Robust and Integrable Time-Varying Metamaterials: A Systematic Survey and Coherent Mapping

Time-varying or temporal metamaterials and metasurfaces, in which electromagnetic parameters are deliberately modulated in time, have emerged as a powerful route to engineer wave-matter interaction beyond what is possible in static media. By enabling the controlled exchange of energy and momentum with the fields, they underpin magnet-free nonreciprocity, low-loss frequency conversion, temporal impedance matching beyond Bode-Fano limit, and unconventional parametric gain and noise control. This survey provides a coherent framework that unifies the main theoretical and experimental developments in the area, from early analyses of velocity-modulated dielectrics to recent demonstrations of temporal photonic crystals, non-Foster temporal boundaries, and spatiotemporally driven metasurfaces relevant to nanophotonic platforms. We systematically compare time-varying permittivity, joint ε-μ modulation, time-varying conductivity, plasmas, and circuit-equivalent implementations, including stochastic and rapidly sign-switching regimes, and relate them to acoustic and quantum analogs using common figures of merit, such as conversion efficiency, isolation versus insertion loss, modulation depth and speed, dynamic range, and stability. Our work concludes by outlining key challenges, loss and pump efficiency, high-speed modulation at the nanoscale, dispersion engineering for broadband operation, and fair benchmarking, which must be addressed for robust, integrable temporal metasurfaces.