Split-ring resonator

A split-ring resonator. Notice the current, denoted by the small letter "i", is in the clockwise direction.

Split ring resonators (SRRs) consist of a pair of concentric metallic rings, etched on a dielectric substrate, with slits etched on opposite sides. SRRs can produce an effect of being electrically smaller when responding to an oscillating electromagnetic field. These resonators have been used for the synthesis of left-handed and negative refractive index media, where the necessary value of the negative effective permeability is due to the presence of the SRRs. When an array of electrically small SRRs is excited by means of a time varying magnetic field, the structure behaves as an effective medium with negative effective permeability in a narrow band above SRR resonance. SRRs have also been coupled to planar transmission lines, for the synthesis of metamaterials transmission line .[7] [8] [9] [10]

The split ring resonator was a microstructure design featured in the paper by Pendry et al in 1999 called, "Magnetism from Conductors and Enhanced Nonlinear Phenomena".[11] It proposed that the split ring resonator design, built out of nonmagnetic material, could enhance the magnetic activity unseen in natural materials. In the simple microstructure design, it is shown that in an array of conducting cylinders, with an applied external ${\displaystyle H_{0}}$ field parallel to the cylinders, the effective permeability can be written as the following. (This model is very limited and the effective permeability cannot be less than zero or greater than one.)[8]

${\displaystyle \mu _{eff}=1-{\frac {\pi r^{2}}{a^{2}}}\ \left(1+i{\frac {2\sigma }{\omega r\mu _{0}}}\ \right)^{-1}}$

Where ${\displaystyle \sigma }$ is the resistance of the cylinder surface per unit area, a is the spacing of the cylinders, ${\displaystyle \omega }$ is the angular frequency, ${\displaystyle \mu _{0}}$ is the permeability of free space and r is the radius. Moreover, when gaps are introduced to a double cylinder design similar to the image above, we see that the gaps produce a capacitance. This capacitor and inductor microstructure design introduces a resonance that amplifies the magnetic effect. The new form of the effective permeability resembles a familiar response[12] known in plasmonic materials.

${\displaystyle \mu _{eff}=1-{\frac {{\frac {\pi r^{2}}{a^{2}}}\ }{1+{\frac {2\sigma i}{\omega r\mu _{0}}}\ -{\frac {3dc_{0}^{2}}{\pi ^{2}\omega ^{2}r^{3}}}\ }}\ }$

Where d is the spacing of the concentric conducting sheets. The final design replaces the double concentric cylinders with a pair of flat concentric c-shaped sheets, placed on each side of a unit cell. The unit cells are stacked on top of each other by a length, l. The final result of the effective permeability can be seen below.

${\displaystyle \mu _{eff}=1-{\frac {{\frac {\pi r^{2}}{a^{2}}}\ }{1+{\frac {2l\sigma _{1}i}{\omega r\mu _{0}}}\ -{\frac {3lc_{0}^{2}}{\pi \omega ^{2}r^{3}ln({\frac {2c}{d}}\ )}}\ }}\ }$

where c is the thickness of the c-shaped sheet and ${\displaystyle \sigma }$ is the resistance of unit length of the sheets measured around the circumference.[8]

The split ring resonator and the metamaterial itself are composite materials. Each SRR has an individual tailored response to the electromagnetic field. However, the periodic construction of many SRR cells is such that the electromagnetic wave interacts as if these were homogeneous materials. This is similar to how light actually interacts with everyday materials; materials such as glass or lenses are made of atoms, an averaging or macroscopic effect is produced.

The SRR is designed to mimic the magnetic response of atoms, only on a much larger scale. Also, as part of periodic composite structure these are designed to have a stronger magnetic coupling than is found in nature. The larger scale allows for more control over the magnetic response, while each unit is smaller than the radiated electromagnetic wave.

