Perturbation theory for Maxwell's equations with shifting material boundaries

被引：368

作者：

Johnson, Steven G. ^{[1
]}

Ibanescu, M. ^{[1
]}

Skorobogatiy, M.A. ^{[1
]}

Weisberg, O. ^{[1
]}

Joannopoulos, J.D. ^{[1
]}

Fink, Y. ^{[1
]}

机构：

[1] OmniGuide Communications, Building 100, No. 3, One Kendall Square, Cambridge, MA 02139

来源：

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | 2002年 / 65卷 / 06期

关键词：

Approximation theory - Boundary conditions - Eigenvalues and eigenfunctions - Electromagnetism - Green's function - Integral equations - Maxwell equations - Permittivity;

D O I：

10.1103/PhysRevE.65.066611

中图分类号：

学科分类号：

摘要：

Perturbation theory permits the analytic study of small changes on known solutions, and is especially useful in electromagnetism for understanding weak interactions and imperfections. Standard perturbation-theory techniques, however, have difficulties when applied to Maxwell's equations for small shifts in dielectric interfaces (especially in high-index-contrast, three-dimensional systems) due to the discontinous field boundary conditions - in fact, the usual methods fail even to predict the lowest-order behavior. By considering a sharp boundary as a limit of anisotropically smoothed systems, we are able to derive a correct first-order perturbation theory and mode-coupling constants, involving only surface integrals of the unperturbed fields over the perturbed interface. In addition, we discuss further considerations that arise for higher-order perturbative methods in electromagnetism. ©2002 The American Physical Society.

引用

页码：1 / 066611