nonlinear nanocomposites with electric field tunability,” Appl. Phys. Lett. 97, 041903 (2010).
    [Crossref]
  21. W. J. Wild and C. L. Giles, “Goos-Hänchen shifts from absorbing media,” Phys. Rev. A 25, 2099 (1982).
    [Crossref]
  22. P. T Leung, Z.W Chen, and H. -P Chiang, “Large negative Goos-Hänchen shift at metal surfaces,” Opt. Commun. 276, 206–208 (2007).
    [Crossref]
  23. 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. Express 15, 15928–15934 (2007).
    [Crossref] [PubMed]
  24. R. Macêdo and T. Dumelow, “Beam shifts on reflection of electromagnetic radiation off anisotropic crystals at optic phonon frequencies,” Journal of Optics 15, 014013 (2013).
    [Crossref]
  25. F. Lima, T. Dumelow, J. A. P. da Costa, and E. L. Albuquerque, “Lateral shift on normal incidence reflection off an antiferromagnet,” Europhys. Lett. 83, 17003 (2008).
    [Crossref]
  26. F. Lima, T. Dumelow, J. A. P. da Costa, and E. L. Albuquerque, “Power flow associated with the Goos-Hänchen shift of a normally incident electromagnetic beam reflected off an antiferromagnet,” Phys. Rev. B 79155124 (2009).
    [Crossref]
  27. D. L. Mills and E. Burstein, “Polaritons: the electromagnetic modes of media,” Rep. Prog. Phys. 37, 817 (1974).
    [Crossref]
  28. M. McGuirk and C. K. Carniglia, “An angular spectrum approach to the Goos-Hänchen shift,” J. Opt. Soc. Am.. 67, 103–107 (1977).
    [Crossref]
  29. K. Artmann, “Berechnung der seitenversetzung des totalrelektierten strahles,” Ann. Phys. 437, 87–102 (1948).
    [Crossref]
  30. T. Dumelow and M. C. Oliveros, “Continuum model of confined magnon polaritons in superlattices of antiferromagnets,” Phys. Rev. B 55, 994 (1997).
    [Crossref]
  31. R. Macêdo and T. Dumelow, “Tunable all-angle negative refraction using antiferromagnets,” Phys. Rev. B 89, 035135 (2014).
    [Crossref]
  32. R. Macêdo, R. Rodrigues da Silva, T. Dumelow, and J. A. P. da Costa, “MgF2 as a material exhibiting all-angle negative refraction and subwavelength imaging due to the phonon response in the far infrared,” Opt. Commun. 31094–99 (2014).
    [Crossref]

2014 (2)

R. Macêdo and T. Dumelow, “Tunable all-angle negative refraction using antiferromagnets,” Phys. Rev. B 89, 035135 (2014).
[Crossref]

R. Macêdo, R. Rodrigues da Silva, T. Dumelow, and J. A. P. da Costa, “MgF2 as a material exhibiting all-angle negative refraction and subwavelength imaging due to the phonon response in the far infrared,” Opt. Commun. 31094–99 (2014).
[Crossref]

2013 (1)

R. Macêdo and T. Dumelow, “Beam shifts on reflection of electromagnetic radiation off anisotropic crystals at optic phonon frequencies,” Journal of Optics 15, 014013 (2013).
[Crossref]

2012 (1)

Y. Huang, B. Zhao, and L. Gao, “Goos-Hänchen shift of the reflected wave through an anisotropic metamaterial containing metal/dielectric nanocomposites,” J. Opt. Soc. Am. 291436–1444 (2012)
[Crossref]

2011 (2)

X. -Q Jiang, Z. W Lu, and X. -D Sun, “Control of direction of Goos-Hänchen shift on reflection from a weakly absorbing medium,” Optik 122, 2140–2142 (2011).
[Crossref]

F. Lima, T. Dumelow, E. L. Albuquerque, and J. A. P. da Costa, “Nonreciprocity in the Goos–Hänchen shift on oblique incidence reflection off antiferromagnets,” J. Opt. Soc. Am. B 28, 306–313 (2011).
[Crossref]

2010 (1)

D. Gao and L. Gao, “Goos-Hänchen shift of the reflection from nonlinear nanocomposites with electric field tunability,” Appl. Phys. Lett. 97, 041903 (2010).
[Crossref]

2009 (2)

B. Zhao and L. Gao, “Temperature-dependent Goos-Hänchen shift on the interface of metal/dielectric composites,” Opt. Express 17, 21433–21441 (2009).
[Crossref] [PubMed]

F. Lima, T. Dumelow, J. A. P. da Costa, and E. L. Albuquerque, “Power flow associated with the Goos-Hänchen shift of a normally incident electromagnetic beam reflected off an antiferromagnet,” Phys. Rev. B 79155124 (2009).
[Crossref]

2008 (2)

2007 (2)

1998 (1)

