  The properties of space-time modulated media operating in the sub-sonic
regime are discussed based on rigorous Bloch-Floquet theory. A geometrical
description in the frequency-wavenumber plane is developed to provide insight
into the possible interactions and their nature. It is shown that the secular
equation has a singularity, which results in a weak/passive second harmonic
generation process. Additionally bandgaps arising from the strong/active
parametric interaction between an incident wave and its space-time harmonic,
result in an inelastic Brillouin like scattering process. Hence when the
incident frequency is inside a forward (backward) bandgap, a Stokes'
(Anti-Stokes') scattered wave bounces back to the source. Although the forward
and backward bandgaps do not generally occur at the same frequency bands, the
insertion loss and gap width are equal. Requiring that both gaps do not
overlap, enforces a lower bound on the modulation speed. It is shown that
although an increase in the modulation index is desirable, as it enhances the
non-reciprocal behaviour, it also limits the range of possible modulation
speeds. The effective complex refractive index is calculated over a wide
frequency range. It is shown that peaks appear in the extinction coefficient,
indicating scattering to Stokes' and Anti-Stokes' waves. Finally, a
comprehensive numerical analysis based on the Finite Difference Time Domain
method is developed to verify and demonstrate the intriguing properties of
space-time modulated media.
