Propagation and interaction of ultrashort electromagnetic pulses in nonlinear media with a quadratic-cubic nonlinearity

Propagation of extremely short unipolar pulses of electromagnetic field ("v ideopulses") is considered in the framework of a model in which the materia l medium is represented by anharmonic oscillators (approximating bound elec trons) with quadratic and cubic nonlinearities. Two families of exact analy tical solutions (with positive or negative polarity) are found for the movi ng solitary pulses. Direct simulations demonstrate that the pulses are very robust against perturbations. Two unipolar pulses collide nearly elastical ly, while collisions between pulses with opposite polarities and a small re lative velocity are inelastic, leading to emission of radiation and generat ion of a small-amplitude additional pulse. (C) 2001 Published by Elsevier S cience B.V.