Abstract

An explicit formula for the normal-incidence polar Kerr magneto-optical coefficient in a general multilayer structure consisting of a magnetic film and multilayers has been derived. The optimum condition of the multilayer-medium structure for maximizing the signal-to-noise ratio in the readout system is analytically derived by means of an equivalent bilayer treatment. For the case of the quarter-wave multilayer structure, numerical examples are given. It is shown that the optimization of both the multilayer structure and the readout optical components can greatly increase the signal-to-noise ratio in the readout system.

© 1984 Optical Society of America

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References

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  1. Research on the magneto-optical storage is described by D. O. Smith, “Magnetic films and optics in computer memories,” IEEE Trans. Magn. MAG-3, 433–452 (1967); Y. Togami, “Magneto-optic disk storage,” IEEE Trans. Magn. MAG-18, 1233–1237 (1982).
    [CrossRef]
  2. D. O. Smith, “Magneto-optical scattering from multilayer magnetic and dielectric films. Part I. General theory,” Opt. Acta 12, 13–45 (1965).
    [CrossRef]
  3. T. Yoshino, S. Tanaka, “Theory of polar magneto-optic effects in thin films,” Oyo Butsuri 34, 572–581 (1965) (in Japanese).
  4. T. Yoshino, S. Tanaka, “Polar and longitudinal magneto-optical Kerr and Faraday coefficients of bi-gyrotropic thin films,” Jpn. J. Appl. Phys. 9, 1282–1283 (1970).
    [CrossRef]
  5. C. C. Robinson, “Polar and longitudinal magneto-optic effects in a planar geometry,” J. Opt. Soc. Am. 58, 1342–1347 (1968).
    [CrossRef]
  6. 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]
  7. M. Mansuripur, G. A. N. Connell, J. W. Goodman, “Signal and noise in magneto-optical readout,” J. Appl. Phys. 53, 4485–4494 (1982).
    [CrossRef]
  8. The main part of this study was presented at the 1982 Fall Meeting of the Japan Society of Applied Physics, Kyushu, Japan, September 1982.
  9. Counterclockwise rotation is defined as being positive when the reflected or transmitted light is viewed toward the light traveling from a light source.
  10. O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965), pp. 63–65.
  11. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 51–70.
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 544–555.
  13. W. D. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), pp. 204–218.
  14. R. J. McIntyre, “Multiplication noise in uniform avalanche diode,” IEEE Trans. Electron Devices ED-13, 164–168 (1966).
    [CrossRef]
  15. When m= 2M− 1, i.e., for odd multilayers, it follows from Eq. (18) that Δ1= Δ2= π/2 and thatr=Uρ+ρ0(1-2∣ρ∣2)U-ρρ0andk=(1 -∣ρ∣2)U(U-ρρ0)2k0,whereρ=PM′-QM′PM′+QM′,in whichPM′=(n2′n4′…n2M-2′)2nandandQM′=(n1′n3′…n2M-1′)2.
  16. S. D. Personick, “Receiver design for digital fiber optic communication system I,” Bell Syst. Tech J. 52, 843–876 (1973).

1982 (1)

M. Mansuripur, G. A. N. Connell, J. W. Goodman, “Signal and noise in magneto-optical readout,” J. Appl. Phys. 53, 4485–4494 (1982).
[CrossRef]

1973 (1)

S. D. Personick, “Receiver design for digital fiber optic communication system I,” Bell Syst. Tech J. 52, 843–876 (1973).

