Floquet-Wave-Based Analysis of Transient Scattering From Doubly Periodic Structures

147 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2004.In the past, transient scattering from doubly periodic structures has been analyzed predominantly using finite difference time domain methods. Unfortunately, for obliquely excited periodic structures, these solvers call for future field values to update current ones, and therefore cannot be applied directly. Several avenues for tackling this problem have been suggested. It appears, however, that most fixes proposed to date are either hard to implement or somewhat limited in scope. This thesis starts with a study of classically formulated time domain integral equation (TDIE) based schemes for analyzing transient scattering from doubly periodic, free-standing or substrate imprinted perfectly electrically conducting (PEC) elements. Like in their finite difference counterparts, noncausal terms appear in the update equations that result upon discretizing periodic structure TDIEs by classical marching-on-in-time (MOT) procedures. Luckily, however, these noncausal terms are easily eliminated through the introduction of time-shifted temporal basis functions in combination with a bandlimited extrapolation method. However, like all MOT-based TDIE solvers, these "classically" constructed MOT-based TDIE solvers for doubly periodic structures are computationally expensive, which renders them inapplicable to the analysis of real-world structures. This thesis then focuses on a Floquet-wave-based scheme to relieve this computational burden by using blocked fast Fourier transform based accelerators to efficiently evaluate transient Floquet-wave decomposed electromagnetic fields generated by doubly periodic and temporally bandlimited source distributions. The resulting scheme produces an efficient mean for analyzing transient scattering from doubly periodic, discretely planar, free-standing PEC structures. However, it is not directly applicable to the analysis of nonplanar doubly periodic structures. Therefore, an improved Floquet-wave-based scheme that relies on a time-marching scheme to efficiently evolve the modal amplitudes of time-domain Floquet waves along one-dimensional domains using a spectral time-stepping scheme supplemented with Huygens' based boundary conditions is proposed. The resulting scheme applies without difficulty to the analysis of transient scattering from nonplanar doubly periodic structures comprising PEC elements and sculptured dielectric volumes. Numerous numerical examples demonstrate the capabilities and accuracy of the proposed schemes.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD