Evolution of ultra-short and extremely short electromagnetic pulses in quadratic-cubic nonlinear medium

摘要

An objective of the present work is considering of the unidirectional propagation and interactions of linearly polarized extremely short pulses in a nonlinear dispersive medium modeled by an anharmonic oscillator combining quadratic and cubic nonlinearities. Two families of exact analytical solutions (with a positive or negative polarity) are found for the moving solitary pulses. Direct simulations demonstrate that the pulses are very robust against weak perturbations, and collide nearly elastically, irrespective of their relative polarity.