1970 (1)

T. Yoshino, S. Tanaka, “Polar and longitudinal magneto-optical Kerr and Faraday coefficients of bi-gyrotropic thin films,” Jpn. J. Appl. Phys. 9, 1282–1283 (1970).
[CrossRef]

1968 (2)

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]

C. C. Robinson, “Polar and longitudinal magneto-optic effects in a planar geometry,” J. Opt. Soc. Am. 58, 1342–1347 (1968).
[CrossRef]

1967 (1)

Research on the magneto-optical storage is described by D. O. Smith, “Magnetic films and optics in computer memories,” IEEE Trans. Magn. MAG-3, 433–452 (1967); Y. Togami, “Magneto-optic disk storage,” IEEE Trans. Magn. MAG-18, 1233–1237 (1982).
[CrossRef]

1966 (1)

R. J. McIntyre, “Multiplication noise in uniform avalanche diode,” IEEE Trans. Electron Devices ED-13, 164–168 (1966).
[CrossRef]

1965 (2)

D. O. Smith, “Magneto-optical scattering from multilayer magnetic and dielectric films. Part I. General theory,” Opt. Acta 12, 13–45 (1965).
[CrossRef]

T. Yoshino, S. Tanaka, “Theory of polar magneto-optic effects in thin films,” Oyo Butsuri 34, 572–581 (1965) (in Japanese).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 51–70.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 544–555.

Connell, G. A. N.

M. Mansuripur, G. A. N. Connell, J. W. Goodman, “Signal and noise in magneto-optical readout,” J. Appl. Phys. 53, 4485–4494 (1982).
[CrossRef]

Davenport, W. D.

W. D. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), pp. 204–218.

Goodman, J. W.

M. Mansuripur, G. A. N. Connell, J. W. Goodman, “Signal and noise in magneto-optical readout,” J. Appl. Phys. 53, 4485–4494 (1982).
[CrossRef]

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965), pp. 63–65.

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]

Lissberger, P. H.

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]

Mansuripur, M.

M. Mansuripur, G. A. N. Connell, J. W. Goodman, “Signal and noise in magneto-optical readout,” J. Appl. Phys. 53, 4485–4494 (1982).
[CrossRef]

McIntyre, R. J.

R. J. McIntyre, “Multiplication noise in uniform avalanche diode,” IEEE Trans. Electron Devices ED-13, 164–168 (1966).
[CrossRef]

Personick, S. D.

S. D. Personick, “Receiver design for digital fiber optic communication system I,” Bell Syst. Tech J. 52, 843–876 (1973).

Robinson, C. C.

Root, W. L.

W. D. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), pp. 204–218.

Smith, D. O.

Research on the magneto-optical storage is described by D. O. Smith, “Magnetic films and optics in computer memories,” IEEE Trans. Magn. MAG-3, 433–452 (1967); Y. Togami, “Magneto-optic disk storage,” IEEE Trans. Magn. MAG-18, 1233–1237 (1982).
[CrossRef]

D. O. Smith, “Magneto-optical scattering from multilayer magnetic and dielectric films. Part I. General theory,” Opt. Acta 12, 13–45 (1965).
[CrossRef]

Tanaka, S.

T. Yoshino, S. Tanaka, “Polar and longitudinal magneto-optical Kerr and Faraday coefficients of bi-gyrotropic thin films,” Jpn. J. Appl. Phys. 9, 1282–1283 (1970).
[CrossRef]

T. Yoshino, S. Tanaka, “Theory of polar magneto-optic effects in thin films,” Oyo Butsuri 34, 572–581 (1965) (in Japanese).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 544–555.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 51–70.

Yoshino, T.

T. Yoshino, S. Tanaka, “Polar and longitudinal magneto-optical Kerr and Faraday coefficients of bi-gyrotropic thin films,” Jpn. J. Appl. Phys. 9, 1282–1283 (1970).
[CrossRef]

T. Yoshino, S. Tanaka, “Theory of polar magneto-optic effects in thin films,” Oyo Butsuri 34, 572–581 (1965) (in Japanese).

Bell Syst. Tech J. (1)

S. D. Personick, “Receiver design for digital fiber optic communication system I,” Bell Syst. Tech J. 52, 843–876 (1973).

