Search

In this paper a porous 3D system wherein the material porosity forms a percolating spanning cluster is studied. It is considered that the light nanoemitters are randomly incorporated into such a cluster and are pumped to the exited state by an external light beam. To find the optimal optical path between the radiated nanoemitters the Fermat principle was used and it is implemented by means of well-known the travelling salesman (TSP) approach generalized to 3D geometry. With the use of undirected graph mapping the TSP approach is applied for optimizing optical path (for principle of Fermat) to calculate the optimal light paths in such a percolation structure. The convergence of the algorithm for 3D incipient cluster is studied with details to exploit the space of feasible solutions when a collective light radiation of the internal nanoemitters becomes. Finally, the field correlations of the light emission that penetrates the entire 3D percolation cluster is discussed.

By means of the variational approximation (VA) and systematic simulations, we study dynamics and stability boundaries for fundamental solitons in a two-dimensional (2D) self-attracting Bose-Einstein condensate (BEC), trapped in an quasiperiodic optical lattice (OL), with the amplitude subject to periodic time modulation (the modulation frequency, ω. Regions of stability of the solitons against the collapse and decay are identified in the space of the model’s parameters.

It is known that the Maxwell-Lorentz equations with Abraham’s rotating extended electron can be derived from the the Hamilton least action principle applying the variational Poincaré equations on the Lie group SO(3). We prove that, rewritten in the Euler angles, these equations imply the standard Euler-Lagrange and Hamiltonian equations.

We studied numerically the frequency spectrum of photons in a multilayered microsphere coated by a quasiperiodic (Pascal) dielectric stack. It is found that the transmittancy spectrum of such a stack consists of quasiband gaps and narrow resonances caused by re-reflection of optical waves. When the number (Pascal order) of layers increases, the band gaps and resonances split, and the structure of the frequency spectrum acquires a fractal form. Some parts of the spectrum show the self-similarity in the different frequency scales.

We studied the radial distribution of the electromagnetic field and the spectrum of the eigenfrequencies in coated microspheres with alternating quasiperiodic layers having left-handed (LH) materials included. At an increase of the quasiperiodicity parameter $\gamma$, the boundaries of the spectral band gaps acquire the intended shape. When $\gamma$ exceeds the inverse golden mean value, a structure with extremely narrow separated resonant peaks with nearly complete transmittance arises. We find that the field peaks in the radial distribution forbidden band is located not in the center of the microsphere, but in the layers that cover such a microsphere.