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Nonlinear Waves


Nonlinear Optical and Acoustic Waves in Isotropic and Anisotropic Media

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
Tyurin I A

Leading Institute
Georgian Technical University, Georgia, Tbilisi


  • University of Central Florida, USA, FL, Orlando\nUniversity of California / Department of Physics and Astronomy, USA, CA, Irvine

Project summary

The existing theories of the influence of relaxation on the self-induced transparency are contained in the works by McCall-Hahn, Kaup and Adamashvili, which are strictly valid only in gaseous media. A new theory of the influence of transverse relaxation on the electromagnetic and acoustic 2π- and 0π- pulses of the self-induced transparency in solids, in the broad region of spectra, under the condition of the inhomogeneous broadening of spectral lines and based on the formalism of the function of memory will be constructed. A comparison of the theoretical results with different experiments in solids will be made.

A theory of the physical processes of the formation of optical non-resonance double breather in nonlinear and dispersive media will be constructed. The effects leading to instability of non-resonance double breather or changes of their parameters in the presence of its interaction with impurity resonance atoms and a finite conductivity will be considered.

A theory of the formation of optical resonance breathers of the self-induced transparency in a sample of inhomogeneously broadened semiconductor quantum dots (nanostructures) will be constructed.

Anisotropic optical crystals quadratic or cubic susceptibilities with resonance impurity atoms three different (resonance, non-resonance and blended) mechanisms of the formation of nonlinear waves depending on the direction of the extraordinary wave propagation and on the symmetry of the medium, under the condition when the vector of electric dipole moment of impurity atoms and the optical axis of uniaxial crystal do not coincide, will be investigated.

The structure of breathers zones and the conditions for realization of the resonance, non-resonance and blended mechanism of the formation of surface acoustic breathers in different many-layered anisotropic media will be considered.

Expected results and perspectives

After completion of this project, it will be possible to obtain a complete and detailed physical picture of the processes of formation, propagation, stability and evolution of the parameters of the electromagnetic and acoustic nonlinear waves in isotropic and anisotropic solids.

Explicit analytical expressions for the evolution of the forms and parameters of solitons, breathers and double breathers of the self-induced transparency of electromagnetic and acoustic waves in solids, in the broad region of spectra, with inhomogeneous broadening of the spectral line and to taking into account transverse relaxation effects which play very important role in crystals, will be obtained.

The condition of instability and parameters of non-resonance optical double breather in nonlinear and dispersive media will be determined.

The optical breathers under the condition of the self-induced transparency can propagate in realistic semiconductor quantum dot samples without suffering strong losses by analytical and numerical results will be demonstrated.

Explicit analytic expressions (and numerical, where necessary) for the parameters of non-resonance, resonance and blended of nonlinear extraordinary waves, for various mutual orientation of the electric dipole moment of impurity atoms relative to the optical axis of uniaxial crystal, will be obtained. For each group of uniaxial crystals with nonlinear susceptibilities, we will seek to determine the structure of the allowed breathers zones.

The structure of breathers zones and parameters of the resonance, non-resonance and blended surface acoustic breathers will be obtained.

In these systems it is expected to receive qualitatively new theoretical results and their comparison with experiments will allow us to understand and see better, the most interesting directions of the future development of the nonlinear waves theory. These results allow to receive in future the explicit analytic expressions for other kinds of nonlinear waves, for instance for many-photon and many- phonon processes too. This investigation will contribute significantly to our understanding of the properties of nonlinear waves in isotropic and anisotropic solids and will stimulate new theoretical and experimental investigations in this field, as well as to future applications in the physical and engineering sciences.

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 double breathers solutions of nonlinear wave equations, the method of phase functions, the various numerical methods for the nonlinear equations.


Investigations 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, investigators 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.

Basic materials of investigations

Solid dielectrics containing optical active impurity resonance atoms: Al2O3: Cr3+; Organic mixed crystals: diphenyl, with impurity molecules of piren; Diamagnetic solids containing small concentration of paramagnetic impurities: CaF2: U4+, MgO:Fe2+, MgO:Ni2+, LiNbO3:Fe2+; α,β-bisdiphenylene-γ-phenyally; Doped fiber media, for instance an erbium-doped optical fiber; Many-layered system: SiO/LiNbO3:Fe2+. Semiconductor material systems, such as: InP/InGaP, GaSb/GaAs, InSb/GaSb, InAs/Si, InAlAs/AlGaAs, InGaAs quantum-dot waveguides.


The outcome of research on the nonlinear electromagnetic waves could have important implications to optical telecommunications and to photonics, such as for the processing of the images, compression of optical pulses, the transfer of the information on large distances, and others. Particularly is the possibility for applications of low energy breathers, generated by blended mechanisms, propagating in a doped fiber media (for instance an erbium-doped optical fiber), since the parameters of such pulses can have a wide range.

The results of research in semiconductor quantum dots may have applications in future generations of logic and Coulomb blockade based nanostructures devices and also can lead in the future to new classes of devices which offer quantum controlled functions.

The results of research on the nonlinear surface acoustic waves will allow us to create new applications of crystals in different electro-acoustic devices with new properties and possibilities.

Role of Foreign Collaborators

Exchange of information during project implementation, joint investigations, verification of results using independent mathematical methods, and also joint discussion of project results, joint publications, meetings at conferences and direct visits, can be the form of our collaborations.

Rationale and benefits

This proposal is for the theoretical studies of problems of mutual interest. The investigators possess extensive background in the investigation of problems of this sort. They have been studying for a long time, the properties of nonlinear waves but are using different approaches of investigations. Hence their collaborations without doubt will be very important, mutual interesting and fruitful for all sides. These collaborations would give each more experience in this area, as well as more understanding.

Broader Impact

This work will foster cooperation between scientists from the US, France, Japan, Germany and Georgia, with potential benefits of establishing closer ties between the scientific communities in these countries and also foster self-sustaining civilian activities of Georgian scientists.

Competence of the project Manager in the specified area

Professor Adamashvili has been studying the features of nonlinear waves in solids for more than last 25 years. In this time he has published more than 80 original articles in the leading physical journals. Adamashvili is Professor of the Department of 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. He has a lot of pupils, among which participants of the Project and have had with them a lot of joint articles.

Competence of the project team

The investigators possess extensive background in the investigation of problems in the field of the theory of nonlinear waves. They have been studying for a long time, the properties nonlinear waves in solids and are using different modern approaches of investigations. They have received a lot of interesting scientific results, which have been reported in the different international Conferences. Project participants have a number of scientific publications and the majority has dissertations in the specified area.