Abstract

Analytic expressions for the eigenvalues for the four-wave components at an oblique angle of light incidence inside a randomly oriented anisotropic magneto-optic dielectric medium are reported explicitly. In particular, these solutions are valid as long as the dielectric function tensor consists of a symmetric and an antisymmetric part. The normalized Jones reflection and transmission coefficients, i.e., the generalized ellipsometric parameters of homogeneously layered systems having nonsymmetric dielectric properties, are obtained immediately from a recently reviewed 4 × 4 matrix approach. Our explicit solutions allow a future analysis of the generalized ellipsometric data of multilayered magneto-optic media regardless of the orientation of the material magnetization and crystalline axes and the angle of light incidence. Possible experimental thin-film situations are discussed in terms of generalized ellipsometric parameters and illustrated for birefringent free-carrier effects in heavily doped semiconductor thin films and for oblique magnetization directions in magneto-optic multilayer systems.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. C. Boccara, C. Pickering, J. Rivory, eds., Spectroscopic Ellipsometry (Elsevier, Amsterdam, 1993).
  2. R. W. Collins, D. E. Aspnes, E. A. Irene, eds., Spectroscopic Ellipsometry 1997 (Elsevier, Lausanne, 1997).
  3. R. M. A. Azzam, N. M. Bashara, “Generalized ellipsometry for surfaces with directional preferences: application to diffraction gratings,” J. Opt. Soc. Am. 62, 1521–1523 (1972).
    [CrossRef]
  4. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1984).
  5. M. Schubert, B. Rheinländer, J. A. Woollam, B. Johs, C. M. Herzinger, “Extension of rotating-analyzer ellipsometry to generalized ellipsometry: determination of the dielectric function tensor of uniaxial TiO2,” J. Opt. Soc. Am. A 13, 875–883 (1996).
    [CrossRef]
  6. G. E. Jellison, F. A. Modine, “Two-modulator generalized ellipsometry: theory,” Appl. Opt. 36, 8184–8189 (1998); “Two-modulator generalized ellipsometry: experiment and calibration,” Appl. Opt. 36, 8190–8198 (1998).
    [CrossRef]
  7. G. E. Jellison, F. A. Modine, L. A. Boatner, “The measurement of the optical functions of uniaxial materials using two-modulator generalized ellipsometry: rutile (TiO2),” Opt. Lett. 22, 1808–1810 (1997).
    [CrossRef]
  8. D. W. Thompson, M. J. DeVries, T. E. Tiwald, J. A. Woollam, “Determination of optical anisotropy in calcite from ultraviolet to mid-infrared by generalized ellipsometry,” Thin Solid Films 313–314, 341–346 (1998).
  9. B. Lecourt, D. Blaudez, J.-M. Turlet, “Specific approach of generalized ellipsometry for the determination of weak in-plane anisotropy: application to Langmuir–Blodgett ultrathin films,” J. Opt. Soc. Am. A 15, 2769–2782 (1998).
    [CrossRef]
  10. J. F. Elman, J. Greener, C. M. Herzinger, B. Johs, “Characterization of biaxially stretched plastic films by generalized ellipsometry,” Thin Solid Films 313–314, 816–820 (1998).
  11. M. Schubert, B. Rheinländer, C. Cramer, H. Schmiedel, J. A. Woollam, B. Johs, C. M. Herzinger, “Generalized transmission ellipsometry for twisted biaxial dielectric media: application to chiral liquid crystals,” J. Opt. Soc. Am. A 13, 1930–1940 (1996).
    [CrossRef]
  12. P. I. Rovira, R. A. Yarussi, R. W. Collins, R. Messier, V. C. Venugopal, A. Lakhtakia, K. Robbi, M. J. Brett, “Transmission ellipsometry of a thin-film helicoidal bianisotropic medium,” Appl. Phys. Lett. 71, 1180–1182 (1997).
    [CrossRef]
  13. M. Schubert, B. Rheinländer, E. Franke, I. Pietzonka, J. Škriniarova, V. Gottschalch, “Direct-gap reduction and valence band splitting of ordered indirect-gap AlInP2 studied by dark-field spectroscopy,” Phys. Rev. B 54, 17,616–17,619 (1996).
    [CrossRef]
  14. J.-D. Hecht, A. Eifler, V. Riede, M. Schubert, G. Krauss, V. Krämer, “Birefringence and reflectivity of single-crystal CdAl2Se4 by generalized ellipsometry,” Phys. Rev. B 57, 7037–7042 (1998).
    [CrossRef]
  15. M. Schubert, “Generalized ellipsometry and complex optical systems,” Thin Solid Films 313–314, 313–314 (1998).
  16. A. Berger, M. R. Pufall, “Generalized magneto-optical ellipsometry,” Appl. Phys. Lett. 71, 965–967 (1997).
    [CrossRef]
  17. See, for example, W. A. McGahan, “Magneto-optical applications,” in Intermetallic Compounds, J. H. Westbrook, R. L. Fleischer, eds. (Wiley, London, 1994), Vol. 2, Chap. 19, pp. 435–451.
  18. W. A. McGahan, P. He, J. A. Woollam, “Optical and magneto-optical characterization of thin films,” Appl. Phys. Commun. 11, 375–401 (1992).
  19. W. A. McGahan, J. A. Woollam, “Magneto-optics of multilayer systems,” Appl. Phys. Commun. 9, 1–25 (1989).
  20. K. W. Wierman, J. N. Hilfiker, R. F. Sabiryanov, S. S. Jaswal, R. D. Kirby, J. A. Woollam, “Optical and magneto-optical constants of MnPt3,” Phys. Rev. B 55, 3093–3099 (1997).
    [CrossRef]
  21. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).
  22. H. A. Macleod, Thin Film Optical Filters (Macmillan, New York, 1986).
    [CrossRef]
  23. M. Mansuripur, The Physical Principles of Magneto-optical Recording (Cambridge University, Cambridge, England, 1995).
    [CrossRef]
  24. D. W. Berreman, “Optics in stratified and anisotropic media: 4 × 4-matrix formulation,” J. Opt. Soc. Am. 62, 502–510 (1972).
    [CrossRef]
  25. P. Yeh, “Optics of anisotropic layered media: a new 4 × 4 matrix algebra,” Surf. Sci. 96, 41–53 (1980).
    [CrossRef]
  26. See P. J. Lin-Chung, S. Teitler, “4 × 4 matrix formalism for optics in stratified anisotropic media,” J. Opt. Soc. Am. A 1, 703–705 (1984) for a comparison between the 4 × 4 matrix formalisms developed by Berreman24 and by Yeh.25
  27. N. J. Damaskos, A. L. Maffet, P. L. E. Ushlenghi, “Reflection and transmission for gyroelectromagnetic biaxial layered media,” J. Opt. Soc. Am. A 2, 454–461 (1985).
    [CrossRef]
  28. Z.-M. Li, R. R. Parson, “Reflection of strongly focused light beams from magneto-optic multilayer films,” J. Opt. Soc. Am. A 5, 1543–1548 (1988).
    [CrossRef]
  29. Z.-M. Li, B. T. Sullivan, R. R. Parson, “Use of the 4 × 4 matrix method in the optics of multilayer magneto-optic recording media,” Appl. Opt. 27, 1334–1338 (1988).
    [CrossRef] [PubMed]
  30. R. Gamble, P. H. Lissberger, “Electromagnetic field distributions in multilayer thin films for magneto-optic recording media,” J. Opt. Soc. Am. A 5, 1533–1542 (1988).
    [CrossRef]
  31. S. B. Borisov, N. N. Dadoenkova, I. L. Lyubchanskii, “Normal electromagnetic waves in gyrotropic magneto-optic layered structures,” Opt. Spectrosc. 74, 670–682 (1993).
  32. S. Višnovský, “Magneto-optical ellipsometry,” Czech. J. Phys. B 36, 625–650 (1986).
    [CrossRef]
  33. R. P. Hunt, “Magneto-optic scattering from thin solid films,” J. Appl. Phys. 38, 1652–1671 (1967).
    [CrossRef]
  34. M. Mansuripur, “Analysis of multilayer thin film structures containing magneto-optic and anisotropic media at oblique incidence using 2 × 2 matrices,” J. Appl. Phys. 67, 6466–6480 (1990).
    [CrossRef]
  35. S. Višnovský, M. Nývlt, V. Prosser, R. Lopušník, R. Urban, J. Ferré, G. Pénissard, D. Renard, R. Krishnan, “Polar magneto-optics in simple ultrathin-magnetic-film structures,” Phys. Rev. B 52, 1090–1106 (1995).
    [CrossRef]
  36. J. L. Tsalamengas, “Interaction of electromagnetic waves with general bianisotropic slabs,” IEEE Trans. Microwave Theory Tech. 40, 1870–1878 (1992).
    [CrossRef]
  37. Y. Wenyen, W. Wenbing, “The transmission properties of stratified chiroferrite media with obliquely incident plane waves,” Int. J. Infrared Millimeter Waves 15, 593–603 (1994).
    [CrossRef]
  38. J. S. Nefedov, “Microstrip slow-wave structures on the bianisotropic substrate,” Electromagnetics 17, 343–360 (1997).
    [CrossRef]
  39. A. Lakhtakia, W. Weiglhofer, “On light propagation in helicoidal bianisotropic mediums,” Proc. R. Soc. London Ser. A 448, 419–437 (1995).
    [CrossRef]
  40. A. Lakhtakia, W. Weiglhofer, “Further results on light propagation in helicoidal bianisotropic mediums: oblique propagation,” Proc. R. Soc. London Ser. A 453, 93–105 (1997).
    [CrossRef]
  41. H. G. Booker, “Oblique propagation of electromagnetic waves in a slowly-varying nonisotropic medium,” Proc. R. Soc. A 155, 235–257 (1936).
    [CrossRef]
  42. For a definition of the constitutive relations for several anisotropic media, see, e.g., J. A. Kong, Electromagnetic Wave Theory (Wiley, New York, 1990).
  43. L. D. Landau, E. M. Lifschitz, Electrodynamics of Continuous Media (Pergamon, New York, 1960).
  44. M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B 53, 4265–4274 (1996).
    [CrossRef]
  45. S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, S. W. McKnight, A. B. Kale, “Measurement of magnetic fields using the magneto-optic Kerr effect,” Appl. Phys. Lett. 63, 415–417 (1993).
    [CrossRef]
  46. S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, A. B. Kale, “Magnetic field measurements using magneto-optic Kerr effect sensors,” Opt. Eng. 33, 3718–3722 (1994).
    [CrossRef]
  47. J. M. Floraczek, E. Dan Dahlberg, “Detecting two magnetization components by the magneto-optical Kerr effect,” J. Appl. Phys. 67, 7520–7525 (1990).
    [CrossRef]
  48. H. Wöhler, M. Fritsch, G. Haas, D. A. Mlynski, “Faster 4 × 4 matrix method for uniaxial inhomogeneous media,” J. Opt. Soc. Am. A 5, 1554–1557 (1988).
    [CrossRef]
  49. P. S. Hauge, “Generalized rotating-compensator ellipsometry,” Surf. Sci. 56, 148–160 (1976).
    [CrossRef]
  50. D. J. DeSmet, “Generalized ellipsometry and the 4 × 4 matrix formalism,” Surf. Sci. 56, 293–306 (1976).
    [CrossRef]
  51. M. Elshazly-Zaghloul, R. M. A. Azzam, N. M. Bashara, “Explicit solutions for the optical properties of uniaxial materials in generalized ellipsometry,” Surf. Sci. 56, 281–292 (1976).
    [CrossRef]
  52. An introduction to electromagnetic-wave propagation in magneto-optically biaxial materials in application to surface and bulk related plasmons in semiconductors can be found in R. F. Wallis, “Optical properties associated with surface excitations of semiconductors,” in Handbook on Semiconductors, M. Balkanski, ed. (North-Holland, Amsterdam, 1994), Vol. 2, pp. 65–108.
  53. X. Gao, D. W. Glenn, S. Heckens, D. W. Thompson, J. A. Woollam, “Spectroscopic ellipsometry and magneto-optic Kerr effects in Co/Pt multilayers,” J. Appl. Phys. 82, 4525–4531 (1997).
    [CrossRef]
  54. C. R. Pidgeon, “Free carrier optical properties of semiconductors,” in Handbook on Semiconductors, M. Balkanski, ed. (North-Holland, Amsterdam, 1980), Vol. 2, pp. 223–328.
  55. S. M. Sze, Physics of Semiconductor Devices (Wiley, New York, 1981), pp. 29, 849.
  56. E. D. Palik, G. B. Wright, “Free carrier magneto-optical effects,” in R. K. Willardson, A. C. Beer, in Optical Properties of III–V Compounds, Vol. 3 of Semiconductors and Semimetals (Academic, New York, 1967), pp. 457–458.
  57. M. Miyao, T. Motooka, N. Natsuaki, T. Tokuyama, “Change of the electron effective mass in extremely heavily doped n-type Si obtained by ion implantation and laser annealing,” Solid State Commun. 37, 605–608 (1981).
    [CrossRef]
  58. J. S. Blakemore, “Intrinsic density ni(T) in GaAs: Deduced from band gap and effective mass parameters and derived independently from Cr acceptor capture and emission coefficients,” J. Appl. Phys. 53, 520–531 (1982).
    [CrossRef]

