A simple approximate expression is derived for the resonant frequency of a singly split single ring that is among the first microwave resonators designed to be small relative to the wavelength. In addition to the usual gap capacitance the concept of surface capacitance is introduced. The surface capacitance is determined analytically by two different methods, first using analytical expressions for the electric field of a split cylinder, and second by using conformal mapping. Taking two practical examples the resonant frequency, found analytically, is shown to agree with that obtained by numerical simulations. The model could be used for studies of the resonant properties of split rings in the terahertz region.

PACS 07.05. Tp, 81.05.Zx We study experimentally and theoretically coupling mechanisms between metamaterial elements of the split ring resonator (SRR) type. We show that, depending on the orientation of the elements relative to each other, the coupling may be either of magnetic or electric type or a combination of both. Experimental results on SRRs with resonances around 1.7 -1.9 GHz agree quantitatively with results of simulations (CST Microwave Studio). Further simulations provide analysis for a variety of SRRs both in the GHz and in the 20 THz frequency regions. The variety of coupling mechanisms can be employed in designing near field manipulating devices based on propagation of slow waves.

Electrowetting based infrared lens using ionic liquids Appl. Phys. Lett. 99, 213505 (2011) Modulation of negative index metamaterials in the near-IR range Appl. Phys. Lett. 91, 173105 (2007) Mixed metal films with switchable optical properties Appl. Phys. Lett. 80, 1349Lett. 80, (2002 Population dynamics of the threemicron emitting level of Er3+ in YAlO3 J. Appl. Phys. 80, 6610 (1996) Experimental characterization of reactive ion etched germanium diffraction gratings at 10.6 μm Appl. Phys. Lett. 69, 3453 (1996) Additional information on J. Appl. Phys. The coupling between arbitrarily positioned and oriented split ring resonators is investigated up to THz frequencies. Two different analytical approaches are used, one based on circuits and the other on field quantities that includes retardation. These are supplemented by numerical simulations and experiments in the GHz range, and by simulations in the THz range. The field approach makes it possible to determine separately the electric and magnetic coupling coefficients which, depending on orientation, may reinforce or may cancel each other. Maps of coupling are produced for arbitrary orientations of two co-planar split rings resonant at around 2 GHz and then with the geometry scaled down to be resonant at around 100 THz. We prove that the inertia of electrons at high frequencies results in a dramatic change in the maps of coupling, due to reduction of the magnetic contribution. Our approach could facilitate the design of metamaterials in a wide frequency range up to the saturation of the resonant frequency. V C 2012 American Institute of Physics.

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Metamaterials acquire their functionality from the structuring of the small building blocks, "artificial atoms". Our paper provides a study of the resonant behaviour for a variety of metallic nanoparticles in the region of hundreds of THz. Resonant modes for nanorods of rectangular cross section are investigated numerically for different types of excitation and the set of resonant frequencies (fundamental and higher order) are determined for rods of various length. From that the dispersion relationship for surface plasmon-polaritons propagating along the rod is deduced. We analyse resonant-mode near-field distribution of the electric field, including the field lines, to emphasise the underlying physics. Resonant frequencies are also found and field distributions analysed when the rods are combined to form particles of L, U and O shapes. The similarities and differences between those particles, both in the values and in the number of resonances, are discussed. The results of this study may aid the design of nanostructured metamaterials with required properties in the IR and optical domain.