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  1. 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 resonance, implying a nearly perfect conversion of the input light into the frozen mode. The group delay and the effective quality factor at the SIP resonance 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. 
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    Free, publicly-accessible full text available April 11, 2024
  2. Shahriar, Selim M. ; Scheuer, Jacob (Ed.)
    The physics of exceptional points leads to very high sensitivity because the perturbation of an exceptionally degenerate state is highly sensitive to a system’s perturbation. This property is indeed not shared with nondegenerate systems, and it relies in the fractional power expansion (Puiseux series) describing the perturbation of eigenvalues and eigenvectors. We discuss how this property is met in systems made of coupled resonators and with coupled modes in waveguides, whose eigenvalues are the resonant frequencies and the wavenumbers, respectively. We will also discuss the experimental implementation of this principle in unstable nonlinear systems to build extremely sensitive saturated oscillators. 
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  3. Subramania, Ganapathi S. ; Foteinopoulou, Stavroula (Ed.)
    We will discuss two kinds of exceptional points of degeneracy in waveguides and their respective application in lasers. Such exceptional points occur in waveguides with balanced loss and gain (e.g., PT symmetry), and in waveguides without loss and gain (e.g., periodic Si waveguides). Waveguides with such exceptional points have a strong degeneracy of their wavenumbers and polarization states that enables specific wave physics, only found in these degenerate systems. We will discuss advantages and disadvantages of both concepts to conceive laser regimes, related to high power, high spectral purity, high efficiency, etc, and show some realistic designs involving Si ridge waveguides. 
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  4. We present a scheme supporting an exceptional point of degeneracy (EPD) using connected Foster and non-Foster resonators. One resonator contains positive components, whereas the second resonator contains negative components. We show a second-order EPD where two eigenvalues and eigenvectors coalesce. This circuit can be used to make ultra-sensitive sensors. 
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  5. There are two kinds of exceptional points of degeneracy (EPD) in waveguides: those in the absence of loss and gain, related to slow light, and those where the waveguide has distributed gain and/or loss. Here, we discuss both kinds and highlight their differences. We show EPDs of order 2, 3, 4 and 6 in waveguides supporting two or three modes in each direction, and how the coalescence parameter is a good tool to measure the degree of degeneracy by measuring the angle between the eigenvectors (polarization states). In highlighting the differences between the two kinds of EPDs, we also show different sets of applications, which include sensors, delay lines, distributed amplifiers, antennas, and oscillators. 
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