1998 (6)

G. E. Jellison, F. A. Modine, “Two-modulator generalized ellipsometry: theory,” Appl. Opt. 36, 8184–8189 (1998); “Two-modulator generalized ellipsometry: experiment and calibration,” Appl. Opt. 36, 8190–8198 (1998).
[CrossRef]

D. W. Thompson, M. J. DeVries, T. E. Tiwald, J. A. Woollam, “Determination of optical anisotropy in calcite from ultraviolet to mid-infrared by generalized ellipsometry,” Thin Solid Films 313–314, 341–346 (1998).

B. Lecourt, D. Blaudez, J.-M. Turlet, “Specific approach of generalized ellipsometry for the determination of weak in-plane anisotropy: application to Langmuir–Blodgett ultrathin films,” J. Opt. Soc. Am. A 15, 2769–2782 (1998).
[CrossRef]

J. F. Elman, J. Greener, C. M. Herzinger, B. Johs, “Characterization of biaxially stretched plastic films by generalized ellipsometry,” Thin Solid Films 313–314, 816–820 (1998).

J.-D. Hecht, A. Eifler, V. Riede, M. Schubert, G. Krauss, V. Krämer, “Birefringence and reflectivity of single-crystal CdAl2Se4 by generalized ellipsometry,” Phys. Rev. B 57, 7037–7042 (1998).
[CrossRef]

M. Schubert, “Generalized ellipsometry and complex optical systems,” Thin Solid Films 313–314, 313–314 (1998).

1997 (7)

A. Berger, M. R. Pufall, “Generalized magneto-optical ellipsometry,” Appl. Phys. Lett. 71, 965–967 (1997).
[CrossRef]

P. I. Rovira, R. A. Yarussi, R. W. Collins, R. Messier, V. C. Venugopal, A. Lakhtakia, K. Robbi, M. J. Brett, “Transmission ellipsometry of a thin-film helicoidal bianisotropic medium,” Appl. Phys. Lett. 71, 1180–1182 (1997).
[CrossRef]

K. W. Wierman, J. N. Hilfiker, R. F. Sabiryanov, S. S. Jaswal, R. D. Kirby, J. A. Woollam, “Optical and magneto-optical constants of MnPt3,” Phys. Rev. B 55, 3093–3099 (1997).
[CrossRef]

G. E. Jellison, F. A. Modine, L. A. Boatner, “The measurement of the optical functions of uniaxial materials using two-modulator generalized ellipsometry: rutile (TiO2),” Opt. Lett. 22, 1808–1810 (1997).
[CrossRef]

J. S. Nefedov, “Microstrip slow-wave structures on the bianisotropic substrate,” Electromagnetics 17, 343–360 (1997).
[CrossRef]

A. Lakhtakia, W. Weiglhofer, “Further results on light propagation in helicoidal bianisotropic mediums: oblique propagation,” Proc. R. Soc. London Ser. A 453, 93–105 (1997).
[CrossRef]

X. Gao, D. W. Glenn, S. Heckens, D. W. Thompson, J. A. Woollam, “Spectroscopic ellipsometry and magneto-optic Kerr effects in Co/Pt multilayers,” J. Appl. Phys. 82, 4525–4531 (1997).
[CrossRef]

1996 (4)

M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B 53, 4265–4274 (1996).
[CrossRef]

M. Schubert, B. Rheinländer, J. A. Woollam, B. Johs, C. M. Herzinger, “Extension of rotating-analyzer ellipsometry to generalized ellipsometry: determination of the dielectric function tensor of uniaxial TiO2,” J. Opt. Soc. Am. A 13, 875–883 (1996).
[CrossRef]

M. Schubert, B. Rheinländer, C. Cramer, H. Schmiedel, J. A. Woollam, B. Johs, C. M. Herzinger, “Generalized transmission ellipsometry for twisted biaxial dielectric media: application to chiral liquid crystals,” J. Opt. Soc. Am. A 13, 1930–1940 (1996).
[CrossRef]

