Abstract

We investigate a lateral shift of the reflected beam on reflection of far-infrared radiation, at oblique incidence, off an antiferromagnet in an external magnetic field, at frequencies close to the magnon resonances. This shift is nonreciprocal and depends on the direction of the applied field. It occurs both at bulk and reststrahlen frequencies, with or without damping. We illustrate this effect using simulations of reflection off MnF2 at low temperature.

© 2011 Optical Society of America

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  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, 2752-2754 (1986).
    [CrossRef] [PubMed]
  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, 12266-12269 (1994).
    [CrossRef]
  3. 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, 6808-6816 (1994).
    [CrossRef]
  4. D. E. Brown, T. Dumelow, T. J. Parker, K. Abraha, and D. R. Tilley, “Far infrared reflectivity off FeF2,” J. Magn. Magn. Mater. 140-144, 181-182 (1995).
    [CrossRef]
  5. M. R. F. Jensen, S. A. Feiven, T. J. Parker, and R. E. Camley, “Experimental determination of magnetic polariton dispersion curves in FeF2,” Phys. Rev. B 55, 2745-2748 (1997).
    [CrossRef]
  6. M. R. F. Jensen, S. A. Feiven, T. J. Parker, and R. E. Camley, “Experimental observation and interpretation of magnetic polariton modes in FeF2,” J. Phys. Condens. Matter 9, 7233-7247 (1997).
    [CrossRef]
  7. L. Remer, E. Mohler, W. Grill, and B. Lüthi, “Nonreciprocity in the optical reflection of magnetoplasmas,” Phys. Rev. B 30, 3277-3282 (1984).
    [CrossRef]
  8. R. L. Stamps, B. L. Johnson, and R. E. Camley, “Nonreciprocal reflection from semi-infinite antiferromagnets,” Phys. Rev. B 43, 3626-3636 (1991).
    [CrossRef]
  9. T. Dumelow and R. E. Camley, “Nonreciprocal reflection of infrared radiation from structures with antiferromagnets and dielectrics,” Phys. Rev. B 54, 12232-12237 (1996).
    [CrossRef]
  10. 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, 897-908 (1998).
    [CrossRef]
  11. R. E. Camley, “Nonreciprocal surface modes,” Surf. Sci. Rep. 7, 103-188 (1987).
    [CrossRef]
  12. K. Abraha and D. R. Tilley, “Theory of far infrared properties of magnetic surfaces, films and superlattices,” Surf. Sci. Rep. 24, 129-222 (1996).
    [CrossRef]
  13. 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,” K.Y.Kim, ed. (In-Tech, 2010), pp. 143-168, http://www.intechopen.com/articles/show/title/nonreciprocal-phenomena-on-reflection-of-terahertz-radiation-off-antiferromagnets.
  14. 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]
  15. F. Lima, T. Dumelow, E. L. Albuquerque, and J. A. P. da Costa, “Power flow associated with the Goos-Hänchen shift of a normally incident electromagnetic beam reflected off an antiferromagnet,” Phys. Rev. B 79, 155124 (2009).
    [CrossRef]
  16. F. Goos and H. Hänchen, “Ein neuer und fundamentaler versuch zur totalreflexion,” Ann. Phys. 436, 333-346 (1947).
    [CrossRef]
  17. H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect, I,” Optik (Jena) 32, 116-137 (1970).
  18. H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect, II,” Optik (Jena) 32, 189-204 (1970)
    [CrossRef]
  19. H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect, III,” Optik (Jena) 32, 299-319 (1971)
    [CrossRef]
  20. H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect, IV,” Optik (Jena) 32, 553-569 (1971)
  21. H. M. Lai, C. W. Kwok, Y. W. Loo, and B. Y. Xu, “Energy-flux pattern an the Goos-Hänchen effect,” Phys. Rev. E 62, 7330-7339 (2000).
    [CrossRef]
  22. T. Dumelow and M. C. Oliveros, “Continuum model of confined magnon polaritons in superlattices of antiferromagnets,” Phys. Rev. B 55, 994-1005 (1997).
    [CrossRef]
  23. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon , 1984).
    [CrossRef]
  24. K. Artmann, “Berechnung der seitenversetzung des totalrelektierten strahles,” Ann. Phys. 437, 87-102 (1948).
    [CrossRef]
  25. B. R. Horowitz and T. Tamir, “Lateral displacement of a light beam at a dielectric interface,” J. Opt. Soc. Am. 61, 586-594(1971).
    [CrossRef] [PubMed]
  26. M. McGuirk and C. K. Carniglia, “An angular spectrum representation approach to the Goos-Hänchen shift,” J. Opt. Soc. Am. 67, 103-107 (1977).
    [CrossRef] [PubMed]
  27. X. Chen and C.-F. Li, “Lateral shift of the transmitted light beam through a left-handed slab,” Phys. Rev. E 69, 066617(2004).
    [CrossRef]
  28. M. Rosenbluh, R. J. Temkin, and K. J. Button, “Submillimeter laser wavelength tables,” Appl. Opt. 15, 2635-2644(1976).
  29. A. Dobroiu, M. Yamashita, Y. N. Ohshima, Y. Morita, C. Otani, and K. Kawase, “Terahertz imaging system based on a backward-wave oscillator,” Appl. Opt. 43, 5637-5646 (2004).
  30. D. Kurtxz, T. Crowe, J. Hesier, D. Porterfield, V. Inc, and V. Charlottesville, “Frequency domain terahertz spectroscopy” in Joint 30th International Conference on Infrared and Millimeter Waves and 13th International Conference on Terahertz Electronics (IEEE, 2005), pp. 76-77, doi: 10.1109/ICIMW.2005.1572414

