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**A mathematical framework for tunable metasurfaces. II.**
*(English)*
Zbl 1442.35443

Summary: This paper is concerned with wave propagation inside a cavity with a tunable boundary condition. It is a follow-up of [the authors, ibid. 114, No. 3–4, 129–179 (2019; Zbl 1443.35153)]. Cavities, because they trap waves for long times due to their reflecting walls, are used in a vast number of scientific domains. Indeed, in these closed media and due to interferences, the free space continuum of solutions becomes a discrete set of stationary eigenmodes. These enhanced stationary fields are commonly used in fundamental physics to increase wave-matter interactions. The eigenmodes and associated eigenfrequencies of a cavity are imposed by its geometrical properties throughthe boundary conditions. In this paper, we show the effect of a small change of boundary condition on the Green’s function of the cavity. This is achieved through the use of a tunable reflecting metasurface. The boundary condition can be switched from Dirichlet to Neumann at some specific resonant frequencies.

### MSC:

35Q61 | Maxwell equations |

74F15 | Electromagnetic effects in solid mechanics |

35J08 | Green’s functions for elliptic equations |

78A40 | Waves and radiation in optics and electromagnetic theory |

35P15 | Estimates of eigenvalues in context of PDEs |