Abstract

It is shown how the electric field amplitude distributions that are due to radiation incident upon multilayer coatings containing magnetic (gyrotropic) films can be calculated, with particular emphasis on the magneto-optical components. The relevance of the electric field amplitudes for the evaluation of absorption in the layers, interfacial scattering, and the signal-to-noise ratio associated with the detection of magneto-optical effects is discussed. Two sets of examples of electric field amplitude distributions in multilayer coatings are given, and it is concluded that multilayer structures designed to enhance the shot-noise-limited signal-to-noise ratio in magneto-optical recording may also increase the noise associated with surface roughness scattering.

© 1988 Optical Society of America

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References

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  1. D. Kossel, K. Deutscher, K. Hirschberg, “Interference photocathodes,” in Physics of Thin Films, G. Hass, R. E. Thun, eds. (Academic, New York, 1969), Vol. 5, pp. 1–44.
  2. P. H. Berning, A. F. Turner, “Induced transmission in absorbing films applied to band pass filter design,” J. Opt. Soc. Am. 47, 230–239 (1957).
    [CrossRef]
  3. D. Keay, P. H. Lissberger, “Longitudinal Kerr magneto-optic effect in multilayer structures of dielectric and magnetic films,” Opt. Acta 15, 373–388 (1968).
    [CrossRef]
  4. P. H. Lissberger, “Optical applications of dielectric thin films,” Rep. Prog. Phys. 33, 197–268 (1970).
    [CrossRef]
  5. P. H. Lissberger, “Magneto-optics in convergent beams,” IBM unclassified rep. (IBM, San Jose, Calif., 1969).
  6. P. H. Lissberger, “The relationship between optical absorptance and electric field of the radiation in multilayer thin films,” Opt. Acta 28, 187–200 (1981).
    [CrossRef]
  7. P. H. Lissberger, “Kerr magneto-optic effect in nickel-iron films. II. Theoretical,” J. Opt. Soc. Am. 51, 957–966 (1961).
    [CrossRef]
  8. 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, 1651–1653 (1985).
    [CrossRef]
  9. R. Atkinson, R. Gamble, P. F. Gu, P. H. Lissberger, “Ellipso-metric comparisons of rare earth-transition metal alloy films in connection with magneto-optical recording,” Thin Solid Films (to be published).
  10. D. Y. Smith, E. Shiles, M. Inokuti, “The optical properties of metallic aluminum,” in Handbook of Optical Constants of Metals, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 369–406.
  11. C. C. Robinson, “Longitudinal Kerr magneto-optic effect in thin films of iron, nickel and permalloy,” J. Opt. Soc. Am. 53, 681–689 (1962).
    [CrossRef]
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1965), pp. 81–84.
  13. M. Ojima, A. Saito, T. Kaku, M. Ito, Y. Tsunoda, S. Takayama, Y. Sugita, “Compact magnetooptical disk for coded data storage,” Appl. Opt. 25, 483–489 (1986).
    [CrossRef] [PubMed]
  14. M. H. Kryder, “Magneto-optic recording technology,” J. Appl. Phys. 57, 3913–3918 (1985).
    [CrossRef]
  15. D. R. Gibson, P. H. Lissberger, “Light scattering from multilayer filter coatings,” in Thin Film Technologies, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.401, 257–265 (1983).
    [CrossRef]

1986

1985

M. H. Kryder, “Magneto-optic recording technology,” J. Appl. Phys. 57, 3913–3918 (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, 1651–1653 (1985).
[CrossRef]

1981

P. H. Lissberger, “The relationship between optical absorptance and electric field of the radiation in multilayer thin films,” Opt. Acta 28, 187–200 (1981).
[CrossRef]

1970

P. H. Lissberger, “Optical applications of dielectric thin films,” Rep. Prog. Phys. 33, 197–268 (1970).
[CrossRef]

1968

D. Keay, P. H. Lissberger, “Longitudinal Kerr magneto-optic effect in multilayer structures of dielectric and magnetic films,” Opt. Acta 15, 373–388 (1968).
[CrossRef]

1962

1961

1957

Atkinson, R.

R. Atkinson, R. Gamble, P. F. Gu, P. H. Lissberger, “Ellipso-metric comparisons of rare earth-transition metal alloy films in connection with magneto-optical recording,” Thin Solid Films (to be published).

Berning, P. H.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1965), pp. 81–84.

Deutscher, K.

D. Kossel, K. Deutscher, K. Hirschberg, “Interference photocathodes,” in Physics of Thin Films, G. Hass, R. E. Thun, eds. (Academic, New York, 1969), Vol. 5, pp. 1–44.

