Multiresolution Homogenization of Field and Network Formulations for Multiscale Laminate Dielectric Slabs—Part 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 vaManuscript received June 11, 2002. This work was supported in part by the US-Israel Binational Science Foundation, Jerusalem, Israel, under Grant 9900448 and in part by the Israel Ministry of Science. The work of L. B. Felsen was supported in part by ODDR&E under MURI Grants ARO DAAG55-97-1-0013 and AFOSRF49620-1-0028, in part by the Engineering Research Centers Program of the National Science Foundation under Award EEC-9986821, and in part by Polytechnic University, Brooklyn, NY. V. Lomakin was with the Department of Interdisciplinary Studies, Faculty of Engineering, Tel Aviv University, 69978 Tel Aviv, Israel. He is now with the Center for Computational Electromagnetics, University of Illinois at UrbanaChampaign, Urbana, IL 61801-2991 USA (e-mail: [email protected]). B. Z. Steinberg and E. Heyman are with the School of Electrical Engineering, Tel Aviv University, 69978 Tel Aviv, Israel (e-mail: [email protected]; [email protected]). L. B. Felsen is with the Department of Aerospace and Mechanical Engineering and Department of Electrical and Computer Engineering, Boston University, Boston, MA 02215 USA and with the Polytechnic University, Brooklyn, NY 11201 USA. Digital Object Identifier 10.1109/TAP.2003.816356 lidity of the conventional-to-MRH conversion for these alternative field representations. This lays the 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.