Properties of a metamaterial element: Analytical solutions and numerical simulations for a singly split double ring

Abstract

An equivalent circuit, consisting of bulk and distributed elements, is derived for describing the properties of a potential metamaterial element capable of providing negative effective permeability. It is the singly split double ring (SSDR), a special case of the split ring resonator (J. B. Pendry et al., IEEE Trans. Microwave Theory Tech. 47, 2075 (1999)), obtained when the gap capacitance in the inner ring is infinitely large. The variables are the inter-ring voltage and the currents flowing in the inner and outer rings. The excitation is assumed in the form of a spatially constant temporally varying magnetic field. The functions, showing the angular variation of the variables, are found by solving a set of differential equations with boundary conditions imposed at the position of the split. It is shown from the analytical solution that the SSDR can have resonant frequencies in the full spectrum from very low to very high frequencies. It is pointed out in particular that whenever the mean diameter of the ring is equal to an odd multiple of the half wavelength it is always possible to find a set of parameters which will give rise to resonance. As examples the resonant frequencies are determined for eight sets of parameters. Results are also derived by replacing the distributed circuit with a number of discrete circuits. It is finally shown that the results obtained from the equivalent circuit model are in excellent agreement with those derived from the MICRO-STRIPES numerical package which solves Maxwell’s equations in the time domain.

Transmission Properties of Stacked SRR Metasurfaces in Free Space

“…The SRRs metasurfaces displayed in Figure 1(a) were fabricated with a total size of 200 mm × 200 mm (25 × 25 elements), see Figure 1(b). The free space transmission measurements were performed using an Agilent 8722ES vector network analyzer and different microwave standard horn antennas to cover the frequency bandwidth (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20). The distance between horn antennas is maintained at 500 mm.…”

“…To our knowledge study of the high order resonances interactions is very limited in the literature [14][15][16]. With the present work, we aim to bridge this gap with a detailed study of the transmission properties across stacked SRRs (axial configuration) metasurfaces putting particular emphasis on the interaction between adjacent SRRs metasurfaces.…”

“…Owing to those landmark properties, i.e., negative permeability and subwavelength dimension, the SRR has been recently the subject of intensive research activities [2][3][4] either for designing negative refractive index medium notably with the addition of metallic wires [2], compact microwave planar circuits [3] or perfect lens [4]. Moreover, the SRR is found to support the propagation of the so-called magnetoinductive waves (MIWs) [5][6][7][8] at the quasistatic resonance when nearest-neighbor coupling is included in the analysis of arrays of SRRs. It is found that MIWs in the axial configuration are forward waves with the phase and group velocities in the same direction, that is, right-handed propagation.…”

Analytical model for double split ring resonators with arbitrary ring width

“…An accurate analytical model for the SRR's has the potential to drastically lower the design time and will make high performance microwave filters based on SRR's a practical option in many commercial applications. The model presented in [12], [13] provides a wideband analysis, but, unfortunately, doesn't take into account the presence of a ground plane in planar structures.…”

“…The coupled line sections are a compact representation of the model in [12], [13]. The coupled line sections are described in terms of even and odd mode impedance and propagation parameters, which are available for a large range of different realizations using standard microwave theory.…”