Multiresolution homogenization of field and network formulations for multiscale laminate dielectric slabs .I. Field theory

Conventional theories addressing the wave-dynamic behavior of plane-stratified multilayer environments usually involve wavenumber spectral and asymptotic techniques, which apply to layer thickness of the same "macroscale" order as the wavelengths in the spectrum of the excitation. However, in applications of multilayer bonded laminates (for example, in biological and other "exotic" materials") wherein the layer structure contains extremely fine "microscale" constituents as well as the conventional macroscales, the desired "observables" involve the macroscale response, which accounts self-consistently for the macroscale loading by the microscales. A novel multiresolution homogenization (MRH) has been presented previously to provide the self-consistent rigorous analytic micro-macro scale framework for calibrated parameterization of the wave dynamics in terms of a microscale-loaded macroscale medium with corresponding "effective" field observables. The outcome has been an algorithm that allows the conversion of the conventional macroscale propagation models to their "effective" micro-macroscale versions by direct substitution of the MRH-based effective fields, media, etc., in place of the corresponding conventional quantities, with error bounds that quantify the quality of the substitution. This theory may accommodate broad ranges, discrete and continuous, of wavenumber spectra and thus can be applied in conjunction with the spectral techniques noted above. In this paper, relevant "pragmatic" results of the MRH-based field theory are extracted from the previous formal treatment and are extended to accommodate alternative physics-matched MRH field representations. The reflection, transmission, and waveguiding properties, in free space, of a dipole-excited laminate slab whose scales span a wide continuum from micro to macro are examined in detail, with emphasis on alternative MRH field representations (ray, guided mode, etc.) that are best matched to the wave physics for specified ranges of operating frequencies, source-observer locations, etc. Extensive numerical experiments have been performed to calibrate, via quantified error bounds, the quality and range of validity of the conventional-to-MRH conversion for these alternative field representations. This lays t- he foundation for an MRH-based effective network theory for multiscale laminate conglomerates comprising a sequence of micro-macroscale laminate constituents, to be presented in part II of this paper.