T. Dumelow, R. E. Camley, K. Abraha, and D. R. Tilley, “Nonreciprocal phase behavior in reflection of electromagnetic waves from magnetic materials,” Phys. Rev. B 58, 897 (1998).
[Crossref]

1997 (1)

T. Dumelow and M. C. Oliveros, “Continuum model of confined magnon polaritons in superlattices of antiferromagnets,” Phys. Rev. B 55, 994 (1997).
[Crossref]

1996 (2)

K. Abraha and D. R. Tilley, “Theory of far infrared properties of magnetic surfaces, films and superlattices,” Surf. Sci. Rep. 24, 129 (1996).
[Crossref]

T. Dumelow and R. E. Camley, “Nonreciprocal reflection of infrared radiation from structures with antiferromagnets and dielectrics,” Phys. Rev. B 54, 12232 (1996).
[Crossref]

1995 (1)

M. R. F. Jensen, T. J. Parker, Kamsul Abraha, and D. R. Tilley, “Experimental observation of magnetic surface polaritons in FeF2 by attenuated total reflection’,’ Phys. Rev. Lett. 75, 3756 (1995).
[Crossref] [PubMed]

1994 (2)

D. E. Brown, T. Dumelow, T. J. Parker, K. Abraha, and D. R. Tilley, “Nonreciprocal reflection by magnons in FeF2: a high resolution study,” Phys. Rev. B 49, 12266 (1994).
[Crossref]

K. Abraha, D. E. Brown, T. Dumelow, T. J. Parker, and D. R. Tilley, “Oblique incidence far-infrared reflectivity study of the uniaxial antiferromagnet FeF2,” Phys. Rev. B 50, 6808 (1994).
[Crossref]

1991 (1)

R. L. Stamps, B. L. Johnson, and R. E. Camley, “Nonreciprocal reflection from semi-infinite antiferromagnets,” Phys. Rev. B 43, 3626 (1991).
[Crossref]

1988 (1)

N. S. Almeida and D. L. Mills, “Dynamical response of antiferromagnets in an oblique magnetic field: application to surface magnons,” Phys. Rev. B 37, 3400 (1988).
[Crossref]

1987 (1)

R. E. Camley, “Nonreciprocal surface modes,” Surf. Sci. Rep. 7, 103–188 (1987).
[Crossref]

1986 (1)

L. Remer, B. Lüthi, H. Sauer, R. Geick, and R. E. Camley, “Nonreciprocal optical reflection of the uniaxial antiferromagnet MnF2,” Phys. Rev. Lett.. 56, 2752 (1986).
[Crossref] [PubMed]

1982 (1)

W. J. Wild and C. L. Giles, “Goos-Hänchen shifts from absorbing media,” Phys. Rev. A 25, 2099 (1982).
[Crossref]

1977 (1)

M. McGuirk and C. K. Carniglia, “An angular spectrum approach to the Goos-Hänchen shift,” J. Opt. Soc. Am.. 67, 103–107 (1977).
[Crossref]

1974 (1)

D. L. Mills and E. Burstein, “Polaritons: the electromagnetic modes of media,” Rep. Prog. Phys. 37, 817 (1974).
[Crossref]

1971 (1)

1970 (1)

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect,” Optik 32, 116 (1970).

1948 (1)

K. Artmann, “Berechnung der seitenversetzung des totalrelektierten 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(7–8), 33–46 (1947).
[Crossref]

’t Hooft, G. W

Abraha, K.

T. Dumelow, R. E. Camley, K. Abraha, and D. R. Tilley, “Nonreciprocal phase behavior in reflection of electromagnetic waves from magnetic materials,” Phys. Rev. B 58, 897 (1998).
[Crossref]

K. Abraha and D. R. Tilley, “Theory of far infrared properties of magnetic surfaces, films and superlattices,” Surf. Sci. Rep. 24, 129 (1996).
[Crossref]

K. Abraha, D. E. Brown, T. Dumelow, T. J. Parker, and D. R. Tilley, “Oblique incidence far-infrared reflectivity study of the uniaxial antiferromagnet FeF2,” Phys. Rev. B 50, 6808 (1994).
[Crossref]

D. E. Brown, T. Dumelow, T. J. Parker, K. Abraha, and D. R. Tilley, “Nonreciprocal reflection by magnons in FeF2: a high resolution study,” Phys. Rev. B 49, 12266 (1994).
[Crossref]

Abraha, Kamsul

M. R. F. Jensen, T. J. Parker, Kamsul Abraha, and D. R. Tilley, “Experimental observation of magnetic surface polaritons in FeF2 by attenuated total reflection’,’ Phys. Rev. Lett. 75, 3756 (1995).
[Crossref] [PubMed]

Aiello, A.

Albuquerque, E. L.

