Claude Amra,1
Joseph H. Apfel,2
and Emile Pelletier1
1Laboratoire d’Optique des Surfaces et des Couches Minces, Unité Associée au Centre National de la Recherche Scientifique, Ecole Nationale Supérieure de Physique de Marseille, Domaine Universitaire de St. Jérôme, 13397 Marseille Cedex 13, France.
2Optical Coating Laboratory, Inc., 2789 Northpoint Parkway, Santa Rosa, California 95407-7397.
Claude Amra, Joseph H. Apfel, and Emile Pelletier, "Role of interface correlation in light scattering by a multiplayer," Appl. Opt. 31, 3134-3151 (1992)
Four industries prepared optical coatings with a common design that permits an easy determination of cross-correlation laws between the rough interfaces in the stack. Different pairs of materials and deposition processes were used. After clarifying the differences between scalar and vector theories of light scattering caused by rough interfaces in optical multilayers, we compare the experimental values with both theories. Factors such as variations of correlation with spatial frequency, residual roughness, and slight errors in the design are taken into account for comparison with the vector theory of angular scattering. Correlation of the interface roughnesses is found to be high for practically all coatings. However, at low scatter-loss levels, scattering by localized defects in the coatings appears to dominate over the scattering caused by rough interfaces.
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Vector value Dv is calculated with a Gaussian autocorrelation function for all surface defects: Γ(τ) = δg2 exp −(τ/Lg)2, with δg, 0.5 nm; ppm, parts in 10−6.
Scalar value Ds′ is calculated with the measurable roughness δv (Ds′ is further explained in text).
Scalar value Ds is calculated with a roughness δs = δg = 0.5 nm.
Table II
Participants, Deposition Techniques, and Materials, with the Associated Values of Scattering, Correlation, and Residual Roughness
D is the value of total scattering losses.
η is the ratio of scattering after coating to scattering before coating.
α′ is the value of correlation that corresponds to η. The values of η are closer to unity (theoretical value for α′ = 1) rather than 30 (theoretical value for α′ = 0), which indicates high correlation for all samples.
The residual roughness δr is responsible for the slight lack of correlation.
Samples that were kept uncoated.
Table III
Values of Refractive Indices n(λ) = A + (B/λ2) + (C/λ4) (λ in nm) and of Layer Thicknesses (e in nm) of the Stack: Glass, nHe1, nLe2, nHe3, Air Calculated from Reflectance Measurements
Indices
Sample
Compound
A
B
C
017
ZrO2
2.1124
0.1428 105
−0.1877 108
SiO2
1.4779
0.4045 104
−0.5450 108
e1 = 142.5
e2 = 215.8
e3 = 143.7
30
TiO2
2.0685
0.2116 105
0.3683 1010
SiO2
1.4779
0.4045 104
−0.5450 108
e1 = 156.8
e2 = 220.1
e3 = 156.4
22
TiO2
2.1970
0.3780 105
0.3492 1010
SiO2
1.4779
0.4045 104
−0.5450 108
e1 = 130.1
e2 = 224.9
e3 = 137.9
003
Ta2O5
2.1558
0.2368 105
0.1098 1010
SiO2
1.4779
0.4045 104
−0.5450 108
e1 = 153.9
e2 = 201.4
e3 = 147.1
Tables (3)
Table I
Comparison of Scalar and Vector Values of Total Scattering Losses from a 2H 2L 2H Stack at λo in the Limits of Correlation (α = 0 and α = 1)
Vector value Dv is calculated with a Gaussian autocorrelation function for all surface defects: Γ(τ) = δg2 exp −(τ/Lg)2, with δg, 0.5 nm; ppm, parts in 10−6.
Scalar value Ds′ is calculated with the measurable roughness δv (Ds′ is further explained in text).
Scalar value Ds is calculated with a roughness δs = δg = 0.5 nm.
Table II
Participants, Deposition Techniques, and Materials, with the Associated Values of Scattering, Correlation, and Residual Roughness
D is the value of total scattering losses.
η is the ratio of scattering after coating to scattering before coating.
α′ is the value of correlation that corresponds to η. The values of η are closer to unity (theoretical value for α′ = 1) rather than 30 (theoretical value for α′ = 0), which indicates high correlation for all samples.
The residual roughness δr is responsible for the slight lack of correlation.
Samples that were kept uncoated.
Table III
Values of Refractive Indices n(λ) = A + (B/λ2) + (C/λ4) (λ in nm) and of Layer Thicknesses (e in nm) of the Stack: Glass, nHe1, nLe2, nHe3, Air Calculated from Reflectance Measurements