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, 1651–1653 (1985).
[CrossRef]

R. Atkinson, R. Gamble, P. F. Gu, P. H. Lissberger, “Ellipso-metric comparisons of rare earth-transition metal alloy films in connection with magneto-optical recording,” Thin Solid Films (to be published).

Gibson, D. R.

D. R. Gibson, P. H. Lissberger, “Light scattering from multilayer filter coatings,” in Thin Film Technologies, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.401, 257–265 (1983).
[CrossRef]

Gu, P. F.

R. Atkinson, R. Gamble, P. F. Gu, P. H. Lissberger, “Ellipso-metric comparisons of rare earth-transition metal alloy films in connection with magneto-optical recording,” Thin Solid Films (to be published).

Hirschberg, K.

D. Kossel, K. Deutscher, K. Hirschberg, “Interference photocathodes,” in Physics of Thin Films, G. Hass, R. E. Thun, eds. (Academic, New York, 1969), Vol. 5, pp. 1–44.

Inokuti, M.

D. Y. Smith, E. Shiles, M. Inokuti, “The optical properties of metallic aluminum,” in Handbook of Optical Constants of Metals, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 369–406.

Ito, M.

Kaku, T.

Keay, D.

D. Keay, P. H. Lissberger, “Longitudinal Kerr magneto-optic effect in multilayer structures of dielectric and magnetic films,” Opt. Acta 15, 373–388 (1968).
[CrossRef]

Kossel, D.

D. Kossel, K. Deutscher, K. Hirschberg, “Interference photocathodes,” in Physics of Thin Films, G. Hass, R. E. Thun, eds. (Academic, New York, 1969), Vol. 5, pp. 1–44.

Kryder, M. H.

M. H. Kryder, “Magneto-optic recording technology,” J. Appl. Phys. 57, 3913–3918 (1985).
[CrossRef]

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, 1651–1653 (1985).
[CrossRef]

P. H. Lissberger, “The relationship between optical absorptance and electric field of the radiation in multilayer thin films,” Opt. Acta 28, 187–200 (1981).
[CrossRef]

P. H. Lissberger, “Optical applications of dielectric thin films,” Rep. Prog. Phys. 33, 197–268 (1970).
[CrossRef]

D. Keay, P. H. Lissberger, “Longitudinal Kerr magneto-optic effect in multilayer structures of dielectric and magnetic films,” Opt. Acta 15, 373–388 (1968).
[CrossRef]

P. H. Lissberger, “Kerr magneto-optic effect in nickel-iron films. II. Theoretical,” J. Opt. Soc. Am. 51, 957–966 (1961).
[CrossRef]

R. Atkinson, R. Gamble, P. F. Gu, P. H. Lissberger, “Ellipso-metric comparisons of rare earth-transition metal alloy films in connection with magneto-optical recording,” Thin Solid Films (to be published).

P. H. Lissberger, “Magneto-optics in convergent beams,” IBM unclassified rep. (IBM, San Jose, Calif., 1969).

D. R. Gibson, P. H. Lissberger, “Light scattering from multilayer filter coatings,” in Thin Film Technologies, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.401, 257–265 (1983).
[CrossRef]

Ojima, M.

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, 1651–1653 (1985).
[CrossRef]

Robinson, C. C.

Saito, A.

Shiles, E.

D. Y. Smith, E. Shiles, M. Inokuti, “The optical properties of metallic aluminum,” in Handbook of Optical Constants of Metals, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 369–406.

Smith, D. Y.

D. Y. Smith, E. Shiles, M. Inokuti, “The optical properties of metallic aluminum,” in Handbook of Optical Constants of Metals, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 369–406.

Sugita, Y.

Takayama, S.

Tsunoda, Y.

Turner, A. F.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1965), pp. 81–84.

Appl. Opt.

IEEE Trans. Magn.

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, 1651–1653 (1985).
[CrossRef]

J. Appl. Phys.

M. H. Kryder, “Magneto-optic recording technology,” J. Appl. Phys. 57, 3913–3918 (1985).
[CrossRef]

J. Opt. Soc. Am.

Opt. Acta

D. Keay, P. H. Lissberger, “Longitudinal Kerr magneto-optic effect in multilayer structures of dielectric and magnetic films,” Opt. Acta 15, 373–388 (1968).
[CrossRef]

P. H. Lissberger, “The relationship between optical absorptance and electric field of the radiation in multilayer thin films,” Opt. Acta 28, 187–200 (1981).
[CrossRef]

Rep. Prog. Phys.

P. H. Lissberger, “Optical applications of dielectric thin films,” Rep. Prog. Phys. 33, 197–268 (1970).
[CrossRef]

Other

P. H. Lissberger, “Magneto-optics in convergent beams,” IBM unclassified rep. (IBM, San Jose, Calif., 1969).

D. Kossel, K. Deutscher, K. Hirschberg, “Interference photocathodes,” in Physics of Thin Films, G. Hass, R. E. Thun, eds. (Academic, New York, 1969), Vol. 5, pp. 1–44.