2009 (1)

F. Lima, T. Dumelow, E. L. Albuquerque, and J. A. P. da Costa, “Power flow associated with the Goos-Hänchen shift of a normally incident electromagnetic beam reflected off an antiferromagnet,” Phys. Rev. B 79, 155124 (2009).
[CrossRef]

2008 (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]

2004 (2)

X. Chen and C.-F. Li, “Lateral shift of the transmitted light beam through a left-handed slab,” Phys. Rev. E 69, 066617(2004).
[CrossRef]

A. Dobroiu, M. Yamashita, Y. N. Ohshima, Y. Morita, C. Otani, and K. Kawase, “Terahertz imaging system based on a backward-wave oscillator,” Appl. Opt. 43, 5637-5646 (2004).

2000 (1)

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

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, 897-908 (1998).
[CrossRef]

1997 (3)

M. R. F. Jensen, S. A. Feiven, T. J. Parker, and R. E. Camley, “Experimental determination of magnetic polariton dispersion curves in FeF2,” Phys. Rev. B 55, 2745-2748 (1997).
[CrossRef]

M. R. F. Jensen, S. A. Feiven, T. J. Parker, and R. E. Camley, “Experimental observation and interpretation of magnetic polariton modes in FeF2,” J. Phys. Condens. Matter 9, 7233-7247 (1997).
[CrossRef]

T. Dumelow and M. C. Oliveros, “Continuum model of confined magnon polaritons in superlattices of antiferromagnets,” Phys. Rev. B 55, 994-1005 (1997).
[CrossRef]

1996 (2)

T. Dumelow and R. E. Camley, “Nonreciprocal reflection of infrared radiation from structures with antiferromagnets and dielectrics,” Phys. Rev. B 54, 12232-12237 (1996).
[CrossRef]

K. Abraha and D. R. Tilley, “Theory of far infrared properties of magnetic surfaces, films and superlattices,” Surf. Sci. Rep. 24, 129-222 (1996).
[CrossRef]

1995 (1)

D. E. Brown, T. Dumelow, T. J. Parker, K. Abraha, and D. R. Tilley, “Far infrared reflectivity off FeF2,” J. Magn. Magn. Mater. 140-144, 181-182 (1995).
[CrossRef]

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, 12266-12269 (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, 6808-6816 (1994).
[CrossRef]

1991 (1)

R. L. Stamps, B. L. Johnson, and R. E. Camley, “Nonreciprocal reflection from semi-infinite antiferromagnets,” Phys. Rev. B 43, 3626-3636 (1991).
[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, 2752-2754 (1986).
[CrossRef] [PubMed]

1984 (1)

L. Remer, E. Mohler, W. Grill, and B. Lüthi, “Nonreciprocity in the optical reflection of magnetoplasmas,” Phys. Rev. B 30, 3277-3282 (1984).
[CrossRef]

1977 (1)

1976 (1)

1971 (3)

B. R. Horowitz and T. Tamir, “Lateral displacement of a light beam at a dielectric interface,” J. Opt. Soc. Am. 61, 586-594(1971).
[CrossRef] [PubMed]

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect, III,” Optik (Jena) 32, 299-319 (1971)
[CrossRef]

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect, IV,” Optik (Jena) 32, 553-569 (1971)

1970 (2)

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect, I,” Optik (Jena) 32, 116-137 (1970).

