Role of interface correlation in light scattering by a multiplayer

Abstract

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.

Reflectance and transmittance model for multilayer optical coatings with roughness at oblique incidence

“…Many researchers have studied the cross-correlation properties of different interfaces, such as Thomas A. Germer [17], J. M.Elson [18], C. Amra [19,20] and etc., which will give us lots of guidance in our future work.…”

Statistical distribution of the field scattered by rough layered interfaces: formulae derived from the small perturbation method

“…The study of electromagnetic scattering by a stack of rough layers has many applications in remote sensing [1][2][3][4][5][6] as in optics [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Such structures can be analysed by means of approximated models and of exact methods [27][28][29][30][31][32][33].…”

“…Let us emphasise that, over the past several years, first-order perturbation theory have been used to predict scattering from multilayer stacks and especially light scattering from multilayer optical coatings [7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Elson has developed a vector theory of scattering from a stack of two-dimensional slightly rough interfaces which allows the angular distribution of scattered light to be determined [7][8][9][10].…”

“…The vector theory can be used with fully or partially correlated or uncorrelated surface roughness. Many authors of the optical thin film community have studied the role of correlation lengths and roughness cross-correlation properties on the angular scattering [7][8][9][10][11][13][14][15][16][17] and studied the relationship of the scattering from optical coatings to angle of incidence and polarisation [9,17] and compared results of the perturbation theory with experimental ones [8,[11][12][13][14][15][16]. In references , the perturbation method has been used to determine the first-order complex amplitude of the scattered far-field and the statistical average of the radiation intensity but not the probability laws of the farfield.…”

Grazing angle enhanced backscattering from a dielectric film on a reflecting metal substrate

“…In the papers of Elson, [39][40][41][42] Elson et al, [43][44][45] Bousquet et al, 46 and Duparre et al 47 it was developed for electromagnetic wave scattering ("vector scattering model") by rough interfaces of multilayer dielectric stacks. This model was successfully applied and developed by Amra [48][49][50] and Amra et al [51][52][53][54] for a theoretical interpretation of numerous experimental results.…”