Homogenization and Characterization of Additive Manufactured Dielectric Crystals for High-Frequency Electromagnetic Applications

Abstract

Today, state-of-the-art device manufacturing for high-frequency (HF) electromagnetic (EM) applications is primarily dominated by subtractive techniques, including milling, laser cutting, electric discharge machining, and chemical etching, among others. While these methods are well established and enable remarkable accuracy, they are fundamentally constrained in terms of the geometric complexity they can achieve. The growing demand for more compact, efficient, and high-bandwidth EM devices challenges these limitations. Consequently, there has been a surge in alternative manufacturing techniques that leverage three-dimensional space to unlock additional design freedoms. The present work explores the unique capabilities of extrusion-based additive manufacturing (AM) to realize complex periodic dielectric structures for modern high-frequency EM applications. Specifically, this thesis investigates the homogenization, characterization, and practical implementation of periodic dielectric structures—also referred to as dielectric crystals—for advanced EM applications at microwave and millimeter-wave frequencies.
The thesis opens with a comprehensive review of AM applications in HF electromagnetics, highlighting significant potential while also identifying critical gaps in the current state of the art. These gaps guide the original contributions of the presented research, summarized below.

First, a comprehensive overview and comparison of homogenization and experimental characterization techniques for evaluating dielectric material properties is provided. While literature offers treatments on numerous analytical, numerical, and experimental methods, there is a lack of a systematic comparison tailored specifically to AM periodic dielectric structures. This thesis bridges that gap by rigorously comparing selected homogenization methods against experimental characterization results. It provides an analysis of the advantages and limitations of each approach and identifies their suitability for analysing AM periodic dielectrics.

Second, the impact of additive fabrication on the anisotropy of dielectric material properties is studied. The phenomenon of mechanical anisotropy resulting from the layer-by-layer additive fabrication approach is well-documented in literature, while its implications for dielectric properties remain unexplored. The presented research addresses this critical gap by thoroughly investigating the effective permittivity tensor. For this purpose, an analytical model is presented and its predictions validated through numerical simulations and experimental characterization using various materials and printing parameters. The results confirm significant anisotropy with negative birefringence, aligning well with theoretical predictions.

Third, although previous studies have utilized volumetric infill variations to influence the effective dielectric properties of periodic structures, the fundamental connection between crystallographic theory and dielectric behavior has remained largely unexplored. This thesis systematically investigates how lattice symmetries affect the effective permittivity tensor. A detailed parametric study of selected Bravais lattices and crystal centerings is conducted, demonstrating precise control over dielectric anisotropy. These findings are confirmed experimentally through careful characterization of several lattice structures exhibiting distinct uniaxial and biaxial anisotropic properties.

Fourth, spatially modulated dielectric structures have mostly been employed in graded-index (GRIN) lenses for long-wavelength applications. This work expands significantly beyond this scope, exploring new applications in both the long- and short-wavelength operating regimes. For long-wavelength scenarios, cylindrical heterogeneous dielectric resonator antennas (DRAs) with radially and vertically varying permittivity profiles are investigated. Experimental results demonstrate that spatial modulation enhances both the impedance and axial ratio bandwidth compared to homogeneous DRAs. Furthermore, heterogeneous dielectric slabs within rectangular waveguides are explored, demonstrating practical control over transmission and reflection characteristics, exemplified through the realization of a third-order Chebyshev bandpass filter.
Regarding short-wavelength applications, this research explores 3D periodic dielectric bandgap materials. A thorough numerical and experimental verification of the bandgap properties of woodpile structures is conducted, culminating in a novel dielectric rod antenna that significantly suppresses third harmonic radiation through combined long- and short-wavelength concepts. Collectively, these examples demonstrate the vast potential for innovative device performance enabled by spatially modulated periodic dielectric structures.

Fifth, integrating conductive and dielectric materials in a single AM process is highly advantageous yet underutilized, primarily due to the prohibitive cost of specialized equipment. Addressing this limitation, the thesis introduces an accessible, open-source inspired approach to hybrid AM. A custom-built AM system incorporating a micro-dispensing head for conductive ink deposition is successfully demonstrated through the fabrication of a fully additive-manufactured dielectric resonator phased array antenna operating at $20$\si{\giga\hertz}. This practical demonstration confirms the viability and effectiveness of hybrid AM technology for advanced antenna applications.

In summary, this research underscores the transformative potential and enables new opportunities of additive manufacturing in EM device engineering. While recognizing the ongoing challenges related to material and equipment limitations, the thesis illustrates that these can be effectively managed through careful selection of homogenization, characterization, and design methodologies. Promising future directions identified include further exploration of hybrid AM for high-frequency EM applications, innovations in communications, radar, and sensing technologies, and continued advancements in integrated material processes. Ultimately, this work significantly advances additive manufacturing for electromagnetic applications, laying a strong foundation for future innovations in communication, radar, and sensing technologies.