Broadband Effective Permittivity Simulation and Measurement Techniques for 3-D-Printed Dielectric Crystals

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.