Coherent propagation of an optical pulse in a Bragg plasmon grating

The propagation of ultrashort pulses in a dielectric medium with periodically arranged metal nanoparticles is considered theoretically. Plasmon oscillations in these particles are described by the model of an anharmonic oscillator with the driving force proportional to the electric-field strength of an electromagnetic pulse. A system of equations determining the behaviour of electromagnetic waves is obtained in the approximation of slowly varying envelopes of ultrashort pulses and medium polarisation. Under the assumption that the frequencies of the carrier wave and oscillators coincide and the Bragg resonance condition is fulfilled, the solution of the obtained equations is found, which corresponds to the solitary wave of the ultrashort-pulse field and the medium polarisation (Bragg soliton). The numerical simulation shows the formation of a Bragg soliton (from the initial Gaussian pulse of the sufficient energy) and a nonstationary solitary wave with the vanishing group velocity.