Bernhard Maier (Karlsruhe Institute of Technology), Marlis Hochbruck, Marvin Müller, Carsten Rockstuhl

We study the interaction of electromagnetic waves with rf-SQUIDs aligned on a thin film [1]. This yields a system of Maxwell’s equations coupled with an anharmonic oscillator via a jump condition for the normal derivative at the interface. Since our main interest is the calculation of the reflection and transmission coefficients of the film, we introduce transparent boundary conditions [2], which drastically reduce the computational effort. In fact, the spatial resolution of our numerical examples does not affect the computational cost.

In this talk, we show well-posedness using [3] for a first order reformulation of this system. We further discuss the discretization with finite elements in space and the Crank-Nicolson method in time and prove convergence results. Finally, we confirm these results presenting numerical examples.

References

[1] J.-G. Caputo, I. Gabitov and A. I. Maimistov, Polarization rotation by an rf-squid metasurface, Phys. Rev. B (2015)

[2] M. J. Grote and I. Sim, On local nonreflecting boundary conditions for time dependent wave propagation, Chinese Annals of Mathematics, Series B (2009)

[3] J. Leibold, Semilineare Wellengleichungen mit dynamischen Randbedingungen, Master’s thesis, Karlsruhe Institute of Technology (2017)