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Nonlinear Waves in Nanostructures


Nonlinear Optical and Acoustic Waves in Nanostructures

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
Taylor 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 Project aim. The goal of this project is to develop a theory of the processes of the formation and propagation of the nonlinear optical and acoustic waves in nanostructures. To construct more general theory of the ultrafast nonlinear wave phenomena in semiconductor quantum dots (SQDs) and anisotropic metamaterials under strong nonequilibrium conditions and dissipation in order to consider wide class of the physical phenomena and to adequately describe new experimental results. It is particular interest to study the transition between the dissipative (diffusive) and ballistic limit, or between near equilibrium and far from equilibrium conditions.

The project’s influence on progress in this area. After the implementation 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 SQDs and anisotropic metamaterials under strong nonequilibrium conditions and dissipation. These results would allow one to construct explicit analytic expressions for other kinds of nonlinear waves, for instance for many-photon and many- phonon processes. Thus this investigation will contribute significantly to our understanding of the properties of nonlinear waves in SQDs and anisotropic metamaterials and will stimulate new theoretical and experimental investigations in this field. Although the research program concentrates on basic research, it is also motivated by potential applications in the physical and engineering sciences and also in biology and medicine.

Expected results and perspectives. After the implementation of this project, explicit analytical expressions for the evolution of the shapes and parameters of solitons of both electromagnetic and acoustic waves will be obtained, both in the presence of inhomogeneous broadening of the spectral line and transverse non-Markovian relaxation, each of which plays a very important role in solids.

Explicit analytic (and numerical, where necessary) expressions for the parameters of resonance nonlinear extraordinary surface plasmon-polaritons will be obtained, for various mutual orientations of the electric dipole moment of the SQDs relative to the optical axis of the uniaxial anisotropic crystal.

Explicit analytic expressions for the parameters of dissipative optical solitons in SQDs under strong nonequilibrium conditions and dissipation, to study the transition between the dissipative and ballistic limit, will be obtained.

The properties and features of the wave processes near the point where a refractive index changes its sign will be obtained, for the propagation of electromagnetic extraordinary waves in uniaxial anisotropic “positive to negative transition” metamaterials.

Explicit analytic expressions for the parameters of the SIT breathers and optical nonlinear waves with special phase modulation in an ensemble of the SQDs will be obtained, when there is a distribution of the transition dipole moments in the ensemble of the quantum dots.

The general solution for the Bloch-Maxwell equations for SQDs when there are distributions of transition dipole moments in the SQDs will be obtained.

Explicit analytic expressions for the parameters of dissipative acoustic solitons in SQDs under strong nonequilibrium conditions and dissipation, to study the transition between the dissipative and ballistic limit, will be obtained.

Scope of activities. The following activities will be implemented under the Project:

  1. Influence of non-Markovian relaxation on self-induced transparency (SIT) solitons in SQDs;
  2. The influence of the distribution of transition dipole moments in SQDs on the small amplitude breather and dounle-breather of SIT;
  3. Dissipative optical solitons in the ensemble of SQDs;
  4. Optical nonlinear waves with special phase modulation in SQDs;
  5. The general solution for the semiconductor Maxwell-Bloch equations when there are distributions of transition dipole moments in SQDs;
  6. A theory of nonlinear extraordinary surface plasmon-polaritons in anisotropic metamaterials;
  7. A theory of the extraordinary waves in uniaxially anisotropic “positive to negative transition” metamaterials;
  8. Influence of non-Markovian relaxation on acoustic SIT;
  9. Dissipative acoustic solitons in solids.

The participants’ expertise.

Competence of the project Manager in the specified area.

Professor Adamashvili has been studying nonlinear waves in solids for more than last 30 years. He has published more than 120 original articles in the leading physical journals. He has produced many interesting scientific results which have been reported in international Conferences. Professor Adamashvili is head of the center of the “Theoretical Physics and Nanooptics” of the Technical University of Georgia. He has had extensive experience in leading scientific centers of the former SU, USA and Germany. Many students have participated in this Project and have collaborated with him on joint articles.

