Numerical Modeling and Design of Gradient-Index Lens and Radome Antennas

QC 20260902

Abstract

This thesis investigates the numerical modeling and design of gradient-index (GRIN) lens antennas and radome-integrated phased array antennas (PAAs) at millimeter-wave frequencies. The research encompasses the analysis of periodic structures, the development of efficient ray-tracing and physical-optics (RT-PO) tools, and the design of high-performance GRIN lens and radome antennas.

First, a comprehensive methodology is established to obtain the dispersion diagrams of structures periodic in all three spatial dimensions and characterized by various lattice arrangements. Analysis shows that symmetries in body-centered and face-centered cubic lattices lead to improved isotropy and maintain low-dispersion characteristics over a wider frequency range than conventional simple cubic lattices. These properties facilitate the implementation of high-performance GRIN lenses based on suitable lattice arrangements, as demonstrated through fully metallic Luneburg lens and dielectric truncated virtual image lens designs.

Second, an efficient RT-PO model is developed to provide a rapid tool for analyzing lens radiation properties. This framework applies geometric optics to calculate ray trajectories and determine the corresponding phase distributions, followed by amplitude evaluation via ray-tube power conservation theory and radiation-field computation using the field equivalence principle. For azimuthally symmetric three-dimensional GRIN lenses with directive feeds for collimation or focusing, RT is reduced to a two-dimensional (2D) axial cross section, while PO is performed on a circular integration surface at the lens output. If the field on this surface is uniformly linearly polarized, the PO formulation is further simplified from vector to scalar integration. This approach enables accurate evaluation of both quasi-nondiffracting near-field and collimated far-field distributions, with computation times significantly shorter than those required by commercial full-wave simulators.

Lastly, this research explores lens-based radomes integrated with PAAs to enhance directivity within the desired scanning range without modifying the existing arrays. The initial dielectric lens (DL) designs are based on full-wave simulations; however, the high computational cost of these simulations motivates the development of efficient RT-PO models for radome analysis and design. Using the 2D RT-PO model, a DL is designed and validated through prototype measurements, confirming improved gain and beam-pointing accuracy for a realistic PAA at wide scanning angles. Beyond standalone DLs, a hybrid dome combining DLs and metadomes (MDs) is introduced to exploit the benefits of both structures, achieving lower weight and volume than standalone DLs and a broader bandwidth than standalone MDs. The capability of the hybrid dome to extend the PAA scanning range is demonstrated in both single-beam scanning scenarios and steerable flat-top beam applications.

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