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arXiv · 2501.07229

Limiting absorption principle of Helmholtz equation with sign changing coefficients under periodic structure

Wenjing Zhang·Yu Chen·Yixian Gao
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Abstract

Negative refractive index materials have attracted significant research attention due to their unique electromagnetic response characteristics. In this paper, we employ the complementing boundary condition to establish rigorous a priori estimates for the Helmholtz equation, from which the limiting absorption principle is analytically derived. Within this mathematical framework, we conclusively establish the well-posedness of the electromagnetic transmission problem at the interface between conventional materials and negative refractive index materials in two-dimensional periodic structures.

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Wenjing Zhang, Yu Chen, Yixian Gao. 2025-01-13. Limiting absorption principle of Helmholtz equation with sign changing coefficients under periodic structure. https://arxiv.org/abs/2501.07229

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