Asymptotics for metamaterial cavities and their effect on scattering
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It is well-known that optical cavities can exhibit localized phenomena responsible for numerical instabilities in approximating scattering problems. In classic optical cavities, those localized phenomena concentrate at the inner boundary of the cavity and are called whispering gallery modes. In this paper we consider cavities made of Negative-Index Metamaterials (NIM). Those manufactured materials can exhibit unusual optical properties, leading to the appearance of exotic waves at the interface of metamaterial-dielectric interface, such as surface plasmons. There is a great interest in controlling and guiding surface plasmons to design the next-generation of nano-antennas, sensors, and others. Surface plasmons have been usually characterized in the context of the specific quasi-static case. Using asymptotic analysis, we provide a systematic mathematical characterization of emerging surface plasmons for general metamaterial cavities for the full wave problem, and answer the following questions: can surface plasmons be always excited in scattering problems? Can they create numerical instabilities? Our asymptotic analysis reveals that the nature of surface plasmons changes depending on the metamaterial's properties, leading to different effects on scattering problems. Numerical results for several metamaterial cavities are provided.
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