OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 38, Iss. 1 — Jan. 1, 1999
  • pp: 177–187

Explicit solutions for the optical properties of arbitrary magneto-optic materials in generalized ellipsometry

Mathias Schubert, Thomas E. Tiwald, and John A. Woollam  »View Author Affiliations


Applied Optics, Vol. 38, Issue 1, pp. 177-187 (1999)
http://dx.doi.org/10.1364/AO.38.000177


View Full Text Article

Enhanced HTML    Acrobat PDF (457 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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

OCIS Codes
(210.3820) Optical data storage : Magneto-optical materials
(230.4170) Optical devices : Multilayers
(260.1180) Physical optics : Crystal optics
(260.1440) Physical optics : Birefringence
(260.2130) Physical optics : Ellipsometry and polarimetry
(310.6860) Thin films : Thin films, optical properties

History
Original Manuscript: June 15, 1998
Revised Manuscript: August 17, 1998
Published: January 1, 1999

Citation
Mathias Schubert, Thomas E. Tiwald, and John A. Woollam, "Explicit solutions for the optical properties of arbitrary magneto-optic materials in generalized ellipsometry," Appl. Opt. 38, 177-187 (1999)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-38-1-177


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  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]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited