Polarization instability of femtosecond pulse-splitting in normally dispersive self-focusing media

Summary form only given. Through many numerical, analytical and recently also experimental investigations it has been verified that the collapse of self-focusing femtosecond pulses propagating through normally dispersive bulk third-order media is arrested by temporal dispersion due to the positive value of the GVD constant. In simple intuitive terms the arrest of the collapse may be explained as follows: for common experimental setups temporal dispersion may be neglected initially, thus making self-focusing induced by the combined effect of diffraction and nonlinearity the dominant effect throughout the early stages of pulse propagation. Hence, in the central part of the pulse (center in time) where the power in the transverse plane is above the threshold for self-focusing, off-axis energy is moved towards the peak of the pulse thereby increasing the peak-amplitude. Along with the increase in the peak-amplitude self-phase modulation starts to create significant gradients in the phase along the time-axis-a process which results in a flow of energy directed away from the peak, eventually bringing the peak power below the threshold for collapse. The majority of the studies of femtosecond pulse propagation in the past have used scalar models. A limitation of the various scalar models used is the restriction to the modelling of either linearly or circularly polarized pulses. It is the aim of the present work to illustrate how the inclusion of vectorial effects into the model may significantly alter the propagation scenarios known from the scalar case. In particular, we show how the linearly polarized solutions of the usual scalar models are unstable with respect to perturbations of the polarization state, and how self-focusing and pulse splitting in general may be controlled by altering the polarization state.