Third order modal exceptional degeneracy in waveguides with glide-time symmetry

The dispersion of a three-way waveguide is engineered to exhibit exceptional modal characteristics. Two coupled waveguides with parity-time (PT) symmetry have been previously demonstrated to exhibit second order exceptional points of degeneracy (EPDs). In this work, we introduce and investigate a particular class of EPDs, applicable from radio frequency to optical wavelengths, whereby three coupled waveguides satisfy glide-time (GT) symmetry to exhibit a third order modal degeneracy with a real-valued wave number. GT symmetry involves glide symmetry of lossless and gainless components of the waveguide in addition to changing the sign of passive and active elements while applying a glide-symmetry operation. This GT-symmetry condition allows three Floquet-Bloch eigenmodes of the structure to coalesce to a real-valued wave number at a single frequency, in addition to having one branch of the dispersion diagram with a purely real wave number. The proposed scheme may have applications including but not limited to distributed amplifiers, radiating arrays, and sensors, from radio frequency to optics.