IEEE Trans. Electron Devices (1)

R. J. McIntyre, “Multiplication noise in uniform avalanche diode,” IEEE Trans. Electron Devices ED-13, 164–168 (1966).
[CrossRef]

IEEE Trans. Magn. (1)

Research on the magneto-optical storage is described by D. O. Smith, “Magnetic films and optics in computer memories,” IEEE Trans. Magn. MAG-3, 433–452 (1967); Y. Togami, “Magneto-optic disk storage,” IEEE Trans. Magn. MAG-18, 1233–1237 (1982).
[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, 4485–4494 (1982).
[CrossRef]

J. Opt. Soc. Am. (1)

Jpn. J. Appl. Phys. (1)

T. Yoshino, S. Tanaka, “Polar and longitudinal magneto-optical Kerr and Faraday coefficients of bi-gyrotropic thin films,” Jpn. J. Appl. Phys. 9, 1282–1283 (1970).
[CrossRef]

Opt. Acta (2)

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]

D. O. Smith, “Magneto-optical scattering from multilayer magnetic and dielectric films. Part I. General theory,” Opt. Acta 12, 13–45 (1965).
[CrossRef]

Oyo Butsuri (1)

T. Yoshino, S. Tanaka, “Theory of polar magneto-optic effects in thin films,” Oyo Butsuri 34, 572–581 (1965) (in Japanese).

Other (7)

The main part of this study was presented at the 1982 Fall Meeting of the Japan Society of Applied Physics, Kyushu, Japan, September 1982.

Counterclockwise rotation is defined as being positive when the reflected or transmitted light is viewed toward the light traveling from a light source.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965), pp. 63–65.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 51–70.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), pp. 544–555.

W. D. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), pp. 204–218.

When m= 2M− 1, i.e., for odd multilayers, it follows from Eq. (18) that Δ1= Δ2= π/2 and thatr=Uρ+ρ0(1-2∣ρ∣2)U-ρρ0andk=(1 -∣ρ∣2)U(U-ρρ0)2k0,whereρ=PM′-QM′PM′+QM′,in whichPM′=(n2′n4′…n2M-2′)2nandandQM′=(n1′n3′…n2M-1′)2.

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Figures (10)

Fig. 1
Fig. 1

Polar magneto-optical Kerr effect.

Fig. 2
Fig. 2

General multilayer structure involving a magnetic thin film.

Fig. 3
Fig. 3

Schematic diagram of upper dielectric multilayer stack.

Fig. 4
Fig. 4

Schematic diagram of magneto-optical readout system. PBS, polarizing beam splitter; OL, objective lens; R retarder; D, photodetector.

Fig. 5
Fig. 5

Equivalent bilayer structure.

Fig. 6
Fig. 6

Magneto-optical interference factor Γ calculated as functions of real and imaginary parts of effective refractive index of substrate Ns for four different values of GdTbFe thickness h.

Fig. 7
Fig. 7

Magneto-optical interference factor Γ calculated as functions of real effective refractive index of substrate Ns and GdTbFe thickness h.

Fig. 8
Fig. 8

Medium structure using quarter-wave multilayers.

Fig. 9
Fig. 9

Magnetic-film-thickness dependence of optical responses. θk, Kerr rotation angle; χk, Kerr ellipticity; δk, phase difference; R, Fresnel reflectivity; K, Kerr reflectivity; Γ, magneto-optical interference factor.

Fig. 10
Fig. 10

Magnetic-film-thickness dependence of optimum system values and maximum SNR. APD denotes an avalanche photodiode; PD denotes a photodiode.

Tables (4)

Tables Icon

Table 1 Optimum Values of Medium and System Parameters

Tables Icon

Table 2 Optical and Magneto-Optical Constants of Materials at λ = 830 nm

Tables Icon

Table 3 Numerical Values of System Parameters

Tables Icon

Table 4 Improvement of SNR for Seven Medium Structures

Equations (95)