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect, II,” Optik (Jena) 32, 189-204 (1970)
[CrossRef]

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, 333-346 (1947).
[CrossRef]

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, 897-908 (1998).
[CrossRef]

K. Abraha and D. R. Tilley, “Theory of far infrared properties of magnetic surfaces, films and superlattices,” Surf. Sci. Rep. 24, 129-222 (1996).
[CrossRef]

D. E. Brown, T. Dumelow, T. J. Parker, K. Abraha, and D. R. Tilley, “Far infrared reflectivity off FeF2,” J. Magn. Magn. Mater. 140-144, 181-182 (1995).
[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, 12266-12269 (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, 6808-6816 (1994).
[CrossRef]

Albuquerque, E. L.

F. Lima, T. Dumelow, E. L. Albuquerque, and J. A. P. da Costa, “Power flow associated with the Goos-Hänchen shift of a normally incident electromagnetic beam reflected off an antiferromagnet,” Phys. Rev. B 79, 155124 (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, 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,” K.Y.Kim, ed. (In-Tech, 2010), pp. 143-168, http://www.intechopen.com/articles/show/title/nonreciprocal-phenomena-on-reflection-of-terahertz-radiation-off-antiferromagnets.

Artmann, K.

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

Brown, D. E.

D. E. Brown, T. Dumelow, T. J. Parker, K. Abraha, and D. R. Tilley, “Far infrared reflectivity off FeF2,” J. Magn. Magn. Mater. 140-144, 181-182 (1995).
[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, 6808-6816 (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, 12266-12269 (1994).
[CrossRef]

Button, K. J.

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, 897-908 (1998).
[CrossRef]

M. R. F. Jensen, S. A. Feiven, T. J. Parker, and R. E. Camley, “Experimental observation and interpretation of magnetic polariton modes in FeF2,” J. Phys. Condens. Matter 9, 7233-7247 (1997).
[CrossRef]

M. R. F. Jensen, S. A. Feiven, T. J. Parker, and R. E. Camley, “Experimental determination of magnetic polariton dispersion curves in FeF2,” Phys. Rev. B 55, 2745-2748 (1997).
[CrossRef]

T. Dumelow and R. E. Camley, “Nonreciprocal reflection of infrared radiation from structures with antiferromagnets and dielectrics,” Phys. Rev. B 54, 12232-12237 (1996).
[CrossRef]

R. L. Stamps, B. L. Johnson, and R. E. Camley, “Nonreciprocal reflection from semi-infinite antiferromagnets,” Phys. Rev. B 43, 3626-3636 (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, 2752-2754 (1986).
[CrossRef] [PubMed]

Carniglia, C. K.

Charlottesville, V.

D. Kurtxz, T. Crowe, J. Hesier, D. Porterfield, V. Inc, and V. Charlottesville, “Frequency domain terahertz spectroscopy” in Joint 30th International Conference on Infrared and Millimeter Waves and 13th International Conference on Terahertz Electronics (IEEE, 2005), pp. 76-77, doi: 10.1109/ICIMW.2005.1572414

Chen, X.

X. Chen and C.-F. Li, “Lateral shift of the transmitted light beam through a left-handed slab,” Phys. Rev. E 69, 066617(2004).
[CrossRef]

Crowe, T.

D. Kurtxz, T. Crowe, J. Hesier, D. Porterfield, V. Inc, and V. Charlottesville, “Frequency domain terahertz spectroscopy” in Joint 30th International Conference on Infrared and Millimeter Waves and 13th International Conference on Terahertz Electronics (IEEE, 2005), pp. 76-77, doi: 10.1109/ICIMW.2005.1572414

da Costa, J. A. P.

F. Lima, T. Dumelow, E. L. Albuquerque, and J. A. P. da Costa, “Power flow associated with the Goos-Hänchen shift of a normally incident electromagnetic beam reflected off an antiferromagnet,” Phys. Rev. B 79, 155124 (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, 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,” K.Y.Kim, ed. (In-Tech, 2010), pp. 143-168, http://www.intechopen.com/articles/show/title/nonreciprocal-phenomena-on-reflection-of-terahertz-radiation-off-antiferromagnets.

Dobroiu, A.

