Attenuation of waveguide modes of thin films: separation of contributions of absorption and surface scattering of the light
A.B. Sotsky, P.Ya. Chudakouski

Full text of article: Russian language.

Abstract:
Analytical solution for the problem on separation of contributions of the material effects of absorption and surface scattering of the light in the attenuation coefficients of TE polarization modes is obtained under the assumption of a good localization of the energy of waveguide modes in a thin film and mean square deviations and the autocorrelation intervals of rough boundaries of film are small than the wavelength of the radiation. Based on this solve the algorithm of reconstruction of the imaginary part of the complex refractive index for the film is formulated. This algorithm uses of the real parts of the propagation constants and attenuation coefficients for the two TE modes of film, that are measured by means the waveguide spectroscopy. Effectiveness of the approach is confirmed by calculation of the diffraction fields arising at the propagation of waveguide modes along the film with rough boundaries.

Key words:
waveguide spectroscopy, waveguide mode, attenuation coefficient of waveguide modes, thin film.

References:

  1. Glyanko, M.S. Software for the device for detection of cleanliness and roughness of optical substrates / M.S. Glyanko, P.Yu. Izotov // Computer Optics. – 2012. – Vol. 36, N 2. – P. 242-248. – (In Russian).
  2. Khomchenko, A. Waveguide spectroscopy of thin films / A. Khomchenko. – Elsevier, 2005. – 236 p.
  3. Cardin, J. Determination of refractive index, thickness, and the optical losses of thin films from prism-film coupling measurements/ J. Cardin, D. Leduc // Appl. Opt. – 2008. – Vol. 47, N 7. – P. 894-900.
  4. Bilenko, D.I. Determination of optical properties and thickness of the nanolayers on the angular dependence of the reflection coefficient / D.I. Bilenko, A.A. Sagaidach­ny, V.V. Galuska, V.P. Polyanskaya // The Journal of Technical Physics. – 2010. – Vol. 80, N 10. – P. 89-94. – (In Russian).
  5. Tarasov, I.A. Ellipsometric express method for determining the thickness and optical constants of the profiles in the growth process of nanostructures Fe/SiO2/Si (100) / I.A. Tarasov, N.N. Kosyrev, S.N. Varnakov, S.G. Ovchinnikov, S.M. Zharkov, V.A. Shvets, S.G. Bondarenko, O.E. Tereshchenko // The Journal of Technical Physics. – 2012. – Vol. 82, N 9. – P. 44-48. – (In Russian).
  6. Hunsperger, R. Integrated optics: Theory and Technology / R. Hunsperger. – Moscow: “Mir” Publisher, 1985. – 384 p. – (In Russian).
  7. Unger, H.G. Planar optical waveguides and fibers / H.G. Unger. – Moscow: “Mir” Publisher, 1980. – 656 p. – (In Russian).
  8. Sotsky, A.B. Analysis of the reflected beam intensity distribution in the scheme of prism excitation of dielectric waveguides / A.B. Sotsky, A.A. Romanenko, A.V. Khomchenko, I.U. Primak // Radiotekh. Electron. – 1999. – Vol. 44, N 6. – P. 687-695. – (In Russian).
  9. Khomchenko, A.V. The waveguide method of measuring the parameters of thin films / A.V. Khomchenko, A.B. Sot­sky, A.A. Romanenko, E.V. Glazunov, .V. Shulga // The Journal of Technical Physics. – 2005. – Vol. 75, N 6. – P. 98-106. – (In Russian).
