The Project aim. The goal of this project is to develop a theory of the processes of the excitation and propagation of the nonlinear optical and acoustic waves of self-induced transparency (SIT) in graphene nanostructures: mono- and bilayer graphene, graphene ribbons and graphene quantum dots (QDs). To construct general theory of the ultrafast optical nonlinear wave phenomena in graphene nanostructures, anisotropic semiconductor QDs and bi-anisotropic (chiral) negative index metamaterials (NIM) under strong nonequilibrium conditions and dissipation in order to study wide class of the physical phenomena and to adequately describe new experimental results. It is particular important to consider the transition between the ballistic and dissipative (diffusive) limit, or between far from equilibrium and near equilibrium conditions. With this project we set out to prove that a new direction of graphene plasmonics and graphene acoustics based on resonance and blended nonlinear surface plasmon-polaritons (SPPs) and resonance surface acoustic solitons is viable.
Current status. At the present time the nonlinear resonance waves of SIT in graphene monolayer have been considered by Adamashvili [2014, 2015] only for SPPs and waveguide modes. But the nonlinear resonance and blended optical and acoustic waves (solitons, breathers, vector solitons) of SIT in graphene nanostructure, anisotropic semiconductor QDs and bi-anisotropic NIM have not been considered.
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 resonance, non-resonance and blended nonlinear waves in graphene nanostructures (and graphene-like two-dimensional materials such as, silicene, germanene, hafnene and etc.) and also in anisotropic semiconductor QDs and bi-anisotropic NIM under strong nonequilibrium conditions and dissipation. These results would allow one to construct explicit analytic expressions for other kinds of nonlinear waves in these systems, for instance, for many-photon and many- phonon processes in many-layer graphene sheets. The investigation of of the nonlinear graphene plasmonics basically focused on nonlinear resonance and blended SPPs in graphene nanostructures. Thus these investigations will contribute significantly to our understanding of the properties of nonlinear waves in graphene nanostructures, anisotropic semiconductor QDs and bi-anisotropic NIM 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. An adequate theory of the SIT in graphene nanostructures, anisotropic semiconductor QDs and bi-anisotropic NIM under strong nonequilibrium conditions and dissipation will be constructed. After the implementation of this project,, it will be possible to obtain more complete and detail physical picture of the processes of formation, propagation, stability and evolution of the parameters of the of 2? - and 0? - pulses of SIT in these nanostructures. Explicit analytic (and numerical, where necessary) expressions for the parameters of nonlinear SPPs both in conservative as well as in dissipative physical systems of the graphene nanostructures, anisotropic semiconductor QDs and bi-anisotropic NIM in the presence the optical conductivity and strong optical nonlinearity of graphene will be obtained. The parameters of dissipative optical solitons under strong nonequilibrium conditions and dissipation, to study the transition between the ballistic and dissipative limit, will be obtained. The conditions of instability of the nonlinear waves in graphene nanostructures will be determined. These outcomes are important and will contribute significantly to our understanding of the properties of resonance nonlinear waves in graphene, QDs and NIM. A comparison of the new theoretical results with the experiments will allow us to understand better the most interesting directions of the future development of the theory of SIT, in particular, and of the nonlinear waves theory generally. The properties of the wave processes near the point where a refractive index changes its sign will be considered, for the propagation of electromagnetic waves in bi-anisotropic (chiral) negative to positive transition metamaterials with a two-dimensional sheet of anisotropic semiconductor QDs and graphene monolayer. Explicit analytic expressions for the parameters of dissipative surface acoustic solitons in graphene 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:
- optical resonance solitons of SIT of the SPPs in graphene nanostructures;
- optical blended breathers of SPPs in graphene;
- optical resonance vector soliton with the sum and difference of the frequencies of SPPs in graphene;
- optical non-resonance vector solitons with the sum and difference of the frequencies of SPPs in graphene;
- optical dissipative solitons of SPPs in graphene;
- the electromagnetic waves in bi-anisotropic (chiral) negative to positive transition metamaterials with a two-dimensional sheet of anisotropic semiconductor QDs and monolayer graphene;
- acoustic surface solitons in monolayer graphene.
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 40 years. He has published more than 160 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 research center of the “Theoretical Physics and Nano-optics” 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 and research projects.
Competence of the project team. The former “weapons” scientists taking part in the project have considerable experience in the nature of nonlinear waves in nanostructures: semiconductor QDs, NIM, 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 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 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 6 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 and vector soliton 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 modulators, photodetectors, polarizers, optical memory devices based on anisotropic semiconductor QDs and bi-anisotropic NIM, the transfer of the information over large distances, and others. The results of research on anisotropic semiconductor QDs 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. The anisotropic semiconductor QDs and graphene QDs have also been suggested as implementations of qubits for quantum information processing and also as material for cascade lasers. Graded-index transition bi-anisotropic or chiral 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. Doping graphene QDs with heteroatoms provides an attractive means of effectively tuning their intrinsic properties and exploiting new phenomena for advanced device applications. The fabrication of graphene-based transistors, solar cells, photodetectors, batteries, light emitting devices, ultrafast lasers, optical sensors, acoustic transducers, gas sensors and frequency-tunable surface acoustic soliton devices.
Basic materials of investigations. The typical materials to be used as models in these theoretical investigations will be anisotropic semiconductor QDs in InGaAs. Dilute paramagnetic dielectrics, 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. Bi-anisotropic negative to positive transition metamaterials. The mono- and bilayer graphene. Graphene ribbons. Graphene/ZnO, a graphene sheet is fabricated on dielectric wafer (e.g., SiO2). The doped Mn2+ in ZnS:Mn quantum dots. Doping graphene QDs with heteroatoms.
