1. Electromagnetic interactions in a pair of coupled split ring resonators S. Seetharaman, I. R. Hooper, W. L. Barnes Department of Physics & Astronomy, University of Exeter, Stocker Road, Exeter, United Kingdom, EX4 4QL ss693@exeter.ac.uk ex.ac.uk/SSeetharaman www.exeter.ac.uk/metamaterials Abstract: We study experimentally the strength and nature of the coupling between two identical metallic split ring resonators (SRRs) operating at microwave frequencies. We show that two SRRs in close proximity exhibit a rich coupling that involves both electric and magnetic interactions and that depending on their relative orientation, the couplings can either reinforce each other or act in competition. Introduction: Split Ring Resonators are a fundamental building block of many electromagnetic metamaterials [1, 2]. In the current study, we aim to understand the nature of the competition between the electric and magnetic field interactions in pairs of split-ring resonators. A single SRR can be excited by either the electric or magnetic field component of an incident electromagnetic field. The electric field component incident on the ring as shown in figure 1 (a) causes opposite charges to accumulate on the inner surface of the ring on either side of split. The potential difference created by opposite charges induces an oscillating electric current in the ring, which gives rise to a magnetic moment normal to the plane of the ring. When two SRRs are close enough to couple, the coupled resonant modes are influenced by the relative orientations of the electric and magnetic dipole moments of the coupled system. Experiment – Setup and Method: References [1] Pendry J. et al., Magnetism from Conductors, and Enhanced Non-Linear Phenomena, IEEE Transactions on Microwave Theory and Techniques, 47, 11 (1999). [2] Solymar L., Shamonina E., Waves in Metamaterials, Oxford University Press. [3] Powell D. A. et al. Near-field interaction of twisted split-ring resonators, Phys. Rev. B 83, 235420 (2011). (a) Fig 1 (a) Schematic of a split-ring resonator excited by the electric field component of incident field. The red and blue arrows represent the direction of induced electric and magnetic dipole moments in the ring respectively while the circular red arrow represents the direction of the oscillating circular current in the ring, all at one instant in the phase of the alternating EM field, (b) A SRR placed next to a penny for scale. The designed SRRs have an outer ring radius of 3.5 mm, ring width 0.37 mm, with the gap of the split being 1 mm. (b) Fig 2 (a) Experimental setup where the Vector Network Analyzer (VNA) is used to excite the fundamental mode of the waveguide and record both reflected and transmitted field amplitudes, (b) Top view of two SRR samples inside the customized rectangular waveguide that permits easy control of relative orientation and separation distances between them. SRR samples are designed to operate at a resonant frequency of 5.8 GHz and fabricated on PCB substrate by laser writing, followed by wet etching. For ease of experimentation, a pair of the fabricated SRRs are placed in a rectangular waveguide operating in the frequency range of 4.5 GHz to 8 GHz. The resonant response of the coupled SRRs is analysed by exciting the fundamental TE10 mode of the waveguide and recording the reflected and transmitted power. The response is recorded for three relative rotation angles 0 o, 90 o, and 180 o (refer to insets of figure 3) for increasing distances of separation. Absorption of power in the coupled modes in each of the three cases is calculated from the recorded transmitted and reflected power (presented in figure 3). Results and Discussion: (a)(b) (a)(c) Fig 3 Experimentally measured absorption for coupled pairs of SRRs, plotted on a logarithmic scale, with relative rotation angles of (a) 0 o, (b) 90 o and (c) 180 o for increasing distances of separation. (Insets) Orientation of the coupled SRRs with respect to each other and with respect to the incident electromagnetic field. The red arrows represent the transversely coupled electric dipole moments and the blue arrows represent the longitudinally coupled magnetic dipole moments. Anti-symmetric mode ( ω - in inset) is highly absorptive. Absorption in the symmetric mode ( ω + in inset) is weak due to strong scattering. Crossing between symmetric and anti-symmetric modes suggests competition between the electric and magnetic field interactions with increase in separation. Crossing of modes for increasing rotation angles at fixed separation has been previously observed [3]. Only magnetic interactions matter between the split- ring resonators as the excited electric dipole moments in the rings correspond to different resonant modes. Both coupled modes are strongly absorptive at lower separations. Higher energy mode fades slowly at higher separations suggesting the weakening of coupling. Wide separation between the symmetric and anti-symmetric mode frequencies at lower separations suggests that the electric and magnetic interactions are working with each other. This is possible due to the positioning of splits on opposite sides to each other. Without conflict between interactions, no crossing behaviour is observed. Relative rotation angle - 0 o Relative rotation angle - 90 o Relative rotation angle - 180 o ω-ω- ω+ω+ ω-ω- ω+ω+ ω-ω- ω+ω+