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Perturbation theory for Maxwell’s equations with shifting material boundaries
Abstract
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 discontinuous 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.
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Jackson, J. D., & Fox, R. F. (1999) · American Journal of Physics · doi:10.1119/1.19136 · Cited by 3,073
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Metadata
- Authors
- Johnson, S. G., Ibanescu, M., Skorobogatiy, M. A., Weisberg, O., Joannopoulos, J. D., & Fink, Y.
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2002-06-20
- Volume
- 65
- Issue
- 6
- Pages
- 066611-066611
- ISSN
- 1063-651X (ISSN-L)
- 1095-3787
- OpenAlex
- W1986349933
- Cited by
- 483
- References
- 1
- FWCI
- 7.61
- Type
- journal article
- Language
- en
- Open access
- closed
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- Johnson, S. G., Ibanescu, M., Skorobogatiy, M. A., Weisberg, O., Joannopoulos, J. D., & Fink, Y. (2002). Perturbation theory for Maxwell’s equations with shifting material boundaries. Physical Review E. https://doi.org/10.1103/physreve.65.066611
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