Here τ is the time delay between the pulses, ε ε ε pu and ε ε ε pr are the unit vectors of the linear polarization of the pulses, A pu and A pr are the pulse amplitudes, E pu (t) and E pr (t) are the dimensionless envelope functions, k pu and k pr are the wave vectors and ω pu and ω pr are the pulse carrier frequencies.