Frequency-dependent dielectric properties of 3-D-printed structured dielectrics (dielectric crystals) with engineered effective permittivity for micro-and mmWave applications are studied. Different modeling and measurement techniques for broadband dielectric properties of such 3-D-printed crystals are reviewed, their tradeoffs discussed, and individual results compared. Numerically obtained results from the plane wave expansion method (PWEM) and Floquet port scattering are compared with traveling-wave measurements in both guided and free-space setups. Furthermore, the shortcomings of effective media theories (EMTs) and resonance measurement methods are addressed and contrasted against broadband methods. Individual simulation and measurement setups are reviewed with respect to dielectric crystals with simple cubic (SC) and face-centered cubic (FCC) symmetry, with different unit cell sizes and volumetric infill fractions. Extracted effective permittivity values from PWEM and Floquet port simulations show excellent agreement with traveling-wave measurements in both guided and free-space scenarios. Furthermore, the discussed broadband methods predict and measure frequency-dependent effects that are not covered by EMTs and resonance measurement setups, highlighting the necessity to adopt more sophisticated simulation tools for the design of graded-index devices. It is shown that the effective media bandwidth of dielectric crystals depends on the respective unit cell symmetry and that FCC symmetry obtains a significantly increased bandwidth compared with SC symmetry.

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Additive manufactured structured dielectrics with engineered permittivity tensors are promising tools for novel microwave components and are drawing increasing attention from researchers. However, design modeling and experimental verification of anisotropic materials are challenging and have not yet been thoroughly explored in the literature. In this work, a design approach based on superimposed spatial harmonics for the design of anisotropic lattices called dielectric crystals is used. Furthermore, the plane wave expansion method (PWEM) is identified as a powerful tool for modeling the effective permittivity tensor. A wideband material characterization measurement setup based on rectangular waveguides is utilized for experimental verification. Experiments with uniaxial anisotropic dielectric crystals are carried out and are shown to be in satisfying agreement with our theoretical modeling.@en