Half-cycle optical soliton in quadratic nonlinear media

We show that a few-cycle pulse launched in a quadratic medium may result in a half-cycle soliton in the form of a single hump, with no oscillating tail. The analysis involves the derivation of a Korteweg-de Vries (KdV) equation from both a classical and a quantum mechanical simple model of matter-radiation interaction. The sign of the electric field in the half-cycle KdV soliton is fully determined by the properties of the material, which definitely breaks the phase invariance