  10. Zhang, X.-J. Simple and efficient technique for evaluating the optical losses from surface scattering and volume attenuation in a thin film / Xi-Jing Zhang, Xi-Zhi Fan, Hui-Tian Wang, Jing-Liang He, N.B. Ming // Opt. Express. – 2002. – Vol. 10, N 25. – P. 1485-1490.
  11. Sotsky, A.B. Light beam reflection from the prism-film coupler. Part I. Theoretical model / A.B. Sotsky, P.J. Chu­da­kouski, I.U. Primak, L.I. Sotskaya // Vestnik Mogilev State University. – 2012. – Vol. 19, N 1. – P. 44-59. – (In Russian).
  12. Sotsky, A.B. Light beam reflection from the prism-film coupler. Part II. The solution of the inverse problem for the waveguide / A.B. Sotsky, P.J. Chudakouski, I.U. Primak, L.I. Sotskaya // Vestnik Mogilev State University. – 2012. – Vol. 40, N 2. – P .45-59. – (In Russian).
  13. Tamir, T.Integrated optics / T. Tamir. – Moscow: “Mir” Publisher, 1978. – 344 p. – (In Russian).
  14. Marcuse, D. Light transmission optics / D. Marcuse. – Moscow: “Mir” Publisher, 1972. – 576 p. – (In Russian).
  15. Lahad, L.S.A. Dispersion of light in the gradient wave guides with rough border / L.S.A. Lahad, A.N. Osovitsky // Vestnik RUDN (Physics). – 2005. – Vol. 13, N 1. – P. 60-67. – (In Russian).
  16. Ilyinsky, A.S. Mathematical models of electrodynamics / A.S. Ilyinsky, V.V. Kravtsov, A.G. Sveshnikov. – Moscow: ”Vysshaya Shkola” Publisher, 1991. – 224 p. – (In Russian).
  17. Elson, J.M. Propagation in planar waveguides and the effects of wall roughness / J.M. Elson // Opt. Express. – 2001. – Vol. 9, N 9. – P. 461-475.
  18. Silberstein, E. Use of grating theories in integrated optics / E. Silberstein, P. Lallane, J.P. Hugonin, Q. Cao // J. Opt. Soc. Am. A. – 2001. – Vol. 18, N 11. – P. 2865-2875.
  19. Sotsky, A.B. Diffraction of light in planar structures with perfectly matched layers / A.B. Sotsky, P.J. Chudakouski, I.U. Primak // Vestnik Mogilev State University. – 2010. – Vol. 29, N 1. – P. 45-50. – (In Russian).
  20. Shevchenko, V.V. Smooth transitions in open waveguides / V.V. Shevchenko. – Moscow: “Nauka” Publisher, 1969. – 192 p. – (In Russian).
  21. Sacks, Z.S. A perfectly matched anisotropic absorber for use as an absorbing boundary condition / Z.S. Sacks, D.M. Kingsland, R. Lee, J. Lee // IEEE Trans. Antennas Propagat. – 1995. –Vol. 43, N 12. – P. 1460-1463.
  22. Shevchenko, V.V. About a spectral resolution on characteristic and associated functions of one non self-conjugate problem of type of Sturm-Liouville on all axis / V.V. Shevchenko // Differential Equations. – 1979. – Vol. 15, N 11. – P. 2004-2020. – (In Russian).
  23. Sotsky, A.B. Theory of optical waveguide elements / A.B. Sotsky. – Mogilev: MSU Publisher, 2011. – 456 p. – (In Russian).
  24. Strasser, T.A. Optical loss measurement of low-loss thin-film waveguides by photographic analysis / T.A. Strasser, M.C. Gupta // Appl. Opt. – 1992. – Vol. 31, N 12. – P. 2041-2046.
  25. Weber, .P. Loss measurement in thin-film optical waveguides / H.P. Weber, F.A. Dunn, W.N. Leibolt // Appl. Opt. – 1973. – Vol. 12, N 4.– P. 755-757.

© 2009, IPSI RAS
Institution of Russian Academy of Sciences, Image Processing Systems Institute of RAS, Russia, 443001, Samara, Molodogvardeyskaya Street 151; E-mail: ko@smr.ru; Phones: +7 (846 2) 332-56-22, Fax: +7 (846 2) 332-56-20