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

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

2007-08-07

arxiv.org/abs/0708.1031v1

Physics

Optics

10 pages

Scientific paper

10.1103/PhysRevE.77.036611

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.

Affiliated with

Also associated with

No associations

Rating

Perturbation theory for anisotropic dielectric interfaces, and application to sub-pixel smoothing of discretized numerical methods does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Perturbation theory for anisotropic dielectric interfaces, and application to sub-pixel smoothing of discretized numerical methods, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Perturbation theory for anisotropic dielectric interfaces, and application to sub-pixel smoothing of discretized numerical methods will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-215337