Tam et al. [271]. Ultimately, applications are limited by the low-
dimensionality of these materials which leads to small interaction volume and
short interaction time. On the other hand, nanostructuring can again be used
to enhance the response from these systems: enhanced light-matter interaction
has been shown in monolayers coupled with plasmonic nanoantennas [276, 277,
278] as well as with a Si waveguide [279]. Nonlinear antennas built from bulk
TMDs could also provide a platform for time-varying experiments in the same
fashion as GaAs or Si [280]. Another alternative would be van der Waals
heterostructures, stacked layers of TMDs which have also exhibited short rise
times of about 50 fs [281, 282], with no dependence of the response time on
the twisting angle between layers [283, 284].More information on the specific
spin and valley dynamics at the origin of the ultrafast dynamics in van der
Vaals heterostructures can be found in Jin et al.’s review [285].

###  5.3 Outlook

All-optical implementations of time-varying metasurfaces are of great interest
for the creation of new miniaturized technologies for the control of light
both in space and time. ENZ materials such as ITO and AZO, along with high-
index dielectrics, have proven to be solid platforms for time-varying
experiments and will surely be the ground for more complex investigations.
These nanophotonic architectures can boost both light coupling to the
nonlinear medium and field enhancement. Multilayered ENZ metamaterials could
provide new solutions to the practical problems posed by the nature of more
classical time-varying systems, such as resonance-engineering or high
permittivity contrast. New materials and systems could pave the way for
further development of time-varying experiments, expanding the spectral range
of operation, increasing the efficiency and the damage threshold. Quantum well
polaritons and monolayer 2D materials could exhibit time-varying effects at
lower energies, while magneto-optical effects would open a new framework
including time-varying magnetic effects, which are ignored in current
nonlinear optical experiments.

##  6 Conclusions

In this Review Article, we have presented a comprehensive overview of photonic
time-varying media. We started by reviewing the basic phenomenological and
mathematical considerations rooted in the behaviour of Maxwell’s Equations in
the presence of temporal material discontinuities, discussing the main
directions of ongoing research on electromagnetic time-switching for several
applications such as time-reversal, energy manipulation, frequency conversion,
bandwidth enhancement and wave routing, amongst many others. We then continued
our discussion to consider photonic time-crystals, discussing the basic
phenomenology underlying periodic time-scattering and parametric amplification
to develop an insight which we deployed in addressing more advanced instances
of time-modulation in particular for topological physics, non-Hermitian
systems and disorder, concluding with some brief remarks on time-modulated
surfaces. We then extended our discussion to combinations of spatial and
temporal degrees of freedom, providing an overview of the basic properties of
space-time crystals, and their application to nonreciprocity, as well as the
engineering of synthetic motion and its applications to optical drag and giant
bianisotropic responses, highlighting the concept of luminal amplification and
spatiotemporal localization as a new form of wave amplification physically
distinct from the conventional parametric gain, and concluding with an
overview of the wealth of opportunities and applications for space-time
metasurfaces. Finally, we reviewed some of the most successful materials and
paradigms for experimental realizations of time-varying effects in the visible
and IR, indicating some of the most promising avenues recently unveiled for
future optical experiments with time-varying media. While the latter
undoubtedly constitute the greatest long-term challenge for this rising field
of research, we believe that, as in many other instances of scientific
enquiry, the quest for time-varying photonic systems will prove a prolific one
from both the point of view of unveiling fundamentally novel wave phenomena
and for revealing new and unexpected windows of opportunity for technological
advancement.

### Acknowledgments

E.G. acknowledges funding from the Engineering and Physical Sciences Research
Council via an EPSRC Doctoral Prize Fellowship (Grant No. EP/T51780X/1) and a
Junior Fellowship of the Simons Society of Fellows (855344,EG). P.A.H. and M.
S. acknowledge funding from Fundação para a Ciência e a Tecnologia and
Instituto de Telecomunicações under project UIDB/50008/2020 and the CEEC
Individual program from Fundação para a Ciência e a Tecnologia with reference
CEECIND/02947/2020. R.S. J.P. and S.V. acknowledges funding from the
Engineering and Physical Sciences Research Council (EP/V048880). J.P.
acknowledges funding from the Gordon and Betty More Foundation. A.A., S.Y. and
H.L. acknowledge funding from the Department of Defense, the Simons Foundation
and the Air Force Office of Scientific Research MURI program.

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