F. Lima, T. Dumelow, E. L. Albuquerque, and J. A. P. da Costa, “Nonreciprocity in the Goos–Hänchen shift on oblique incidence reflection off antiferromagnets,” J. Opt. Soc. Am. B 28, 306–313 (2011).
[Crossref]

F. Lima, T. Dumelow, J. A. P. da Costa, and E. L. Albuquerque, “Power flow associated with the Goos-Hänchen shift of a normally incident electromagnetic beam reflected off an antiferromagnet,” Phys. Rev. B 79155124 (2009).
[Crossref]

F. Lima, T. Dumelow, J. A. P. da Costa, and E. L. Albuquerque, “Lateral shift on normal incidence reflection off an antiferromagnet,” Europhys. Lett. 83, 17003 (2008).
[Crossref]

Almeida, N. S.

N. S. Almeida and D. L. Mills, “Dynamical response of antiferromagnets in an oblique magnetic field: application to surface magnons,” Phys. Rev. B 37, 3400 (1988).
[Crossref]

Artmann, K.

K. Artmann, “Berechnung der seitenversetzung des totalrelektierten strahles,” Ann. Phys. 437, 87–102 (1948).
[Crossref]

Bertoni, H. L.

Brown, D. E.

K. Abraha, D. E. Brown, T. Dumelow, T. J. Parker, and D. R. Tilley, “Oblique incidence far-infrared reflectivity study of the uniaxial antiferromagnet FeF2,” Phys. Rev. B 50, 6808 (1994).
[Crossref]

D. E. Brown, T. Dumelow, T. J. Parker, K. Abraha, and D. R. Tilley, “Nonreciprocal reflection by magnons in FeF2: a high resolution study,” Phys. Rev. B 49, 12266 (1994).
[Crossref]

Burstein, E.

D. L. Mills and E. Burstein, “Polaritons: the electromagnetic modes of media,” Rep. Prog. Phys. 37, 817 (1974).
[Crossref]

Camley, R. E.

T. Dumelow, R. E. Camley, K. Abraha, and D. R. Tilley, “Nonreciprocal phase behavior in reflection of electromagnetic waves from magnetic materials,” Phys. Rev. B 58, 897 (1998).
[Crossref]

T. Dumelow and R. E. Camley, “Nonreciprocal reflection of infrared radiation from structures with antiferromagnets and dielectrics,” Phys. Rev. B 54, 12232 (1996).
[Crossref]

R. L. Stamps, B. L. Johnson, and R. E. Camley, “Nonreciprocal reflection from semi-infinite antiferromagnets,” Phys. Rev. B 43, 3626 (1991).
[Crossref]

R. E. Camley, “Nonreciprocal surface modes,” Surf. Sci. Rep. 7, 103–188 (1987).
[Crossref]

L. Remer, B. Lüthi, H. Sauer, R. Geick, and R. E. Camley, “Nonreciprocal optical reflection of the uniaxial antiferromagnet MnF2,” Phys. Rev. Lett.. 56, 2752 (1986).
[Crossref] [PubMed]

Carniglia, C. K.

M. McGuirk and C. K. Carniglia, “An angular spectrum approach to the Goos-Hänchen shift,” J. Opt. Soc. Am.. 67, 103–107 (1977).
[Crossref]

Chen, Z.W

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

da Costa, J. A. P.

R. Macêdo, R. Rodrigues da Silva, T. Dumelow, and J. A. P. da Costa, “MgF2 as a material exhibiting all-angle negative refraction and subwavelength imaging due to the phonon response in the far infrared,” Opt. Commun. 31094–99 (2014).
[Crossref]

F. Lima, T. Dumelow, E. L. Albuquerque, and J. A. P. da Costa, “Nonreciprocity in the Goos–Hänchen shift on oblique incidence reflection off antiferromagnets,” J. Opt. Soc. Am. B 28, 306–313 (2011).
[Crossref]

F. Lima, T. Dumelow, J. A. P. da Costa, and E. L. Albuquerque, “Power flow associated with the Goos-Hänchen shift of a normally incident electromagnetic beam reflected off an antiferromagnet,” Phys. Rev. B 79155124 (2009).
[Crossref]

F. Lima, T. Dumelow, J. A. P. da Costa, and E. L. Albuquerque, “Lateral shift on normal incidence reflection off an antiferromagnet,” Europhys. Lett. 83, 17003 (2008).
[Crossref]

Dumelow, T.

