Open Access
Arya, Ravi K
Graduate Program:
Electrical Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
July 06, 2017
Committee Members:
  • Raj Mittra, Dissertation Advisor
  • Raj Mittra, Committee Chair
  • Ram Mohan Narayanan, Committee Member
  • Victor P Pasko, Committee Member
  • Michael T Lanagan, Outside Member
  • Lens Antenna
  • antenna
  • statistical analysis
  • periodic structures
  • FSS
  • FDTD
  • Reflectarray
  • Periodic Boundary Condition
Presently, there is considerable interest in the world of Metamaterial (MTM) and Frequency Selective Surfaces (FSSs) in constructing and using crystals with 3D elements. These elements provide the flexibility in controlling the performance characteristics – in regards to frequency bandwidth, polarization sensitivity and angular range. Frequency selective surfaces (FSSs) are periodic structures with a bandpass or a bandstop frequency response dependent upon the geometrical parameters of its elements. Periodic structures are typically modeled as infinite arrays of scatterers, and are commonly analyzed by imposing periodic boundary conditions to a unit cell to reduce the original problem to a manageable size. Analysis of only a single unit cell reduces the computational burden. However, this benefit is marred if the illuminating plane wave has a large incident angle. Large incident angles in numerical simulations require lowering of the step size, which in turn might lead to instability. Even though several Finite-Difference Time-Domain (FDTD)/ Periodic Boundary Condition (PBC) methods are capable of handling the large angle condition in different ways, solving the unit cell remains a computationally intensive problem. The conventional Method of Moments (MoM) approach provides an efficient means to simulating FSSs though given the caveat that the periodic elements are PEC and not inhomogeneous, complex objects, which are more amenable to convenient analysis through the use of Finite Methods (FM). This dissertation starts by presenting a novel approach that is numerically efficient and accurate for the analysis of three–dimensional arbitrarily shaped periodic structures with arbitrary incidence angles. This technique does not suffer from the stability issues encountered in the FDTD/PBC algorithm, which can become unstable and computationally intensive with wide angles of incidence. Next, the design of the flat lenses is explored using modified commercial off-the- shelf (COTS) materials, as opposed to metamaterials (MTMs) that are often required in lens designs based on the Transformation Optics (TO) approach. While lens designs based on Ray Optics (RO) do not suffer from the drawback of having to use metamaterials, they still require dielectric materials that may not be commercially available off-the-shelf. A systematic procedure for realizing the desired materials is demonstrated by modifying the COTS types of materials, and illustrates its application with some practical examples. This dissertation investigates the use of 3D–printing for such examples and illustrates its benefits by combining it with the proposed method. Normally, the FSS structure is numerically simulated during the design process and then fabricated to verify if indeed it has the predicted characteristics. It is not unusual to find that there is considerable discrepancy between the simulated and measured results, even when there is only a minor difference between the designed and fabricated structures. This is especially true for Metamaterials used at optical wavelengths, where the difficulties in fabrication almost always introduce small variations in the dimensions of the elements that comprise the “periodic” array. This dissertation explores the resulting effect to the performance of the presence of this type of variation in the unit cell parameters by using the Polynomial Chaos method instead of the traditional Monte Carlo method, which can be extremely expensive in terms of computational resources. Finally, two designs of offset–fed dielectric reflectarray are presented. Both reflectarrays feature broadband designs realized by using dielectric blocks backed by a PEC plane. One of these arrays uses a phase compensating flat lens to reduce the maximum permittivity of the dielectric blocks covering the PEC plane. We compare the performances of both reflectarrays and list their benefits as compared to traditional reflectarrays that use resonant elements for their designs, which render them narrowband.