Ordering of ferroelectric polarization and its trajectory in response to an electric field are essential for the operation of non-volatile memories, transducers and electro-optic devices. However, for voltage control of capacitance and frequency agility in telecommunication devices, domain walls have long been thought to be a hindrance because they lead to high dielectric loss and hysteresis in the device response to an applied electric field. To avoid these effects, tunable dielectrics are often operated under piezoelectric resonance conditions, relying on operation well above the ferroelectric Curie temperature, where tunability is compromised. Therefore, there is an unavoidable trade-off between the requirements of high tunability and low loss in tunable dielectric devices, which leads to severe limitations on their figure of merit. Here we show that domain structure can in fact be exploited to obtain ultralow loss and exceptional frequency selectivity without piezoelectric resonance. We use intrinsically tunable materials with properties that are defined not only by their chemical composition, but also by the proximity and accessibility of thermodynamically predicted strain-induced, ferroelectric domain-wall variants. The resulting gigahertz microwave tunability and dielectric loss are better than those of the best film devices by one to two orders of magnitude and comparable to those of bulk single crystals. The measured quality factors exceed the theoretically predicted zero-field intrinsic limit owing to domain-wall fluctuations, rather than field-induced piezoelectric oscillations, which are usually associated with resonance. Resonant frequency tuning across the entire L, S and C microwave bands (1-8 gigahertz) is achieved in an individual device-a range about 100 times larger than that of the best intrinsically tunable material. These results point to a rich phase space of possible nanometre-scale domain structures that can be used to surmount current limitations, and demonstrate a promising strategy for obtaining ultrahigh frequency agility and low-loss microwave devices.
The newly introduced parallel-plate ridge gap waveguide consists of a metal ridge in a metamaterial surface, covered by a metallic plate at a small height above it. The gap waveguide is simple to manufacture, especially at millimetre and sub-millimetre wave frequencies. The metamaterial surface is designed to provide a frequency band where normal global parallel-plate modes are in cutoff , thereby allowing a confined gap wave to propagate along the ridge. This paper presents an approximate analytical solution for this confined quasi-TEM dominant mode of the ridge gap waveguide, when the metamaterial surface is an artificial magnetic conductor in the form of a bed of nails. The modal solution is found by dividing the field problem in three regions, the central region above the ridge and the two surrounding side regions above the nails. The fields within the side regions are expressed in terms of two evanescent TE and TM modes obtained by treating the bed of nails as an isotropic impedance surface, and the field in the central ridge region is expanded as a fundamental TEM parallel-plate mode with unknown longitudinal propagation constant. The field solutions are linked together by equalizing longitudinal propagation constants and imposing point-continuity of fields across the region interfaces, resulting in a transcendental dispersion equation. This is solved and presented in a dispersion diagram, showing good agreement with a numerical solution using a general electromagnetic solver. Both the lower and upper cutoff frequencies of the normal global parallel-plate modes are predicted, as well as the quasi-TEM nature of the gap mode between these frequencies. The evanescent fields in the two side regions decay very rapidly away from the ridge, being in the order of 100dB per lower cutoff wavelengths over most of the single-mode bandwidth.
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