Periodicity and modulation lie at the heart of modern electromagnetic, acoustic and mechanical engineering, dramatically altering the way in which waves interact with periodically structured media. The main idea driving the intense research into periodic systems is the fact that periodicity breaks the dependence on natural properties of constituent media and instead allows one to blend the responses of various materials and leverage their geometric shapes to obtain collective responses on demand. In the realm of electromagnetics, over the past two decades there has been an explosive surge of interest to artificially engineered time-invariant periodic structures thanks to numerous fascinating linear and nonlinear effects they enable. In this dissertation, I will present some transformative developments in the area of efficient nonlinear generation and wave mixing in thin 2D periodic structures based on multi-quantum-wells, as well as show the possibility to engineer to the great extent the dispersion topology of surface waves propagating along ideally thin conducting sheets with 1D spatial periodicity such as graphene ribbons. In parallel with the progress in obtaining desired responses in time-invariant periodic structures, significant progress is being made in applying temporal and synchronous spatial and temporal modulation to engage new degrees of freedom and extend the spectrum of achievable electromagnetic phenomena even further. In this dissertation, I will also show that spatiotemporal modulation applied to electronic networks holds a key to obtain ultrawideband and extremely compact delays far beyond those achievable in time-invariant systems. Spatiotemporal modulation also allows for all kinds of nonreciprocal devices to be seamlessly integrated in an electronic chip by overcoming the size and magnetic material incompatibility constraints. This fact holds a truly groundbreaking potential for future electronic devices and wireless systems by enabling their simultaneous transmit-and-receive operation. Finally, I will show that spatiotemporal modulation enables a direct translation of some of the most advanced and intricate concepts of condensed matter physics – topological insulators – to the realm of classical electronic circuits. Compared to standalone nonreciprocal devices, topologically-nontrivial electronic circuits provide an even larger toolbox to obtain various nonreciprocal functionalities by enforcing a wideband unidirectional transmission robust to defects and imperfectionsElectrical and Computer Engineerin