SRRs are much more active than ferromagnetic materials found in nature. The pronounced magnetic response in such lightweight materials demonstrates an advantage over heavier, naturally occurring materials. Each unit can be designed to have its own magnetic response. The response can be enhanced or lessened as desired. In addition, the overall effect reduces power requirements.[4][13]

There are a variety of split-ring resonators and periodic structures: rod-split-rings, nested split-rings, single split rings, deformed split-rings, spiral split-rings, and extended S-structures. The variations of split ring resonators have achieved different results, including smaller and higher frequency structures. The research which involves some of these types are discussed throughout the article.[14]

To date (December 2009) the capability for desired results in the visible spectrum has not been achieved. However, in 2005 it was noted that, physically, a nested circular split-ring resonator must have an inner radius of 30 to 40 nanometers for success in the mid-range of the visible spectrum.[14] Microfabrication and nanofabrication techniques may utilize direct laser beam writing or electron beam lithography depending on the desired resolution.[14]

A split-ring resonator array is configured as a material that produces negative index of refraction. It was constructed of copper split-ring resonators and wires mounted on interlocking sheets of fiberglass circuit board. The total array consists of 3 by 20×20 unit cells with overall dimensions of 10×100×100 mm.[1][15]

Split-ring resonators (SRR) are one of the most common elements used to fabricate metamaterials.[16] Split-ring resonators are non-magnetic materials, which initially were fabricated from circuit board material to create metamaterials.[17]

Looking at the image directly to the right, it can be seen that at first a single SRR looks like an object with two square perimeters, with each perimeter having a small section removed. This results in square "C" shapes on fiberglass printed circuit board material.[16][17] In this type of configuration it is actually two concentric bands of non-magnetic conductor material.[16] There is one gap in each band placed 180° relative to each other.[16] The gap in each band gives it the distinctive "C" shape, rather than a totally circular or square shape.[16][17] Then multiple cells of this double band configuration are fabricated onto circuit board material by an etching technique and lined with copper wire strip arrays.[17] After processing, the boards are cut and assembled into an interlocking unit.[17] It is constructed into a periodic array with a large number of SRRs.[17]

There are now a number of different configurations that use the SRR nomenclature.

On May 1, 2000 conducting wires were placed symmetrically within each cell of a periodic split-ring resonator array which achieved negative propagation of electromagnetic waves in the microwave region. The concept was and still is used to build interacting elements smaller than the applied electromagnetic radiation. In addition, the spacing between, referred to as the lattice constant, is also smaller than the applied radiation.

Additionally, the splits in the ring allow the SRR unit to achieve resonance at wavelengths much larger than the diameter of the ring. The unit is designed to generate a large capacitance, lower the resonant frequency, and concentrate the electric field. Combining units creates a design as a periodic medium. Furthermore, the multiple unit structure has strong magnetic coupling with low radiative losses.[29] Research has also covered variations in magnetic resonances for different SRR configurations.[30][31][32] Research has continued into terahertz radiations with SRRs[33] Other related work fashioned metamaterial configurations with fractals[24] and non-SRR structures. These can be constructed with materials such as periodic metallic crosses, or an ever-widening concentric ring structures known as Swiss rolls.[34][35][36][37] Permeability for only the red wavelength at 780 nm has been analyzed and along with other related work.[38][39][40]

• Ates, Damla; Cakmak, Atilla Ozgur; Colak, Evrim; Zhao, Rongkuo; Soukoulis, C. M.; Ozbay, Ekmel (2010). "Transmission enhancement through deep subwavelength apertures using connected split ring resonators" (Free PDF download). Optics Express. 18 (4): 3952–66. Bibcode:2010OExpr..18.3952A. doi:10.1364/OE.18.003952. hdl:11693/13284. PMID 20389408.
• Shepard, K. W. et al. Split-ring resonator for the Argonne Superconducting Heavy Ion Booster. IEEE Transactions on Nuclear Science, VoL. NS-24, N0.3, JUN 1977.

Look up metamaterials in Wiktionary, the free dictionary.

Look up split-ring resonator in Wiktionary, the free dictionary.

Wikimedia Commons has media related to Metamaterials.

Wikimedia Commons has media related to metamaterials.

• Video: John Pendry lecture: The science of invisibility April 2009, SlowTV
• Split Ring Resonator Calculator: Online tool to calculate the LC equivalent circuit and resonant frequency of SRR and CSRR topologies.