Abstract

Reflectivities for magnetooptical media are measured as functions of angle of incidence in a series of related experiments. Measurements yield sufficient information to determine absolute magnitude and relative phase for the Fresnel amplitude reflection coefficients, r(p) and r(s), as well as for r, which describes the polar Kerr effect on incident polarized light. Using dielectric tensor values measured at normal incidence, theoretical curves for magnitude and phase of r(p),r(s), and r vs angle of incidence are developed. Experimental measurements are compared to theoretical functions of the reflectivities and found to be in good agreement throughout the range of angle of incidence. The theoretical analysis and related experimental procedures explicitly treat the presence of a transparent overcoating layer.

© 1986 Optical Society of America

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References

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  1. P. Chaudhari, J. J. Cuomo, R. J. Gambino, “Amorphous Metallic Films for Magneto-Optic Applications,” Appl. Phys. Lett. 22, 337 (1973).
    [CrossRef]
  2. Y. Mimura, N. Imamura, T. Kobayashi, “Magnetic Properties and Curie Point Writing in Amorphous Metallic Films,” IEEE Trans. Magnet. M-12, 779 (1976).
    [CrossRef]
  3. Y. Mimura, N. Imamura, T. Kobayashi, A. Okada, Y. Kushiro, “Magnetic Properties of Amorphous Alloy Films of Fe with Gd, Tb, Dy, Ho, or Er,” J. Appl. Phys. 49, 1208 (1978).
    [CrossRef]
  4. R. P. Freese, R. N. Gardner, T. A. Rinehart, D. W. Siitari, L. H. Johnson, “An Environmentally Stable, High Performance, High Data Rate Magneto-Optic Media,” Proc. Soc. Photo-Opt. Instrum. Eng. 529, 6 (1985).
  5. M. H. Kryder, W. H. Meiklejohn, R. E. Skoda, “Stability of Perpendicular Domains in Thermomagnetic Recording Materials,” Proc. Soc. Photo-Opt. Instrum. Eng. 420, 236 (1983).
  6. R. J. Meltzer, “Polarization,” in Applied Optics and Optical Engineering, Vol. 1 (Academic, New York, 1965), pp. 362–364.
  7. J. Bennett, H. Bennett, “Polarization,” in Handbook of Optics (McGraw-Hill, New York, 1978), pp. 10–6 to 10–20.
  8. G. A. N. Connell, D. S. Bloomberg, “Amorphous Rare-earth Transition Metal Alloys,” in Mott Festschrift (Plenum, New York, 1985).

1985 (1)

R. P. Freese, R. N. Gardner, T. A. Rinehart, D. W. Siitari, L. H. Johnson, “An Environmentally Stable, High Performance, High Data Rate Magneto-Optic Media,” Proc. Soc. Photo-Opt. Instrum. Eng. 529, 6 (1985).

1983 (1)

M. H. Kryder, W. H. Meiklejohn, R. E. Skoda, “Stability of Perpendicular Domains in Thermomagnetic Recording Materials,” Proc. Soc. Photo-Opt. Instrum. Eng. 420, 236 (1983).

1978 (1)

Y. Mimura, N. Imamura, T. Kobayashi, A. Okada, Y. Kushiro, “Magnetic Properties of Amorphous Alloy Films of Fe with Gd, Tb, Dy, Ho, or Er,” J. Appl. Phys. 49, 1208 (1978).
[CrossRef]

1976 (1)

Y. Mimura, N. Imamura, T. Kobayashi, “Magnetic Properties and Curie Point Writing in Amorphous Metallic Films,” IEEE Trans. Magnet. M-12, 779 (1976).
[CrossRef]

1973 (1)

P. Chaudhari, J. J. Cuomo, R. J. Gambino, “Amorphous Metallic Films for Magneto-Optic Applications,” Appl. Phys. Lett. 22, 337 (1973).
[CrossRef]

Bennett, H.

J. Bennett, H. Bennett, “Polarization,” in Handbook of Optics (McGraw-Hill, New York, 1978), pp. 10–6 to 10–20.

Bennett, J.

J. Bennett, H. Bennett, “Polarization,” in Handbook of Optics (McGraw-Hill, New York, 1978), pp. 10–6 to 10–20.

Bloomberg, D. S.

G. A. N. Connell, D. S. Bloomberg, “Amorphous Rare-earth Transition Metal Alloys,” in Mott Festschrift (Plenum, New York, 1985).

Chaudhari, P.

P. Chaudhari, J. J. Cuomo, R. J. Gambino, “Amorphous Metallic Films for Magneto-Optic Applications,” Appl. Phys. Lett. 22, 337 (1973).
[CrossRef]

Connell, G. A. N.

