Non-Hermitian Wave Mechanics: Application to Integrated Photonics and Electronics

Non-Hermitian wave mechanics is a natural mathematical framework that allows us to describe propagation of classical waves in the presence of gain and loss mechanisms. Recognizing this fact, we aim in this thesis to utilize complex potentials (impedance profiles) with a special spatio-temporal symmetries such that allow us to manage wave propagation. A special class of this type of synthetic structures are the ones which are invariant under joint space-time reflection or PT symmetries. Our work focus on the novel transport properties of these structures. Whenever appropriate, we point the potential technological implications in the frameworks of optics and electronics circuitry. Many of our predictions have already found experimental confirmations. We will also discuss these experimental verifications.