350 rub
Journal Electromagnetic Waves and Electronic Systems №10 for 2010 г.
Article in number:
Propagation of Electromagnetic Wave through an One-Dimensional Layer with an Arbitrary Complex Refractive Index
Keywords: one-dimensional structure electromagnetic wave reflection transmission absorption general approach
Authors:
A.G. Khachatrian
Abstract:
The general approach for consideration of the scattering problem for a plane electromagnetic wave on an one-dimensional layer, having from point to point arbitrary changing complex refractive index. Basing on the one quite general property of the solutions of the one-dimensional wave equation, the problem transfer matrix, which connects the amplitudes of propagating in opposite directions waves in both sides of layer, is constructed. The connection between the elements of the transfer matrix and the transmission and reflection amplitudes of left and right scattering problems is established. Integral equations for the converging and diverging waves are obtained. It is shown, that the connection between the transfer matrix elements exists, which is carried out by means of replacing the sign of the wave number of the incident wave. Generalization of the suggested approach for the case of an arbitrary layered structure is carried out. To illustrate the usefulness of the suggested method, we solve the problem of determination of the wave transmission and reflection amplitudes for the ideal layered structure with an arbitrary structural element.
Pages: 49-65
References
  1. Yablonovitch E. Inhibited spontaneous emission in solid-state physics and electronics Phys. Rev. Lett. 1987. V. 58. № 20. P. 2059-2062.
  2. Joannopoulos J.D., Meade R.D., Winn J.N. Photonic Crystals: Molding the Flow of Light, Singapore, Princeton University Press. 1999.
  3. Быков В.П.Спонтанная эмиссия в периодической структуре // ЖЭТФ. 1972. Т. 35. № 2. С. 269-273.
  4. Адамсон П.В.Антиотражающие поверхностные покрытия с непрерывно изменяющимся комплексным показателем преломления // Письма в ЖТФ. 2000. Т. 26. Вып. 22. С. 50-57.
  5. Thelen A. Equivalent layers in multilayer filters. J.Opt.Soc.Am. 1966. V. 56. P. 1533-1538.
  6. Xu D.P., Mirabednini A., D-Souza M., Li S., Botez D., Lyakh A., Shen Y. J., Zory P., Gmachl. C.Room-temperature, mid-infrared (λ = 4,7 μm) electroluminescence from single-stage intersubband GaAs-based edge emitters, Appl // Phys. Lett. 2004. V. 85. № 20. P. 4573-4575.
  7. Акимов А.В., Вирченко А.В., Голубев В.Г., Каплянский А.А., Курдюков Д.А., Певцов А.Б., Щербаков А.В. Перестройка спектра брэгговской дифракции в композитах под действием лазерных импульсов // ФТТ. 2003. Т. 45. № 2. С. 231-234.
  8. Попов И.Ю., Мельничук О.П. Квантовые волноводы, связанные через периодическую систему малых отверстий: оценка запрещенной зоны // Письма в ЖТФ. 2002. Т. 8. Вып. 22. С. 69-73.
  9. Malis O., Belyanin A., Sivco D.L., Chen J., Sergent A.M. Gmachl C., Cho A.Y. Milliwatt second harmonic generation in quantum cascade lasers with modal phase matching. Appl // Phys. Lett. 2004. V. 84. № 15. P. 2721-2723.
  10. Fan S., Villeneuve P.R., Joannopoulos J.D.Large omnidirectional band gaps in metallodielectric photonic crystals // Phys. Rev. B. 1996. V. 54. № 7. P. 11245-11251.
  11. Арнольд В.И.Дополнительные главы теории обыкновенных дифференциальных уравнений. М.: Наука. 1978.
  12. SedrakianD.M.,KhachatrianA.Zh. On the problem of an electron scattering in an arbitrary one-dimensional potential field // Phys. Lett. A. 2000. V. 265. № 4. Р. 294?296.
  13. SedrakianD.M., Khachatrian A.Zh.Linear differential equations for the one-dimensional scattering problem, Annalen der Physik. 2002. V. 11. № 7. Р. 503-508.
  14. Бабиков В.В.Метод фазовых функций в квантовой механике. М.: Наука. 1976.
  15. Sedrakian D.M., Gevorgyan A.H., Khachatrian A. Zh.Reflection of a plane electromagnetic wave obliquely incident on a one-dimensional isotropic dielectric medium with an arbitrary refractive index. OpticsCommunications. 2001. V. 192. № 3. P. 135-143.
  16. Басс. Ф.Г., Булгаков. А.А., Тетервов А.П. Высокочастотные свойства полупроводников со сверхрешеткой. М.: Наука. 1989.
  17. Wang Z., Chan C.T., Zhang W., et al. Three-dimensional self-assembly of metal nanoparticles: possible photonic crystal with a complete gap below the plasma frequency // Phys. Rev. B. 2001. V. 64. P. 113108-113113.
  18. Gantzounis G., Stefanou N., Yannopapas Y.Optical properties of a periodic monolayer of metallic nanospheres on a dielectric waveguide // J. Phys.: Condens. Matter. 2005. V. 17. P. 1791-1802.
  19. Johnson P.B., Christy R.W. Optical constant of the noble metals // Phys. Rev. B. 1972. V. 6. Р. 4370-4379.