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2013-10-24
Mathematical Models of Electrodynamical Processes of Wave Scattering and Generation on Cubically Polarisable Layers
By
Progress In Electromagnetics Research B, Vol. 56, 109-136, 2013
Abstract
Results of a self-consistent computational analysis based on a mathematical model of resonance scattering and generation of waves on an isotropic nonmagnetic nonlinear layered dielectric structure excited by a packet of plane waves are presented, where the analysis is performed in the domain of resonance frequencies. Physically interesting properties of the nonlinear permittivities of the layers as well as their scattering and generation characteristics are obtained, for instance the characteristic dynamical behaviour of the relative Q-factor of the eigenmodes and the energy of higher harmonics generated by canalising as well as decanalising nonlinear layers. The results demonstrate the possibility to control the scattering and generating properties of a nonlinear structure by means of the excitation intensities.
Citation
Lutz Angermann, and Vasyl V. Yatsyk, "Mathematical Models of Electrodynamical Processes of Wave Scattering and Generation on Cubically Polarisable Layers," Progress In Electromagnetics Research B, Vol. 56, 109-136, 2013.
doi:10.2528/PIERB13090205
References

1. Agranovich, V. and V. Ginzburg, Spatial Dispersion in Crystal, Optics and the Theory of Excitons, Interscience, London, 1966.

2. Angermann, L., Y. V. Shestopalov, and V. V. Yatsyk, "Modeling and analysis of wave packet scattering and generation for a nonlinear layered structure," Multiphysics Modeling in Microwave Power Engineering/14th Seminar Computer, 21-26, Mar. 2012.

3. Angermann, L. and V. V. Yatsyk, "Numerical simulation of the diffraction of weak electromagnetic waves by a Kerr-type nonlinear dielectric layer," Int. J. Electromagnetic Waves and Electronic Systems , Vol. 13, No. 12, 15-30, 2008.

4. Angermann, L. and Mathematical models of the, "Mathematical models of the analysis of processes of resonance scattering and generation of the third harmonic by the di®raction of a plane wave through a layered, cubically polarisable structure," Int. J. Electromagnetic Waves and Electronic Systems, Vol. 15, No. 1, 36-49, 2010.
doi:(in Russian)

5. Angermann, L. and V. V. Yatsyk, "Generation and resonance scattering of waves on cubically polarisable layered structures," Numerical Simulations --- Applications, Examples and Theory, 175-212, 2011.

6. Angermann, L. and V. V. Yatsyk, "Resonance properties of scattering and generation of waves on cubically polarisable dielectric layers," Electromagnetic Waves, 299-340, 2011.

7. Angermann, L. and V. V. Yatsyk, "The influence of weak fields at multiple frequencies on the process of resonant scattering and generation of oscillations by nonlinear layered structures," Physical Bases of Instrumentation, Vol. 2, No. 1, 48-71, 2013.
doi:(in Russian)

8. Angermann, L., V. V. Yatsyk, and M. V. Yatsyk, "Preset field approximation and self-consistent analysis of the scattering and generation of oscillations by a layered structure," Inverse Problems and Large-Scale Computations Springer Proceedings in Mathematics & Statistics, Vol. 52, 41-56, 2013.
doi:10.1007/978-3-319-00660-4_4

9. Chernogor, L. F., Nonlinear Radiophysics, V. N. Karazin Kharkov, National University, Kharkov, 2004.

10. Kleinman, D. A., "Nonlinear dielectric polarization in optical media," Phys. Rev., Vol. 126, No. 6, 1977-1979, 1962.
doi:10.1103/PhysRev.126.1977

11. Kravchenko, V. F. and V. V. Yatsyk, "Effects of resonant scattering of waves by layered dielectric structure with Kerr-type nonlinearity," Int. J. Electromagnetic Waves and Electronic Systems, Vol. 12, No. 12, 17-40, 2007.

12. Miloslavsky, V. K., Nonlinear Optics, V. N. Karazin Kharkov, National University, Kharkov, 2008.

. Schurmann, H. W., V. S. Serov, and Y. V. Shestopalov, "Re°ection and transmission of a TE-plane wave at a lossless nonlinear dielectric film," Physica D, Vol. 158, 197-215, 2001.
doi:10.1016/S0167-2789(01)00310-4

14. Serov, V., H. W. Schurmann, and E. Svetogorova, "Integral equation approach to reflection and transmission of a plane TE-wave at a (linear/nonlinear) dielectric film with spatially varying permittivities," J. Phys. A: Math. Gen., Vol. 37, 3489-3500, 2004.
doi:10.1088/0305-4470/37/10/012

15. Shestopalov, V. and V. V. Yatsyk, "Spectral theory of a dielectric layer and the Morse critical points of dispersion equations," Ukrainian J. of Physics, Vol. 42, No. 7, 861-869, 1997.

16. Shestopalov, V. P. and Y. K. Sirenko, Dynamical Theory of Gratings, Naukova Dumka, Kiev, 1989.
doi:(in Russian)

17. Shestopalov, Y. V. and V. V. Yatsyk, "Resonance scattering of electromagnetic waves by a Kerr nonlinear dielectric layer," Radiotekhnika i Elektronika (J. of Communications Technology and Electronics), Vol. 52, No. 11, 1285-1300, 2007.

18. Shestopalov, Y. V. and V. V. Yatsyk, "Diffraction of electromagnetic waves by a layer filled with a Kerr-type nonlinear medium," J. of Nonlinear Math. Physics, Vol. 17, No. 3, 311-335, 2010.
doi:10.1142/S1402925110000921

19. Smirnov, Y. G., H. W. Schurmann, and Y. V. Shestopalov, "Propagation of TE-waves in cylindrical nonlinear dielectric waveguides," Physical Review E, Vol. 71, 1-10, 2005.
doi:10.1103/PhysRevE.71.036207

20. Vainshtein, L. A., Electromagnetic Waves, Radio i Svyas, Moscow, 1988.
doi:(in Russian)

21. Vinogradova, M. B., O. V. Rudenko, and A. P. Sukhorukov, Wave Theory, Nauka, Moscow, 1990.

22. Yatsyk, V. V., "A constructive approach to construction of local equations of irregular dispersion and evolution of ¯elds in a quasi-homogeneous electrodynamic structure," Usp. Sovr. Radioelektroniki/Telecommunications and Radio Engineering, Vol. 10, 27/89-44/113, 2000.

23. Yatsyk, V. V., "Diffraction by a layer and layered structure with positive and negative susceptibilities of Kerr-nonlinear media," Usp. Sovr. Radioelektroniki, Vol. 8, 68-80, 2006.

24. Yatsyk, V. V., "About a problem of diffraction on transverse non-homogeneous dielectric layer of Kerr-like nonlinearity," Int. J. Electromagnetic Waves and Electronic Systems, Vol. 12, No. 1, 59-69, 2007.