Dumelow, T.

F. Lima, T. Dumelow, E. L. Albuquerque, and J. A. P. da Costa, “Power flow associated with the Goos-Hänchen shift of a normally incident electromagnetic beam reflected off an antiferromagnet,” Phys. Rev. B 79, 155124 (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, 897-908 (1998).
[CrossRef]

T. Dumelow and M. C. Oliveros, “Continuum model of confined magnon polaritons in superlattices of antiferromagnets,” Phys. Rev. B 55, 994-1005 (1997).
[CrossRef]

T. Dumelow and R. E. Camley, “Nonreciprocal reflection of infrared radiation from structures with antiferromagnets and dielectrics,” Phys. Rev. B 54, 12232-12237 (1996).
[CrossRef]

D. E. Brown, T. Dumelow, T. J. Parker, K. Abraha, and D. R. Tilley, “Far infrared reflectivity off FeF2,” J. Magn. Magn. Mater. 140-144, 181-182 (1995).
[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, 12266-12269 (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, 6808-6816 (1994).
[CrossRef]

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,” K.Y.Kim, ed. (In-Tech, 2010), pp. 143-168, http://www.intechopen.com/articles/show/title/nonreciprocal-phenomena-on-reflection-of-terahertz-radiation-off-antiferromagnets.

Feiven, S. A.

M. R. F. Jensen, S. A. Feiven, T. J. Parker, and R. E. Camley, “Experimental determination of magnetic polariton dispersion curves in FeF2,” Phys. Rev. B 55, 2745-2748 (1997).
[CrossRef]

M. R. F. Jensen, S. A. Feiven, T. J. Parker, and R. E. Camley, “Experimental observation and interpretation of magnetic polariton modes in FeF2,” J. Phys. Condens. Matter 9, 7233-7247 (1997).
[CrossRef]

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, 2752-2754 (1986).
[CrossRef] [PubMed]

Goos, F.

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

Grill, W.

L. Remer, E. Mohler, W. Grill, and B. Lüthi, “Nonreciprocity in the optical reflection of magnetoplasmas,” Phys. Rev. B 30, 3277-3282 (1984).
[CrossRef]

Hänchen, H.

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

Hesier, J.

D. Kurtxz, T. Crowe, J. Hesier, D. Porterfield, V. Inc, and V. Charlottesville, “Frequency domain terahertz spectroscopy” in Joint 30th International Conference on Infrared and Millimeter Waves and 13th International Conference on Terahertz Electronics (IEEE, 2005), pp. 76-77, doi: 10.1109/ICIMW.2005.1572414

Horowitz, B. R.

Inc, V.

D. Kurtxz, T. Crowe, J. Hesier, D. Porterfield, V. Inc, and V. Charlottesville, “Frequency domain terahertz spectroscopy” in Joint 30th International Conference on Infrared and Millimeter Waves and 13th International Conference on Terahertz Electronics (IEEE, 2005), pp. 76-77, doi: 10.1109/ICIMW.2005.1572414

Jensen, M. R. F.

M. R. F. Jensen, S. A. Feiven, T. J. Parker, and R. E. Camley, “Experimental determination of magnetic polariton dispersion curves in FeF2,” Phys. Rev. B 55, 2745-2748 (1997).
[CrossRef]

M. R. F. Jensen, S. A. Feiven, T. J. Parker, and R. E. Camley, “Experimental observation and interpretation of magnetic polariton modes in FeF2,” J. Phys. Condens. Matter 9, 7233-7247 (1997).
[CrossRef]

Johnson, B. L.

R. L. Stamps, B. L. Johnson, and R. E. Camley, “Nonreciprocal reflection from semi-infinite antiferromagnets,” Phys. Rev. B 43, 3626-3636 (1991).
[CrossRef]

Kawase, K.

Kurtxz, D.

D. Kurtxz, T. Crowe, J. Hesier, D. Porterfield, V. Inc, and V. Charlottesville, “Frequency domain terahertz spectroscopy” in Joint 30th International Conference on Infrared and Millimeter Waves and 13th International Conference on Terahertz Electronics (IEEE, 2005), pp. 76-77, doi: 10.1109/ICIMW.2005.1572414

Kwok, C. W.

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

Lai, H. M.

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

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon , 1984).
[CrossRef]

Li, C.-F.

X. Chen and C.-F. Li, “Lateral shift of the transmitted light beam through a left-handed slab,” Phys. Rev. E 69, 066617(2004).
[CrossRef]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon , 1984).
[CrossRef]

Lima, F.