M. Schubert, B. Rheinländer, E. Franke, I. Pietzonka, J. Škriniarova, V. Gottschalch, “Direct-gap reduction and valence band splitting of ordered indirect-gap AlInP2 studied by dark-field spectroscopy,” Phys. Rev. B 54, 17,616–17,619 (1996).
[CrossRef]

1995 (2)

A. Lakhtakia, W. Weiglhofer, “On light propagation in helicoidal bianisotropic mediums,” Proc. R. Soc. London Ser. A 448, 419–437 (1995).
[CrossRef]

S. Višnovský, M. Nývlt, V. Prosser, R. Lopušník, R. Urban, J. Ferré, G. Pénissard, D. Renard, R. Krishnan, “Polar magneto-optics in simple ultrathin-magnetic-film structures,” Phys. Rev. B 52, 1090–1106 (1995).
[CrossRef]

1994 (2)

Y. Wenyen, W. Wenbing, “The transmission properties of stratified chiroferrite media with obliquely incident plane waves,” Int. J. Infrared Millimeter Waves 15, 593–603 (1994).
[CrossRef]

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, A. B. Kale, “Magnetic field measurements using magneto-optic Kerr effect sensors,” Opt. Eng. 33, 3718–3722 (1994).
[CrossRef]

1993 (2)

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, S. W. McKnight, A. B. Kale, “Measurement of magnetic fields using the magneto-optic Kerr effect,” Appl. Phys. Lett. 63, 415–417 (1993).
[CrossRef]

S. B. Borisov, N. N. Dadoenkova, I. L. Lyubchanskii, “Normal electromagnetic waves in gyrotropic magneto-optic layered structures,” Opt. Spectrosc. 74, 670–682 (1993).

1992 (2)

J. L. Tsalamengas, “Interaction of electromagnetic waves with general bianisotropic slabs,” IEEE Trans. Microwave Theory Tech. 40, 1870–1878 (1992).
[CrossRef]

W. A. McGahan, P. He, J. A. Woollam, “Optical and magneto-optical characterization of thin films,” Appl. Phys. Commun. 11, 375–401 (1992).

1990 (2)

M. Mansuripur, “Analysis of multilayer thin film structures containing magneto-optic and anisotropic media at oblique incidence using 2 × 2 matrices,” J. Appl. Phys. 67, 6466–6480 (1990).
[CrossRef]

J. M. Floraczek, E. Dan Dahlberg, “Detecting two magnetization components by the magneto-optical Kerr effect,” J. Appl. Phys. 67, 7520–7525 (1990).
[CrossRef]

1989 (1)

W. A. McGahan, J. A. Woollam, “Magneto-optics of multilayer systems,” Appl. Phys. Commun. 9, 1–25 (1989).

1988 (4)

1986 (1)

S. Višnovský, “Magneto-optical ellipsometry,” Czech. J. Phys. B 36, 625–650 (1986).
[CrossRef]

1985 (1)

1984 (1)

1982 (1)

J. S. Blakemore, “Intrinsic density ni(T) in GaAs: Deduced from band gap and effective mass parameters and derived independently from Cr acceptor capture and emission coefficients,” J. Appl. Phys. 53, 520–531 (1982).
[CrossRef]

1981 (1)

M. Miyao, T. Motooka, N. Natsuaki, T. Tokuyama, “Change of the electron effective mass in extremely heavily doped n-type Si obtained by ion implantation and laser annealing,” Solid State Commun. 37, 605–608 (1981).
[CrossRef]

1980 (1)

P. Yeh, “Optics of anisotropic layered media: a new 4 × 4 matrix algebra,” Surf. Sci. 96, 41–53 (1980).
[CrossRef]

1976 (3)

P. S. Hauge, “Generalized rotating-compensator ellipsometry,” Surf. Sci. 56, 148–160 (1976).
[CrossRef]

D. J. DeSmet, “Generalized ellipsometry and the 4 × 4 matrix formalism,” Surf. Sci. 56, 293–306 (1976).
[CrossRef]

M. Elshazly-Zaghloul, R. M. A. Azzam, N. M. Bashara, “Explicit solutions for the optical properties of uniaxial materials in generalized ellipsometry,” Surf. Sci. 56, 281–292 (1976).
[CrossRef]

1972 (2)

1967 (1)

R. P. Hunt, “Magneto-optic scattering from thin solid films,” J. Appl. Phys. 38, 1652–1671 (1967).
[CrossRef]

1936 (1)

H. G. Booker, “Oblique propagation of electromagnetic waves in a slowly-varying nonisotropic medium,” Proc. R. Soc. A 155, 235–257 (1936).
[CrossRef]

Azzam, R. M. A.

M. Elshazly-Zaghloul, R. M. A. Azzam, N. M. Bashara, “Explicit solutions for the optical properties of uniaxial materials in generalized ellipsometry,” Surf. Sci. 56, 281–292 (1976).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, “Generalized ellipsometry for surfaces with directional preferences: application to diffraction gratings,” J. Opt. Soc. Am. 62, 1521–1523 (1972).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1984).

Bashara, N. M.

M. Elshazly-Zaghloul, R. M. A. Azzam, N. M. Bashara, “Explicit solutions for the optical properties of uniaxial materials in generalized ellipsometry,” Surf. Sci. 56, 281–292 (1976).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, “Generalized ellipsometry for surfaces with directional preferences: application to diffraction gratings,” J. Opt. Soc. Am. 62, 1521–1523 (1972).
[CrossRef]

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1984).

Berger, A.

A. Berger, M. R. Pufall, “Generalized magneto-optical ellipsometry,” Appl. Phys. Lett. 71, 965–967 (1997).
[CrossRef]

Berreman, D. W.

Blakemore, J. S.

J. S. Blakemore, “Intrinsic density ni(T) in GaAs: Deduced from band gap and effective mass parameters and derived independently from Cr acceptor capture and emission coefficients,” J. Appl. Phys. 53, 520–531 (1982).
[CrossRef]

Blaudez, D.

Boatner, L. A.

Booker, H. G.

H. G. Booker, “Oblique propagation of electromagnetic waves in a slowly-varying nonisotropic medium,” Proc. R. Soc. A 155, 235–257 (1936).
[CrossRef]

Borisov, S. B.

S. B. Borisov, N. N. Dadoenkova, I. L. Lyubchanskii, “Normal electromagnetic waves in gyrotropic magneto-optic layered structures,” Opt. Spectrosc. 74, 670–682 (1993).

Brett, M. J.

P. I. Rovira, R. A. Yarussi, R. W. Collins, R. Messier, V. C. Venugopal, A. Lakhtakia, K. Robbi, M. J. Brett, “Transmission ellipsometry of a thin-film helicoidal bianisotropic medium,” Appl. Phys. Lett. 71, 1180–1182 (1997).
[CrossRef]

Collins, R. W.

P. I. Rovira, R. A. Yarussi, R. W. Collins, R. Messier, V. C. Venugopal, A. Lakhtakia, K. Robbi, M. J. Brett, “Transmission ellipsometry of a thin-film helicoidal bianisotropic medium,” Appl. Phys. Lett. 71, 1180–1182 (1997).
[CrossRef]

Cramer, C.

Dadoenkova, N. N.

S. B. Borisov, N. N. Dadoenkova, I. L. Lyubchanskii, “Normal electromagnetic waves in gyrotropic magneto-optic layered structures,” Opt. Spectrosc. 74, 670–682 (1993).

Damaskos, N. J.

Dan Dahlberg, E.

J. M. Floraczek, E. Dan Dahlberg, “Detecting two magnetization components by the magneto-optical Kerr effect,” J. Appl. Phys. 67, 7520–7525 (1990).
[CrossRef]

DeSmet, D. J.

D. J. DeSmet, “Generalized ellipsometry and the 4 × 4 matrix formalism,” Surf. Sci. 56, 293–306 (1976).
[CrossRef]

DeVries, M. J.

D. W. Thompson, M. J. DeVries, T. E. Tiwald, J. A. Woollam, “Determination of optical anisotropy in calcite from ultraviolet to mid-infrared by generalized ellipsometry,” Thin Solid Films 313–314, 341–346 (1998).

DiMarzio, C. A.

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, A. B. Kale, “Magnetic field measurements using magneto-optic Kerr effect sensors,” Opt. Eng. 33, 3718–3722 (1994).
[CrossRef]

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, S. W. McKnight, A. B. Kale, “Measurement of magnetic fields using the magneto-optic Kerr effect,” Appl. Phys. Lett. 63, 415–417 (1993).
[CrossRef]

Eifler, A.

