## Abstract

The problem of scattering of electromagnetic waves by a thin dielectric planar structure is considered. If the squared index of refraction of the scatterer scales as 1/h, where h is the thickness of the structure, we show that an approximate solution to the scattering problem can be obtained by a perturbation method. The approximate solution consists of two terms, the zeroth order term and the first order corrector, both of which can be found by solving 2-D integral equations for 3-D problems. We provide error estimates for the approximation. Therefore, the method described in this work can be viewed as a computational approach which can potentially greatly simplify scattering calculations for problems involving thin scatterers.

Original language | English (US) |
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Pages (from-to) | 1329-1342 |

Number of pages | 14 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 38 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2006 |

## Keywords

- Approximate solution
- Asymptotics
- Electromagnetic scattering
- Error estimates
- Maxwell's equations