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We investigate the role of reflection and glide symmetry in periodic lossless waveguides on the dispersion diagram and on the existence of various orders of exceptional points of degeneracy (EPDs). We use an equivalent circuit network to model each unit-cell of the guiding structure. Assuming that a coupled-mode waveguide supports N modes in each direction, we derive the following conclusions. When N is even, we show that a periodic guiding structure with reflection symmetry may exhibit EPDs of maximum order N . To obtain a degenerate band edge (DBE) with only two coupled guiding structures, reflection symmetry must be broken. For odd N,N+1 is the maximum EPD order that may be obtained, and an EPD of order N is not allowed. We present an example of three coupled microstrip transmission lines and show that breaking the reflection symmetry by introducing glide symmetry enables the occurrence of a stationary inflection point (SIP), also called frozen mode, which is an EPD of order three. 

An oscillator made of a periodic waveguide comprising of uniform lossless segments with discrete nonlinear gain and radiating resistive elements prefers to operate at exceptional point of degeneracy (EPD). The steady-state regime is an EPD with π phase shift between unit cells, for various choices of small signal gain of the nonlinear elements and number of unit cells. We demonstrated this fact by monitoring both current and voltage across each nonlinear gain element and finding its effective admittance at the oscillating frequency and checking the degeneracy of the eigenmodes at such point. The EPD studied here is very promising for many applications that incorporate discrete distributed coherent sources and radiation-loss elements. Operating in the vicinity of such special degeneracy conditions may lead to potential performance enhancement in the various microwave, THz and optical systems with distributed gain and radiation, paving the way for a new class of active integrated antenna arrays and radiating laser arrays. 

We demonstrate that a periodic transmission line consisting of uniform lossless segments together with discrete gain and radiation-loss elements supports exceptional points of degeneracy (EPDs). We provide analytical expressions for the conditions that guarantee the coalescence of eigenvalues and eigenvectors. We show the dispersion diagram and discuss the tunability of the EPD frequency. Additionally, a special case is shown where the eigenvectors coalesce for all frequencies when a specific relationship between transmission line characteristic impedance, and gain/loss elements holds; in other words, in this situation, exceptional points merge to a line of frequency. The class of EPDs proposed in this work is very promising in many of applications that incorporate radiation losses. 

We exploit a second order exceptional point of degeneracy (EPD) to enhance frequency purity and oscillation stability in oscillators. The EPD we consider in this paper is a regular band edge (RBE) that exists in lossless and gainless periodic waveguides. We present an example of single-ladder oscillator that may act as a leaky wave antenna (LWA). The oscillator we develop has 8 unit-cells that form a resonant cavity and an active element is used to compensate for the losses and start the oscillation. We show that the oscillation frequency is in proximity of the RBE frequency thanks to the second order degeneracy. 

The degenerate band edge (DBE) is a special fourth-order degenerate point in a dispersion diagram, where four eigenmodes coalesce to a single degenerate eigenmode. It leads to field enhancement of the Bloch mode and to high quality factors, which are useful for high-Q resonators, oscillators and ultrasensitive sensors. The air-filled substrate integrated waveguide (AFSIW) is a novel form of SIW which is low cost and low loss. We propose a design of an AFSIW supporting a degenerate band edge (DBE). We show the occurrence of the so-called “giant resonance” associated to the DBE and we study how losses influence the DBE. 

We propose a pulse generation scheme based on a fourth-order degeneracy in the dispersion relation. We take advantage of the loaded quality factor enhancement and the ultra-sensitivity to external perturbations due to the high order degeneracy in such a structure. The proposed scheme is able to produce a train of nanosecond pulses with several watts of output power. Such a design offers a flexibility that allows to conceive either high output power pulses or high frequency train of pulses.