Circularly polarized few-optical-cycle solitons in Kerr media: A complex modified Korteweg-de Vries model

We consider the propagation of few-cycle pulses (FCPs) in cubic nonlinear media exhibiting a “crystal-like” structure, beyond the slowly varying envelope approximation, taking into account the wave polarization. By using the reductive perturbation method we derive from the Maxwell–Bloch–Heisenberg equations, in the long-wave-approximation regime, a non-integrable complex modified Korteweg-de Vries equation describing the propagation of circularly polarized (CP) FCPs. By direct numerical simulations of the governing nonlinear partial differential equation we get robust CP FCPs and we show that the unstable ones decays into linearly polarized half-cycle pulses, whose polarization direction slowly rotates around the propagation axis.