  Space-time modulation-based metamaterials have recently spurred considerable
interest, owing to the fundamental addition of the time dimension to the medium
parameters, and resulting novel properties and potential applications. However,
the implementation of most related structures -- e.g., involving step, slab or
gradient discontinuities -- has been hindered by the impossible requirement of
infinitely or prohibitively large device sizes. We provide here a solution to
this issue, consisting in a space-time transposition of the conventional
Fresnel prism, whereby a copy of the target modulation is periodically
re-injected at the input of a Fresnel-reduced finite structure, so as to
provide the same anharmonic and nonreciprocal frequency conversion as the
target space-time interface in the case of a modulation step. This concept,
which may readily extend to slab or gradient modulations, as well as
accelerated profiles for space-time chirping operations, may pave the way for
the practical development of a wide range of novel microwave and optical
space-time systems.

Optics