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Perturbation theory for Maxwell's equations with shifting material boundaries
Steven G Johnson1, M Ibanescu, M A Skorobogatiy
1OmniGuide Communications, One Kendall Square, Building 100, No. 3, Cambridge, MA 02139, USA.
Summary
This study introduces a novel perturbation theory for electromagnetism, overcoming challenges with dielectric interfaces. It enables accurate analysis of weak interactions and system imperfections.
Area of Science:
- Electromagnetism
- Mathematical Physics
Background:
- Perturbation theory analyzes small changes in known solutions, crucial for electromagnetism.
- Standard methods struggle with dielectric interfaces in Maxwell's equations, especially in 3D high-index-contrast systems, due to discontinuous boundary conditions.
Purpose of the Study:
- To develop a correct first-order perturbation theory for electromagnetic systems with small shifts in dielectric interfaces.
- To derive mode-coupling constants for such systems.
Main Methods:
- Treating sharp boundaries as a limit of anisotropically smoothed systems.
- Deriving a new perturbation theory involving surface integrals of unperturbed fields.
Main Results:
- A correct first-order perturbation theory is derived for electromagnetic systems with dielectric interface shifts.
- Mode-coupling constants are obtained using only surface integrals of unperturbed fields.
Conclusions:
- The new method accurately predicts behavior, overcoming limitations of standard techniques.
- Further considerations for higher-order perturbation methods in electromagnetism are discussed.