Abstract

The new 4 × 4 matrix method described by Lin-Chung and Teitler [ P. J. Lin-Chung and S. Teitler, J. Opt. Soc. Am. A 1, 703 ( 1984)] is used to study the optics of multilayer magnetooptic recording media. It is demonstrated that the method is capable of handling very complicated optical multilayer structures. For a quadrilayer magnetooptic recording system consisting of an overcoat layer, a magnetic layer, an intermediate dielectric layer, and a reflector, the readout of the system is optimized against the thickness of the overcoat and intermediate layers. As well, cases of oblique angle of incidence, anisotropy in the nonmagnetic part of the dielectric constants, and misalignment of the magnetization are treated.

© 1988 Optical Society of America

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References

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  1. G. A. N. Connell, “Interference Enhanced Kerr Spectroscopy for Very Thin Absorbing Films,” Appl. Phys. Lett. 40, 213 (1982).
    [Crossref]
  2. K. Nakamura, T. Asaka, S. Asari, Y. Ota, A. Itoh, “Enhancement of Kerr Rotation with Amorphous Si Film,” IEEE Trans. Magn. MAG-21, 1654 (1985).
    [Crossref]
  3. M. Mansuripur, G. A. N. Connell, J. W. Goodman, “Signal and Noise in Magneto-Optical Readout,” J. Appl. Phys. 53, 4485 (1982).
    [Crossref]
  4. O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).
  5. R. Gamble, P. H. Lissberger, M. R. Parker, “A Simple Analysis for the Optimization of the Normal Polar Magneto-optical Kerr Effect in Multilayer Coatings Containing a Magnetic Film,” IEEE Trans. Magn. MAG-21, 1651 (1985).
    [Crossref]
  6. D. J. Smet, “Generalized Ellipsometry and the 4 × 4 Matrix Formalism,” Surf. Sci. 56, 293 (1976).
    [Crossref]
  7. J. Kranz, C. Schrodter, “Ellipsometry on Magnetooptic Thin Film Multilayer Systems,” Appl. Phys. B 34, 139 (1984).
    [Crossref]
  8. S. Visnovsky, “Magneto-optical Polar Kerr Effect and Birefringence in Magnetic Crystals of Orthorhombic Symmetry,” Czech. J. Phys. B 34, 155 (1984).
    [Crossref]
  9. G. J. Sprokel, “Reflectivity, Rotation, and Ellipticity of Magnetooptic Film Structures,” Appl. Opt. 23, 3983 (1984).
    [Crossref] [PubMed]
  10. D. O. Smith, “Magneto-Optical Scattering from Multilayer Magnetic and Dielectric Films,” Opt. Acta 12, 13 (1965).
    [Crossref]
  11. D. O. Smith, “Optical Scattering from Cubic Electro-optical Films,” Opt. Acta 13, 195 (1966).
    [Crossref]
  12. D. W. Berreman, “4 × 4-Matrix Formulation for Anisotropic Media,” J. Opt. Soc. Am. 62, 502 (1972).
    [Crossref]
  13. P. Yeh, “Optics of Anisotropic Layered Media: A New 4 × 4 Matrix Algebra,” Surf. Sci. 96, 41 (1980).
    [Crossref]
  14. P. J. Lin-Chung, S. Teitler, “4 × 4 Matrix Formalisms for Optics in Stratified Anisotropic Media,” J. Opt. Soc. Am. A 1, 703 (1984).
    [Crossref]
  15. L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, New York, 1960).
  16. A. H. Lettington, “Optical Properties and Fermi Surfaces of Zinc,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North-Holland, Amsterdam, 1966).
  17. D. Keay, P. H. Lissberger, “Longitudinal Kerr Magnetooptic Effect in Multilayer Structures of Dielectric and Magnetic Films,” Opt. Acta 15, 373 (1968).
    [Crossref]

1985 (2)

K. Nakamura, T. Asaka, S. Asari, Y. Ota, A. Itoh, “Enhancement of Kerr Rotation with Amorphous Si Film,” IEEE Trans. Magn. MAG-21, 1654 (1985).
[Crossref]

R. Gamble, P. H. Lissberger, M. R. Parker, “A Simple Analysis for the Optimization of the Normal Polar Magneto-optical Kerr Effect in Multilayer Coatings Containing a Magnetic Film,” IEEE Trans. Magn. MAG-21, 1651 (1985).
[Crossref]

