Branislav M. Notaros University of Massachusetts Dartmouth
Intellectual Merit. The central goal of this research is to provide the optics and nanotechnology communities, as well as the antenna and RF/microwave communities, with a new electromagnetic (EM) modeling capability for much more efficient analysis and design of realistic planar photonic crystal (PC) or photonic band-gap (PBG) structures, as an alternative to finite-difference time-domain simulations. Two independent higher order large-domain integral-equation (IE) techniques, a general-purpose IE technique and a specialized PBG modeling technique, will be developed, as well as their hybrid. The specialized technique is dedicated to PBG structures involving arbitrary finite non-periodic arrays of air-filled, dielectric-filled, or metalized circular cylindrical holes perforated in an infinite dielectric (semiconductor) slab, and is designed to be extremely rapid, which is crucial for optimization of designs (e.g., using genetic algorithms). The hybrid higher order IE-PBG method will allow arbitrary 3-D electromagnetic structures to be included in the analysis with planar PBG materials.
Broader Impacts. This research has the potential of considerably improving the capabilities of computational electromagnetics for modeling and design of photonic-crystal structures in real-world applications and significantly impacting predicted expansion of research, development, and fabrication activities in this area. Just one example of many great promises of PC materials is their role as enabling technology for future generations of high-density integrated planar lightwave circuits. Two Ph.D. graduate students will be working on the project at all times. A number of other graduate and undergraduate students will be engaged periodically. A new graduate course on EM Metamaterials will be developed.
The central goal of this project is to provide the optics and nanotechnology communities, as well as the antenna and RF/microwave communities, with a new electromagnetic modeling capability for much more efficient analysis and design of photonic crystal or photonic band-gap (PBG) structures with cylindrical and spherical perforations and inclusions, as well as other metamaterial structures, as an alternative to finite-difference time-domain simulations. The major outcomes of the project can be summarized as follows. We have developed a novel specialized higher order large-domain surface integral equation (SIE) method of moments (MoM) coupled with the dyadic layered-media Green’s function (LMGF) technique - for PBG modeling. The LMGF technique is based on the classical exact Sommerfeld formulation. A version of the SIE method implementing special polynomial/exponential higher order entire-domain basis functions for equivalent surface electric and magnetic currents over cylindrical perforations and/or inclusions in photonic crystals is also developed. We have as well developed an alternative approach with PBG cylinders modeled using the volume integral equation (VIE) formulation in the context of MoM, with each cylinder modeled by a single curved volume element. We have developed a novel higher order domain decomposition (DD) method for 3-D electromagnetic analysis of finite periodic structures, such as phontonic crystal materials and devices. This algorithm allows splitting of the original, large, problem into a number of smaller ones (subdomains), which can be analyzed independently, and then stitched together by integral boundary conditions, yet yielding in the process a rigorous solution of Maxwell’s equations for the problem. When compared to the existing DD techniques, it provides the benefits of the higher order modeling; when compared to the higher order MoM-SIE and FEM-MoM techniques, on the other hand, it brings about the common DD advantages. We have developed a novel higher order large-domain FEM and hybrid FEM-MoM techniques for 3-D modeling of electromagnetic and optical structures involving general anisotropic inhomogeneous materials, which is especially important in modeling, analysis, and design of metamaterials. The technique implements large (a couple of wavelengths across) Lagrange-type generalized curved parametric hexahedral finite elements of arbitrary geometrical-mapping orders, filled with anisotropic inhomogeneous materials with continuous spatial variations of complex relative permittivity and permeability tensors described by Lagrange interpolation polynomials of arbitrary material-representation orders, and curl-conforming hierarchical polynomial vector basis functions of arbitrary field-expansion orders for the approximation of the electric field vector within the elements. We have developed a novel highly efficient and versatile computational electromagnetic technique for full-wave rigorous numerical modeling of 3-D transformation-based metamaterial cloaking structures, and have demonstrated it in analysis of spherical invisibility cloaks. We have developed general guidelines and quantitative recipes for adoptions of optimal higher order parameters for MoM and FEM modeling based on an exhaustive series of numerical experiments and comprehensive case studies on higher order hierarchical models of metallic and dielectric scatterers. The goal is to reduce dilemmas and uncertainties associated with the great modeling flexibility of higher order elements and basis and testing functions, to ease and facilitate their use by both MoM/FEM developers and practitioners, and to reduce the gap between the rising academic interest in higher order methods, which evidently show great numerical potential, and their actual usefulness and use in electromagnetics research and engineering applications. The new higher order PBG and metamaterial modeling methodologies and tools and the associated new knowledge will also be a good foundation for further research, development, and code optimization for applications associated with accurate and efficient EM modeling of other classes of optical devices, as well as analysis of antenna arrays and characterization of microwave and millimeter-wave circuits and devices, including mixed-signal and multiphysics modeling. All these applications are at the forefront of research in electrical engineering and communication systems. This research may also be viewed as one of the attempts of pushing the frontiers of conventional computational electromagnetics toward nanoscale, optical, and quantum photonics applications and promoting its tools as an enabling resource for further breakthroughs in these emerging interdisciplinary areas of science and engineering. This project has directly provided research training and development of five graduate students (four Ph.D. students and an M.S. student) fully supported by this grant (during different time periods within the project), as well as two partially supported visiting postdoctoral scholars and two REU undergraduate students. It has also furthered the education of students in advanced level graduate electromagnetics courses taught by the PI. All five graduate students supported by this grant belong to underrepresented groups of students (four female students and a Hispanic student).