G. A. N. Connell, D. S. Bloomberg, “Amorphous Rare-earth Transition Metal Alloys,” in Mott Festschrift (Plenum, New York, 1985).

Cuomo, J. J.

P. Chaudhari, J. J. Cuomo, R. J. Gambino, “Amorphous Metallic Films for Magneto-Optic Applications,” Appl. Phys. Lett. 22, 337 (1973).
[CrossRef]

Freese, R. P.

R. P. Freese, R. N. Gardner, T. A. Rinehart, D. W. Siitari, L. H. Johnson, “An Environmentally Stable, High Performance, High Data Rate Magneto-Optic Media,” Proc. Soc. Photo-Opt. Instrum. Eng. 529, 6 (1985).

Gambino, R. J.

P. Chaudhari, J. J. Cuomo, R. J. Gambino, “Amorphous Metallic Films for Magneto-Optic Applications,” Appl. Phys. Lett. 22, 337 (1973).
[CrossRef]

Gardner, R. N.

R. P. Freese, R. N. Gardner, T. A. Rinehart, D. W. Siitari, L. H. Johnson, “An Environmentally Stable, High Performance, High Data Rate Magneto-Optic Media,” Proc. Soc. Photo-Opt. Instrum. Eng. 529, 6 (1985).

Imamura, N.

Y. Mimura, N. Imamura, T. Kobayashi, A. Okada, Y. Kushiro, “Magnetic Properties of Amorphous Alloy Films of Fe with Gd, Tb, Dy, Ho, or Er,” J. Appl. Phys. 49, 1208 (1978).
[CrossRef]

Y. Mimura, N. Imamura, T. Kobayashi, “Magnetic Properties and Curie Point Writing in Amorphous Metallic Films,” IEEE Trans. Magnet. M-12, 779 (1976).
[CrossRef]

Johnson, L. H.

R. P. Freese, R. N. Gardner, T. A. Rinehart, D. W. Siitari, L. H. Johnson, “An Environmentally Stable, High Performance, High Data Rate Magneto-Optic Media,” Proc. Soc. Photo-Opt. Instrum. Eng. 529, 6 (1985).

Kobayashi, T.

Y. Mimura, N. Imamura, T. Kobayashi, A. Okada, Y. Kushiro, “Magnetic Properties of Amorphous Alloy Films of Fe with Gd, Tb, Dy, Ho, or Er,” J. Appl. Phys. 49, 1208 (1978).
[CrossRef]

Y. Mimura, N. Imamura, T. Kobayashi, “Magnetic Properties and Curie Point Writing in Amorphous Metallic Films,” IEEE Trans. Magnet. M-12, 779 (1976).
[CrossRef]

Kryder, M. H.

M. H. Kryder, W. H. Meiklejohn, R. E. Skoda, “Stability of Perpendicular Domains in Thermomagnetic Recording Materials,” Proc. Soc. Photo-Opt. Instrum. Eng. 420, 236 (1983).

Kushiro, Y.

Y. Mimura, N. Imamura, T. Kobayashi, A. Okada, Y. Kushiro, “Magnetic Properties of Amorphous Alloy Films of Fe with Gd, Tb, Dy, Ho, or Er,” J. Appl. Phys. 49, 1208 (1978).
[CrossRef]

Meiklejohn, W. H.

M. H. Kryder, W. H. Meiklejohn, R. E. Skoda, “Stability of Perpendicular Domains in Thermomagnetic Recording Materials,” Proc. Soc. Photo-Opt. Instrum. Eng. 420, 236 (1983).

Meltzer, R. J.

R. J. Meltzer, “Polarization,” in Applied Optics and Optical Engineering, Vol. 1 (Academic, New York, 1965), pp. 362–364.

Mimura, Y.

Y. Mimura, N. Imamura, T. Kobayashi, A. Okada, Y. Kushiro, “Magnetic Properties of Amorphous Alloy Films of Fe with Gd, Tb, Dy, Ho, or Er,” J. Appl. Phys. 49, 1208 (1978).
[CrossRef]

Y. Mimura, N. Imamura, T. Kobayashi, “Magnetic Properties and Curie Point Writing in Amorphous Metallic Films,” IEEE Trans. Magnet. M-12, 779 (1976).
[CrossRef]

Okada, A.

Y. Mimura, N. Imamura, T. Kobayashi, A. Okada, Y. Kushiro, “Magnetic Properties of Amorphous Alloy Films of Fe with Gd, Tb, Dy, Ho, or Er,” J. Appl. Phys. 49, 1208 (1978).
[CrossRef]

Rinehart, T. A.

