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1. Exceptional Points of Degeneracy in Electromagnetic Periodic Waveguides and the Role of Symmetries

   https://doi.org/10.23919/EuCAP53622.2022.9769037  

   Mealy, Tarek ; Nada, Mohamed Y. ; Abdelshafy, Ahmed F. ; Hafezi, Ehsan ; Capolino, Filippo ( March 2022 , Published in: 2022 16th European Conference on Antennas and Propagation (EuCAP))

   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. 

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2. Exceptional point of sixth-order degeneracy in a modified coupled-resonator optical waveguide

   https://doi.org/10.1364/JOSAB.385198  

   Nada, Mohamed_Y ; Capolino, Filippo ( July 2020 , Journal of the Optical Society of America B)

   We demonstrate for the first time, to our knowledge, the occurrence of asixth-order exceptional point of degeneracy (EPD) in a realistic multimode optical photonic structure by using a modified periodic coupled-resonator optical waveguide (CROW) at the optical wavelength${\mathrm{\lambda <\#comment/>}}_e=1550\text{nm}$. The sixth-order EPD is obtained in a CROW without the need of loss or gain, and such an EPD corresponds to a very special band edge of the periodic photonic structure where six eigenmodes coalesce, so we refer to it as the sixth-order degenerate band edge (6DBE). Moreover, we report a new scaling law of the quality factor$Q$of an optical cavity made of such a periodic 6DBE-CROW with cavity length as$Q\propto <\#comment/>N^7$, when operating near the 6DBE with$N$being the number of unit cells in the periodic finite-length CROW. Furthermore, we elaborate on the application of the 6DBE to ultralow-threshold lasers. We present a novel scaling law of the lasing threshold that scales as$N^{-<\#comment/>7}$when operating near the 6DBE. Also, we show the superiority of the threshold scaling of the 6DBE-CROW to the scaling of another CROW with the same size operating near a fourth-order EPD that is often referred to as the degenerate band edge (DBE). The lasing threshold scaling of the DBE-CROW laser is shown here for the first time to our knowledge. We also discuss the high sensitivity of the proposed 6DBE-CROW to perturbations, which may find applications in sensors, modulators, optical switches, nonlinear devices, and$Q$-switching cavities.

    

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3. Degenerate Band Edge Resonances in Air-filled Substrate Integrated Waveguide

   https://doi.org/10.23919/EuCAP48036.2020.9135497  

   Zheng, Tianyu ; Casaletti, Massimiliano ; Abdelshafy, Ahmed F. ; Capolino, Filippo ; Ren, Zhuoxiang ; Valerio, Guido ( March 2020 , Proc. of 14th European Conference on Antennas and Propagation (EuCAP))

   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. 

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4. Parity-Time Glide-Symmetry and Third Order Exceptional Degeneracy in a Three-Way Microstrip Waveguide

   https://doi.org/10.23919/EuCAP53622.2022.9769390  

   Nikzamir, Alireza ; Marosi, Robert ; Mealy, Tarek ; Yazdi, Farshad ; Capolino, Filippo ( March 2022 , Published in: 2022 16th European Conference on Antennas and Propagation (EuCAP))

   A microstrip-technology three-way waveguide has been conceived to display exceptional modal degeneracy in the presence of periodic gain and radiation losses satisfying parity-time ( PT ) glide-symmetry. A third order exceptional point of degeneracy (EPD) is obtained in the modal dispersion relation, where three Floquet-Bloch eigenmodes coalesce at a single frequency, in their eigenvalues and polarization states. In the proposed structure, PT -glide-symmetry is achieved using periodically spaced lumped (radiation) loss and gain elements, each shifted by half a period. This particular degeneracy can be utilized in the design of devices such as radiating arrays with distributed amplifiers, arrays of oscillators, and sensors. 

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5. Sensing Via Exceptional Points in Space and Time Periodic Systems and in PT-Symmetric Systems

   https://doi.org/10.1109/Metamaterials49557.2020.9285058  

   Nada, M. Y. ; Mealy, T. ; Hafezi, E. ; Nikzamir, A. ; Capolino, F. ( September 2020 , Published in: 2020 Fourteenth International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials))

   We review and explore sensor applications based on electromagnetic systems operating near an exceptional point of degeneracy (EPD). The EPD is defined as the point at which the system eigenmodes coalesce in both their eigenvalues and eigenvectors varying a system parameter. Sensors based on EPDs show sensitivity proportional to δ 1/m , where δ is a perturbation of a system parameter and m is the order of the EPD. EPDs manifest in PT-symmetric systems or periodic systems that can be periodic in either time or space. We review all the methods to obtain EPD based sensors, and we focus on two classes of ultra-sensitive EPD systems: i) periodic linear time-varying single oscillators, and ii) optical gyroscopes based on a modified coupled resonators optical waveguide (CROW) exhibiting 4th order EPD. 

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