F. Lima, T. Dumelow, E. L. Albuquerque, and J. A. P. da Costa, “Power flow associated with the Goos-Hänchen shift of a normally incident electromagnetic beam reflected off an antiferromagnet,” Phys. Rev. B 79, 155124 (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, 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,” K.Y.Kim, ed. (In-Tech, 2010), pp. 143-168, http://www.intechopen.com/articles/show/title/nonreciprocal-phenomena-on-reflection-of-terahertz-radiation-off-antiferromagnets.

Loo, Y. W.

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

Lotsch, H. K. V.

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect, III,” Optik (Jena) 32, 299-319 (1971)
[CrossRef]

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect, IV,” Optik (Jena) 32, 553-569 (1971)

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect, I,” Optik (Jena) 32, 116-137 (1970).

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect, II,” Optik (Jena) 32, 189-204 (1970)
[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, 2752-2754 (1986).
[CrossRef] [PubMed]

L. Remer, E. Mohler, W. Grill, and B. Lüthi, “Nonreciprocity in the optical reflection of magnetoplasmas,” Phys. Rev. B 30, 3277-3282 (1984).
[CrossRef]

McGuirk, M.

Mohler, E.

L. Remer, E. Mohler, W. Grill, and B. Lüthi, “Nonreciprocity in the optical reflection of magnetoplasmas,” Phys. Rev. B 30, 3277-3282 (1984).
[CrossRef]

Morita, Y.

Ohshima, Y. N.

Oliveros, M. C.

T. Dumelow and M. C. Oliveros, “Continuum model of confined magnon polaritons in superlattices of antiferromagnets,” Phys. Rev. B 55, 994-1005 (1997).
[CrossRef]

Otani, C.

Parker, T. J.

M. R. F. Jensen, S. A. Feiven, T. J. Parker, and R. E. Camley, “Experimental observation and interpretation of magnetic polariton modes in FeF2,” J. Phys. Condens. Matter 9, 7233-7247 (1997).
[CrossRef]

M. R. F. Jensen, S. A. Feiven, T. J. Parker, and R. E. Camley, “Experimental determination of magnetic polariton dispersion curves in FeF2,” Phys. Rev. B 55, 2745-2748 (1997).
[CrossRef]

D. E. Brown, T. Dumelow, T. J. Parker, K. Abraha, and D. R. Tilley, “Far infrared reflectivity off FeF2,” J. Magn. Magn. Mater. 140-144, 181-182 (1995).
[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, 6808-6816 (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, 12266-12269 (1994).
[CrossRef]

Porterfield, D.

D. Kurtxz, T. Crowe, J. Hesier, D. Porterfield, V. Inc, and V. Charlottesville, “Frequency domain terahertz spectroscopy” in Joint 30th International Conference on Infrared and Millimeter Waves and 13th International Conference on Terahertz Electronics (IEEE, 2005), pp. 76-77, doi: 10.1109/ICIMW.2005.1572414

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, 2752-2754 (1986).
[CrossRef] [PubMed]

L. Remer, E. Mohler, W. Grill, and B. Lüthi, “Nonreciprocity in the optical reflection of magnetoplasmas,” Phys. Rev. B 30, 3277-3282 (1984).
[CrossRef]

Rosenbluh, M.

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, 2752-2754 (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, 3626-3636 (1991).
[CrossRef]

Tamir, T.

Temkin, R. J.

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, 897-908 (1998).
[CrossRef]

K. Abraha and D. R. Tilley, “Theory of far infrared properties of magnetic surfaces, films and superlattices,” Surf. Sci. Rep. 24, 129-222 (1996).
[CrossRef]

D. E. Brown, T. Dumelow, T. J. Parker, K. Abraha, and D. R. Tilley, “Far infrared reflectivity off FeF2,” J. Magn. Magn. Mater. 140-144, 181-182 (1995).
[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, 12266-12269 (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, 6808-6816 (1994).
[CrossRef]

Xu, B. Y.

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

Yamashita, M.

