Skip to main content

Eigenmodes of Linearised Problems of Scattering and Generation of Oscillations on Cubically Polarisable Layers

  • Conference paper
  • First Online:
Inverse Problems and Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 120))

Abstract

In the frequency domain, the resonant properties of nonlinear structures are determined by the proximity of the scattering/generation frequencies of the nonlinear structures to the complex eigenfrequencies of the corresponding homogeneous linear spectral problems with the induced nonlinear permeability of the medium. Here the case of cubically polarisable, canalising, and decanalising layers is considered.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Angermann, L., Yatsyk V.V.: Mathematical models of the analysis of processes of resonance scattering and generation of the third harmonic by the diffraction of a plane wave through a layered, cubically polarisable structure. Int. J. Electromagn. Waves Electron. Syst. 15(1):36–49, (2010). In Russian.

    Google Scholar 

  2. Angermann, L., Yatsyk, V.V.: Generation and resonance scattering of waves on cubically polarisable layered structures. In Angermann, L. (eds.) Numerical Simulations—Applications, Examples and Theory, pp. 175–212. InTech, Rijeka, (2011).

    Google Scholar 

  3. Angermann, L., Yatsyk, V.V.: Resonance properties of scattering and generation of waves on cubically polarisable dielectric layers. In V. Zhurbenko (eds.) Electromagnetic Waves, pp. 299–340. InTech, Rijeka, (2011).

    Google Scholar 

  4. Angermann, L., Yatsyk, V.V.: The effect of weak fields at multiple frequencies on the scattering and generation of waves by nonlinear layered media. In Kishk, A. (eds.) Solutions and Applications of Scattering, Propagation, Radiation and Emission of Electromagnetic Waves, pp. 303–332 (307–336 electronic). InTech, Rijeka, (2012)

    Google Scholar 

  5. Angermann, L., Yatsyk, V.V.: The influence of weak fields at multiple frequencies on the process of resonant scattering and generation of oscillations by nonlinear layered structures. Phys. Bases Instrum. 2(1):48–71, (2013). In Russian

    Google Scholar 

  6. Angermann, L., Shestopalov, Y.V., Yatsyk, V.V.: Modeling and analysis of wave packet scattering and generation for a nonlinear layered structure. In Kiley, E.M., Yakovlev, V.V. (eds.) Multiphysics Modeling in Microwave Power Engineering, pp. 21–26, University of Bayreuth, Germany, 2012. 14th Seminar Computer Modeling in Microwave Engineering and Applications, Bayreuth, March 5–6, (2012).

    Google Scholar 

  7. Kleinman, D.A.: Nonlinear dielectric polarization in optical media. Phys. Rev. 126(6):1977–1979, (1962)

    Article  Google Scholar 

  8. Miloslavsky, V.K.: Nonlinear Optics. V.N. Karazin Kharkov National University, Kharkov, (2008)

    Google Scholar 

  9. Sánchez-Palencia, E.: Non-Homogeneous Media and Vibration Theory, (vol. 127 of Lecture Notes in Physics). Springer-Verlag, Berlin, (1980)

    MATH  Google Scholar 

  10. Shestopalov V.P., Sirenko Y.K.: Dynamical Theory of Gratings. Naukova Dumka, Kiev, (1989). In Russian

    Google Scholar 

  11. Shestopalov V.P., Yatsyk V.V.: Spectral theory of a dielectric layer and the Morse critical points of dispersion equations. Ukrainian J. Phys. 42(7):861–869, (1997).

    Google Scholar 

  12. Shestopalov, Y.V., Yatsyk V.V.: Diffraction of electromagnetic waves by a layer filled with a Kerr-type nonlinear medium. J. Nonlinear Math. Phys. 17(3):311–335, (2010).

    Article  MATH  MathSciNet  Google Scholar 

  13. Yatsyk, V.V.: A constructive approach to construction of local equations of irregular dispersion and evolution of fields in a quasi-homogeneous electrodynamic structure. Usp. Sovr. Radioelektroniki, 10:27–44, 2000. (Translated in) Telecommun. Radio Eng. 56(8&9): 89–113, (2001).

    Google Scholar 

Download references

Acknowledgments

This work was partially supported by the Visby Program of the Swedish Institute and by the joint Russian-Ukrainian RFBR-NASU grant no. 12.02.90425-2012.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lutz Angermann .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Angermann, L., Shestopalov, Y., Yatsyk, V. (2015). Eigenmodes of Linearised Problems of Scattering and Generation of Oscillations on Cubically Polarisable Layers. In: Beilina, L. (eds) Inverse Problems and Applications. Springer Proceedings in Mathematics & Statistics, vol 120. Springer, Cham. https://doi.org/10.1007/978-3-319-12499-5_5

Download citation

Publish with us

Policies and ethics