R. P. Freese, R. N. Gardner, T. A. Rinehart, D. W. Siitari, L. H. Johnson, “An Environmentally Stable, High Performance, High Data Rate Magneto-Optic Media,” Proc. Soc. Photo-Opt. Instrum. Eng. 529, 6 (1985).

Siitari, D. W.

R. P. Freese, R. N. Gardner, T. A. Rinehart, D. W. Siitari, L. H. Johnson, “An Environmentally Stable, High Performance, High Data Rate Magneto-Optic Media,” Proc. Soc. Photo-Opt. Instrum. Eng. 529, 6 (1985).

Skoda, R. E.

M. H. Kryder, W. H. Meiklejohn, R. E. Skoda, “Stability of Perpendicular Domains in Thermomagnetic Recording Materials,” Proc. Soc. Photo-Opt. Instrum. Eng. 420, 236 (1983).

Appl. Phys. Lett. (1)

P. Chaudhari, J. J. Cuomo, R. J. Gambino, “Amorphous Metallic Films for Magneto-Optic Applications,” Appl. Phys. Lett. 22, 337 (1973).
[CrossRef]

IEEE Trans. Magnet. (1)

Y. Mimura, N. Imamura, T. Kobayashi, “Magnetic Properties and Curie Point Writing in Amorphous Metallic Films,” IEEE Trans. Magnet. M-12, 779 (1976).
[CrossRef]

J. Appl. Phys. (1)

Y. Mimura, N. Imamura, T. Kobayashi, A. Okada, Y. Kushiro, “Magnetic Properties of Amorphous Alloy Films of Fe with Gd, Tb, Dy, Ho, or Er,” J. Appl. Phys. 49, 1208 (1978).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

R. P. Freese, R. N. Gardner, T. A. Rinehart, D. W. Siitari, L. H. Johnson, “An Environmentally Stable, High Performance, High Data Rate Magneto-Optic Media,” Proc. Soc. Photo-Opt. Instrum. Eng. 529, 6 (1985).

M. H. Kryder, W. H. Meiklejohn, R. E. Skoda, “Stability of Perpendicular Domains in Thermomagnetic Recording Materials,” Proc. Soc. Photo-Opt. Instrum. Eng. 420, 236 (1983).

Other (3)

R. J. Meltzer, “Polarization,” in Applied Optics and Optical Engineering, Vol. 1 (Academic, New York, 1965), pp. 362–364.

J. Bennett, H. Bennett, “Polarization,” in Handbook of Optics (McGraw-Hill, New York, 1978), pp. 10–6 to 10–20.

G. A. N. Connell, D. S. Bloomberg, “Amorphous Rare-earth Transition Metal Alloys,” in Mott Festschrift (Plenum, New York, 1985).

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Figures (4)

Fig. 1
Fig. 1

Oblique incidence at the boundary between a magnetooptic medium and dielectric medium.

Fig. 2
Fig. 2

Calculated amplitude and phase for the reflectivity coefficients (a) rp and ϕp; (b) rs and ϕs; (c) r and ϕ. The vertical scale for ϕ is 0 to 4 radians.

Fig. 3
Fig. 3

Schematic diagram of the measurement system.

Fig. 4
Fig. 4

Comparison between theoretical and experimental results for a Tb28Fe72 sample: (a) r p 2 , r s 2, rprs cos(ϕpϕs) vs θ; (b) rpr cos(ϕpϕ) and rpr sin(ϕpϕ) vs θ; (c) rsr cos(ϕsϕ) and rsr sin(ϕsϕ) vs θ.

Equations (34)