Ann. Phys. (2)

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

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

Appl. Opt. (2)

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. Magn. Magn. Mater. (1)

D. E. Brown, T. Dumelow, T. J. Parker, K. Abraha, and D. R. Tilley, “Far infrared reflectivity off FeF2,” J. Magn. Magn. Mater. 140-144, 181-182 (1995).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Phys. Condens. Matter (1)

M. R. F. Jensen, S. A. Feiven, T. J. Parker, and R. E. Camley, “Experimental observation and interpretation of magnetic polariton modes in FeF2,” J. Phys. Condens. Matter 9, 7233-7247 (1997).
[CrossRef]

Optik (Jena) (4)

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect, I,” Optik (Jena) 32, 116-137 (1970).

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect, II,” Optik (Jena) 32, 189-204 (1970)
[CrossRef]

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect, III,” Optik (Jena) 32, 299-319 (1971)
[CrossRef]

H. K. V. Lotsch, “Beam displacement at total reflection: the Goos-Hänchen effect, IV,” Optik (Jena) 32, 553-569 (1971)

Phys. Rev. B (9)

M. R. F. Jensen, S. A. Feiven, T. J. Parker, and R. E. Camley, “Experimental determination of magnetic polariton dispersion curves in FeF2,” Phys. Rev. B 55, 2745-2748 (1997).
[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, 12266-12269 (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, 6808-6816 (1994).
[CrossRef]

L. Remer, E. Mohler, W. Grill, and B. Lüthi, “Nonreciprocity in the optical reflection of magnetoplasmas,” Phys. Rev. B 30, 3277-3282 (1984).
[CrossRef]

R. L. Stamps, B. L. Johnson, and R. E. Camley, “Nonreciprocal reflection from semi-infinite antiferromagnets,” Phys. Rev. B 43, 3626-3636 (1991).
[CrossRef]

T. Dumelow and R. E. Camley, “Nonreciprocal reflection of infrared radiation from structures with antiferromagnets and dielectrics,” Phys. Rev. B 54, 12232-12237 (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, 897-908 (1998).
[CrossRef]

F. Lima, T. Dumelow, E. L. Albuquerque, and J. A. P. da Costa, “Power flow associated with the Goos-Hänchen shift of a normally incident electromagnetic beam reflected off an antiferromagnet,” Phys. Rev. B 79, 155124 (2009).
[CrossRef]

T. Dumelow and M. C. Oliveros, “Continuum model of confined magnon polaritons in superlattices of antiferromagnets,” Phys. Rev. B 55, 994-1005 (1997).
[CrossRef]

Phys. Rev. E (2)

X. Chen and C.-F. Li, “Lateral shift of the transmitted light beam through a left-handed slab,” Phys. Rev. E 69, 066617(2004).
[CrossRef]

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

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, 2752-2754 (1986).
[CrossRef] [PubMed]

Surf. Sci. Rep. (2)

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

K. Abraha and D. R. Tilley, “Theory of far infrared properties of magnetic surfaces, films and superlattices,” Surf. Sci. Rep. 24, 129-222 (1996).
[CrossRef]

Other (3)

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,” K.Y.Kim, ed. (In-Tech, 2010), pp. 143-168, http://www.intechopen.com/articles/show/title/nonreciprocal-phenomena-on-reflection-of-terahertz-radiation-off-antiferromagnets.

D. Kurtxz, T. Crowe, J. Hesier, D. Porterfield, V. Inc, and V. Charlottesville, “Frequency domain terahertz spectroscopy” in Joint 30th International Conference on Infrared and Millimeter Waves and 13th International Conference on Terahertz Electronics (IEEE, 2005), pp. 76-77, doi: 10.1109/ICIMW.2005.1572414

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon , 1984).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Diagrammatic representation of (a) normal incidence Goos–Hänchen shift and (b) oblique incidence Goos– Hänchen shift for reflection off an antiferromagnet (AF) in the presence of an external field B 0 .

Fig. 2
Fig. 2

Oblique incidence ( θ 1 = 30 ° ) simulations around the MnF 2 upper reststrahlen region for Voigt geometry reflection from vacuum in the presence of an external magnetic field of B 0 = ± 0.1 T . (a) Plane-wave reflectivity spectrum, (b) spectrum of reflected phase, (c) angle of refraction θ 2 , (d) Goos–Hänchen shift D calculated from Eq. (1). In each case, the left-hand figures are calculated ignoring damping ( Γ = 0 ), whereas the right-hand figures are for Γ = 0.0007 cm 1 . Solid (red) curves are for B 0 = + 0.1 T , and dashed (blue) curves are for B 0 = 0.1 T . The vertical dotted lines in the left-hand figures separate the bulk (B) regions from the reststrahlen (R) regions.

