Mathematical Study of Novel Wave Phenomena in Optical Waveguides

Optical waveguides are structures that guide the propagation of light. Currently, there exist many different types of optical waveguides for different applications. In recent years, parity-time (PT) symmetric optical waveguides and waveguides supporting bound states in the continuum (BICs) have received significant research interest in the photonics community. PT-symmetric optical waveguides use a balanced gain and loss to realize non-Hermitian degeneracies, also called exceptional points (EPs), in their guided modes. Waveguides supporting BICs can produce arbitrarily strong resonant responses for waves impinging upon the waveguide core. These special optical waveguides have many interesting properties that can be explored in applications. The purpose of this project is to carry out a systematic mathematical study for PT-symmetric waveguides, waveguides with BICs, and waveguides with the so-called complex modes, through rigorous mathematical analysis, accurate numerical simulation, and improved mathematical modeling. We study some important theoretical properties such as existence and robustness, for EPs, BICs and complex modes in optical waveguides, and explore their applications.