Abstract

The level method monitoring technology which is suitable for periodic multilayers is studied theoretically as well as experimentally. Experimental results are given for three multilayer systems.

© 1985 Optical Society of America

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References

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  1. B. W. Smith, “Multilayer Mirrors with High Reflectivity at Fundamental, Second-Harmonic and Third-Harmonic Laser Wavelengths,” Opt. Acta 25, 715 (1978).
    [CrossRef]
  2. H. A. Macleod, E. Pelletier, “Error Compensation Mechanisms in Some Thin Film Monitoring Systems,” Opt. Acta 24, 907 (1977).
    [CrossRef]
  3. H. A. Macleod, “Turning Value Monitoring of Narrow-Band All-Dielectric Thin-Film Optical Filters,” Opt. Acta 19, 1 (1972).
    [CrossRef]
  4. E. Pelletier, P. Giacomo, “Controle et realisation de revetements multidielectriques presentant des caracteristiques spectrales imposees,” Nouv. Rev. Opt. Appl. 3, 133 (1972).
    [CrossRef]

1978 (1)

B. W. Smith, “Multilayer Mirrors with High Reflectivity at Fundamental, Second-Harmonic and Third-Harmonic Laser Wavelengths,” Opt. Acta 25, 715 (1978).
[CrossRef]

1977 (1)

H. A. Macleod, E. Pelletier, “Error Compensation Mechanisms in Some Thin Film Monitoring Systems,” Opt. Acta 24, 907 (1977).
[CrossRef]

1972 (2)

H. A. Macleod, “Turning Value Monitoring of Narrow-Band All-Dielectric Thin-Film Optical Filters,” Opt. Acta 19, 1 (1972).
[CrossRef]

E. Pelletier, P. Giacomo, “Controle et realisation de revetements multidielectriques presentant des caracteristiques spectrales imposees,” Nouv. Rev. Opt. Appl. 3, 133 (1972).
[CrossRef]

Giacomo, P.

E. Pelletier, P. Giacomo, “Controle et realisation de revetements multidielectriques presentant des caracteristiques spectrales imposees,” Nouv. Rev. Opt. Appl. 3, 133 (1972).
[CrossRef]

Macleod, H. A.

H. A. Macleod, E. Pelletier, “Error Compensation Mechanisms in Some Thin Film Monitoring Systems,” Opt. Acta 24, 907 (1977).
[CrossRef]

H. A. Macleod, “Turning Value Monitoring of Narrow-Band All-Dielectric Thin-Film Optical Filters,” Opt. Acta 19, 1 (1972).
[CrossRef]

Pelletier, E.

H. A. Macleod, E. Pelletier, “Error Compensation Mechanisms in Some Thin Film Monitoring Systems,” Opt. Acta 24, 907 (1977).
[CrossRef]

E. Pelletier, P. Giacomo, “Controle et realisation de revetements multidielectriques presentant des caracteristiques spectrales imposees,” Nouv. Rev. Opt. Appl. 3, 133 (1972).
[CrossRef]

Smith, B. W.

B. W. Smith, “Multilayer Mirrors with High Reflectivity at Fundamental, Second-Harmonic and Third-Harmonic Laser Wavelengths,” Opt. Acta 25, 715 (1978).
[CrossRef]

Nouv. Rev. Opt. Appl. (1)

E. Pelletier, P. Giacomo, “Controle et realisation de revetements multidielectriques presentant des caracteristiques spectrales imposees,” Nouv. Rev. Opt. Appl. 3, 133 (1972).
[CrossRef]

Opt. Acta (3)

B. W. Smith, “Multilayer Mirrors with High Reflectivity at Fundamental, Second-Harmonic and Third-Harmonic Laser Wavelengths,” Opt. Acta 25, 715 (1978).
[CrossRef]

H. A. Macleod, E. Pelletier, “Error Compensation Mechanisms in Some Thin Film Monitoring Systems,” Opt. Acta 24, 907 (1977).
[CrossRef]

H. A. Macleod, “Turning Value Monitoring of Narrow-Band All-Dielectric Thin-Film Optical Filters,” Opt. Acta 19, 1 (1972).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Admittance diagram for monitoring by the level method.

Fig. 2
Fig. 2

Relationship between ϕa and ϕb, ϕa/ϕb and ϕa when Na = 2.35, Nb = 1.52, and Ns = 1.52.

