Retrieval of coupling coefficients for dense metamaterials

Broadband Artificial Magnetic Conductors Constructed of Magnetically Coupled Elements

“…Thus for the self-impedance we obtain: (8) where f0 is the resonance frequency of an individual helix, Q its quality factor and L= μ0SN 2 /lhel its self inductance, For the mutual-impedance: (9) where κEa,b and κHa,b are the electric and magnetic couplings between helices (n,m) and (n+a,m+b) respectively, κEgr and κHgr are the electric and magnetic couplings to the ground plane. More information on coupling coefficients can be found in [22] and the way to obtain the coupling values from numerical or experimental data is described in [23]. Now, substituting (6), ( 8) and ( 9) into (7) we obtain the equation for the current in each helix: (10) The magnetic moment of each element is: (11) where Vhel is the intrinsic volume of the helix.…”

Near-field electromagnetic coupling between helices

“…To retrieve the values of both magnetic and electric coupling coefficients separately from measurement or simulation data, a coupling retrieval method has been proposed by one of the current authors in a previous work [23] and then improved upon for the dense metamaterial case in [24]. The retrieval procedure is based on the analysis of equation ( 5).…”

“…This can be implemented both in experiment and in COMSOL modelling which will be discussed in the following section. However for the closely packed structure studied in [24], the voltage induced in the receiver will capture the superposition of the fields produced by the current of the primary element and, to a smaller extent, by the neighbouring element as well, as illustrated in figure 3(a). Moreover the influence of the second element may be different for the data measured next to elements 1 and 2 due to the possible asymmetry of their geometry.…”