Ukrainian Journal of Physical Optics 

Home page

Other articles 

in this issue
Envelopes of optical interference spectra for duplex and triplex layered structures
1Kosobutskyy P.S., 2Kushnir O.P.

1National University “Lviv Polytechnics”, P. O. Box 4544, 79053 Lviv-53, Ukraine
2Lviv State Agrarian University, 1 V. Velykyi St., Dublyany, 80381 Lviv Region, Ukraine

download full version

We have found analytical expressions for the envelopes of maxima and minima of interference reflection and transmission spectra for both transparent and absorbing two- and three-layer structures under the conditions of arbitrary light incidence and polarization state. General regularities for the shape of those spectral envelopes are established, depending on the optical thicknesses of constituent layers.

Keywords: reflection spectra envelopes, thin film, two- and three-layer structures

PACS: 63.22.+m; 78.30-j; 78.30.Fs; 78.66.Hf
Ukr. J. Phys. Opt. 9 73-81   doi: 10.3116/16091833/9/2/73/2008
Received: 10.01.2008


1.Kosobutskyy P S and Morgulis A, 2004. Modelling of reflection and transmission spectroscopies of single-layer Fabri-Perot interferometers using the envelope method. Opt. Zhurn. 71: 63–68.
2. Filippov V V, 2006. Envelope technique for the studies of two-film system lying on reflecting substrate. Opt. Spektrosk. 101: 485–489.
3. Arndt D P, Azzam R M A, Bennett J M, Borgogno JP, Carniglia C K, Case W E, Dobrowolski J A, Gibson U J, Tuttle Hart T, Ho F C, Hodgkin V A, Klapp W P, Macleod H A, Pelletier E, Purvis M K, Quinn D M, Strome D H, Swenson R, Temple P A, Thonn T F, 1984. Multiple determination of the optical constants of thin-film coating materials. Appl. Opt. 23: 3571–3596.
4. Kutavichus V, Filippov V and Huzouski V, 2006. Determination of optical parameters and thickness of weakly absorbing thin films from reflectance and transmittance spectra. Appl. Opt. 45: 4547–4553.
5. Macleod H A Thin-Film Optical Filters. Bristol: Adam Hilger Ltd (1986).
6. Wiktorczyk T and Oles M, 2007. Design, fabrication and optical characterization of cerium oxide-magnesium fluoride double layer antireflection coatings on monocrystalline silicon substrate. Opt. Mater. 29: 1768–1773.
7. Born M and Volf E Fundamentals of Optics Moscow: Nauka (1970).
8. Azzam R. M. A. and Bashara N. M., Ellipsometry and Polarized Light. Moscow: Mir (1981).
9. Kosobutskyy P S and Kushnir O P, 2007. Regularities of manifestation of the Brewster and pseudo-Brewster angular conditions in spectra of light reflection from a thin transparent layer. Ukr. J. Phys. 52: 225–228.
10. Surdutivich G I, Vitlina R Z and Baranauskas V, 1999. Simple reflectometric method for measurement of weakly absorbing films. Thin Solid Films. 355–356: 446–450.
11. Shigeki Takeuchi, Shoji Nitta, Yukihiro Yamada and Shuichi Nonomura, 1996. Brewster Anomalies in Opaque Random Amorphous Multilayers a-Si:H/a-Si3N4+x:H. Opt. Rev. 3: 238–242.

(c) Ukrainian Journal of Physical Optics