Ukrainian Journal of Physical Optics 

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Application of spectral envelope functions of multilayer structures for analytical determination of antireflection conditions 
Kushnir O.P.

Department of Physics, Lviv National Agrarian University, 1 V.Velykogo St., Dublyany, 80381 Lviv region, Ukraine

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Envelope functions for the reflection and transmission spectra of multilayer structures are determined. Analytical expressions for the phase thicknesses of two arbitrary layers ensuring zero reflectance for the whole transparent structure are found with the aid of those envelopes.

Keywords:  antireflection conditions, reflection spectra envelopes, transmission spectra envelopes, multilayer coatings.

PACS:  42.79.Wc; 78.20. UDC: 535.312
Ukr. J. Phys. Opt. 10 82-88 
doi: 10.3116/16091833/10/2/82/2009

Received: 06.02.2009

Анотація. Визначені обвідні функції спектрів відбивання і пропускання багатошарових структур. З допомогою цих обвідних знайдені аналітичні вирази для фазових товщин двох довільних шарів, які забезпечують нульове значення енергетичного коефіцієнта відбивання від всієї прозорої структури.

  1. Minkov D A, 2001. Method for determining the optical constants of thin dielectric films with variable thickness using only their shrunk reflection spectra. J. Phys. D: Appl. Phys. 34: 2489–2496. doi:10.1088/0022-3727/34/16/314
  2. Minkov D A, 1989. Calculation of the optical constants of a thin layer upon a transparent substrate from the reflection spectrum. J. Phys. D: Appl. Phys. 22: 1157–1161. doi:10.1088/0022-3727/22/8/021
  3. Kushev D B and Zheleva N N, 1995. Transmittivity, reflectivities and absorptivities of a semiconductor film with a linear variation in thickness. J. Phys. D: Appl. Phys. 28: 1239–1243. doi:10.1088/0022-3727/28/6/029
  4. Kushev D B, Zheleva N N, Gyulmezov M I and Koparanova M H, 1993. An envelope method for determination of the optical constants of absorptive films on absorptive substrates. Infrared Phys. 34: 163–167. doi:10.1016/0020-0891(93)90005-R
  5. Swanepoel R, 1984. Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films. J. Phys. E: Sci. Instrum. 17: 896–903. doi:10.1088/0022-3735/17/10/023
  6. Caricato A P, Fazzi A and Leggieri G, 2005. A computer program for determination of thin films thickness and optical constants. Appl. Surf. Sci. 248: 440–445. doi:10.1016/j.apsusc.2005.03.069
  7. Minkov D A, 1989. Method for determining the optical constants of a thin film on a transparent substrate. J. Phys. D: Appl. Phys. 22: 199–205. doi:10.1088/0022-3727/22/1/029
  8. 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.
  9. Kosobutskyy P S and Kushnir O P, 2008. Regularities of oblique light reflection by a film caused by a multibeam interference. J. Phys. Stud. 12: 1701-1–1701-5.
  10. Filippov V V, 2006. Envelope technique for the studies of two-film system lying on reflecting substrate. Opt. Spektrosk. 101: 485–489. doi:10.1134/S0030400X06090207
  11. Kosobutskyy P S and Kushnir O P, 2008. Envelopes of optical interference spectra for duplex and triplex layered structures. Ukr. J. Phys. Opt. 9: 73–81. doi:10.3116/16091833/9/2/73/2008
  12. Schuster K, 1949. Anwendung der Vierpoltheorie auf die Probleme der optischen Reflexionsminderung, Reflexionsverstarkung und der Interferenzfilter. Ann. Phys. 4: 352–356. doi:10.1002/andp.19494390607
  13. Catalan L A, 1962. Some computed optical properties of antireflection coatings. J. Opt. Soc. Am. 52: 437–440. doi:10.1364/JOSA.52.000437
  14. Grebenshchikov I V, Vlasov A G, Neporent B S and Sujkovsky N V. Prosvetlenie Optiki (Non-Reflective Coatings on Optical Materials). Moscow: OGIZ (1946).
  15. Dietz N, 2001. Real-time optical characterization of thin film growth. Mat. Sci. Eng. B87: 1–22. doi:10.1016/S0921-5107(01)00711-5
  16. Monz’on J J and S’anchez-Soto L L, 1999. Lossless multilayers and Lorentz transformations: more than an analogy. Opt. Commun. 162: 1–6. doi:10.1016/S0030-4018(99)00065-6
  17. Thelen A. Design of optical interference coatings. New York: McGraw-Hill (2008).

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