R. Macêdo and T. Dumelow, “Tunable all-angle negative refraction using antiferromagnets,” Phys. Rev. B 89, 035135 (2014).
[Crossref]

R. Macêdo, R. Rodrigues da Silva, T. Dumelow, and J. A. P. da Costa, “MgF2 as a material exhibiting all-angle negative refraction and subwavelength imaging due to the phonon response in the far infrared,” Opt. Commun. 31094–99 (2014).
[Crossref]

R. Macêdo and T. Dumelow, “Beam shifts on reflection of electromagnetic radiation off anisotropic crystals at optic phonon frequencies,” Journal of Optics 15, 014013 (2013).
[Crossref]

F. Lima, T. Dumelow, E. L. Albuquerque, and J. A. P. da Costa, “Nonreciprocity in the Goos–Hänchen shift on oblique incidence reflection off antiferromagnets,” J. Opt. Soc. Am. B 28, 306–313 (2011).
[Crossref]

F. Lima, T. Dumelow, J. A. P. da Costa, and E. L. Albuquerque, “Power flow associated with the Goos-Hänchen shift of a normally incident electromagnetic beam reflected off an antiferromagnet,” Phys. Rev. B 79155124 (2009).
[Crossref]

F. Lima, T. Dumelow, J. A. P. da Costa, and E. L. Albuquerque, “Lateral shift on normal incidence reflection off an antiferromagnet,” Europhys. Lett. 83, 17003 (2008).
[Crossref]

T. Dumelow, R. E. Camley, K. Abraha, and D. R. Tilley, “Nonreciprocal phase behavior in reflection of electromagnetic waves from magnetic materials,” Phys. Rev. B 58, 897 (1998).
[Crossref]

T. Dumelow and M. C. Oliveros, “Continuum model of confined magnon polaritons in superlattices of antiferromagnets,” Phys. Rev. B 55, 994 (1997).
[Crossref]

T. Dumelow and R. E. Camley, “Nonreciprocal reflection of infrared radiation from structures with antiferromagnets and dielectrics,” Phys. Rev. B 54, 12232 (1996).
[Crossref]

D. E. Brown, T. Dumelow, T. J. Parker, K. Abraha, and D. R. Tilley, “Nonreciprocal reflection by magnons in FeF2: a high resolution study,” Phys. Rev. B 49, 12266 (1994).
[Crossref]

K. Abraha, D. E. Brown, T. Dumelow, T. J. Parker, and D. R. Tilley, “Oblique incidence far-infrared reflectivity study of the uniaxial antiferromagnet FeF2,” Phys. Rev. B 50, 6808 (1994).
[Crossref]

Eliel, E. R

Gao, D.

D. Gao and L. Gao, “Goos-Hänchen shift of the reflection from nonlinear nanocomposites with electric field tunability,” Appl. Phys. Lett. 97, 041903 (2010).
[Crossref]

Gao, L.

Y. Huang, B. Zhao, and L. Gao, “Goos-Hänchen shift of the reflected wave through an anisotropic metamaterial containing metal/dielectric nanocomposites,” J. Opt. Soc. Am. 291436–1444 (2012)
[Crossref]

D. Gao and L. Gao, “Goos-Hänchen shift of the reflection from nonlinear nanocomposites with electric field tunability,” Appl. Phys. Lett. 97, 041903 (2010).
[Crossref]

B. Zhao and L. Gao, “Temperature-dependent Goos-Hänchen shift on the interface of metal/dielectric composites,” Opt. Express 17, 21433–21441 (2009).
[Crossref] [PubMed]

Geick, R.

L. Remer, B. Lüthi, H. Sauer, R. Geick, and R. E. Camley, “Nonreciprocal optical reflection of the uniaxial antiferromagnet MnF2,” Phys. Rev. Lett.. 56, 2752 (1986).
[Crossref] [PubMed]

Giles, C. L.

W. J. Wild and C. L. Giles, “Goos-Hänchen shifts from absorbing media,” Phys. Rev. A 25, 2099 (1982).
[Crossref]

Goos, F.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436(7–8), 33–46 (1947).
[Crossref]

Hänchen, H.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436(7–8), 33–46 (1947).
[Crossref]

Huang, Y.

Y. Huang, B. Zhao, and L. Gao, “Goos-Hänchen shift of the reflected wave through an anisotropic metamaterial containing metal/dielectric nanocomposites,” J. Opt. Soc. Am. 291436–1444 (2012)
[Crossref]

Jensen, M. R. F.

M. R. F. Jensen, T. J. Parker, Kamsul Abraha, and D. R. Tilley, “Experimental observation of magnetic surface polaritons in FeF2 by attenuated total reflection’,’ Phys. Rev. Lett. 75, 3756 (1995).
[Crossref] [PubMed]

Jiang, X. -Q

X. -Q Jiang, Z. W Lu, and X. -D Sun, “Control of direction of Goos-Hänchen shift on reflection from a weakly absorbing medium,” Optik 122, 2140–2142 (2011).
[Crossref]

Johnson, B. L.

R. L. Stamps, B. L. Johnson, and R. E. Camley, “Nonreciprocal reflection from semi-infinite antiferromagnets,” Phys. Rev. B 43, 3626 (1991).
[Crossref]

Khavasi, A.

Khorasani, S.

Leung, P. T

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

Lima, F.