1984 (4)

J. Kranz, C. Schrodter, “Ellipsometry on Magnetooptic Thin Film Multilayer Systems,” Appl. Phys. B 34, 139 (1984).
[Crossref]

S. Visnovsky, “Magneto-optical Polar Kerr Effect and Birefringence in Magnetic Crystals of Orthorhombic Symmetry,” Czech. J. Phys. B 34, 155 (1984).
[Crossref]

G. J. Sprokel, “Reflectivity, Rotation, and Ellipticity of Magnetooptic Film Structures,” Appl. Opt. 23, 3983 (1984).
[Crossref] [PubMed]

P. J. Lin-Chung, S. Teitler, “4 × 4 Matrix Formalisms for Optics in Stratified Anisotropic Media,” J. Opt. Soc. Am. A 1, 703 (1984).
[Crossref]

1982 (2)

G. A. N. Connell, “Interference Enhanced Kerr Spectroscopy for Very Thin Absorbing Films,” Appl. Phys. Lett. 40, 213 (1982).
[Crossref]

M. Mansuripur, G. A. N. Connell, J. W. Goodman, “Signal and Noise in Magneto-Optical Readout,” J. Appl. Phys. 53, 4485 (1982).
[Crossref]

1980 (1)

P. Yeh, “Optics of Anisotropic Layered Media: A New 4 × 4 Matrix Algebra,” Surf. Sci. 96, 41 (1980).
[Crossref]

1976 (1)

D. J. Smet, “Generalized Ellipsometry and the 4 × 4 Matrix Formalism,” Surf. Sci. 56, 293 (1976).
[Crossref]

1972 (1)

1968 (1)

D. Keay, P. H. Lissberger, “Longitudinal Kerr Magnetooptic Effect in Multilayer Structures of Dielectric and Magnetic Films,” Opt. Acta 15, 373 (1968).
[Crossref]

1966 (1)

D. O. Smith, “Optical Scattering from Cubic Electro-optical Films,” Opt. Acta 13, 195 (1966).
[Crossref]

1965 (1)

D. O. Smith, “Magneto-Optical Scattering from Multilayer Magnetic and Dielectric Films,” Opt. Acta 12, 13 (1965).
[Crossref]

Asaka, T.

K. Nakamura, T. Asaka, S. Asari, Y. Ota, A. Itoh, “Enhancement of Kerr Rotation with Amorphous Si Film,” IEEE Trans. Magn. MAG-21, 1654 (1985).
[Crossref]

Asari, S.

K. Nakamura, T. Asaka, S. Asari, Y. Ota, A. Itoh, “Enhancement of Kerr Rotation with Amorphous Si Film,” IEEE Trans. Magn. MAG-21, 1654 (1985).
[Crossref]

Berreman, D. W.

Connell, G. A. N.

G. A. N. Connell, “Interference Enhanced Kerr Spectroscopy for Very Thin Absorbing Films,” Appl. Phys. Lett. 40, 213 (1982).
[Crossref]

M. Mansuripur, G. A. N. Connell, J. W. Goodman, “Signal and Noise in Magneto-Optical Readout,” J. Appl. Phys. 53, 4485 (1982).
[Crossref]

Gamble, R.

R. Gamble, P. H. Lissberger, M. R. Parker, “A Simple Analysis for the Optimization of the Normal Polar Magneto-optical Kerr Effect in Multilayer Coatings Containing a Magnetic Film,” IEEE Trans. Magn. MAG-21, 1651 (1985).
[Crossref]

Goodman, J. W.

M. Mansuripur, G. A. N. Connell, J. W. Goodman, “Signal and Noise in Magneto-Optical Readout,” J. Appl. Phys. 53, 4485 (1982).
[Crossref]

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).

Itoh, A.

K. Nakamura, T. Asaka, S. Asari, Y. Ota, A. Itoh, “Enhancement of Kerr Rotation with Amorphous Si Film,” IEEE Trans. Magn. MAG-21, 1654 (1985).
[Crossref]

Keay, D.

