Giant Resonance and Anomalous Quality Factor Scaling in Degenerate Band Edge Coupled Resonator Optical Waveguides

Abstract

We propose a novel scheme for enhancing the quality factor of coupled resonators optical waveguides (CROWs) when operating near a degenerate band edge (DBE). A DBE is a four-mode exceptional point of degeneracy (EPD) occurring when four Bloch eigenmodes coalesce providing a resonance condition with a giant enhancement in fields. We report an unprecedented scaling law of quality factor of CROWs when operating at the DBE, even in the presence of losses and structural perturbations. Remarkably, the Q factor of the proposed CROW can be engineered to exceed that of a single ring resonator having a diameter equal to the CROW length, hence having an overall strong area reduction. The findings reported in this letter are critical for enhancing field's amplitudes to giant levels and the Q factor of ring resonators and are very beneficial for various applications including four wave mixing, Q switching, lasers, and highly sensitive sensors.

Degenerate band edge laser

“…In the example shown in Fig. 1(c) the DBE cavity is made of waveguides coupled to a chain of coupled resonator optical waveguide (CROW) as shown in [50]. (The conventional CROW topology would support only an RBE [59][60][61].)…”

“…However, it is important to stress that the DBE, which is a fourth order EPD, occurs in a passive and lossless system, i.e., without the need of gain or loss. Some DBE characteristics have been shown to occur at optical frequencies using perturbed coupled silicon waveguides [48,49], or a chain of ring resonators coupled to a waveguide [50]; as well as in metallic waveguides at microwaves [39]. There have been also significant efforts in analysis, design, and experimental realization of the DBE structures and its slow-wave properties at both microwave [51][52][53] and optical frequencies [54,55].…”

“…There have been also significant efforts in analysis, design, and experimental realization of the DBE structures and its slow-wave properties at both microwave [51][52][53] and optical frequencies [54,55]. It is important to point out that even though DBE is a precise EPD condition occurring in lossless waveguides, experimental studies made both at microwaves [53] and optical frequencies [50,51] have confirmed the existence of features associated with the DBE in the presence of losses and fabrication tolerances. Indeed, the robustness of DBE features against perturbations due to possible fabrication tolerances that may arise during fabrication was demonstrated for DBE CROWs in [50].…”

“…It is important to point out that even though DBE is a precise EPD condition occurring in lossless waveguides, experimental studies made both at microwaves [53] and optical frequencies [50,51] have confirmed the existence of features associated with the DBE in the presence of losses and fabrication tolerances. Indeed, the robustness of DBE features against perturbations due to possible fabrication tolerances that may arise during fabrication was demonstrated for DBE CROWs in [50]. The DBE has led to observing giant gains in optical cavities [47]; however here we leverage a general EPD concept, for the first time, to propose the new regime of lasing, resulting in low-threshold and single frequency operation of the degenerate band edge laser.…”

A New Amplification Regime for Traveling Wave Tubes With Third-Order Modal Degeneracy

“…See Refs. [31]- [33], [38] for more details on the generalized Pierce theory of multimodal periodic SWS interaction with an electron beam, including a Lagrangian formalism in [37]. We employ such general framework to investigate a specific SWS that develops an SIP.…”