Scattering of light with quartz rough surface covered by thin gold film which has sine wave form
Calculation of light scattering by rough quartz surface covered with the gold film is shown. 2D vector Helmholtz equation solved using finite element approach is proposed. The interface between quartz and gold film is chosen as a surface which has sine wave form. It is shown that if using the surface highlight from the side of the quartz (complete internal reflection of light is required) and rms of rough gold thin film surface is insignificant ( nm) then (a) energy streams, caused the falling wave, are substantially disturbed near-by this surface only, (b) the crest of falling wave changes own position depending on the phase of the wave, (c) the size of the given wave crest in the rough surface peak is higher than the one in the valley, (d) the energy of the wave which dissipates on a thin film of gold in the far scattering zone is much smaller than the energy of the incident wave, (e) the contrast of quartz rough surface diminishes when its correlation length increases, (f) the contrast is practically independent of the length of the incident wave in the case where the conditions for the existence of a surface plasmon resonance are not fulfilled.
1. Zolotarev V.M. Polnoe vnutrennee otrashenie. Fizitcheskaya entsiklopedia. V.4. (Moscow: Bolshaya Rosiyskaya entsiklopedia, 1994). [in Russian].
2. Shestopalov V.D., Yatsuk K.P. Metodi izmereniya dielektritcheskix pronitsaemostei vestchestva na sverxvisokix tchastotax. UFN. 1961. 74(4): 721. [in Russian]. https://doi.org/10.3367/UFNr.0074.196108e.0721
3. Arma C. From light scattering to the microstructure of thin-film multilayers. Appl. Opt. 1993. 32(28): 5481. https://doi.org/10.1364/AO.32.005481
4. Volakis J.L., Cbatterjee A., Kempel L.C. Finite Element Method for Electromagnetics. (IEEE Press, 1998). https://doi.org/10.1109/9780470544655
5. Johnson P.W., Christy R.W. Optical Constants of the Noble Metals. Phys. Rev. B. 1972. 6(12): 4370. https://doi.org/10.1103/PhysRevB.6.4370
6. Jin J. The Finite Element Method in Electromagnetics. Second Edition. (New York: Wiley, 2002).
7. 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: 599. https://doi.org/10.1002/mop.4650071304
8. 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. https://doi.org/10.1109/8.477075
9. Raether H. Surface Plasmons on Smooth and Rough Surfaces and on Gratings. (Springer-Verlag, 1988). https://doi.org/10.1007/BFb0048317
10. Novotnii L., Xext B. Osnovi nanooptiki. (Moscow: Fizmatlit, 2009) [in Russian].
11. Quinten M. Optical Properties of Nanoparticle Systems: Mie and Beyond. (Willey: VCH Verlag&Co. KGaA, Weinhein, 2011). https://doi.org/10.1002/9783527633135
12. Adams M. Vvedenie v teoriyu opticheskix volnovodov. (Moscow: Mir, 1984). [in Russian].