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= ( x i x y 0 - i x y y 0 0 0 z ) .
V ( r , t ) = V 0 exp { i [ ( 2 π n / λ 0 ) S · r - ω t ] } .
Δ × E = - 1 c B t ,
Δ × H = 1 c D t ,
× × E = ω 2 c 2 D .
n 2 [ E 0 - ( S · E 0 ) S ] = D 0 .
( x - n 2 S z 2 i x y n 2 S x S z - i x y x - n 2 0 n 2 S x S z 0 z - n 2 S x 2 ) ( E x 0 E y 0 E z 0 ) = 0.
( x S x 2 + z S z 2 ) n 4 - [ ( x 2 - x y 2 ) S x 2 + x z ( 1 + S z 2 ) ] n 2 + z ( x 2 - x y 2 ) = 0
n o 2 = x             ordinary ray ,
n e 2 = ( S x 2 z + S z 2 x ) - 1 extraordinary ray .
n 2 = x ± x y .
E x 0 = ± i E y 0 ,
H 0 = n ( S × E 0 ) .
n 0 sin θ = n 1 S x 1 = n 2 S x 2 .
n 2 = x + 1 2 ( 1 - x z ) n 0 2 sin 2 θ ± { [ 1 2 ( 1 - x z ) n 0 2 sin 2 θ ] 2 + ( 1 - n 0 2 sin 2 θ z ) x y 2 } 1 / 2 .
a i = ( n i / n 0 ) 2 - x n o 2             i = 1 , 2 ;
b i = { ( n i / n o ) 2 + [ ( n i / n o ) 2 - 1 ] tan 2 θ } 1 / 2 ;             i = 1 , 2 ;
c = 1 + ( 1 - n o 2 z ) tan 2 θ .
r ( p ) = E p ( r ) E p ( i ) = a 1 ( c - b 1 ) ( 1 + b 2 ) - a 2 ( c - b 2 ) ( 1 + b 1 ) a 1 ( c + b 1 ) ( 1 + b 2 ) - a 2 ( c + b 2 ) ( 1 + b 1 ) ,
r ( p ) = E s ( r ) E p ( i ) = 2 i c ( b 1 - b 2 ) ( x y / n 0 2 ) cos θ a 1 ( c + b 1 ) ( 1 + b 2 ) - a 2 ( c + b 2 ) ( 1 + b 1 ) .
r ( s ) = E s ( r ) E s ( i ) = a 1 ( c + b 1 ) ( 1 - b 2 ) - a 2 ( c + b 2 ) ( 1 - b 1 ) a 1 ( c + b 1 ) ( 1 + b 2 ) - a 2 ( c + b 2 ) ( 1 + b 1 ) ,
r ( s ) = E p ( r ) E s ( i ) = 2 i a 1 a 2 ( b 1 - b 2 ) ( n 0 2 / x y ) ( 1 / cos θ ) a 1 ( c + b 1 ) ( 1 + b 2 ) - a 2 ( c + b 2 ) ( 1 + b 1 ) .
r ( p ) = - r ( s ) ,
σ 0 = S 1 + S 2 = 1 / 2 α A 2 .
r ( p ) = r p exp ( i ϕ p ) , r ( s ) = r s exp ( i ϕ s ) , r = r exp ( i ϕ ) .
σ / σ 0 = r p 2 cos 2 2 β + r s 2 sin 2 2 β + r 2 + [ r p r cos ( ϕ p - ϕ ) - r s r cos ( ϕ s - ϕ ) ] sin 4 β ,
Δ S / σ 0 = [ ( r p 2 cos 2 2 β - r s 2 sin 2 2 β ) cos 2 ζ - r 2 cos ( 4 β - 2 ζ ) ] cos ( 2 η - 2 ζ ) + r p r s [ sin 2 ζ cos ( ϕ p - ϕ s ) cos ( 4 η - 2 ζ ) + sin ( ϕ p - ϕ s ) sin ( 4 η - 2 ζ ) ] sin 4 β - 2 r p r [ cos 2 β sin ( ϕ p - ϕ ) sin ( 4 η - 2 ζ ) + sin ( 2 ζ - 2 β ) cos ( ϕ p - ϕ ) cos ( 4 η - 2 ζ ) ] cos 2 β - 2 r s r [ sin 2 β sin ( ϕ s - ϕ ) sin ( 4 η - 2 ζ ) - cos ( 2 ζ - 2 β ) cos ( ϕ s - ϕ ) cos ( 4 π - 2 ζ ) ] sin 2 β .
σ / σ 0 = r p 2 + r 2 r p 2 .
σ / σ 0 = r s 2 + r 2 r s 2 .
Δ S / σ 0 = r p r s sin ( ϕ p - ϕ s ) - r p r sin ( ϕ p - ϕ ) - r s r sin ( ϕ s - ϕ ) r p r s sin ( ϕ p - ϕ s ) ,
- Δ S / σ 0 = r 2 sin 4 η + r p r s sin ( ϕ p - ϕ s - 4 η ) - r p r sin ( ϕ p - ϕ - 4 η ) - r s r sin ( ϕ s - ϕ + 4 η ) r p r s sin ( ϕ p - ϕ s - 4 η ) .
Δ S / σ 0 = 2 r p r sin ( ϕ p - ϕ - 4 η ) .
δ / σ 0 = Δ S - Δ S σ 0 = 4 r p r sin ( ϕ p - ϕ - 4 η ) .
δ / σ 0 = Δ S - Δ S σ 0 = 4 r s r sin ( ϕ s - ϕ + 4 η ) ,

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