Frozen Mode in Three-Way Periodic Microstrip Coupled Waveguide

We demonstrate theoretically and experimentally that a simple periodic fully planar three-way microstrip coupled waveguide exhibits a stationary inflection point (SIP). The SIP is a third-order exceptional point of degeneracy where three eigenmodes of the guiding system coalesce to form a stationary frozen mode with zero group velocity. Here, the frozen mode is shown in a reciprocal three-way waveguide supporting three modes in each direction. We illustrate the occurrence of the frozen mode regime by observing the dispersion diagram and by the coalescence parameter that is a measure of the separation of the three coalescing eigenvectors. Results based on full-wave simulations and measurements demonstrate the coalescence of three modes and how this coalescence is not perfect due to the presence of losses in the microstrip structure at 2 GHz. The coalescence parameter is used to determine how close the three-way system is to the ideal frozen mode condition.