Design of a Modified Coupled Resonators Optical Waveguide Supporting a Frozen Mode
We design a three-way silicon optical waveguide with the Bloch dispersion relation supporting a stationary inflection point (SIP). The SIP is a third order exceptional point of degeneracy (EPD) where three Bloch modes coalesce forming the frozen mode with greatly enhanced amplitude. The proposed design consists of a coupled resonators optical waveguide (CROW) coupled to a parallel straight waveguide. At any given frequency, this structure supports three pairs of reciprocal Bloch eigenmodes, propagating and/or evanescent. In addition to full-wave simulations, we also employ a so-called ''hybrid model'' that uses transfer matrices obtained from full-wave simulations of sub-blocks of the unit cell. This allows us to account for radiation losses and enables a design procedure based on minimizing the eigenmodes' coalescence parameter. The proposed finite-length CROW displays almost unitary transfer function at the SIP frequency, implying a nearly perfect conversion of the input light into the frozen mode. The group delay and the effective quality factor at the SIP frequency show an $N^{3}$ scaling, where $N$ is the number of unit cells in the cavity. The frozen mode in the CROW can be utilized in various applications like sensors, lasers and optical delay lines.