F. Lima, T. Dumelow, E. L. Albuquerque, and J. A. P. da Costa, “Nonreciprocity in the Goos–Hänchen shift on oblique incidence reflection off antiferromagnets,” J. Opt. Soc. Am. B 28, 306–313 (2011).
[Crossref]

F. Lima, T. Dumelow, J. A. P. da Costa, and E. L. Albuquerque, “Power flow associated with the Goos-Hänchen shift of a normally incident electromagnetic beam reflected off an antiferromagnet,” Phys. Rev. B 79155124 (2009).
[Crossref]

F. Lima, T. Dumelow, J. A. P. da Costa, and E. L. Albuquerque, “Lateral shift on normal incidence reflection off an antiferromagnet,” Europhys. Lett. 83, 17003 (2008).
[Crossref]

Lotsch, H. K. V.

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect,” Optik 32, 116 (1970).

Lu, Z. W

X. -Q Jiang, Z. W Lu, and X. -D Sun, “Control of direction of Goos-Hänchen shift on reflection from a weakly absorbing medium,” Optik 122, 2140–2142 (2011).
[Crossref]

Lüthi, B.

L. Remer, B. Lüthi, H. Sauer, R. Geick, and R. E. Camley, “Nonreciprocal optical reflection of the uniaxial antiferromagnet MnF2,” Phys. Rev. Lett.. 56, 2752 (1986).
[Crossref] [PubMed]

Macêdo, R.

R. Macêdo and T. Dumelow, “Tunable all-angle negative refraction using antiferromagnets,” Phys. Rev. B 89, 035135 (2014).
[Crossref]

R. Macêdo, R. Rodrigues da Silva, T. Dumelow, and J. A. P. da Costa, “MgF2 as a material exhibiting all-angle negative refraction and subwavelength imaging due to the phonon response in the far infrared,” Opt. Commun. 31094–99 (2014).
[Crossref]

R. Macêdo and T. Dumelow, “Beam shifts on reflection of electromagnetic radiation off anisotropic crystals at optic phonon frequencies,” Journal of Optics 15, 014013 (2013).
[Crossref]

McGuirk, M.

M. McGuirk and C. K. Carniglia, “An angular spectrum approach to the Goos-Hänchen shift,” J. Opt. Soc. Am.. 67, 103–107 (1977).
[Crossref]

Mehrany, K.

Merano, M.

Mills, D. L.

N. S. Almeida and D. L. Mills, “Dynamical response of antiferromagnets in an oblique magnetic field: application to surface magnons,” Phys. Rev. B 37, 3400 (1988).
[Crossref]

D. L. Mills and E. Burstein, “Polaritons: the electromagnetic modes of media,” Rep. Prog. Phys. 37, 817 (1974).
[Crossref]

Miri,

Naqavi, A.

Oliveros, M. C.

T. Dumelow and M. C. Oliveros, “Continuum model of confined magnon polaritons in superlattices of antiferromagnets,” Phys. Rev. B 55, 994 (1997).
[Crossref]

Parker, T. J.

M. R. F. Jensen, T. J. Parker, Kamsul Abraha, and D. R. Tilley, “Experimental observation of magnetic surface polaritons in FeF2 by attenuated total reflection’,’ Phys. Rev. Lett. 75, 3756 (1995).
[Crossref] [PubMed]

D. E. Brown, T. Dumelow, T. J. Parker, K. Abraha, and D. R. Tilley, “Nonreciprocal reflection by magnons in FeF2: a high resolution study,” Phys. Rev. B 49, 12266 (1994).
[Crossref]

K. Abraha, D. E. Brown, T. Dumelow, T. J. Parker, and D. R. Tilley, “Oblique incidence far-infrared reflectivity study of the uniaxial antiferromagnet FeF2,” Phys. Rev. B 50, 6808 (1994).
[Crossref]

Rashidian, B.

Remer, L.

L. Remer, B. Lüthi, H. Sauer, R. Geick, and R. E. Camley, “Nonreciprocal optical reflection of the uniaxial antiferromagnet MnF2,” Phys. Rev. Lett.. 56, 2752 (1986).
[Crossref] [PubMed]

Rodrigues da Silva, R.

R. Macêdo, R. Rodrigues da Silva, T. Dumelow, and J. A. P. da Costa, “MgF2 as a material exhibiting all-angle negative refraction and subwavelength imaging due to the phonon response in the far infrared,” Opt. Commun. 31094–99 (2014).
[Crossref]

Sauer, H.

L. Remer, B. Lüthi, H. Sauer, R. Geick, and R. E. Camley, “Nonreciprocal optical reflection of the uniaxial antiferromagnet MnF2,” Phys. Rev. Lett.. 56, 2752 (1986).
[Crossref] [PubMed]

Stamps, R. L.

R. L. Stamps, B. L. Johnson, and R. E. Camley, “Nonreciprocal reflection from semi-infinite antiferromagnets,” Phys. Rev. B 43, 3626 (1991).
[Crossref]

Sun, X. -D

X. -Q Jiang, Z. W Lu, and X. -D Sun, “Control of direction of Goos-Hänchen shift on reflection from a weakly absorbing medium,” Optik 122, 2140–2142 (2011).
[Crossref]

Tamir, T.

