  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 wavenumber. GT symmetry involves
glide symmetry of lossless/gainless components of the waveguide in addition to
changing the sign of passive/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 wavenumber at a single frequency, in
addition of having one branch of the dispersion diagram with a purely real
wavenumber. The proposed scheme may have applications including but not limited
to distributed amplifiers, radiating arrays, and sensors, from radio frequency
to optics.