R. Atkinson, R. Gamble, P. F. Gu, P. H. Lissberger, “Ellipso-metric comparisons of rare earth-transition metal alloy films in connection with magneto-optical recording,” Thin Solid Films (to be published).

D. Y. Smith, E. Shiles, M. Inokuti, “The optical properties of metallic aluminum,” in Handbook of Optical Constants of Metals, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 369–406.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1965), pp. 81–84.

D. R. Gibson, P. H. Lissberger, “Light scattering from multilayer filter coatings,” in Thin Film Technologies, J. R. Jacobsson, ed., Proc. Soc. Photo-Opt. Instrum. Eng.401, 257–265 (1983).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

Definition of boundary field matrices.

Fig. 2
Fig. 2

Electromagnetic field vectors of incident and reflected waves: (a) p-polarized waves (∥), (b) s-polarized waves (⊥).

Fig. 3
Fig. 3

Magneto-optical configurations.

Fig. 4
Fig. 4

Matrices for the evaluation of the electric field at a plane in layer l of a multilayer containing N layers.

Fig. 5
Fig. 5

Parameters of a multilayer system containing a single magneto-optic (M.O.) film.

Fig. 6
Fig. 6

Amplitudes of incident and reflected waves for the system shown in Fig. 5.

Fig. 7
Fig. 7

Normalized electric field amplitude distribution for p-polarized radiation incident normally upon a thick film of RE-TM alloy (24.4% Tb, 53.8% Fe, 21.8% Co). λ = 614.9 nm, n = 3.02 + 2.46i (see Ref. 9).

Fig. 8
Fig. 8

Normalized electric field amplitude distribution for the s-polarized polar Kerr component corresponding to Fig. 7. Q = (−1.90 + 1.32i) × 10−2 (see Ref. 9).

Fig. 9
Fig. 9

Normalized electric field amplitude distributions for p-polarized radiation incident normally upon a quadrilayer structure containing a thin (23.6-nm) film of RE–TM alloy. λ = 614.9 nm, nAl = 1.35 + 7.35i,10 n MgF 2 = 1.38, nZnS = 2.36, nPMMA = 1.49.

Fig. 10
Fig. 10

Normalized electric field amplitude distribution for the s-polarized polar Kerr component corresponding to Fig. 9.

Fig. 11
Fig. 11

Normalized electric field amplitude distribution for p-polarized radiation incident at an angle of 42° upon a multilayer structure3 containing a single thin (14.7-nm) layer (the sixth from the air side) of permalloy (83% Ni, 17% Fe). λ = 506.4 nm, n = 1.64 + 2.80i (see Ref. 11), nL = 1.35, nH = 2.37, nL = 1.31. L, L, and H are quarter-wave layers at normal incidence, and λ0 = 546 nm. m = 0.771H.

Fig. 12
Fig. 12

Normalized electric field amplitude distribution for the s-polarized longitudinal Kerr component corresponding to Fig. 11. Q = (9.03 − 8.72i) × 10−3 (see Ref. 11).

Fig. 13
Fig. 13

Normalized electric field amplitude distribution for s-polarized radiation incident at an angle of 42° upon the multilayer structure3 defined in the caption for Fig. 11. λ = 506.4 nm.

Fig. 14
Fig. 14

Normalized electric field distribution for the p-polarized longitudinal Kerr component corresponding to Fig. 13.

Fig. 15
Fig. 15

Interfacial roughness geometry.

Tables (1)

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Table 1 Characteristic Matrix Elements of a Single Magnetic (Gyrotropic) Layer

Equations (66)