J.-D. Hecht, A. Eifler, V. Riede, M. Schubert, G. Krauss, V. Krämer, “Birefringence and reflectivity of single-crystal CdAl2Se4 by generalized ellipsometry,” Phys. Rev. B 57, 7037–7042 (1998).
[CrossRef]

Elman, J. F.

J. F. Elman, J. Greener, C. M. Herzinger, B. Johs, “Characterization of biaxially stretched plastic films by generalized ellipsometry,” Thin Solid Films 313–314, 816–820 (1998).

Elshazly-Zaghloul, M.

M. Elshazly-Zaghloul, R. M. A. Azzam, N. M. Bashara, “Explicit solutions for the optical properties of uniaxial materials in generalized ellipsometry,” Surf. Sci. 56, 281–292 (1976).
[CrossRef]

Ferré, J.

S. Višnovský, M. Nývlt, V. Prosser, R. Lopušník, R. Urban, J. Ferré, G. Pénissard, D. Renard, R. Krishnan, “Polar magneto-optics in simple ultrathin-magnetic-film structures,” Phys. Rev. B 52, 1090–1106 (1995).
[CrossRef]

Floraczek, J. M.

J. M. Floraczek, E. Dan Dahlberg, “Detecting two magnetization components by the magneto-optical Kerr effect,” J. Appl. Phys. 67, 7520–7525 (1990).
[CrossRef]

Franke, E.

M. Schubert, B. Rheinländer, E. Franke, I. Pietzonka, J. Škriniarova, V. Gottschalch, “Direct-gap reduction and valence band splitting of ordered indirect-gap AlInP2 studied by dark-field spectroscopy,” Phys. Rev. B 54, 17,616–17,619 (1996).
[CrossRef]

Fritsch, M.

Gamble, R.

Gao, X.

X. Gao, D. W. Glenn, S. Heckens, D. W. Thompson, J. A. Woollam, “Spectroscopic ellipsometry and magneto-optic Kerr effects in Co/Pt multilayers,” J. Appl. Phys. 82, 4525–4531 (1997).
[CrossRef]

Glenn, D. W.

X. Gao, D. W. Glenn, S. Heckens, D. W. Thompson, J. A. Woollam, “Spectroscopic ellipsometry and magneto-optic Kerr effects in Co/Pt multilayers,” J. Appl. Phys. 82, 4525–4531 (1997).
[CrossRef]

Gottschalch, V.

M. Schubert, B. Rheinländer, E. Franke, I. Pietzonka, J. Škriniarova, V. Gottschalch, “Direct-gap reduction and valence band splitting of ordered indirect-gap AlInP2 studied by dark-field spectroscopy,” Phys. Rev. B 54, 17,616–17,619 (1996).
[CrossRef]

Greener, J.

J. F. Elman, J. Greener, C. M. Herzinger, B. Johs, “Characterization of biaxially stretched plastic films by generalized ellipsometry,” Thin Solid Films 313–314, 816–820 (1998).

Haas, G.

Hauge, P. S.

P. S. Hauge, “Generalized rotating-compensator ellipsometry,” Surf. Sci. 56, 148–160 (1976).
[CrossRef]

He, P.

W. A. McGahan, P. He, J. A. Woollam, “Optical and magneto-optical characterization of thin films,” Appl. Phys. Commun. 11, 375–401 (1992).

Hecht, J.-D.

J.-D. Hecht, A. Eifler, V. Riede, M. Schubert, G. Krauss, V. Krämer, “Birefringence and reflectivity of single-crystal CdAl2Se4 by generalized ellipsometry,” Phys. Rev. B 57, 7037–7042 (1998).
[CrossRef]

Heckens, S.

X. Gao, D. W. Glenn, S. Heckens, D. W. Thompson, J. A. Woollam, “Spectroscopic ellipsometry and magneto-optic Kerr effects in Co/Pt multilayers,” J. Appl. Phys. 82, 4525–4531 (1997).
[CrossRef]

Herzinger, C. M.

Hilfiker, J. N.

K. W. Wierman, J. N. Hilfiker, R. F. Sabiryanov, S. S. Jaswal, R. D. Kirby, J. A. Woollam, “Optical and magneto-optical constants of MnPt3,” Phys. Rev. B 55, 3093–3099 (1997).
[CrossRef]

Hunt, R. P.

R. P. Hunt, “Magneto-optic scattering from thin solid films,” J. Appl. Phys. 38, 1652–1671 (1967).
[CrossRef]

Jaswal, S. S.

K. W. Wierman, J. N. Hilfiker, R. F. Sabiryanov, S. S. Jaswal, R. D. Kirby, J. A. Woollam, “Optical and magneto-optical constants of MnPt3,” Phys. Rev. B 55, 3093–3099 (1997).
[CrossRef]

Jellison, G. E.

Johs, B.

Kale, A. B.

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, A. B. Kale, “Magnetic field measurements using magneto-optic Kerr effect sensors,” Opt. Eng. 33, 3718–3722 (1994).
[CrossRef]

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, S. W. McKnight, A. B. Kale, “Measurement of magnetic fields using the magneto-optic Kerr effect,” Appl. Phys. Lett. 63, 415–417 (1993).
[CrossRef]

Kirby, R. D.

K. W. Wierman, J. N. Hilfiker, R. F. Sabiryanov, S. S. Jaswal, R. D. Kirby, J. A. Woollam, “Optical and magneto-optical constants of MnPt3,” Phys. Rev. B 55, 3093–3099 (1997).
[CrossRef]

Kong, J. A.

For a definition of the constitutive relations for several anisotropic media, see, e.g., J. A. Kong, Electromagnetic Wave Theory (Wiley, New York, 1990).

Krämer, V.

J.-D. Hecht, A. Eifler, V. Riede, M. Schubert, G. Krauss, V. Krämer, “Birefringence and reflectivity of single-crystal CdAl2Se4 by generalized ellipsometry,” Phys. Rev. B 57, 7037–7042 (1998).
[CrossRef]

Krauss, G.

J.-D. Hecht, A. Eifler, V. Riede, M. Schubert, G. Krauss, V. Krämer, “Birefringence and reflectivity of single-crystal CdAl2Se4 by generalized ellipsometry,” Phys. Rev. B 57, 7037–7042 (1998).
[CrossRef]

Krishnan, R.

S. Višnovský, M. Nývlt, V. Prosser, R. Lopušník, R. Urban, J. Ferré, G. Pénissard, D. Renard, R. Krishnan, “Polar magneto-optics in simple ultrathin-magnetic-film structures,” Phys. Rev. B 52, 1090–1106 (1995).
[CrossRef]

Lakhtakia, A.

A. Lakhtakia, W. Weiglhofer, “Further results on light propagation in helicoidal bianisotropic mediums: oblique propagation,” Proc. R. Soc. London Ser. A 453, 93–105 (1997).
[CrossRef]

P. I. Rovira, R. A. Yarussi, R. W. Collins, R. Messier, V. C. Venugopal, A. Lakhtakia, K. Robbi, M. J. Brett, “Transmission ellipsometry of a thin-film helicoidal bianisotropic medium,” Appl. Phys. Lett. 71, 1180–1182 (1997).
[CrossRef]

A. Lakhtakia, W. Weiglhofer, “On light propagation in helicoidal bianisotropic mediums,” Proc. R. Soc. London Ser. A 448, 419–437 (1995).
[CrossRef]

Landau, L. D.

L. D. Landau, E. M. Lifschitz, Electrodynamics of Continuous Media (Pergamon, New York, 1960).

Lecourt, B.

Li, Z.-M.

Lifschitz, E. M.

L. D. Landau, E. M. Lifschitz, Electrodynamics of Continuous Media (Pergamon, New York, 1960).

Lin-Chung, P. J.

Lindberg, S. C.

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, A. B. Kale, “Magnetic field measurements using magneto-optic Kerr effect sensors,” Opt. Eng. 33, 3718–3722 (1994).
[CrossRef]

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, S. W. McKnight, A. B. Kale, “Measurement of magnetic fields using the magneto-optic Kerr effect,” Appl. Phys. Lett. 63, 415–417 (1993).
[CrossRef]

Lissberger, P. H.

Lopušník, R.

S. Višnovský, M. Nývlt, V. Prosser, R. Lopušník, R. Urban, J. Ferré, G. Pénissard, D. Renard, R. Krishnan, “Polar magneto-optics in simple ultrathin-magnetic-film structures,” Phys. Rev. B 52, 1090–1106 (1995).
[CrossRef]

Lyubchanskii, I. L.

S. B. Borisov, N. N. Dadoenkova, I. L. Lyubchanskii, “Normal electromagnetic waves in gyrotropic magneto-optic layered structures,” Opt. Spectrosc. 74, 670–682 (1993).

Macleod, H. A.