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n ( ± ) = n ( 1 ± ½ Q ) ,             Q 1 ,
n = n - i n ,
^ = n 2 [ 1 - i Q 0 i Q 1 0 0 0 1 ] ,
r = ½ [ r ( + ) + r ( - ) ]
k = ½ i [ r ( + ) - r ( - ) ] ,
r r Q = 0
k ½ i Q n d r d n | Q = 0 ,
θ k = - Re ( k / r )
χ k = Im ( k / r ) .
δ k = arg ( k / r ) .
r j = ρ 1             for j = 1 ,
r j = ρ j + r j - 1 exp ( - i δ j - 1 ) 1 + r j - 1 ρ j exp ( - i δ j - 1 )             for 2 j l + 1 ,
ρ j = n j - n j - 1 n j + n j - 1
δ j - 1 = 4 π λ n j - 1 z j - 1 ,
n 0 = n s ( refractive index of substrate )
n l + 1 = n ( refractive index of magnetic film ) .
N s = 1 - r l + 1 1 + r l + 1 n ,
r = ρ + t t ¯ ρ 0 exp ( - i δ ) [ 1 + ρ ¯ ρ 0 exp ( - i δ ) + ] = ρ + ( t t ¯ - ρ ρ ¯ ) ρ 0 exp ( - i δ ) 1 - ρ ¯ ρ 0 exp ( - i δ ) ,
δ = 4 π λ n d d
ρ 0 = V ρ + ρ V + ρ ρ ,
ρ = n d - n n d + n ,
ρ = n - N s n + N s ,
V = exp ( i 4 π λ n h ) .
M = [ A i B i C D ]
ρ = ( n a A - n d D ) + i ( n a n d B - C ) ( n a A + n d D ) + i ( n a n d B + C ) ,
ρ ¯ = - ( n a A - n d D ) + i ( n a n d B - C ) ( n a A + n d D ) - i ( n a n d B + C ) ,
t = 2 n a ( n a A + n d D ) + i ( n a n d B + C ) ,
t ¯ = 2 n d ( n a A + n d D ) - i ( n a n d B + C ) .
r = U ρ + ρ 0 { 1 - ρ 2 [ 1 - exp ( i 2 Δ 1 ) ] } U + ρ ρ 0 exp ( i 2 Δ 2 ) ,
Δ 1 = tan - 1 ( n a n d B - C n a A - n d D ) ,
Δ 2 = tan - 1 ( n a n d B + C n a A + n d D ) ,
U = exp ( i 4 π λ n d d ) .
n d n a t 2 + ρ 2 = 1
d r d n = r ρ 0 d ρ 0 d n = r ρ 0 ( ρ 0 ρ d ρ d n + ρ 0 ρ d ρ d n + ρ 0 V d V d n ) .
ρ = ρ exp [ i ( Δ 1 - Δ 2 ) ] .
r ρ 0 = U ( 1 - ρ 2 ) [ U + ρ ρ 0 exp ( i 2 Δ 2 ) ] 2 ,
d ρ 0 d n = - i ( 1 - ρ 2 ) 2 n ( V + ρ ρ ) 2 × { 8 π λ n h ρ V - i [ V 2 - ρ 2 - ( 1 - ρ 2 ) V ] } .
k = U ( 1 - ρ 2 ) [ U + ρ ρ 0 exp ( i 2 Δ 2 ) ] 2 k 0 ,
k 0 = Q ( 1 - ρ 2 ) 4 ( V + ρ ρ ) { 8 π λ n h ρ V - i [ V 2 - ρ 2 - ( 1 - ρ 2 ) V ] } .
PBS 1 :             A ( t / r ) = [ a x ( t / r ) 0 0 a y ( t / r ) ] ,
PBS 2 :             B ( t / r ) = [ b x ( t / r ) 0 0 b y ( t / r ) ] ,
Retarder :             R = [ exp ( i ϕ ) 0 0 1 ] ,
Medium :             M = [ - r k k r ] .
T ( t / r ) ( ψ ) = C ( - ψ ) B ( t / r ) C ( ψ ) R A ( r ) M A ( t ) ,
