Using the transfer matrix method we analyse the transmission of time-modulated Gaussian beam through the
RHM-LHM layered structures with dispersive, lossy, and magnetic layers. The modulated parts of the beam
are subject to a complex temporal and spatial shape transformation, which may be characterised in terms of
spectral and spatial filtering, while the layered structure itself is entirely described with the respective transfer
function or equivalently with the impulse response. Due to strong dispersion and absorption of the LHM layers,
it is possible to identify higher order dispersion effects taking place within very short distances. This opens the
possibility of designing novel filters capable of complex reshaping of the beam envelope.