  This paper addresses the problem of wave scattering at a moving interface
formed by a space-time modulation step. Specifically, it derives, using the
technique of frame hopping with Lorentz transformation, the formula for the
corresponding critical angle beyond which the transmitted field is evanescent.
It shows that this angle is smaller (resp. larger) than $\pi/2$ (position of
the interface) for a modulation that is codirectional (resp. contradirectional)
to the direction of wave propagation, and that the critical angle versus the
modulation velocity function monotonically decreases to zero at the velocity
where the incident wave cannot catch up any more with the interface. The theory
is illustrated and validated by full-wave FDTD simulation.
