Waveguides with Exceptional Points of Degeneracy of Order 2, 3, 4 and 6 without Loss and Gain

We show various examples of fully-planar two-way and three-way microstrip coupled waveguides that exhibit second, third, fourth and sixth order exceptional points of degeneracy (EPD). EPDs are shown in reciprocal waveguides that do not have gain or loss. The occurrence of EPDs is observed using three methods: (i) the mathematical description of modes and the similarity of the system matrix to a Jordan block; (ii) the dispersion diagram with prescribed flatness; (iii) the coalescence of eigenvectors that is observed analytically or experimentally. We have defined a coalescence parameter that is used in conjunction with experimental results to measure the separation of the coalescing eigenvectors (polarization states). The presented structures can serve various applications like leaky-wave antennas, distributed amplifiers, oscillators, delay lines, pulse generators, and sensors.