Starting with the spinor representation of the electromagnetic field, we consider the propagation of a light beam along the Oz axis of a nonlinear medium. We first prove that for nonstationary processes in a one-dimensional space, the energy conservation takes the form of a conservation equation of kinematic waves. Then, using the method of characteristics, we discuss the self-steepening problem for initial value and boundary condition problems. We give the shock conditions and the shock velocity. The paper ends with a discus-sion of self-modulation.
"Self-Steepening And Self-Modulation Of Optical Beams In The Spinor Theory Of Light," Optical Engineering 24(1), 241153 (1 February 1985). https://doi.org/10.1117/12.7973443