Experimental Validation of Frozen Modes Guided on Printed Coupled Transmission Lines

Previous work has theoretically demonstrated that nonreciprocal slow-wave modes, namely, "frozen modes," can be supported on a pair of coupled transmission lines printed on a magnetic substrate. Small antennas have also been designed by exploiting these modes. However, to date, we have yet to demonstrate and observe their existence experimentally. To this end, we construct two printed prototypes comprised of several unit-cells and employ the " T -matrix method" to determine the dispersion properties by measuring the S -parameters of these finite periodic prototypes. The printed unit-cell is designed to exhibit a unique stationary inflection point in the dispersion diagram corresponding to a frozen mode with almost zero group velocity. Through careful measurements and calculations, the frozen mode is observed to propagate at a significantly slower speed (286 times slower) than the speed of light. Importantly, this extraction method can be applied to any other periodic layout to obtain related dispersion properties.