Theory and Applications of Exceptional Points of Degeneracy in Coupled Mode Structures
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Theory and Applications of Exceptional Points of Degeneracy in Coupled Mode Structures

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High quality (Q) factor optical resonators offer a practical testbed for new advances in various applications, including photonics and sensing applications. One way to realize high Q factor devices is the utilization of the slow-light phenomenon associated with exceptional points of degeneracy (EPD). An EPD is a point in a system parameter space at which two or more eigenmodes coalesce in both the eigenvalues and eigenvectors. We present a novel approach and a theoretical framework for generating high order EPDs in optical photonic structures based on periodic coupled resonators optical waveguides (CROWs). We propose a novel CROW design by coupling the chain of ring resonators from one side to a straight waveguide. Then we present the mathematical theory of EPDs in the proposed CROW where we adopt the transfer matrix formalism. The proposed CROW design exhibits various EPD orders (2, 3, 4, and 6) and we show the dispersion relation of the proposed CROW unit cell and the necessary conditions governing the CROW parameters to exhibit each of such orders. Then we focus on CROW finite-length cavities operating in the vicinity of the DBE, where we explore the transfer function characteristics near the DBE. We show that the Q factor of DBE cavities of N unit cells scales with N5 when operating at the resonance frequency closest to the DBE, even in the presence of losses. Moreover, we show that the obtained Q factor at the DBE resonance is higher in designs with flatter dispersion at the DBE, and we derive an analytic expression of the flatness parameter. We also demonstrate the robustness of the CROW Q factor at the DBE resonance against perturbations and disorders that could arise from tolerances in fabrication. In addition, we explore the sensitivity of the DBE-CROW and discuss the utilization of such unique sensitivity to design ultra-sensitive optical CROW gyroscopes. We present a mathematical model of the rotating CROW gyroscope based on the transfer matrix (T-matrix) formalism. Further on, we demonstrate for the first time the occurrence of a sixth order EPD (6DBE) in the proposed CROW with practical dimensions at the optical wavelength λ_e=1550nm. Moreover, we report a new scaling law of the Q factor of an N unit cells periodic CROW cavity as N^7 when operating in the vicinity of the 6DBE. Furthermore, we elaborate on the applications of the 6DBE-CROW to ultra-low-threshold mirrorless lasers. In addition, we show the high sensitivity of the 6DBE-CROW eigenvalues to perturbations, that may find applications in sensors, modulators, optical switches, nonlinear devices, and Q-switching cavities. We have also introduced a new CROW geometry based on racetrack resonators with different radii in each resonator to realize the stationary inflection point (SIP) at optical frequencies, which is a third order EPD. We have verified the existence of the SIP through full wave simulations. We have explored different unique properties associated with the existence of the SIP in finite-length cavities and show that the group delay at the SIP frequency scales with the number of unit cells in the finite CROW cavity as N3. This SIP-CROW might find applications in optical delay lines, sensors and laser. In the microwave realm, we demonstrate theoretically and experimentally a novel simple periodic fully planar three-way microstrip coupled waveguide that exhibits a stationary inflection point (SIP). We verify experimentally the existence of the SIP in the proposed design where the coalescence parameter is used to determine how close the three-way system is to the ideal frozen mode condition.

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