H. A. Macleod, Thin Film Optical Filters (Macmillan, New York, 1986).
[CrossRef]

Maffet, A. L.

Mansuripur, M.

M. Mansuripur, “Analysis of multilayer thin film structures containing magneto-optic and anisotropic media at oblique incidence using 2 × 2 matrices,” J. Appl. Phys. 67, 6466–6480 (1990).
[CrossRef]

M. Mansuripur, The Physical Principles of Magneto-optical Recording (Cambridge University, Cambridge, England, 1995).
[CrossRef]

McGahan, W. A.

W. A. McGahan, P. He, J. A. Woollam, “Optical and magneto-optical characterization of thin films,” Appl. Phys. Commun. 11, 375–401 (1992).

W. A. McGahan, J. A. Woollam, “Magneto-optics of multilayer systems,” Appl. Phys. Commun. 9, 1–25 (1989).

See, for example, W. A. McGahan, “Magneto-optical applications,” in Intermetallic Compounds, J. H. Westbrook, R. L. Fleischer, eds. (Wiley, London, 1994), Vol. 2, Chap. 19, pp. 435–451.

McKnight, S. W.

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, S. W. McKnight, A. B. Kale, “Measurement of magnetic fields using the magneto-optic Kerr effect,” Appl. Phys. Lett. 63, 415–417 (1993).
[CrossRef]

Messier, R.

P. I. Rovira, R. A. Yarussi, R. W. Collins, R. Messier, V. C. Venugopal, A. Lakhtakia, K. Robbi, M. J. Brett, “Transmission ellipsometry of a thin-film helicoidal bianisotropic medium,” Appl. Phys. Lett. 71, 1180–1182 (1997).
[CrossRef]

Miyao, M.

M. Miyao, T. Motooka, N. Natsuaki, T. Tokuyama, “Change of the electron effective mass in extremely heavily doped n-type Si obtained by ion implantation and laser annealing,” Solid State Commun. 37, 605–608 (1981).
[CrossRef]

Mlynski, D. A.

Modine, F. A.

Motooka, T.

M. Miyao, T. Motooka, N. Natsuaki, T. Tokuyama, “Change of the electron effective mass in extremely heavily doped n-type Si obtained by ion implantation and laser annealing,” Solid State Commun. 37, 605–608 (1981).
[CrossRef]

Natsuaki, N.

M. Miyao, T. Motooka, N. Natsuaki, T. Tokuyama, “Change of the electron effective mass in extremely heavily doped n-type Si obtained by ion implantation and laser annealing,” Solid State Commun. 37, 605–608 (1981).
[CrossRef]

Nefedov, J. S.

J. S. Nefedov, “Microstrip slow-wave structures on the bianisotropic substrate,” Electromagnetics 17, 343–360 (1997).
[CrossRef]

Nývlt, M.

S. Višnovský, M. Nývlt, V. Prosser, R. Lopušník, R. Urban, J. Ferré, G. Pénissard, D. Renard, R. Krishnan, “Polar magneto-optics in simple ultrathin-magnetic-film structures,” Phys. Rev. B 52, 1090–1106 (1995).
[CrossRef]

Oliver, S. A.

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, A. B. Kale, “Magnetic field measurements using magneto-optic Kerr effect sensors,” Opt. Eng. 33, 3718–3722 (1994).
[CrossRef]

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, S. W. McKnight, A. B. Kale, “Measurement of magnetic fields using the magneto-optic Kerr effect,” Appl. Phys. Lett. 63, 415–417 (1993).
[CrossRef]

Palik, E. D.

E. D. Palik, G. B. Wright, “Free carrier magneto-optical effects,” in R. K. Willardson, A. C. Beer, in Optical Properties of III–V Compounds, Vol. 3 of Semiconductors and Semimetals (Academic, New York, 1967), pp. 457–458.

Parson, R. R.

Pénissard, G.

S. Višnovský, M. Nývlt, V. Prosser, R. Lopušník, R. Urban, J. Ferré, G. Pénissard, D. Renard, R. Krishnan, “Polar magneto-optics in simple ultrathin-magnetic-film structures,” Phys. Rev. B 52, 1090–1106 (1995).
[CrossRef]

Pidgeon, C. R.

C. R. Pidgeon, “Free carrier optical properties of semiconductors,” in Handbook on Semiconductors, M. Balkanski, ed. (North-Holland, Amsterdam, 1980), Vol. 2, pp. 223–328.

Pietzonka, I.

M. Schubert, B. Rheinländer, E. Franke, I. Pietzonka, J. Škriniarova, V. Gottschalch, “Direct-gap reduction and valence band splitting of ordered indirect-gap AlInP2 studied by dark-field spectroscopy,” Phys. Rev. B 54, 17,616–17,619 (1996).
[CrossRef]

Prosser, V.

S. Višnovský, M. Nývlt, V. Prosser, R. Lopušník, R. Urban, J. Ferré, G. Pénissard, D. Renard, R. Krishnan, “Polar magneto-optics in simple ultrathin-magnetic-film structures,” Phys. Rev. B 52, 1090–1106 (1995).
[CrossRef]

Pufall, M. R.

A. Berger, M. R. Pufall, “Generalized magneto-optical ellipsometry,” Appl. Phys. Lett. 71, 965–967 (1997).
[CrossRef]

Renard, D.

S. Višnovský, M. Nývlt, V. Prosser, R. Lopušník, R. Urban, J. Ferré, G. Pénissard, D. Renard, R. Krishnan, “Polar magneto-optics in simple ultrathin-magnetic-film structures,” Phys. Rev. B 52, 1090–1106 (1995).
[CrossRef]

Rheinländer, B.

Riede, V.

J.-D. Hecht, A. Eifler, V. Riede, M. Schubert, G. Krauss, V. Krämer, “Birefringence and reflectivity of single-crystal CdAl2Se4 by generalized ellipsometry,” Phys. Rev. B 57, 7037–7042 (1998).
[CrossRef]

Robbi, K.

P. I. Rovira, R. A. Yarussi, R. W. Collins, R. Messier, V. C. Venugopal, A. Lakhtakia, K. Robbi, M. J. Brett, “Transmission ellipsometry of a thin-film helicoidal bianisotropic medium,” Appl. Phys. Lett. 71, 1180–1182 (1997).
[CrossRef]

Rovira, P. I.

P. I. Rovira, R. A. Yarussi, R. W. Collins, R. Messier, V. C. Venugopal, A. Lakhtakia, K. Robbi, M. J. Brett, “Transmission ellipsometry of a thin-film helicoidal bianisotropic medium,” Appl. Phys. Lett. 71, 1180–1182 (1997).
[CrossRef]

Sabiryanov, R. F.

K. W. Wierman, J. N. Hilfiker, R. F. Sabiryanov, S. S. Jaswal, R. D. Kirby, J. A. Woollam, “Optical and magneto-optical constants of MnPt3,” Phys. Rev. B 55, 3093–3099 (1997).
[CrossRef]

Schmiedel, H.

Schubert, M.

J.-D. Hecht, A. Eifler, V. Riede, M. Schubert, G. Krauss, V. Krämer, “Birefringence and reflectivity of single-crystal CdAl2Se4 by generalized ellipsometry,” Phys. Rev. B 57, 7037–7042 (1998).
[CrossRef]

M. Schubert, “Generalized ellipsometry and complex optical systems,” Thin Solid Films 313–314, 313–314 (1998).

M. Schubert, B. Rheinländer, E. Franke, I. Pietzonka, J. Škriniarova, V. Gottschalch, “Direct-gap reduction and valence band splitting of ordered indirect-gap AlInP2 studied by dark-field spectroscopy,” Phys. Rev. B 54, 17,616–17,619 (1996).
[CrossRef]

M. Schubert, B. Rheinländer, C. Cramer, H. Schmiedel, J. A. Woollam, B. Johs, C. M. Herzinger, “Generalized transmission ellipsometry for twisted biaxial dielectric media: application to chiral liquid crystals,” J. Opt. Soc. Am. A 13, 1930–1940 (1996).
[CrossRef]

M. Schubert, B. Rheinländer, J. A. Woollam, B. Johs, C. M. Herzinger, “Extension of rotating-analyzer ellipsometry to generalized ellipsometry: determination of the dielectric function tensor of uniaxial TiO2,” J. Opt. Soc. Am. A 13, 875–883 (1996).
[CrossRef]

M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B 53, 4265–4274 (1996).
[CrossRef]

Škriniarova, J.

M. Schubert, B. Rheinländer, E. Franke, I. Pietzonka, J. Škriniarova, V. Gottschalch, “Direct-gap reduction and valence band splitting of ordered indirect-gap AlInP2 studied by dark-field spectroscopy,” Phys. Rev. B 54, 17,616–17,619 (1996).
[CrossRef]

Sullivan, B. T.

