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Analytical and numerical analysis of linear and nonlinear properties of an rf-SQUID based metasurface

Müller, Marvin M. ORCID iD icon; Maier, Bernhard; Rockstuhl, Carsten; Hochbruck, Marlis


We derive a model to describe the interaction of an rf-SQUID (radio frequency Superconducting QUantum Interference Device) based metasurface with free space electromagnetic waves. The electromagnetic fields are described on the base of Maxwell’s equations. For the rf-SQUID metasurface we rely on an equivalent circuit model. After a detailed derivation, we show that the problem that is described by a system of coupled differential equations is wellposed and, therefore, has a unique solution. In the small amplitude limit, we provide analytical expressions for reflection, transmission, and absorption depending on the frequency. To investigate the nonlinear regime, we numerically solve the system of coupled differential equations using a finite element scheme with transparent boundary conditions and the Crank-Nicolson method. We also provide a rigorous error analysis that shows convergence of the scheme at the expected rates. The simulation results for the adiabatic increase of either the field’s amplitude or its frequency show that the metasurface’s response in the nonlinear interaction regime exhibits bistable behavior both in transmission and reflection.

Volltext §
DOI: 10.5445/IR/1000088565
Veröffentlicht am 17.12.2018
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Institut für Nanotechnologie (INT)
Institut für Theoretische Festkörperphysik (TFP)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2018
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000088565
HGF-Programm 43.23.01 (POF III, LK 01) Advanced Optical Lithography+Microscopy
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 13 S.
Serie CRC1173 ; 2018/47
Projektinformation SFB 1173/1 (DFG, DFG KOORD, SFB 1173/1 2015)
Schlagwörter SQUIDs, photonic structures, metamaterials, electromagnetic wave propagation, transparent boundary conditions, time integration
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