C ( ψ ) = [ cos ψ - sin ψ sin ψ cos ψ ] ,
I ( t / r ) = Tr ( T ( t / r ) J i T ( t / r ) ) ,
J i = P 0 [ 1 0 0 0 ] ,
b x ( t ) 2 = b y ( r ) 2 = 1
b x ( r ) 2 = b y ( t ) 2 = 0.
I ( t / r ) = P 0 2 a x ( t ) 2 a x ( r ) 2 R ± P 0 a x ( t ) 2 a x ( r ) a y ( r ) R K cos δ ,
R = r 2 ,
K = k 2 ,
δ = ϕ + arg ( r + k * + a x ( r ) + a y ( r ) * ) ,
a x ( t ) 2 = 1 - a x ( r ) 2 .
I F = ½ P 0 α ( 1 - α ) R
I K = P 0 α β ( 1 - α ) R K cos δ ,
α = a x ( r ) 2 ,
β = a y ( r ) 2 .
i dc = e η h ν s M I F
i p - p = e η h ν s 2 M I K ,
p - p signal power : i s 2 = 4 i p - p 2 ,
mean - square shot - noise power : i ¯ shot 2 = 4 e M 2 F M B ( i dc M = 1 ) ,
mean - square thermal - noise power : i ¯ th 2 = 8 k T e B R L ,
F M = M - ( 1 - κ ) ( M - 1 ) 2 M ,
SNR = i ¯ s 2 i ¯ shot 2 + i ¯ th 2
= 16 ( e η h ν s ) 2 M 2 P 0 2 α β ( 1 - α ) 2 R K [ 2 e 2 η h ν s P 0 F M α ( 1 - α ) M 2 R + i ¯ th 2 ] B ,
SNR = 8 η h ν s P 0 ( 1 - α ) β K B F M ,
N s = ( n 2 n 4 n 2 L n 1 n 3 n 2 L - 1 ) 2 n s             for l = 2 L ,
N s = ( n 1 n 3 n 2 L - 1 n 2 n 4 n 2 L - 2 ) 2 1 n s             for l = 2 L - 1 ,
A = ( - 1 ) M n 1 n 3 n 2 M - 1 n 2 n 4 n 2 M , D = ( - 1 ) M n 2 n 4 n 2 M n 1 n 3 n 2 n 2 M - 1 , B = C = 0 ,
A = D = 0 , B = ( - 1 ) M n 2 n 4 n 2 M - 2 n 1 n 3 n 2 M - 1 , C = ( - 1 ) M n 1 n 3 n 2 M - 1 n 2 n 4 n 2 M - 2 ,
r = U ρ + ρ 0 U + ρ ρ 0 ,
k = ( 1 - ρ 2 ) U ( U + ρ ρ 0 ) 2 k 0 ,
ρ = P M - Q M P M + Q M ,
P M = ( n 1 n 3 n 2 M - 1 ) 2 n a ,
Q M = ( n 2 n 4 n 2 M ) 2 n d .
ρ = N a - n d N a + n d ,
N a = ( n 1 n 3 n 2 M - 1 n 2 n 4 n 2 M ) 2 n a .
r = U r 1 + r 0 U + r 0 r 1 ,
k = ( 1 - r 1 2 ) U ( U + r 0 r 1 ) 2 k 0 ,
U = exp ( i 4 π λ n d d ) ,
r 1 = N a - n d N a + n d ,
r 0 = V r + r V + r r .
V = exp ( i 4 π λ n h ) ,
r = n d - n n d + n ,
r = n - N s n + N s .
K = Γ K 0 ( 1 - R ) 2 ,
K 0 = Q 2 n 2 16 n 2
Γ = | { 8 π λ n h r V - i [ V 2 - r 2 - ( 1 - r 2 ) V ] } | 2 [ V 2 - r 2 - 2 n n Re ( i r * V ) ] 2 .
F M M x ,
r=Uρ+ρ0(1-2ρ2)U-ρρ0
k=(1-ρ2)U(U-ρρ0)2k0,
ρ=PM-QMPM+QM,
PM=(n2n4n2M-2)2nand
QM=(n1n3n2M-1)2.

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