Scattering of light by quartz rough surface described as sequence of surface three-cornered form irregularities

  • V. I. Grigoruk Kyiv National Taras Shevchenko University
  • V. I. Kanevskii Chuiko Institute of Surface Chemistry of National Academy of Sciences of Ukraine
  • S. A. Kolenov Kyiv National Taras Shevchenko University
  • V. S. Sidorenko Kyiv National Taras Shevchenko University


Calculation of evanescent field in near-zone of quartz rough surface is presented. 2D vector Helmholtz equation by means of finite element approach is used. Shape of quartz surface is chosen as sequence of surface three-cornered form irregularities. It shown that (a) contrast range of evanescent field practically does not depend on length of scattering wave at illumination of quartz rough surface on condition of total light reflection especially in the case of height of irregularities ()is insignificant (£1nm); (b) the reflection light coefficient does not depend on the   parameter; (c) the contrast of quartz rough surface diminishes when its correlation length increases; (d) on the average, distribution of evanescent field along the surface of quartz repeats the form of the rough surface.


1. Ali I., Roy S.R., Shinn G. Chemical-mechanical polishing of interlayer dielectric: a review. Solid State Technology. 1994. 37(10): 63.

2. Ivanovsky G.F., Petrov V.I. Ionno-plazmennaya obrabotka materialov. (Moscow: Radio i svyaz', 1986). [in Russian].

3. Patent Japan JP2014-022411A. Genichi O., Takashi Y., Ko N. Etching method using near-field light. 2014.

5. Nomura W., Yatsui T., Ohtsu M. Nonadiabatic Near-Field Optical Polishing and Energy Transfers in Spherical Quantum Dots. In: Progress in Nano–Electro–Optics VII. (Berlin: Springer-Verlag, 2010).

7. Volakis J.L., Cbatterjee A., Kempel L.C. Finite Element Method for Electromagnetics. (IEEE Press, 1998).

8. Johnson P.W., Christy R.W. Optical constants of the noble metals. Phys. Rev. B. 1972. 6(12): 4370.

9. Jin J. The Finite Element Method in Electromagnetics. Second Edition. (New York: Wiley, 2002).

10. Chew W.C., Weedon W.C. A 3D perfectly matched medium from modified Maxwell's equations with stretched coordinates. Microwave Opt. Technol. Lett. 1994. 7(13): 599.

11. Sacks Z.S., Kingsland D.M., Lee R., Lee J.F. A perfectly matched anisotropic absorber for use as an absorbing boundary condition. IEEE Trans. Antennas Propag. 1995. 43(12): 1460.

12. Raether H. Surface Plasmons on Smooth and Rough Surfaces and on Gratings. (Springer-Verlag, 1988).

13. Sergienko A.B. Tsifrovaya obrabotka signalov. (Moscow: Piter, 2003). [in Russian].

14. Novotny L., Hecht B. Osnovy nanooptiki. (Moscow: FIZMATLIT, 2009). [in Russian].

15. Quinten M. Optical Properties of Nanoparticle Systems: Mie and Beyond. (Willey, VCH Verlag&Co. KGaA, Weinhein, 2011).

16. Agranovich V.M., Mills D.L. Surface Polaritons: Electromagnetic Waves at Surface and Interfaces. (Amsterdam, New York, North-Holland, 1982).

How to Cite
Grigoruk, V., Kanevskii, V., Kolenov, S., & Sidorenko, V. (2017). Scattering of light by quartz rough surface described as sequence of surface three-cornered form irregularities. Surface, (9(24), 69-80.
Theory of surface chemical structure and reactivity.