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

Abstract

3D-printed structured dielectrics, or dielectric crystals, with engineered effective permittivity, are currently receiving much research attention to create novel graded index devices for micro- and mmWave applications. However, the design, modeling, and experimental verification of the dielectric properties of such crystals are not trivial. Promising results have been achieved using parametrically defined unit cells, effective media theories (EMT), and resonative measurement setups. However, more generalized design approaches and sophisticated simulation and measurement methods that provide insight into frequency-dependent behavior are needed to fully expoint the potential of structured dielectrics. This work discusses the plane wave expansion method (PWEM), Flochet port simulations, and traveling wave measurements in both guided and free-space setups to address the shortcomings of effective media theories like the Maxwell-Garnett approximation (MGA) and resonative measurement methods. Furthermore, a generalized design method for the dielectric crystals is utilized to create unit cells with different crystal symmetries. Results of the individual simulation and measurement setups are discussed concerning dielectric crystals in simple cubic (SC) and face-centered cubic (FCC) symmetry with different unit cell sizes and volumetric infill fractions. PWEM and Flochet port simulations and traveling wave measurements show excellent agreement for the extracted effective permittivity of structured dielectrics. Furthermore, the discussed methods predict and measure frequency-dependent effects that are not covered by effective media theories and resonative measurement setups, highlighting the necessity to adopt more sophisticated simulation tools for the design of graded index devices.