Fig. 3
Fig. 3

(a) The results of error simulation calculations for the system G[(2A/3)(2B/3)(2A/3)]9M with Na = 2.35, Nb = 1.58, Nm = 1, Ng = 1.52, A = 1428 Å, B = 1428 Å, and E = 0.005. (b) The results of error simulation calculations for the system GAB′[(B/3)(4A/3)(B/3)]6M with Na′ = Na = 2.35, Nb = Nb′ = 1.38, Nm = 1, Ng = 1.52, B = A = 1500 Å, A′ = 1967 Å, B′ = 933 Å, E = 0.005, λc = 4900 Å.

Fig. 4
Fig. 4

(a) The results of error simulation calculations for the system GAB′[(B/2)A(B/2)]7M with A′ = 2221Å, B′ = 1142 Å, A = B = 1859 Å, Nb′ = Nb = Ng = 1.52, Nm = 1, Na′ = Na, Na = 2.252 + 1.575 × 1062 + 5.422 × 10134 (4), E = 0.005, λc = 5950 Å. (b) The results of error simulation calculations for the system GAB′[(B/2)A(B/2)]7M with A′ = 2122 Å, B′ = 721 Å, A = B = 1859 Å, Nb′ = Nb = Ng = 1.52, Nm = 1, Na′ = Na, Na = 2.252 + 1.575 × 1062 + 5.422 × 10134 (4).

Fig. 5
Fig. 5

Admittance diagram when an error exists in the monitoring signal.

Fig. 6
Fig. 6

Three experimental results for the system GAB′[(B/3)(4A/3)(B/3)]6M with Na′ = Na = 2.35, Nb′ = Nb = 1.38, Ng = 1.52, Nm = 1, A = 1987 Å, B′ = 933 Å, B = A = 1500 Å, λc = 4800 Å, –* denotes calculation.

Fig. 7
Fig. 7

Three experimental results for the system G[(2A/3)(2B/3)(2A/3)]8BM with Na = 2.35, Nb = Ng = 1.52, Nb′ = 1.38, Nm = 1, B′ = 2170 Å, A = B = 1170 Å, λc = 6050 Å, ** denotes calculation.

Fig. 8
Fig. 8

Three experimental results for the system GB′[(B/2)A(B/2)]7M with Na = 2.35, Nb = Ng = 1.52, Nb = 1.38, Nm = 1, B′ = 1370 Å, B = A = 1860 Å, λc = 5850 Å, ** denotes calculation.

Equations (8)

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tan 2 ϕ b N a N b sin 2 ϕ a N a 4 N s 2 N b 2 N a 2 N s 2 ( N a 2 + N b 2 ) cos 2 ϕ a .
ϕ a ϕ b = C 1 C 2 .
N s = N a [ N a N b sin 2 ϕ a + ( N b 2 cos 2 ϕ a N a 2 sin 2 ϕ a ) tan 2 ϕ b N a N b sin 2 ϕ a + ( N a 2 cos 2 ϕ a N b 2 sin 2 ϕ a ) tan 2 ϕ b ] 1 / 2 .
R 0 = ( N s N m ) 2 + ( N a N m N s / N a ) 2 tan 2 ϕ a ( N s + N m ) 2 + ( N a + N m N s / N a ) 2 tan 2 ϕ a .
tan ϕ = [ N a N b N s 2 N a 2 N b N s 2 / N a ] 1 / 2 .
cos ϕ a = [ N a 4 N b 2 N s 2 ( N a 2 N s 2 ) ( N a 2 + N b ) 2 ] 1 / 2 .
Δ R 0 = F 5 + F 3 F 4 R 1 + F 2 F 3 Δ R e ,
F 1 = 4 N e ( N e 1 ) ( 2 N e k ) ( 1 + N e ) 3 ( 1 N b 2 + β 2 α 2 ) , F 2 = 8 β N e ( N e 1 ) α ( 2 N e k ) ( 1 + N e ) 3 , F 3 = 1 2 β ( N a 2 + N s 2 N s 2 α ) , F 4 = 8 α β [ ( α + 1 ) 2 + β 2 ] 2 , F 5 = 4 ( α 2 β 2 1 ) [ ( α + 1 ) 2 + β 2 ] 2 , k = N b 2 + α 2 + β 2 α .

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