D. Keay, P. H. Lissberger, “Longitudinal Kerr Magnetooptic Effect in Multilayer Structures of Dielectric and Magnetic Films,” Opt. Acta 15, 373 (1968).
[Crossref]

Kranz, J.

J. Kranz, C. Schrodter, “Ellipsometry on Magnetooptic Thin Film Multilayer Systems,” Appl. Phys. B 34, 139 (1984).
[Crossref]

Landau, L. D.

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

Lettington, A. H.

A. H. Lettington, “Optical Properties and Fermi Surfaces of Zinc,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North-Holland, Amsterdam, 1966).

Lifshitz, E. M.

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

Lin-Chung, P. J.

Lissberger, P. H.

R. Gamble, P. H. Lissberger, M. R. Parker, “A Simple Analysis for the Optimization of the Normal Polar Magneto-optical Kerr Effect in Multilayer Coatings Containing a Magnetic Film,” IEEE Trans. Magn. MAG-21, 1651 (1985).
[Crossref]

D. Keay, P. H. Lissberger, “Longitudinal Kerr Magnetooptic Effect in Multilayer Structures of Dielectric and Magnetic Films,” Opt. Acta 15, 373 (1968).
[Crossref]

Mansuripur, M.

M. Mansuripur, G. A. N. Connell, J. W. Goodman, “Signal and Noise in Magneto-Optical Readout,” J. Appl. Phys. 53, 4485 (1982).
[Crossref]

Nakamura, K.

K. Nakamura, T. Asaka, S. Asari, Y. Ota, A. Itoh, “Enhancement of Kerr Rotation with Amorphous Si Film,” IEEE Trans. Magn. MAG-21, 1654 (1985).
[Crossref]

Ota, Y.

K. Nakamura, T. Asaka, S. Asari, Y. Ota, A. Itoh, “Enhancement of Kerr Rotation with Amorphous Si Film,” IEEE Trans. Magn. MAG-21, 1654 (1985).
[Crossref]

Parker, M. R.

R. Gamble, P. H. Lissberger, M. R. Parker, “A Simple Analysis for the Optimization of the Normal Polar Magneto-optical Kerr Effect in Multilayer Coatings Containing a Magnetic Film,” IEEE Trans. Magn. MAG-21, 1651 (1985).
[Crossref]

Schrodter, C.

J. Kranz, C. Schrodter, “Ellipsometry on Magnetooptic Thin Film Multilayer Systems,” Appl. Phys. B 34, 139 (1984).
[Crossref]

Smet, D. J.

D. J. Smet, “Generalized Ellipsometry and the 4 × 4 Matrix Formalism,” Surf. Sci. 56, 293 (1976).
[Crossref]

Smith, D. O.

D. O. Smith, “Optical Scattering from Cubic Electro-optical Films,” Opt. Acta 13, 195 (1966).
[Crossref]

D. O. Smith, “Magneto-Optical Scattering from Multilayer Magnetic and Dielectric Films,” Opt. Acta 12, 13 (1965).
[Crossref]

Sprokel, G. J.

Teitler, S.

Visnovsky, S.

S. Visnovsky, “Magneto-optical Polar Kerr Effect and Birefringence in Magnetic Crystals of Orthorhombic Symmetry,” Czech. J. Phys. B 34, 155 (1984).
[Crossref]

Yeh, P.

P. Yeh, “Optics of Anisotropic Layered Media: A New 4 × 4 Matrix Algebra,” Surf. Sci. 96, 41 (1980).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (1)

J. Kranz, C. Schrodter, “Ellipsometry on Magnetooptic Thin Film Multilayer Systems,” Appl. Phys. B 34, 139 (1984).
[Crossref]

Appl. Phys. Lett. (1)

G. A. N. Connell, “Interference Enhanced Kerr Spectroscopy for Very Thin Absorbing Films,” Appl. Phys. Lett. 40, 213 (1982).
[Crossref]

Czech. J. Phys. B (1)

S. Visnovsky, “Magneto-optical Polar Kerr Effect and Birefringence in Magnetic Crystals of Orthorhombic Symmetry,” Czech. J. Phys. B 34, 155 (1984).
[Crossref]

IEEE Trans. Magn. (2)

R. Gamble, P. H. Lissberger, M. R. Parker, “A Simple Analysis for the Optimization of the Normal Polar Magneto-optical Kerr Effect in Multilayer Coatings Containing a Magnetic Film,” IEEE Trans. Magn. MAG-21, 1651 (1985).
[Crossref]

