Numerical Modeling of Omnidirectional Reflectivity

We will provide convenient and accurate time-domain modeling capabilities for electromagnetics (EM) in dielectric media with regions having oblique boundary conditions, specifically for devices exhibiting omnidirectional reflectivity. Omnidirectional reflectors, constructed with layers of dielectrics, reflect electromagnetic radiation with 100% efficiency for all incident angles and polarizations. The Phase I effort analyzed this system in both the time domain and the frequency domain. To provide time-domain modeling capabilities, we extended the VORPAL EM modeling code to include dielectrics and to allow nonplanar boundaries, and we used this capability to model photonic band gap systems. We further identified the algorithm to be used to obtain oblique boundary conditions accurate to second order in the grid size. In the frequency domain, Chiping Chen of MIT, our Phase I partner, advanced their PBGSS code for obtaining band gaps for dielectric crystals. In Phase II, we propose to implement higher-order boundary conditions, to model active media, and to provide a graphical user interface. In Phase II we will additionally work with Prof. Hesthaven of Brown University and Dan Barnes of the University of Colorado to develop and implement higher-order EM solvers. This part of the work may have applications for particle-in-cell methods.