Physics and mathematics of dispersion-managed optical solitons

We review the main physical and mathematical properties of dispersion-managed (DM) optical solitons. Theory of DM solitons can be presented at two levels of accuracy: first, simple, but nevertheless, quantitative models based on ordinary differential equations governing evolution of the soliton width and phase parameter (the so-called chirp); and second, a comprehensive path-average theory that is capable of describing in detail both the fine structure of DM soliton form and its evolution along the fiber line. An analogy between DM soliton and a macroscopic nonlinear quantum oscillator model is also discussed. © 2003 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. All rights reserved.

Total solution of Gibilaro and Rowe model for a segregating fluidised bed

This study re-examines the one-dimensional equilibrium model of Gibilaro and Rowe (1974) for a segregating gas fluidized bed. The model was based on volumetric jetsam concentration and divided the bed contents into bulk and wake phases, taking account of bulk and wake flux, segregation, exchange between the bulk and wake phases, and axial mixing. Due to the complex nature of the model and its unstable solution, the lack of computing power at the time prevented the authors from doing little more than the analytical solutions to specific cases of this model. This paper provides a numerical total solution and allows the effect of the respective parameters to be compared for the first time. There is also a comparison with experimental results, which showed a reasonable agreement.

Analytical model for active metamaterials with quantum ingredients

We present an analytical model for describing complex dynamics of a hybrid system consisting of resonantly coupled classical resonator and quantum structures. Classical resonators in our model correspond to plasmonic metamaterials of various geometries, as well as other types of nano- and microstructure, the optical responses of which can be described classically. Quantum resonators are represented by atoms or molecules, or their aggregates (for example, quantum dots, carbon nanotubes, dye molecules, polymer or bio-molecules etc), which can be accurately modelled only with the use of the quantum mechanical approach. Our model is based on the set of equations that combines well established density matrix formalism appropriate for quantum systems, coupled with harmonic-oscillator equations ideal for modelling sub-wavelength plasmonic and optical resonators. As a particular example of application of our model, we show that the saturation nonlinearity of carbon nanotubes increases multifold in the resonantly enhanced near field of a metamaterial. In the framework of our model, we discuss the effect of inhomogeneity of the carbon-nanotube layer (bandgap value distribution) on the nonlinearity enhancement. © 2012 IOP Publishing Ltd.