Fig. 3
Fig. 3

(a) Overall power intensity, normalized with respect to the center of the incident beam at its focus, and flux lines for reflection of a obliquely incident ( θ 1 = 30 ° ) Gaussian beam of width g = 2 λ , focused onto the surface of a semi-infinite sample of MnF 2 in an external magnetic field of B 0 = ± 0.1 T at a frequency of 9.0769 cm 1 (reststrahlen region), in the absence of damping. (b) Overall power intensity and direction with damping included. In both figures, the solid vertical black line represents the surface of the sample.

Fig. 4
Fig. 4

Details of power flow near the interface for the situation shown in Fig. 3. (a) Γ = 0 , (b) Γ = 0.0007 cm 1 . Note that intensities are shown on a logarithmic scale for clarity.

Fig. 5
Fig. 5

Power flow at a frequency of 9.0705 cm 1 (bulk region). Conditions are the same as those in Fig. 3. (a) Γ = 0 , (b) Γ = 0.0007 cm 1 .

Fig. 6
Fig. 6

Power flow for reflection of a Gaussian beam, of width g = 2 λ , off MnF 2 , when the beam focus lies in the y = 1.0 cm plane, after reflection. Other conditions are the same as those in Figs. 3, 5. (a) ω = 9.0769 cm 1 (reststrahlen region), (b) ω = 9.0705 cm 1 (bulk region). A damping of Γ = 0.0007 cm 1 has been included in both cases.

Fig. 7
Fig. 7

Power intensity profile along y = 1.0 cm for the situation shown in Fig. 6. (a) ω = 9.0769 cm 1 (reststrahlen region), (b) ω = 9.0705 cm 1 (bulk region). Solid (red) curves are for B 0 = + 0.1 T , and dashed (blue) curves are for B 0 = 0.1 T . The vertical dotted line shows the position of the beam center in the absence of any Goos–Hänchen shift.

Equations (27)

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D = d ϕ d k x ,
μ = ( μ 1 i μ 2 0 i μ 2 μ 1 0 0 0 1 ) ,
μ 1 = 1 + μ 0 γ 2 B A M S ( Y + + Y ) ,
μ 2 = μ 0 γ 2 B A M S ( Y + Y ) ,
Y ± = [ ω r 2 ( ω ± γ B 0 + i Γ ) 2 ] 1 .
ω r = γ ( 2 B A B E + B A 2 ) 1 / 2 ,
r = k 1 y μ v k 2 y i k x ( μ 2 / μ 1 ) k 1 y μ v + k 2 y + i k x ( μ 2 / μ 1 ) ,
k x = k 0 sin θ 1 ,
k 1 y = [ k 0 2 k x 2 ] 1 / 2 ,
k 2 y = [ ϵ μ v k 0 2 k x 2 ] 1 / 2 .
μ v = ( μ 1 2 μ 2 2 ) / μ 1 .
r = ρ exp ( i ϕ ) ,
ϕ ( B 0 ) = ϕ ( B 0 ) ,
S = 1 / 2 Re ( E × H * ) .
S 2 x = | E z | 2 2 ω μ 0 Re [ k x i k 2 y ( μ 2 / μ 1 ) μ v ] ,
S 2 y = | E z | 2 2 ω μ 0 Re [ k 2 y + i k x ( μ 2 / μ 1 ) μ v ] .
tan θ 2 = S 2 x S 2 z .
S 2 x = | E z | 2 k x 2 ω μ 0 μ v ,
S 2 y = | E z | 2 k 2 y 2 ω μ 0 μ v .
S 2 x = | E z | 2 [ k x i k 2 y ( μ 2 / μ 1 ) ] 2 ω μ 0 μ v ,
S 2 y = 0 ,
D ( B 0 ) = D ( B 0 ) .
E i ( x , y ) = k 0 k 0 ψ ( k x ) exp [ i ( k x x + k 1 y y ) ] d k x .
ψ ( k x ) = g 2 cos θ 0 π exp [ g 2 ( k x k 0 sin θ 0 ) 2 4 cos 2 θ 0 ] ,
E r ( x , y ) = k 0 k 0 r ( k x ) ψ ( k x ) exp [ i ( k x x k 1 y y ) ] d k x ,
E t ( x , y ) = k 0 k 0 t ( k x ) ψ ( k x ) exp [ i ( k x x + k 2 y y ) ] d k x ,
t ( k x ) = 1 + r ( k x ) .

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