Competence of the project team.

The scientists taking part in the project have considerable experience in the nature of nonlinear waves in SQDs and left-handed metamaterials, and will apply different approaches to the investigation. The scientists who have participated in the different projects, have assisted in producing a number of scientific publications, and many of them have also produced dissertations in these various areas.

Role of Foreign Collaborator.

The foreign collaborator will be kept informed of the progress on the project and his opinions and suggestions will be regularly solicited. He will also be involved in joint discussions about the verification of results, will use independent mathematical methods and will be involved in the publication of results. There will be meetings between him and the project participants at conferences as well as in direct visits.

Rationale and benefits

This proposal is for the theoretical studies of problems of mutual interest to all sides. The investigators possess extensive background in the investigation of problems of this manner. They have long experience in nonlinear wave phenomena in solids, and have used various different approaches in their investigations. Hence their collaboration will certainly be very important as well as mutually interesting and fruitful for all sides. This collaboration would give each more experience in this area, as well as more understanding.

Broader Impact

This work will foster cooperation between an American, EU and a Georgian scientists, with potential benefits of establishing closer ties between the scientific communities in the these countries and also foster self-sustaining civilian activities of Georgian scientists.

Meeting the ISTC goals and objectives. Since former “weapons” scientists will be taking part in the Project the goal of which are peaceful purposes and applications, the Project meets the ISTC goals. Adherence to these objectives will be maintained by means of continuing wide dissemination of the project results to other scientists and participating institutions of the international scientific community by providing information on the Project at international conferences.

Technical approach and methodology.

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, a special type of many-scale reductive perturbation method for the investigation of breathers solutions of nonlinear wave equations, the method of phase functions, the various numerical methods for solving nonlinear equations, the computer symbolic software Mathematica.

Methodology: Investigations of mathematical models and the construction of corresponding nonlinear wave equations which describe the physical phenomena being considered. Following that, one would study solutions of these equations. When in the process of the investigations, whenever some mathematical problems arises, the opinions of appropriate mathematicians will be sought. All results will be presented as original articles for publication and reports to conferences and seminars in leading scientific centers.

Applications. The results of research on nonlinear electromagnetic waves could have important implications to optical telecommunications and nano-photonic devices (e.g. semiconductor nano-lasers), such as the processing of the images, compression of optical pulses, optical memory devices based on metamaterials and SQDs, the transfer of the information over large distances, and others. The results of research on SQDs may have applications in future generations of logic and Coulomb blockade based nanostructures devices and also could lead to new classes of devices which offer quantum controlled functions. SQDs have also been suggested as implementations of qubits for quantum information processing and also as material for cascade lasers. Graded-index transition metamaterials provide a novel platform for potential applications for wave concentrators and polarization sensitive devices. The results of research on nonlinear acoustic waves will allow us to create new applications of crystals in different electro-acoustic devices with new properties and possibilities.

Basic materials of investigations. The typical materials to be used as models in these theoretical investigations will be SQDs in InGaAs. Superlattices and GaAs-AlAs metamaterials which use silver as a constituent material. Diamagnetic solids containing small concentration of paramagnetic impurities, such as CaF2:U4+, MgO:Fe2+, MgO:Ni2+, LiNbO3:Fe2+. Also many-layered systems such as SiO/LiNbO3:Fe2+ and semiconductor material systems, such as InP/InGaP, GaSb/GaAs, InSb/GaSb, InAs/Si, InAlAs/AlGaAs and InGaAs quantum-dot waveguides.


The International Science and Technology Center (ISTC) is an intergovernmental organization connecting scientists from Kazakhstan, Armenia, Tajikistan, Kyrgyzstan, and Georgia with their peers and research organizations in the EU, Japan, Republic of Korea, Norway and the United States.


ISTC facilitates international science projects and assists the global scientific and business community to source and engage with CIS and Georgian institutes that develop or possess an excellence of scientific know-how.

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