Theory of Coupled Resonator Optical Waveguides (CROW) Exhibiting High Order Exceptional Points of Degeneracy

TL;DR

This paper introduces a new theoretical framework for creating high order exceptional points in coupled resonator optical waveguides without gain or loss, enabling enhanced modal properties and potential applications.

Contribution

It presents the first demonstration of high order exceptional points in CROWs through symmetry breaking, expanding the understanding of EPDs in passive photonic structures.

Findings

EPDs can be achieved without gain/loss by symmetry breaking in CROWs.

CROWs exhibit high Q-factors and field enhancement near EPDs.

Q-factor scales anomalously with CROW length near the degenerate band edge.

Abstract

We present a novel approach and a theoretical framework for generating high order exceptional points of degeneracy (EPD) in photonic structures based on periodic coupled resonators optical waveguides (CROWs). Such EPDs involve the coalescence of Floquet-Bloch eigenwaves in CROWs, without the presence of gain and loss, which is in contrast to the requirement of Parity-Time (PT) symmetry to develop exceptional points based on gain and loss balance. The EPDs arise here by introducing symmetry breaking in a conventional chain of coupled resonators through coupling the chain of resonators to an adjacent uniform optical waveguide, which leads to unique modal characteristics that cannot be realized in conventional CROWs. Such remarkable characteristics include high quality factors (Q-factor) and strong field enhancement, even without any mirrors at the two ends of a cavity. We show for the first time the capability of CROWs to exhibit EPDs of various order; including the degenerate band edge (DBE) and the stationary inflection point (SIP). The proposed CROW of finite length shows enhanced quality factor when operating near the DBE, and the Q-factor exhibits an anomalous scaling with the CROW's length. We develop the theory of EPDs in such unconventional CROW using coupled-wave equations, and we derive an analytical expression for the dispersion relation. The proposed unconventional CROW concepts have various potential applications including Q-switching, nonlinear devices, lasers, and extremely sensitive sensors.