Perturbation theory for anisotropic dielectric interfaces, and application to sub-pixel smoothing of discretized numerical methods

We derive a correct first-order perturbation theory in electromagnetism for cases where an interface between two anisotropic dielectric materials is slightly shifted. Most previous perturbative methods give incorrect results for this case, even to lowest order, because of the complicated discontinuous boundary conditions on the electric field at such an interface. Our final expression is simply a surface integral, over the material interface, of the continuous field components from the unperturbed structure. The derivation is based on a "localized" coordinate-transformation technique, which avoids both the problem of field discontinuities and the challenge of constructing an explicit coordinate transformation by taking a limit in which a coordinate perturbation is infinitesimally localized around the boundary. Not only is our result potentially useful in evaluating boundary perturbations, e.g. from fabrication imperfections, in highly anisotropic media such as many metamaterials, but it also has a direct application in numerical electromagnetism. In particular, we show how it leads to a sub-pixel smoothing scheme to ameliorate staircasing effects in discretized simulations of anisotropic media, in such a way as to greatly reduce the numerical errors compared to other proposed smoothing schemes.Comment: 10 page

Balancing accuracy against computation time: 3–D FDTD for nanophotonics device optimization

The finite–difference time–domain (FDTD) approach is now widely used to simulate the expected performance of photonic crystal, plasmonic, and other nanophotonic devices. Unfortunately, given the computational demands of full 3–D simulations, researchers can seldom bring this modeling tool to bear on more than a few isolated design points. Thus 3-D FDTD—as it stands now—is merely a verification rather than a design optimization tool. Over the long term, continuing improvements in available computing power can be expected to bring structures of current interest within general reach. In the meantime, however, many researchers appear to be exploring alternative modeling techniques, trading off flexibility of approach in return for more rapid turnaround on the devices of specific interest to them. In contrast, we are trying to improve the efficiency of 3–D FDTD by reducing its computational expense without sacrificing accuracy. We believe that these two approaches are completely complementary — even with vast amounts of computational power, any real–world system will still require a modular approach to modeling, spanning from the nanometer to the millimeter scale or beyond

Meep: A flexible free-software package for electromagnetic simulations by the FDTD method

This paper describes Meep, a popular free implementation of the finite-difference time-domain (FDTD) method for simulating electromagnetism. In particular, we focus on aspects of implementing a full-featured FDTD package that go beyond standard textbook descriptions of the algorithm, or ways in which Meep differs from typical FDTD implementations. These include pervasive interpolation and accurate modeling of subpixel features, advanced signal processing, support for nonlinear materials via Pad´e approximants, and flexible scripting capabilities.National Science Foundation (U.S.) (Grant No. DMR-9400334)National Science Foundation (U.S.) (Grant No. DMR- 0819762)United States. Army Research Office. Institute for Soldier Nanotechnologies (Contract No. DAAD- 19-02-D0002)United States. Office of Naval Research (Award N00014-05-1-0700