Sze, S. M.

S. M. Sze, Physics of Semiconductor Devices (Wiley, New York, 1981), pp. 29, 849.

Teitler, S.

Thompson, D. W.

D. W. Thompson, M. J. DeVries, T. E. Tiwald, J. A. Woollam, “Determination of optical anisotropy in calcite from ultraviolet to mid-infrared by generalized ellipsometry,” Thin Solid Films 313–314, 341–346 (1998).

X. Gao, D. W. Glenn, S. Heckens, D. W. Thompson, J. A. Woollam, “Spectroscopic ellipsometry and magneto-optic Kerr effects in Co/Pt multilayers,” J. Appl. Phys. 82, 4525–4531 (1997).
[CrossRef]

Tiwald, T. E.

D. W. Thompson, M. J. DeVries, T. E. Tiwald, J. A. Woollam, “Determination of optical anisotropy in calcite from ultraviolet to mid-infrared by generalized ellipsometry,” Thin Solid Films 313–314, 341–346 (1998).

Tokuyama, T.

M. Miyao, T. Motooka, N. Natsuaki, T. Tokuyama, “Change of the electron effective mass in extremely heavily doped n-type Si obtained by ion implantation and laser annealing,” Solid State Commun. 37, 605–608 (1981).
[CrossRef]

Tsalamengas, J. L.

J. L. Tsalamengas, “Interaction of electromagnetic waves with general bianisotropic slabs,” IEEE Trans. Microwave Theory Tech. 40, 1870–1878 (1992).
[CrossRef]

Turlet, J.-M.

Urban, R.

S. Višnovský, M. Nývlt, V. Prosser, R. Lopušník, R. Urban, J. Ferré, G. Pénissard, D. Renard, R. Krishnan, “Polar magneto-optics in simple ultrathin-magnetic-film structures,” Phys. Rev. B 52, 1090–1106 (1995).
[CrossRef]

Ushlenghi, P. L. E.

Venugopal, V. C.

P. I. Rovira, R. A. Yarussi, R. W. Collins, R. Messier, V. C. Venugopal, A. Lakhtakia, K. Robbi, M. J. Brett, “Transmission ellipsometry of a thin-film helicoidal bianisotropic medium,” Appl. Phys. Lett. 71, 1180–1182 (1997).
[CrossRef]

Višnovský, S.

S. Višnovský, M. Nývlt, V. Prosser, R. Lopušník, R. Urban, J. Ferré, G. Pénissard, D. Renard, R. Krishnan, “Polar magneto-optics in simple ultrathin-magnetic-film structures,” Phys. Rev. B 52, 1090–1106 (1995).
[CrossRef]

S. Višnovský, “Magneto-optical ellipsometry,” Czech. J. Phys. B 36, 625–650 (1986).
[CrossRef]

Wallis, R. F.

An introduction to electromagnetic-wave propagation in magneto-optically biaxial materials in application to surface and bulk related plasmons in semiconductors can be found in R. F. Wallis, “Optical properties associated with surface excitations of semiconductors,” in Handbook on Semiconductors, M. Balkanski, ed. (North-Holland, Amsterdam, 1994), Vol. 2, pp. 65–108.

Weiglhofer, W.

A. Lakhtakia, W. Weiglhofer, “Further results on light propagation in helicoidal bianisotropic mediums: oblique propagation,” Proc. R. Soc. London Ser. A 453, 93–105 (1997).
[CrossRef]

A. Lakhtakia, W. Weiglhofer, “On light propagation in helicoidal bianisotropic mediums,” Proc. R. Soc. London Ser. A 448, 419–437 (1995).
[CrossRef]

Wenbing, W.

Y. Wenyen, W. Wenbing, “The transmission properties of stratified chiroferrite media with obliquely incident plane waves,” Int. J. Infrared Millimeter Waves 15, 593–603 (1994).
[CrossRef]

Wenyen, Y.

Y. Wenyen, W. Wenbing, “The transmission properties of stratified chiroferrite media with obliquely incident plane waves,” Int. J. Infrared Millimeter Waves 15, 593–603 (1994).
[CrossRef]

Wierman, K. W.

K. W. Wierman, J. N. Hilfiker, R. F. Sabiryanov, S. S. Jaswal, R. D. Kirby, J. A. Woollam, “Optical and magneto-optical constants of MnPt3,” Phys. Rev. B 55, 3093–3099 (1997).
[CrossRef]

Wöhler, H.

Woollam, J. A.

D. W. Thompson, M. J. DeVries, T. E. Tiwald, J. A. Woollam, “Determination of optical anisotropy in calcite from ultraviolet to mid-infrared by generalized ellipsometry,” Thin Solid Films 313–314, 341–346 (1998).

K. W. Wierman, J. N. Hilfiker, R. F. Sabiryanov, S. S. Jaswal, R. D. Kirby, J. A. Woollam, “Optical and magneto-optical constants of MnPt3,” Phys. Rev. B 55, 3093–3099 (1997).
[CrossRef]

X. Gao, D. W. Glenn, S. Heckens, D. W. Thompson, J. A. Woollam, “Spectroscopic ellipsometry and magneto-optic Kerr effects in Co/Pt multilayers,” J. Appl. Phys. 82, 4525–4531 (1997).
[CrossRef]

M. Schubert, B. Rheinländer, J. A. Woollam, B. Johs, C. M. Herzinger, “Extension of rotating-analyzer ellipsometry to generalized ellipsometry: determination of the dielectric function tensor of uniaxial TiO2,” J. Opt. Soc. Am. A 13, 875–883 (1996).
[CrossRef]

M. Schubert, B. Rheinländer, C. Cramer, H. Schmiedel, J. A. Woollam, B. Johs, C. M. Herzinger, “Generalized transmission ellipsometry for twisted biaxial dielectric media: application to chiral liquid crystals,” J. Opt. Soc. Am. A 13, 1930–1940 (1996).
[CrossRef]

W. A. McGahan, P. He, J. A. Woollam, “Optical and magneto-optical characterization of thin films,” Appl. Phys. Commun. 11, 375–401 (1992).

W. A. McGahan, J. A. Woollam, “Magneto-optics of multilayer systems,” Appl. Phys. Commun. 9, 1–25 (1989).

Wright, G. B.

E. D. Palik, G. B. Wright, “Free carrier magneto-optical effects,” in R. K. Willardson, A. C. Beer, in Optical Properties of III–V Compounds, Vol. 3 of Semiconductors and Semimetals (Academic, New York, 1967), pp. 457–458.

Yarussi, R. A.

P. I. Rovira, R. A. Yarussi, R. W. Collins, R. Messier, V. C. Venugopal, A. Lakhtakia, K. Robbi, M. J. Brett, “Transmission ellipsometry of a thin-film helicoidal bianisotropic medium,” Appl. Phys. Lett. 71, 1180–1182 (1997).
[CrossRef]

Yeh, P.

P. Yeh, “Optics of anisotropic layered media: a new 4 × 4 matrix algebra,” Surf. Sci. 96, 41–53 (1980).
[CrossRef]

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

Appl. Opt. (2)

Appl. Phys. Commun. (2)

W. A. McGahan, P. He, J. A. Woollam, “Optical and magneto-optical characterization of thin films,” Appl. Phys. Commun. 11, 375–401 (1992).

W. A. McGahan, J. A. Woollam, “Magneto-optics of multilayer systems,” Appl. Phys. Commun. 9, 1–25 (1989).

Appl. Phys. Lett. (3)

P. I. Rovira, R. A. Yarussi, R. W. Collins, R. Messier, V. C. Venugopal, A. Lakhtakia, K. Robbi, M. J. Brett, “Transmission ellipsometry of a thin-film helicoidal bianisotropic medium,” Appl. Phys. Lett. 71, 1180–1182 (1997).
[CrossRef]

A. Berger, M. R. Pufall, “Generalized magneto-optical ellipsometry,” Appl. Phys. Lett. 71, 965–967 (1997).
[CrossRef]

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, S. W. McKnight, A. B. Kale, “Measurement of magnetic fields using the magneto-optic Kerr effect,” Appl. Phys. Lett. 63, 415–417 (1993).
[CrossRef]

Czech. J. Phys. B (1)

S. Višnovský, “Magneto-optical ellipsometry,” Czech. J. Phys. B 36, 625–650 (1986).
[CrossRef]

Electromagnetics (1)

J. S. Nefedov, “Microstrip slow-wave structures on the bianisotropic substrate,” Electromagnetics 17, 343–360 (1997).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. L. Tsalamengas, “Interaction of electromagnetic waves with general bianisotropic slabs,” IEEE Trans. Microwave Theory Tech. 40, 1870–1878 (1992).
[CrossRef]