Tilley, D. R.

T. Dumelow, R. E. Camley, K. Abraha, and D. R. Tilley, “Nonreciprocal phase behavior in reflection of electromagnetic waves from magnetic materials,” Phys. Rev. B 58, 897 (1998).
[Crossref]

K. Abraha and D. R. Tilley, “Theory of far infrared properties of magnetic surfaces, films and superlattices,” Surf. Sci. Rep. 24, 129 (1996).
[Crossref]

M. R. F. Jensen, T. J. Parker, Kamsul Abraha, and D. R. Tilley, “Experimental observation of magnetic surface polaritons in FeF2 by attenuated total reflection’,’ Phys. Rev. Lett. 75, 3756 (1995).
[Crossref] [PubMed]

D. E. Brown, T. Dumelow, T. J. Parker, K. Abraha, and D. R. Tilley, “Nonreciprocal reflection by magnons in FeF2: a high resolution study,” Phys. Rev. B 49, 12266 (1994).
[Crossref]

K. Abraha, D. E. Brown, T. Dumelow, T. J. Parker, and D. R. Tilley, “Oblique incidence far-infrared reflectivity study of the uniaxial antiferromagnet FeF2,” Phys. Rev. B 50, 6808 (1994).
[Crossref]

van Exter, M. P

Wild, W. J.

W. J. Wild and C. L. Giles, “Goos-Hänchen shifts from absorbing media,” Phys. Rev. A 25, 2099 (1982).
[Crossref]

Woerdman, J. P

Zhao, B.

Y. Huang, B. Zhao, and L. Gao, “Goos-Hänchen shift of the reflected wave through an anisotropic metamaterial containing metal/dielectric nanocomposites,” J. Opt. Soc. Am. 291436–1444 (2012)
[Crossref]

B. Zhao and L. Gao, “Temperature-dependent Goos-Hänchen shift on the interface of metal/dielectric composites,” Opt. Express 17, 21433–21441 (2009).
[Crossref] [PubMed]

Ann. Phys. (2)

F. Goos and H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. 436(7–8), 33–46 (1947).
[Crossref]

K. Artmann, “Berechnung der seitenversetzung des totalrelektierten strahles,” Ann. Phys. 437, 87–102 (1948).
[Crossref]

Appl. Phys. Lett. (1)

D. Gao and L. Gao, “Goos-Hänchen shift of the reflection from nonlinear nanocomposites with electric field tunability,” Appl. Phys. Lett. 97, 041903 (2010).
[Crossref]

Europhys. Lett. (1)

F. Lima, T. Dumelow, J. A. P. da Costa, and E. L. Albuquerque, “Lateral shift on normal incidence reflection off an antiferromagnet,” Europhys. Lett. 83, 17003 (2008).
[Crossref]

J. Opt. Soc. Am. (2)

T. Tamir and H. L. Bertoni, “Lateral displacement of optical beams at multilayered and periodic structures,” J. Opt. Soc. Am. 61, 1397–1413 (1971).
[Crossref]

Y. Huang, B. Zhao, and L. Gao, “Goos-Hänchen shift of the reflected wave through an anisotropic metamaterial containing metal/dielectric nanocomposites,” J. Opt. Soc. Am. 291436–1444 (2012)
[Crossref]

J. Opt. Soc. Am. B (1)

J. Opt. Soc. Am.. (1)

M. McGuirk and C. K. Carniglia, “An angular spectrum approach to the Goos-Hänchen shift,” J. Opt. Soc. Am.. 67, 103–107 (1977).
[Crossref]

Journal of Optics (1)

R. Macêdo and T. Dumelow, “Beam shifts on reflection of electromagnetic radiation off anisotropic crystals at optic phonon frequencies,” Journal of Optics 15, 014013 (2013).
[Crossref]

Opt. Commun. (2)

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

R. Macêdo, R. Rodrigues da Silva, T. Dumelow, and J. A. P. da Costa, “MgF2 as a material exhibiting all-angle negative refraction and subwavelength imaging due to the phonon response in the far infrared,” Opt. Commun. 31094–99 (2014).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Optik (2)

X. -Q Jiang, Z. W Lu, and X. -D Sun, “Control of direction of Goos-Hänchen shift on reflection from a weakly absorbing medium,” Optik 122, 2140–2142 (2011).
[Crossref]

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect,” Optik 32, 116 (1970).

