  Photonic time interfaces, as the temporal analogue of spatial interfaces
between two media, consist of a rapid change of the electromagnetic properties
of a material (such as permittivity {\epsilon}, and permeability {\mu}) while
the wave is present in the material. Here we exploit cascading of such time
interfaces in spatially cascaded guided-wave structures such as slab waveguides
and ring resonators by considering that the relative permittivity of the
cladding of dielectric waveguides is rapidly changed at different moments of
time from {\epsilon}clad_1 to {\epsilon}clad_2 , while the material of the core
remains unchanged in time. It is shown how such time-dependent cladding can
enable frequency conversion within the space-time dielectric ring resonator and
slab waveguides due to an induced modification of the effective refractive
index of the mode propagating within such photonic device. Cascaded frequency
conversion is achieved in such cascaded space-time dielectric waveguides and
ring resonators, showing how the combination of space and time interfaces can
offer further opportunities for manipulation of light-matter interaction using
four-dimensional (4D) photonic structures.