Int. J. Infrared Millimeter Waves (1)

Y. Wenyen, W. Wenbing, “The transmission properties of stratified chiroferrite media with obliquely incident plane waves,” Int. J. Infrared Millimeter Waves 15, 593–603 (1994).
[CrossRef]

J. Appl. Phys. (5)

R. P. Hunt, “Magneto-optic scattering from thin solid films,” J. Appl. Phys. 38, 1652–1671 (1967).
[CrossRef]

M. Mansuripur, “Analysis of multilayer thin film structures containing magneto-optic and anisotropic media at oblique incidence using 2 × 2 matrices,” J. Appl. Phys. 67, 6466–6480 (1990).
[CrossRef]

J. M. Floraczek, E. Dan Dahlberg, “Detecting two magnetization components by the magneto-optical Kerr effect,” J. Appl. Phys. 67, 7520–7525 (1990).
[CrossRef]

X. Gao, D. W. Glenn, S. Heckens, D. W. Thompson, J. A. Woollam, “Spectroscopic ellipsometry and magneto-optic Kerr effects in Co/Pt multilayers,” J. Appl. Phys. 82, 4525–4531 (1997).
[CrossRef]

J. S. Blakemore, “Intrinsic density ni(T) in GaAs: Deduced from band gap and effective mass parameters and derived independently from Cr acceptor capture and emission coefficients,” J. Appl. Phys. 53, 520–531 (1982).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (8)

B. Lecourt, D. Blaudez, J.-M. Turlet, “Specific approach of generalized ellipsometry for the determination of weak in-plane anisotropy: application to Langmuir–Blodgett ultrathin films,” J. Opt. Soc. Am. A 15, 2769–2782 (1998).
[CrossRef]

M. Schubert, B. Rheinländer, J. A. Woollam, B. Johs, C. M. Herzinger, “Extension of rotating-analyzer ellipsometry to generalized ellipsometry: determination of the dielectric function tensor of uniaxial TiO2,” J. Opt. Soc. Am. A 13, 875–883 (1996).
[CrossRef]

M. Schubert, B. Rheinländer, C. Cramer, H. Schmiedel, J. A. Woollam, B. Johs, C. M. Herzinger, “Generalized transmission ellipsometry for twisted biaxial dielectric media: application to chiral liquid crystals,” J. Opt. Soc. Am. A 13, 1930–1940 (1996).
[CrossRef]

See P. J. Lin-Chung, S. Teitler, “4 × 4 matrix formalism for optics in stratified anisotropic media,” J. Opt. Soc. Am. A 1, 703–705 (1984) for a comparison between the 4 × 4 matrix formalisms developed by Berreman24 and by Yeh.25

N. J. Damaskos, A. L. Maffet, P. L. E. Ushlenghi, “Reflection and transmission for gyroelectromagnetic biaxial layered media,” J. Opt. Soc. Am. A 2, 454–461 (1985).
[CrossRef]

Z.-M. Li, R. R. Parson, “Reflection of strongly focused light beams from magneto-optic multilayer films,” J. Opt. Soc. Am. A 5, 1543–1548 (1988).
[CrossRef]

R. Gamble, P. H. Lissberger, “Electromagnetic field distributions in multilayer thin films for magneto-optic recording media,” J. Opt. Soc. Am. A 5, 1533–1542 (1988).
[CrossRef]

H. Wöhler, M. Fritsch, G. Haas, D. A. Mlynski, “Faster 4 × 4 matrix method for uniaxial inhomogeneous media,” J. Opt. Soc. Am. A 5, 1554–1557 (1988).
[CrossRef]

Opt. Eng. (1)

S. A. Oliver, C. A. DiMarzio, S. C. Lindberg, A. B. Kale, “Magnetic field measurements using magneto-optic Kerr effect sensors,” Opt. Eng. 33, 3718–3722 (1994).
[CrossRef]

Opt. Lett. (1)

Opt. Spectrosc. (1)

S. B. Borisov, N. N. Dadoenkova, I. L. Lyubchanskii, “Normal electromagnetic waves in gyrotropic magneto-optic layered structures,” Opt. Spectrosc. 74, 670–682 (1993).

Phys. Rev. B (5)

S. Višnovský, M. Nývlt, V. Prosser, R. Lopušník, R. Urban, J. Ferré, G. Pénissard, D. Renard, R. Krishnan, “Polar magneto-optics in simple ultrathin-magnetic-film structures,” Phys. Rev. B 52, 1090–1106 (1995).
[CrossRef]

K. W. Wierman, J. N. Hilfiker, R. F. Sabiryanov, S. S. Jaswal, R. D. Kirby, J. A. Woollam, “Optical and magneto-optical constants of MnPt3,” Phys. Rev. B 55, 3093–3099 (1997).
[CrossRef]

M. Schubert, B. Rheinländer, E. Franke, I. Pietzonka, J. Škriniarova, V. Gottschalch, “Direct-gap reduction and valence band splitting of ordered indirect-gap AlInP2 studied by dark-field spectroscopy,” Phys. Rev. B 54, 17,616–17,619 (1996).
[CrossRef]

J.-D. Hecht, A. Eifler, V. Riede, M. Schubert, G. Krauss, V. Krämer, “Birefringence and reflectivity of single-crystal CdAl2Se4 by generalized ellipsometry,” Phys. Rev. B 57, 7037–7042 (1998).
[CrossRef]

M. Schubert, “Polarization-dependent optical parameters of arbitrarily anisotropic homogeneous layered systems,” Phys. Rev. B 53, 4265–4274 (1996).
[CrossRef]

Proc. R. Soc. A (1)

H. G. Booker, “Oblique propagation of electromagnetic waves in a slowly-varying nonisotropic medium,” Proc. R. Soc. A 155, 235–257 (1936).
[CrossRef]

Proc. R. Soc. London Ser. A (2)

A. Lakhtakia, W. Weiglhofer, “On light propagation in helicoidal bianisotropic mediums,” Proc. R. Soc. London Ser. A 448, 419–437 (1995).
[CrossRef]

A. Lakhtakia, W. Weiglhofer, “Further results on light propagation in helicoidal bianisotropic mediums: oblique propagation,” Proc. R. Soc. London Ser. A 453, 93–105 (1997).
[CrossRef]

Solid State Commun. (1)

M. Miyao, T. Motooka, N. Natsuaki, T. Tokuyama, “Change of the electron effective mass in extremely heavily doped n-type Si obtained by ion implantation and laser annealing,” Solid State Commun. 37, 605–608 (1981).
[CrossRef]

Surf. Sci. (4)

P. S. Hauge, “Generalized rotating-compensator ellipsometry,” Surf. Sci. 56, 148–160 (1976).
[CrossRef]

D. J. DeSmet, “Generalized ellipsometry and the 4 × 4 matrix formalism,” Surf. Sci. 56, 293–306 (1976).
[CrossRef]

M. Elshazly-Zaghloul, R. M. A. Azzam, N. M. Bashara, “Explicit solutions for the optical properties of uniaxial materials in generalized ellipsometry,” Surf. Sci. 56, 281–292 (1976).
[CrossRef]

P. Yeh, “Optics of anisotropic layered media: a new 4 × 4 matrix algebra,” Surf. Sci. 96, 41–53 (1980).
[CrossRef]

Thin Solid Films (3)

M. Schubert, “Generalized ellipsometry and complex optical systems,” Thin Solid Films 313–314, 313–314 (1998).

D. W. Thompson, M. J. DeVries, T. E. Tiwald, J. A. Woollam, “Determination of optical anisotropy in calcite from ultraviolet to mid-infrared by generalized ellipsometry,” Thin Solid Films 313–314, 341–346 (1998).

J. F. Elman, J. Greener, C. M. Herzinger, B. Johs, “Characterization of biaxially stretched plastic films by generalized ellipsometry,” Thin Solid Films 313–314, 816–820 (1998).

Other (13)

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1984).

A. C. Boccara, C. Pickering, J. Rivory, eds., Spectroscopic Ellipsometry (Elsevier, Amsterdam, 1993).

R. W. Collins, D. E. Aspnes, E. A. Irene, eds., Spectroscopic Ellipsometry 1997 (Elsevier, Lausanne, 1997).

See, for example, W. A. McGahan, “Magneto-optical applications,” in Intermetallic Compounds, J. H. Westbrook, R. L. Fleischer, eds. (Wiley, London, 1994), Vol. 2, Chap. 19, pp. 435–451.

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).

