Exceptional Points of Degeneracy in Periodic Coupled Waveguides and the Interplay of Gain and Radiation Loss: Theoretical and Experimental Demonstration

Abstract

We present a novel paradigm for dispersion engineering in coupled transmission lines (CTLs) based on exceptional points of degeneracy (EPDs). We develop a theory for fourth-order EPDs consisting of four Floquet-Bloch eigenmodes coalescing into one degenerate eigenmode. We present unique wave propagation properties associated to the EPD and develop a figure of merit to assess the practical occurrence of fourth-order EPDs in CTLs with tolerances and losses. We experimentally verify for the first time the existence of a fourth EPD (the degenerate band edge), through dispersion and transmission measurements in microstrip-based CTLs at microwave frequencies. In addition, we report that based on experimental observation and the developed figure of merit, the EPD features are still observable in structures that radiate (leak energy away), even in the presence of fabrication tolerances and dissipative losses. We investigate the gain and loss balance regime in CTLs as a mean of recovering an EPD in the presence of radiation and/or dissipative losses, without necessarily resorting to Parity-Time (PT)-symmetry regimes. The versatile EPD concept is promising in applications such as high intensity and power-efficiency oscillators, spatial power combiners, or low-threshold oscillators and opens new frontiers for boosting the performance of large coherent sources.

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• General Conditions to Realize Exceptional Points of Degeneracy in Two Uniform Coupled Transmission Lines
• Exceptional Point of Degeneracy in Backward-Wave Oscillator with Distributed Power Extraction
• Frozen mode in an asymmetric serpentine optical waveguide
• Exceptional Point of Sixth Order Degeneracy in a Modified Coupled Resonators Optical Waveguide
• Chiral terahertz lasing with Berry curvature dipoles
• Exceptional Degeneracy in a Waveguide Periodically Loaded with Discrete Gain and Radiation Loss Elements
• High Power Backward Wave Oscillator using Folded Waveguide with Distributed Power Extraction Operating at an Exceptional Point
• Lasing at a Stationary Inflection Point
• Low-Threshold Lasing with Frozen Mode Regime and Stationary Inflection Point in Three Coupled Waveguide Structure
• Triple Ladder Lumped Circuit with Sixth Order Modal Exceptional Degeneracy
• Degenerate Distributed Feedback Photonic Structure with Double Grating Exhibiting Degenerate Band Edge
• Frozen Mode Regime in an Optical Waveguide With Distributed Bragg Reflector
• Third Order Modal Exceptional Degeneracy in Waveguides with Glide-Time Symmetry
• One-transmitter Multiple-receiver Wireless Power Transfer System Using an Exceptional Point of Degeneracy
• Three-Way Serpentine Slow-Wave Structures with Stationary Inflection Point and Enhanced Interaction Impedance