Dynamics of oscillator populations globally coupled with distributed phase shifts

We consider a population of globally coupled oscillators in which phase shifts with respect to the global force are different. Such a setup appears for spatially distributed oscillators with different propagation times of the global forcing signal. In the presence of independent noises and in the thermodynamic limit, we show that the dynamics can be reduced, for arbitrary coupling function, to an effective ensemble of units with identical phase shifts but with a proper renormalization of the order parameters. The same reduction is shown to be valid, by virtue of an analysis of Ott-Antonsen equations, for oscillators with a Cauchy distribution of natural frequencies and with the first harmonics coupling. However, the reduction to an effective ensemble may fail if the coupling function is complex enough to ensure the multistability of locked states

Multipolar third-harmonic generation driven by optically-induced magnetic resonances

We analyze third-harmonic generation from high-index dielectric nanoparticles and discuss the basic features and multipolar nature of the parametrically generated electromagnetic fields near the Mie-type optical resonances. By combining both analytical and numerical methods, we study the nonlinear scattering from simple nanoparticle geometries such as spheres and disks in the vicinity of the magnetic dipole resonance. We reveal the approaches for manipulating and directing the resonantly enhanced nonlinear emission with subwavelength all-dielectric structures that can be of a particular interest for novel designs of nonlinear optical antennas and engineering the magnetic optical nonlinear response at nanoscale.Comment: 24 pages, 6 figure

Electron Spin Dynamics in Semiconductors without Inversion Symmetry

We present a microscopic analysis of electron spin dynamics in the presence of an external magnetic field for non-centrosymmetric semiconductors in which the D'yakonov-Perel' spin-orbit interaction is the dominant spin relaxation mechanism. We implement a fully microscopic two-step calculation, in which the relaxation of orbital motion due to electron-bath coupling is the first step and spin relaxation due to spin-orbit coupling is the second step. On this basis, we derive a set of Bloch equations for spin with the relaxation times T_1 and T_2 obtained microscopically. We show that in bulk semiconductors without magnetic field, T_1 = T_2, whereas for a quantum well with a magnetic field applied along the growth direction T_1 = T_2/2 for any magnetic field strength.Comment: to appear in Proceedings of Mesoscopic Superconductivity and Spintronics (MS+S2002