Phys. Rev. A (1)

W. J. Wild and C. L. Giles, “Goos-Hänchen shifts from absorbing media,” Phys. Rev. A 25, 2099 (1982).
[Crossref]

Phys. Rev. B (9)

F. Lima, T. Dumelow, J. A. P. da Costa, and E. L. Albuquerque, “Power flow associated with the Goos-Hänchen shift of a normally incident electromagnetic beam reflected off an antiferromagnet,” Phys. Rev. B 79155124 (2009).
[Crossref]

T. Dumelow and M. C. Oliveros, “Continuum model of confined magnon polaritons in superlattices of antiferromagnets,” Phys. Rev. B 55, 994 (1997).
[Crossref]

R. Macêdo and T. Dumelow, “Tunable all-angle negative refraction using antiferromagnets,” Phys. Rev. B 89, 035135 (2014).
[Crossref]

N. S. Almeida and D. L. Mills, “Dynamical response of antiferromagnets in an oblique magnetic field: application to surface magnons,” Phys. Rev. B 37, 3400 (1988).
[Crossref]

R. L. Stamps, B. L. Johnson, and R. E. Camley, “Nonreciprocal reflection from semi-infinite antiferromagnets,” Phys. Rev. B 43, 3626 (1991).
[Crossref]

T. Dumelow and R. E. Camley, “Nonreciprocal reflection of infrared radiation from structures with antiferromagnets and dielectrics,” Phys. Rev. B 54, 12232 (1996).
[Crossref]

T. Dumelow, R. E. Camley, K. Abraha, and D. R. Tilley, “Nonreciprocal phase behavior in reflection of electromagnetic waves from magnetic materials,” Phys. Rev. B 58, 897 (1998).
[Crossref]

D. E. Brown, T. Dumelow, T. J. Parker, K. Abraha, and D. R. Tilley, “Nonreciprocal reflection by magnons in FeF2: a high resolution study,” Phys. Rev. B 49, 12266 (1994).
[Crossref]

K. Abraha, D. E. Brown, T. Dumelow, T. J. Parker, and D. R. Tilley, “Oblique incidence far-infrared reflectivity study of the uniaxial antiferromagnet FeF2,” Phys. Rev. B 50, 6808 (1994).
[Crossref]

Phys. Rev. Lett. (1)

M. R. F. Jensen, T. J. Parker, Kamsul Abraha, and D. R. Tilley, “Experimental observation of magnetic surface polaritons in FeF2 by attenuated total reflection’,’ Phys. Rev. Lett. 75, 3756 (1995).
[Crossref] [PubMed]

Phys. Rev. Lett.. (1)

L. Remer, B. Lüthi, H. Sauer, R. Geick, and R. E. Camley, “Nonreciprocal optical reflection of the uniaxial antiferromagnet MnF2,” Phys. Rev. Lett.. 56, 2752 (1986).
[Crossref] [PubMed]

Rep. Prog. Phys. (1)

D. L. Mills and E. Burstein, “Polaritons: the electromagnetic modes of media,” Rep. Prog. Phys. 37, 817 (1974).
[Crossref]

Surf. Sci. Rep. (2)

K. Abraha and D. R. Tilley, “Theory of far infrared properties of magnetic surfaces, films and superlattices,” Surf. Sci. Rep. 24, 129 (1996).
[Crossref]

R. E. Camley, “Nonreciprocal surface modes,” Surf. Sci. Rep. 7, 103–188 (1987).
[Crossref]

Other (1)