H. A. Macleod, Thin Film Optical Filters (Macmillan, New York, 1986).
[CrossRef]

M. Mansuripur, The Physical Principles of Magneto-optical Recording (Cambridge University, Cambridge, England, 1995).
[CrossRef]

An introduction to electromagnetic-wave propagation in magneto-optically biaxial materials in application to surface and bulk related plasmons in semiconductors can be found in R. F. Wallis, “Optical properties associated with surface excitations of semiconductors,” in Handbook on Semiconductors, M. Balkanski, ed. (North-Holland, Amsterdam, 1994), Vol. 2, pp. 65–108.

For a definition of the constitutive relations for several anisotropic media, see, e.g., J. A. Kong, Electromagnetic Wave Theory (Wiley, New York, 1990).

L. D. Landau, E. M. Lifschitz, Electrodynamics of Continuous Media (Pergamon, New York, 1960).

C. R. Pidgeon, “Free carrier optical properties of semiconductors,” in Handbook on Semiconductors, M. Balkanski, ed. (North-Holland, Amsterdam, 1980), Vol. 2, pp. 223–328.

S. M. Sze, Physics of Semiconductor Devices (Wiley, New York, 1981), pp. 29, 849.

E. D. Palik, G. B. Wright, “Free carrier magneto-optical effects,” in R. K. Willardson, A. C. Beer, in Optical Properties of III–V Compounds, Vol. 3 of Semiconductors and Semimetals (Academic, New York, 1967), pp. 457–458.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Schematic representation of a multilayered sample and incident, reflected, and transmitted p and s modes of plane waves with wave vectors k a , k a ′, and k f , respectively. D p and D s indicate the modes of backtraveling waves (k f ′) within the substrate (exit medium) that are assumed to be zero. If the exit medium is anisotropic k f may split into different wave vectors, k f,p and k f,s , associated with C p and C s , respectively.

Fig. 2
Fig. 2

Model parameters and coordinate systems used for the oblique magnetization Kerr-effect calculations of a Co/Au system. A p , A s and B p , B s are the p and the s modes of the incident and the reflected plane waves, respectively. The Euler angles Θ and φ rotate the sample frame of reference, i.e., the sample magnetization direction H. In our notation the special sets (Θ = 0°, φ = 0°), (Θ = 90°, φ = 0°), and (Θ = 90°, φ = 90°) refer to the polar, transverse, and longitudinal Kerr effect, respectively.

Fig. 3
Fig. 3

Magneto-optic Kerr effect for our three-layer structure at normal incidence (Φ a = 0°) as a function of the magnetization direction in terms of the generalized ellipsometric ratio R pp . (a) Ψ pp and (b) Δ pp versus sample magnetization azimuth φ at various inclinations Θ of the magnetization (see Fig. 2). The data points for the transverse, longitudinal (TK, LK; Θ = 90°: open squares at φ = 0°, 180° and φ = 90°, 270°, respectively), and polar (PK; Θ = 0°: solid lines and independent from φ) Kerr-effect generalized ellipsometric angles are indicated by insets. Note that the twofold-degenerate modulation amplitudes in Ψ pp and Δ pp increase as the magnetization in-plane component increases (Θ → 90°).

Fig. 4
Fig. 4

Same as Fig. 3 for (a) Ψ ps and (b) Δ ps . Ψ ps decreases strongly and becomes fourfold degenerate as Θ approaches 90°. Note the right scale in (b), which is valid for Δ ps at Θ = 90° only. It is observed that at normal incidence one cannot distinguish between the reversed transverse (longitudinal) Kerr-effect generalized ellipsometric angles at φ = 0°(90°) and φ = 180°(270°).

Fig. 5
Fig. 5

Same as Fig. 4 for (a) Re{R ps } and (b) Im{R ps }, which in our notation are identical to the usual Kerr rotation Θ K and ellipticity η K parameters as defined, e.g., in Refs. 18 and 19.

Fig. 6
Fig. 6

Same as Fig. 3 for Φ a = 65°. R pp is nondegenerate. Note that the effect of modulation versus φ is much stronger at Φ a = 65° than at normal incidence.

Fig. 7
Fig. 7

Same as Fig. 4 for Φ a = 65°. R ps is now asymmetric with respect to φ and twofold degenerate at Θ = 90° only. Note that R ps is zero in the transverse configuration only, whereas R ps at Φ a = 0° vanishes at the longitudinal magnetization as well. Note again the right scale in Fig. 7(b), which is valid for Θ = 90° only.

Fig. 8
Fig. 8

Same as Fig. 5 for Φ a = 65°. A more pronounced modulation of R pp versus φ at Φ a = 65° than at Φ a = 0° is observed as Θ increases. Obviously, at oblique incidence the generalized ellipsometric parameters are more sensitive to oblique sample magnetization effects than at normal incidence.

Fig. 9
Fig. 9

Birefringent free-carrier magneto-optic effect in a heavily doped semiconductor thin film with nonscalar (spatially dispersive) scattering rates (γ0x = γ0z = 0.01 eV, 2γ0y = γ0x ) in terms of the generalized ellipsometric parameters R ps ps only) at longitudinal magnetization geometry versus incident photon energy and sample azimuth angle φ. The angle of incidence is Φ a = 40°. The scattering tensor γ coincides at φ = 0° with the laboratory coordinate system. A twofold-degenerate variation occurs in Ψ ps when the sample rotates between 0° < φ < 360° with respect to the magnetization direction that remains in the plane of incidence and the sample surface (longitudinal Kerr geometry). At ω ∼ ω p /√ε the incident plane waves cause cyclotron resonance for right and left circularly polarized radiation. At φ = 0°, 90°, 180°, 270° the optical response is similar to the longitudinal Kerr effect. At φ = 45°, 135°, 225°, 315° Ψ ps refers to the polar Kerr effect where cyclotron resonance is observed for right circularly polarized light only, and absorption for left circularly polarized radiation increases monotonically as ω approaches 0 (see, e.g., Ref. 54).

Equations (22)

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

As Bs Ap BpT=TCs 0 Cp 0T.
BpBs=rApAs=rpprsprpsrssApAs, CpCs=tApAs=tpptsptpstssApAs.
T=La-1i=1NTpidi-1Lf=La-1i=1N Tpi-diLf.
ρ=Rpp+Rspχ-11+RppRpsχ-1,
rpprssRpp=tan Ψpp expiΔpp, rpsrppRps=tan Ψps expiΔps, rsprssRsp=tan Ψsp expiΔsp.
Rpp=T11T43-T41T13T21T33-T23T31, Rps=T11T23-T21T13T11T43-T41T13, Rsp=T41T33-T43T31T21T33-T23T31.
zΨz=ik0ΔΨz, Ψz=Ex, Ey, Hx, HyTz, k0ωc,
Ψz+d=expi ωc ΔdΨz=TpΨz, Tpexpi ωc Δd,
Tpexpi ωc Δd=β0I+β1Δ+β2Δ2+β3Δ3,
expi ωc qkd=j=03 βjqkj, k=1,, 4.
εij=sij+aij; sij=sji, aij=-aji, i.e.,  sij=1/2εij+εji; aij=1/2εij-εji.
Δ=-kxs13-a13s33-kxs23-a23s3301-kx2s3300-10s23+a23s13-a13s33-s12-a12kx2-s22+s23-a23s23+a23s330kxs23+a23s33s11-s13+a13s13-a13s33s12+a12-s23-a23s13+a13s330-kxs13+a13s33, kxna sin Φa.
q1/2+=12-kxs13s33--23 t1+kxs13s332+S1/2±-43 t1+2kxs13s332-S-S34-23 t1+kxs13s332+S1/21/2,
q1/2-=12-kxs13s33+-23 t1+kxs13s332+S1/2±-43 t1+2kxs13s332-S+S34-23 t1+kxs13s332+S1/21/2,
S=12S112S2+S22-4S131/2-1/3+12S2+S22-4S131/21/3, S1=t12+12kxs13s33 t2+t3, S2=2t13+36kxs13s33 t1t2+108t22+kxs13s332t3-72t1t3, S3=-8kxs13s33kxs13s332-t1+16t2,
t1=1s33s132+s232-s33s11+s22-kx21+s11s33-a232+a132, t2=kxs33s13s22-s12s23-s13kx2-a23a12, t3=1s33+s11a232-s232+s22a132-s132+s33a122-s122+2s12s13s23-s12a13a23+s13a12a23-s23a13a12+kx2s122+s132-s11s22+s33-kx2-a132+a122+s11s22s33.
ε=ε-i 4πω σ,
μ 1qγ+tv=E+1cv×H.
σ=14πH-1ωp2
H=γ-iωI-qc μ-10-H3H2H30-H1-H2H10, I=δij,
ωp2=4πq2Nμ-1,
γ=AΘ,φ,ψdiagγ0x,γ0y,γ0zA-Θ,-φ,-ψ.

Metrics