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Nonlinear Optical and Acoustical Waves


Nonlinear Optical and Acoustical Waves in Dielectrics and Semiconductors

Tech Area / Field

  • PHY-OPL/Optics and Lasers/Physics
  • PHY-SSP/Solid State Physics/Physics

8 Project completed

Registration date

Completion date

Senior Project Manager
Malakhov Yu I

Leading Institute
Georgian Technical University, Georgia, Tbilisi

Supporting institutes

  • American-European Academy of Science (Georgian Branch), Georgia, Tbilisi


  • Clarkson University, USA, NY, Potsdam\nInstitut Fresnel / Faculte des Sciences Saint Jerome, France, Marseille

Project summary

A theory of optical and acoustical nonlinear waves of different kinds in nonlinear and disperse media will be developed. Some new physical processes of formation of solitons or/and breathers, when two different mechanisms of formation of nonlinear waves are simultaneously effective will be considered. Specific peculiarity propagation of optical (acoustical) breathers under condition of one-photon (one-phonon) excitations of optical active impurity atoms (paramagnetic impurities) will be investigated in detailed. Influence of finite conductivity and some other dissipation effects on the formation and stability of double breather of self-induced transparency will be considered. The explicit analytical expressions for nonlinear magneto-acoustic waves and their polarization in a magnetically ordered medium will be investigated. The solitons in exciton region of spectrum and their polarization in the presence of an external constant magnetic field will be investigated too.
The following new results are expected:
1. Explicit analytical expressions for optical solitons or/and breathers when two different mechanisms of formation of nonlinear waves are simultaneously effective, to reveal the competition between the effects of optical self-induced transparency, second-harmonic generation and dispersion and the mutual influence of these mechanisms.
2.Explicit analytical expressions for solitons or/and breathers of nonlinear surface acoustic waves in a nonmetallic diamagnetic many-layer system which contains a small concentration of paramagnetic impurities in the presence of an external constant magnetic field under the condition of acoustic second-harmonic generation, self-induced transparency and dispersion.
3. Explicit analytical expressions for the form and parameters of optical double breather of self-induced transparency when the finite conductivity or some other dissipation effects are presented. Condition of instability of the double breathers.
4.Explicit analytic expressions for the forms and parameters of nonlinear magneto-acoustic waves and dynamics of change of polarization of nonlinear magneto-acoustic wave in a magnetically ordered medium. Assume that these expressions will be expressed by means of elliptical integrals and full elliptical integrals of the third kind for the nonlinear periodical waves. Study correspondence between the phenomenological and microscopic parameters.
5.Explicit analytic expressions for the forms and parameters of nonlinear magneto-optical wave and compared with the results of the linear theory of polaritons. Dynamics of change of polarization of nonlinear linearly polarized transverse wave in molecular crystals and semiconductors.
Approximations and mathematical methods.
Approximations: Rotating wave approximation and the slowly varying envelope approximation.
Mathematical methods: The inverse scattering transform, a perturbation expansion for the inverse scattering transform, the reductive perturbation method, the various modification of the reductive perturbation method, the special type of many-scale reductive perturbation method for investigation of breathers and superbreathers solutions of nonlinear wave equations, the method of phase functions, the various numerical methods for the nonlinear equations and the method of Goll, Haken and Schenzle.
Methodology: Investigation of mathematical models and construction corresponding nonlinear wave equations, which describe considered physical phenomena. After this solutions of these equations. In the process of investigations if arise some mathematical problems and will be need opinion of some mathematicians, investigator will be pay a visit to corresponding research center. Definitively will be write corresponding original article for publication and reports on the Conferences and seminars in the leading scientific centers.
Some perspectives: After complete this project will be possible obtain more full and detail physical picture the processes of formation, propagation, change of polarization and other parameters of nonlinear waves in solids. This results allow receive in future explicit analytic expressions for other kinds of nonlinear wave too. At this will be interesting consider these effects for many-photon and many- phonon processes too.
Competence of the project Manager in the specified area:
Professor G.T. Adamashvili has been studying the features of nonlinear waves in solids for more than last 20 years. In this time he has published more than 70 original articles in the leading physical journals. Professor G.T. Adamashvili is Professor of the Department of General Physics of the Georgian Technical University and Scientific Director of the Research Laboratory "Physics of nonlinear Processes" at Tbilisi State University. He has gained great experience in the leading scientific centers of the former SU, USA, Germany. So in the Institutes of the Academy of Sciences of the former SU: The Institute of Metallurgy (from which he received diploma), the L.D. Landau Institute of Theoretical Physics (in the group of academician V.E. Zakharov), and the Institute of Spectroscopy (in the group of Professor V.M. Agranovich). In the University of California, Irvine, CA, USA professor G. Adamashvili worked with Professor A.A. Maradudin. In the University of Regensburg, Institute of Theoretical Physics, Regensburg, Germany (with Dr. A. Mayer). He has a lot of pupils.


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