T. Dumelow, J. A. P. da Costa, F. Lima, and E. L. Albuquerque., “Nonreciprocal phenomena on reflection of terahertz radiation off antiferromagnets,” in Recent Optical and Photonic Technologies, Ki Young Kim, ed. (InTech, Vukovar, 2010), Chap. 8. http://www.intechopen.com/books/recent-optical-and-photonic-technologies/nonreciprocal-phenomena-on-reflection-of-terahertz-radiation-off-antiferromagnets .
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 Schematic representation of an oblique incident beam with an angle θ1 being displaced on the reflection by a distance D at the interface between vacuum and an antiferromagnet, where Si and Sr are the incident and reflected Poynting vector respectively.
Fig. 2
Fig. 2 (a) Calculations of s-polarized oblique incidence (θ1 = ±60°) reflection from the interface between vacuum and MnF2 and (b) Goos-Hänchen shift D. Reflected (c) phase and (d) amplitude, as a function of in-plane wavevector kx, at the frequency marked as A in (a) (9.0103 cm−1) for the configuration shown in Fig. 1. Dashed lines are calculated for Γ = 0, whereas solid lines are for calculations in which Γ = 0.0007 cm−1. The shaded regions show where transmission is possible in the absence of damping. In case (a) the curves corresponding to θ1 = ±60° are coincident, so only a blue curve is seen in the case of the solid lines. Note that, in part (c), ϕ = π is represented as ϕ = −π in the Γ = 0 curve for consistency with the Γ = 0.0007 cm−1 curve.
Fig. 3
Fig. 3 Calculated overall power intensity (in terms of the magnitude of the time-averaged Poynting vector) showing intensities for a beam of width g = 0.2 cm obliquely incident (θ1 = +60°) on a vacuum/MnF2 interface at the frequency marked as A in Fig. 2 (9.0103 cm−1). The arrows represent the incident and reflected beams, positioned according to Eq. (15), with angle of reflection assumed equal to angle of incidence.
Fig. 4
Fig. 4 Goos-Hänchen shift D for different values of applied external field (a) B0 = 0.0 T, (b) B0 = 0.5 T, (c) B0 = 1.0 T and (d) B0 = 1.5 T. Blue lines are calculated for θ1 = +60°, whereas red lines are calculated for θ1 = −60°
Fig. 5
Fig. 5 (a) Calculations of s-polarized oblique incidence (θ1 = ±60°) reflection from the interface between vacuum and MnF2 in the presence of an external magnetic field of 1.5 T and (b) Goos-Hänchen shift D. Reflected (c) phase and (d) amplitude, as a function of in-plane wavevector kx, at frequency marked as B (9.125 cm−1) in (a). Dashed lines are calculated ignoring damping, whereas solid lines are for calculations in which damping is included. The shaded region shows frequencies where transmission can occur in the absence of damping.
Fig. 6
Fig. 6 Calculated overall power intensity (in terms of the magnitude of the time-averaged Poynting vector) showing intensities for a beam of width g = 0.2 cm obliquely incident on a vacuum/MnF2 interface at frequency B (ω = 9.125 cm−1) in the presence of a magnetic field B0 = 1.5 T. (a) θ1 = +60°; (b) θ1 = −60°.The arrows represent the incident and reflected beams, positioned according to Eq. (15), with angle of reflection assumed equal to angle of incidence.
Fig. 7
Fig. 7 Normal incidence calculations in the presence of an external magnetic field of 1.5 T. (a) Plane wave reflectivity spectrum; (b) Goos-Hänchen shift D. Reflected (a) phase and (b) amplitude, as a function of in-plane wavevector kx, for s-polarized reflection from a MnF2 crystal at the frequency marked in C as (a) (9.1204 cm−1), in the presence of an external magnetic field of 1.5 T. Dashed lines are calculated ignoring damping, whereas solid lines are for calculations in which damping is included. The shaded regions show where transmission can occur in the absence of damping.
Fig. 8
Fig. 8 Intensity profiles of the incident (solid curve) and reflected (dashed curve) gaussian beam of width g = 0.5 cm, at the frequency marked as C as Fig. 7 (9.1204 cm−1), normally incident on MnF2 in the presence of a magnetic field B0 = 1.5 T, with damping effects taken into account. The vertical solid line represents the center of the incident beam (x = 0) and the vertical dashed line represents the center of the reflected beam (x = −0.04 cm).

Equations (19)

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sin α = B 0 B A + 2 B E .
ω = ( ω r 2 cos 2 α + 2 γ 2 B 0 sin α ) 1 / 2 .
μ = ( μ x x 0 μ x z 0 μ y y 0 μ x z 0 μ z z ) .
μ x x = 1 + 2 μ 0 γ 2 M S B 0 sin α ω 2 ( ω + i Γ ) 2 ,
μ z z = 1 + 2 μ 0 γ 2 M S ( B 0 sin α + B A cos 2 α ) ω 2 ( ω + i Γ ) 2 ,
μ x z = μ x z = i 2 μ 0 γ 2 M S ( ω + i Γ ) sin α ω 2 ( ω + i Γ ) 2 .
r = k z 1 ( μ x x μ z z + μ x z 2 ) k z 2 μ z z k x μ x z k z 1 ( μ x x μ z z + μ x z 2 ) + k z 2 μ z z + k x μ x z .
k z 1 2 = k 0 2 k x 2
k z 2 2 = ε k 0 2 ( μ x x μ z z + μ x z 2 ) k x 2 μ x x μ z z
E i ( x , z ) = k 0 k 0 ψ ( k x ) e i ( k x x + k 1 z z ) d k x ,
E i ( x , 0 ) = k 0 + k 0 ψ ( k x ) e k x x d k x ,
E r ( x , 0 ) = k 0 + k 0 r ( k x ) ψ ( k x ) e i k x x d k x .
r ( k x ) = ρ ( k x ) e i ϕ ( k x ) ,
E r ( x ) = r ( k x 0 ) k 0 + k 0 ψ ( k x ) exp [ k x ( x + d ϕ d k x | k x = k x 0 ) ] d k x ,
D = d ϕ d k x | k x = k x 0 .
r = ( μ x x k z 1 k z 2 ) ( μ x x k z 1 + k z 2 ) ,
k z 2 2 = ε μ x x k 0 2 μ x x μ z z k x 2 .
ψ ( k x ) = g 2 cos θ 1 π exp [ g 2 ( k x k x 0 ) 2 4 cos 2 θ 1 ] ,
ψ ( k x ) = g 2 π exp ( g 2 k x 2 4 ) .

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