V.V. Shagaev - Dr. Sc. (Phys.-Math.), Professor, Kaluga branch of the Bauman MSTU E-mail: shagaev_vv@rambler.ru

It is known that the angular dependence of a reflection coefficient of the p polarised electromagnetic wave from a homogeneous medium has the zero value minimum. The corresponding angle is named as Brewster,s angle. The presence of thin transitive layer near a partition boundary results in the fact that the reflection coefficient, as before, has the minimum in angular dependence, which, however, doesn\'t reach zero. Thus the descriptions of reflection near the Bryuster,s angle are defined by the properties of transitive layer. In the present work results establishing a connection of the electrodynamic properties of the layer with the reflection coefficient are expounded. It is possible to deduce the analytical expression for electromagnetic wave reflection coefficient from a non-homogeneous medium only in the exclusive cases. The simplest example is the Drude,s model in which the permittivity changes by the jump at some depth. The reflection coefficient in this case can be expressed through the amplitude reflection coefficients from the semi-infinite homogeneous media with the sharp boundaries of partition (Fresnel,s coefficients). The numerical methods for arbitrary profile of the permittivity go out on the first plan. The method in which the non-homogeneous part of a medium breaks into the thin homogeneous layers is the most often used. The number of layers depends on the permittivity profile, and the reflection coefficient is calculated on the recurrent formula expressed through Fresnel,s coefficients. In the given article features of reflection near the Bryuster,s angle for a medium with a nonmonotonic profile of the permittivity are considered. The analysis is divided into two parts. A method of segmentation into the thin homogeneous layers was used for the first. In the second part analytical expression for a reflectivity is deduced in case when the thickness of the nonuniform layer is much less than the length of an electromagnetic wave. As an example of the developed theory use the problem of the terahertz radiation reflection from the implanted layer is considered. The obtained results are of interest to development of control methods of the technological operations modifying the materials surface properties.

 

1. Zinchenko S.P., Kovtun A.P., Tolmachev G.N. O vozmozhnosti kontrolja rosta tonkikh plenok metodom uglovojj reflektometrii v oblasti ugla Brjustera // ZHTF. 2009. T. 79. № 11. S. 128−133.
2. Erokhin N.S., Zueva JU.M., SHvarcburg A.B. Poljarizacionnye ehffekty v gradientnojj nanooptike // Kvantovaja ehlektronika. 2013. T. 43. № 9. S. 785−790.
3. SHvarcburg A.B. Dispersija ehlektromagnitnykh voln v sloistykh i nestacionarnykh sredakh (tochno reshaemye modeli) // UFN. 2000. T. 170. № 12. S. 1297−1324.
4. SHvarcburg A.B., Agranat M.B., CHefonov O.V. Nanooptika gradientnykh diehlektricheskikh plenok // Kvantovaja ehlektronika. 2009. T. 39. № 10. S. 948−952.
5. Naurzalin R.EH. Priblizhennye analiticheskie vyrazhenija dlja koehfficientov otrazhenija ehlektromagnitnojj volny ot neodnorodnogo kiralnogo sloja // ZHurnal radioehlektroniki. 2007. № 7. URL: http://jre.cplire.ru/win/jul07/4/text.html (07.09.2016).
6. Kravcov JU.A., Orlov JU.I. Geometricheskaja optika neodnorodnykh sred. M: Nauka. 1980. 306 s.
7. Antonec I.V., Kotov L.N., SHavrov V.G., SHHeglov V.I. Metod iskljuchenija dlja rascheta rasprostranenija voln cherez sredy so stupenchatymi neodnorodnostjami // ZHurnal radioehlektroniki. 2013. № 4. S. 38 URL: http://jre.cplire.ru/alt/apr13/6/text.pdf (07.09.2016).
8. Bilenko D.I., Poljanskaja V.P., Gecman M.A., Gorin D.A., Neveshkin A.A., JAshhenok A.M. Vlijanie perekhodnogo sloja na rezultaty ehllipsometricheskikh issledovanijj nanorazmernykh sloev // ZHTF. 2005. T. 75. № 6. S. 69−73.
9. SHagaev V.V. Raschet reflektometricheskikh kharakteristik s uchetom profilnojj neodnorodnosti perekhodnogo sloja // ZHTF. 2015. T. 85. № 12. S. 6−11.
10. Babikov V.V. Metod fazovykh funkcijj v kvantovojj mekhanike. M: Nauka. 1976. 286 s.