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( F 0 ) = [ C 1 ] ( F 1 ) ,
( F ) = [ E z H x E x H z ] = [ β ( E + + E ) 1 Z ( E + E ) ( E + + E ) 1 Z ( E + E ) ]
n γ = n 0 γ 0 .
B = μ 0 H
D = 0 [ K ] E ,
[ K ] p = n 2 [ 1 0 i Q 0 1 0 i Q 0 1 ] ,
[ C ] = [ [ C I ] g Q [ C A ] g Q [ C A ] [ C I ] ] .
[ C ] = [ [ C I ] + g Q [ C A ] [ 0 ] [ 0 ] [ C I ] ] .
c = cos δ , s = sin δ , δ = ( 2 π / λ ) d n β ,
( F 0 ) = [ C 1 , N ] ( F S ) ,
( F 0 ) = [ C ] ( F ) = [ C 1 , N ] ( F S ) .
[ β 0 k 0 1 Z 0 k 0 ( 1 + r 0 ) 1 Z 0 ( 1 r 0 ) ] = [ C ] [ β ( E + + E ) 1 Z ( E + E ) ( E + + E ) 1 Z ( E + E ) ] = [ C 1 , N ] [ β S E S + 1 Z S E S + E S + 1 Z S E S + ] .
| E 0 + | = 1 , E 0 = k 0 , E 0 + = 0 , E 0 = r 0 ,
E S = 0 , E S = 0.
ξ = | β ( E + + E ) + γ ( E + E ) | ,
ξ = | E + + E | .
A = 4 π h λ β 0 0 d ξ 2 d y ,
h = Im ( n β ) Re ( n / β ) / ( 1 + | γ / β | 2 )
h = Im ( n β ) Re ( n β ) .
h = h = h = n n .
ξ = ( λ β 0 4 π n n A y ) 1 / 2 .
a = ( ζ r ± k ) / 2 ,
T S ( ± M ) = a a * = [ ζ 2 | r | 2 + | k | 2 ± 2 ζ | k | | r | cos Δ ] / 2 ,
T S = [ T S ( + M ) + T S ( M ) ] / 2 = ζ 2 | r | 2 / 2 ,
Δ T s = T s ( + M ) T s ( M ) = 2 ζ | k | | r | cos Δ .
T s = T p ( ζ 2 + 2 c ) | r | 2 / 2
Δ T s = 2 T p ζ | k | | r | cos Δ .
S = ϕ P e Δ T s ,
N ¯ = b 2 T s + b 1 T s + b 0 ,
b 1 = ( ϕ P e 2 / 4 τ ) ,
( S / N ¯ ) s = η 1 / 2 4 T p [ ζ / ( ζ 2 + 2 c ) 1 / 2 ] | k | cos Δ ,
( S / N ¯ ) s = η 1 / 2 4 T p | k | .
| k | = ψ k [ ( 1 | r | 2 ) ( 1 | r | 2 ) ] 1 / 2 ,
T = ψ ( 1 R ) ,
| k | = ψ k ( 1 R ) ,
1 R = A ,
| k | = ψ k A .
d s = λ / ( 4 π n ) ,
E 1 = E 1 + + E 1 ,
E 2 = E 1 = E .
δ P 12 = 0 [ ( K 1 1 ) E 1 ( K 2 1 ) E 2 ] Δ 12 δ X δ Z ,
P eff = 0 ( K 1 K 2 ) E S exp [ i 2 π λ ( α 0 x + β 0 y + γ 0 z ) ] Δ 12 δ X δ Z ,
P = ω 4 | P eff | 2 ( 1 γ 0 2 ) r ˆ 32 π 2 0 c 3 | r | 2 ,
δ ϕ SC = P · δ a .
δ ϕ SC = π 2 λ 4 | K 1 K 2 | 2 | E | 2 2 Z υ ( 1 γ 0 2 ) S g δ Ω ,
δ Ω = r ˆ · δ a / | r | 2
g ( σ , L ) = 1 S | s exp [ i 2 π λ ( α 0 x + γ 0 z ) ] Δ 12 d x d z | 2
AC ( L x , L z ) = 1 S s Δ 12 ( x , z ) Δ 12 ( x + L x , z + L z ) d x d z .
g = π L 2 σ 2 ,
DFC = δ ϕ SC / ϕ I δ Ω = π 3 [ | K 1 K 2 | ξ ( L / λ ) ( σ / λ ) ] 2 ( 1 γ 0 2 ) ,
N ¯ SC ϕ I π 3 F [ | K 1 K 2 | ξ ( L / λ 2 ) ] 2 V ( σ 2 ) ,
F = N . A . ( 1 γ 0 2 ) d Ω
Γ / Γ = ( 1 | γ / β | 2 ) / ( 1 + | γ / β | 2 ) ,
Γ = Im ( n / β ) / Re ( n / β )
Γ = Im ( n β ) / Re ( n β ) .
h = [ Im ( n / β ) Re ( n β ) + Im ( n β ) Re ( n / β ) ] / 2 .
h = n n ,
n = | n | cos ρ n ,
n = | n | sin ρ n .
n β = ( n 2 n 0 2 γ 0 2 ) 1 / 2 ,
β 2 = 1 γ 2
n 2 γ 2 = n 0 2 γ 0 2 ( Snell's law ) .
n β = K 1 / 2 ,
K = K + i K = ( n 2 n 2 n 0 2 γ 0 2 ) + 2 i n n .
n β = [ ( | K | + K ) / 2 ] 1 / 2 + i [ ( | K | | K ) / 2 ] 1 / 2 .
h = Im ( n β ) Re ( n β ) = K / 2 = n n .

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