K. Nakamura, T. Asaka, S. Asari, Y. Ota, A. Itoh, “Enhancement of Kerr Rotation with Amorphous Si Film,” IEEE Trans. Magn. MAG-21, 1654 (1985).
[Crossref]

J. Appl. Phys. (1)

M. Mansuripur, G. A. N. Connell, J. W. Goodman, “Signal and Noise in Magneto-Optical Readout,” J. Appl. Phys. 53, 4485 (1982).
[Crossref]

J. Opt. Soc. Am. (1)

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

Opt. Acta (3)

D. Keay, P. H. Lissberger, “Longitudinal Kerr Magnetooptic Effect in Multilayer Structures of Dielectric and Magnetic Films,” Opt. Acta 15, 373 (1968).
[Crossref]

D. O. Smith, “Magneto-Optical Scattering from Multilayer Magnetic and Dielectric Films,” Opt. Acta 12, 13 (1965).
[Crossref]

D. O. Smith, “Optical Scattering from Cubic Electro-optical Films,” Opt. Acta 13, 195 (1966).
[Crossref]

Surf. Sci. (2)

P. Yeh, “Optics of Anisotropic Layered Media: A New 4 × 4 Matrix Algebra,” Surf. Sci. 96, 41 (1980).
[Crossref]

D. J. Smet, “Generalized Ellipsometry and the 4 × 4 Matrix Formalism,” Surf. Sci. 56, 293 (1976).
[Crossref]

Other (3)

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).

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

A. H. Lettington, “Optical Properties and Fermi Surfaces of Zinc,” in Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North-Holland, Amsterdam, 1966).

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Figures (6)

Fig. 1
Fig. 1

Schematic for the reiterative formalism, ri−1,i is the Fresnel coefficient between the (i − 1)th and ith layer and r i T is the contribution from the reflectivity of all the layers below the ith layer.

Fig. 2
Fig. 2

Structure of a typical, quadrilayer magnetooptic disk. It consists of SiO2 as the overcoat layer and the intermediate phase matching layer, MnBi as the magnetic layer, and Al as the reflector. The refractive indices are taken from Ref. 3 at a wavelength of 840 nm. The superscripts + and − denote the refractive index for left-handed and right-handed circularly polarized light, respectively.

Fig. 3
Fig. 3

Contour plot of 2000 |rsp|2 as a function of the thickness of the intermediate layer ti and that of the overcoat layer tc.

Fig. 4
Fig. 4

Same as Fig. 3 except (a) the imaginary part of the refractive index, n″, is reduced by ½ and (b) n″ is increased by ½.

Fig. 5
Fig. 5

Effect of anisotropy on 2000 |rsp|2 as a function of the incident angle θ0. Based on the optimized quadrilayer in Fig. 2, the principal axis value of the dielectric tensor, 3 0, is varied for the intermediate layer. In the figure, K i = 3 0 / 1 0 for the intermediate layer with the principal axis of 3 0 chosen to be parallel to the z axis.

Fig. 6
Fig. 6

Dependence of 2000 |rsp|2 on θm, the angle between the direction of magnetization and the normal to the film. Also shown in the plot is 2000 〈|rsp|2〉 averaged over a Gaussian distribution as a function of the standard deviation of the distribution θσ.

Equations (12)

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

r i T = r i 1 , i + r i + 1 T exp ( 2 i δ i ) 1 + r i 1 , i r i + 1 T exp ( 2 i δ i ) ,
r i 1 , i = n i 1 n i n i 1 + n i
ψ = ( E x H y E y H x )
n z ψ = Δ ψ ,
= 0 + m ,
m = ( 0 g z i g y i g z i 0 g x i g y i g x i 0 ) ,
ψ = Ψ ϕ ,
C p = | E x | 2 | E x | 2 + | E y | 2
( E s r E p r ) = ( r s s r s p r p s r p p ) ( E s i E p i ) ,
G = | r s p | ( 1 R m s ) | r s p | m s ( 1 R ) ,
3 0 = K i 1 0
f ( θ m ) = 1 2 π θ σ exp [ 1 2 ( θ m θ σ ) 2 ] .

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