CEE Seminar: Time-Domain Simulation of Dispersive Maxwell's Equations with Application to Optical Metamaterial Design
September 16, 2019 - 12:00pm to 1:00pm
Jeffrey Banks, Professor, Rennselaer Polytechnic Institute, Dept. of Mathematical Sciences
Recent advances in manufacturing at the micro-scale has made possible the creation of composite materials that exhibit electromagnetic properties unattainable in nature, such as materials with a negative index of refraction. These new engineered metamaterials have the potential to revolutionize the field of optical design leading to smaller and lighter-weight devices that use less power, are multi-functional and tunable, and that cost less than devices based on conventional optics and materials. The overall research program in optical metamaterials is vast, and encompasses myriad disciplines. In the present talk I will focus on one critical aspect; specifically time-domain simulation of dispersive optical materials. Our approach is based on the second-order formulation of Maxwell's equations, and uses auxiliary differential equations to evolve the wave polarization vectors for a generalized dispersion material model, with material parameters determined to fit the frequency domain material response. The numerical scheme is built around an efficient 3-level time stepping algorithm, and both second- and fourth-order accurate schemes are presented. Overlapping grids are used to address geometric complexity, and a novel form of stabilizing upwind dissipation is added to the equations. The efficacy of the overall approach is demonstrated on a series of electromagnetic wave propagation problems including scattering from perfect conductors as well as scattering from dielectric...
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