and Computational Methods

doi: 10.18698/2309-3684-2014-2-327

The paper considers two-dimensional boundary value problem of propagation of plane electromagnetic wave through a periodic stratified medium with one-dimensional photonic crystal structure. The structure contains a finite number of slabs. Each periodicity cell consists of two layers with different real values of constant dielectric permittivity and different thicknesses. We show that under certain additional condition, which connects the angle of incidence of the plane wave, thicknesses of the layers, frequencies and dielectric permittivity of the layers, we can solve the problem completely and explicitly, the solution leading to simple expressions for both the field reflected from the structure, and the field which has passed through it. Herewith in case of H-polarized field, unlike E-polarization, properties of this medium depend on the ratio of thickness of the layers multiplied by their dielectric permittivity (with E-polarization they depend on thickness ratio only). As a result, depending on the field frequency, photonic crystal can behave as perfectly reflecting structure, while with the same ratio of thicknesses of the layers in case of E-polarization, it becomes a wave guiding structure, and vice-versa. We have compared numerical computations with those for cases of E-polarization.

[1] Apeltsin V.F., Mozzhorina T.Yu. Inzhenerny zhurnal: nauka i innovatsii — Engineering Journal: Science and Innovations, 2013, no. 9. Available at: http://engjournal.ru/articles/966/966.pdf

[2] Dimitrienko Yu.I., Sokolov A.P., Markevitch M.N. Nauka i obrazovanie. Elektronnoe nauchno-tekhnicheskoe izdanie — Science and Education. Electronic Scientific and Technical Journal, 2013, no. 1, doi: 10.7463/0113.0531682.

[3] Dimitrienko Yu.I., Sokolov A.P., Markevitch M.N. Nauka i obrazovanie. Elektronnoe nauchno-tekhnicheskoe izdanie — Science and Education. Electronic Scientific and Technical Journal, 2013, no.10, doi: 10.7463/1013.0623343.

[4] Joannopoulos J.D., Meade R.D., Winn J.N. Photonic Crystals: Molding the Flow of Light. Princeton Univ. Press, 1995.

[5] Sakoda R., ed. Optical properties of photonic crystals. Berlin, Springer-Verlag, 2001.

[6] Zarubin V.S., Kuvyrkin G.N. Matematicheskoie Modelirovanie i Chislennye Metody — Mathematical Modeling and Computational Methods, 2014, no. 1, pp. 5–17.

[7] Bogolyubov A.N., Butkarev I.A., Dementyeva Yu.S. Vestnik Moskovskogo Universiteta. Seriya 3. Fizika. Astronomiya — Moscow State University Bulletin. Series 3. Phisics. Astronomy, 2010, no. 6, pp. 3–8.

[8] Dementyeva Yu.S. Vychislitel’nye Metody i Programmirovanie — Numerical Methods and Programming, 2011, vol. 12, pp. 375–378.

Apeltsin V., Mozzhorina T. Properties of one-dimensional photonic crystal as a reflective or wave guiding structure when excited by H-polarization. Маthematical Modeling and Coтputational Methods, 2014, №2 (2), pp. 3-27

Количество скачиваний: 608