  Self-phase modulation (SPM) of light pulses is found to occur strongly, at
low incident intensities, in the coupling of light with superconductors. We
develop a theory from a synthesis of the time-dependent Ginzburg-Landau (TDGL)
equation and basic electrodynamics which shows the strongly non-linear phase
accumulated in the interaction. Unusually, the SPM of the pulse in this system
is found to be highly asymmetric, producing a strongly redshifted spectrum when
interacting with a superconducting thin film, and it develops in just a few
nanometers of propagation. In this paper we present theoretical results and
simulations in the THz regime, for both hyperbolic secant and
supergaussian-shaped pulses.
