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Split-ring resonator

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Split-ring resonator consisting of an inner square with a split on one side embedded in an outer square with a split on the other side. Split-ring resonators are on the front and right surfaces of the square grid, and single vertical wires are on the back and left surfaces.[1][2]

A split-ring resonator (SRR) is a component part of a negative index metamaterial (NIM), also known as Double Negative metamaterials (DNG). They are also component parts of other types of metamaterial such as Single Negative metamaterial (SNG). SRRs are also used for research in Terahertz metamaterials, Acoustic metamaterials, and Metamaterial antennas. SRR is a pair of concentric annular rings with splits in them at opposite ends. The rings are made of nonmagnetic metal like copper and have a small gap between them.

A magnetic flux penetrating the metal rings will induce rotating currents in the rings, which produce their own flux to enhance or oppose the incident field (depending on the SRRs resonant properties). This field pattern is dipolar. Due to splits in the rings the structure can support resonant wavelengths much larger than the diameter of the rings. This would not happen in closed rings. The small gaps between the rings produces large capacitance values which lower the resonating frequency, as the time constant is large. The dimensions of the structure are small compared to the resonant wavelength. This results in low radiative losses, and very high quality factors.

At frequencies below the resonant frequency, the real part of the magnetic permeability of the SRR becomes large (positive), and at frequencies higher than resonance it will become negative. This negative permeability can be used with the negative dielectric constant of another structure to produce negative refractive index materials.

SRR electromagnetic metamaterials

In 2005, using modern micro and nanofabrication techniques, the manufacturing of electromagnetic metamaterials with structure sizes < 100 μm and critical dimensions < 100 nm had become possible.[3]

In 1967 a paper was published that was written by Victor G. Veselago. In a straightforward manner he stated that ε (permittivity) as a dielctric constant and µ (magnetic permeability) "are the fundamental characteristic quantities which determine the propagation of electromagnetic waves in matter." Furthermore, these quantities determine the index of refraction "n". He realized, that materials with simultaneous negative values for ε and µ can exist within the laws of physics, and that these substances have some properties different from materials with positive values for ε and µ. Vesaglo described the unsusal consequences of such a left-handed substance; a refraction that is reversed, an inversion of the Doppler and Cerenkov effects, the vectors E, H, and k occur as a left handed set, a sign change of the group velocity, bi-concave and bi-convex lenses change roles, and the reversal of radiation pressure to radiation tension. In other words, dramatically different propagation characteristics. [3]

Thirty years later physcists would agree when practical structures that exhibit negative values for ε,µ, and n were fabricated and demonstrated in the year 2000. These are called electromagnetic metamaterials, and the first of these used a nested split ring resonator design and are still in use today for research. (see illustration at the beginning of this article). However, the research has gone from negative values for ε,µ, and n in the microwave - gigahertz range up to terahertz and infared frequencies.[3]

There is a variety of split-ring resonators - 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.[3]

To date (December 2009) the capability for desired results in visible spectrum has not been achieved. However, in 2005, it was noted that, physically, a nested circular split-ring resonator must have an inner radii of 30 to 40 nanometers for success in the mid-range of the visible spectrum. [3]

Micro-fabrication and nano-fabrication techniques utilize direct laser beam writing or electron beam lithography, and this depends on the desired resolution.[3]

First demonstrations with the SRR

May 2000. A composite medium, based on a periodic array of interspaced conducting nonmagnetic split ring resonators and continuous wires, that exhibits a frequency region in the microwave regime with simultaneously negative values of effective permeability and permittivity.[4]

SRR configuration

Left-handed metamaterial array configuration, which 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][5]

Split-ring resonators (SRR) are one of the most common elements used to fabricate metamaterials.[6] Split-ring resonators are non-magnetic materials, which are usually fabricated from circuit board material to create metamaterials.[7]

Often a single SRR looks like a ring with small segment removed which results in a "C" shape, on fiberglass, printed circuit board material.[6][7] In this type of configuration it is actually two concentric bands of non-magnetic conductor material.[6] There is one gap in each band placed 180° relative to each other.[6] The gap in each band gives it the distinctive "C" shape, rather than a totally circular or square shape.[6][7] Then multiple cells of this double band configuration are fabricated onto circuit board material by an etching technique and lined with copper wire strips (along the edges).[7] After processing, the boards are cut and assembled into an interlocking unit.[7] It is constructed into a periodic array with a large number of SRRs.[7]

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

A periodic array of SRRs was used for the first actual demonstration of a negative index of refraction.[7] For this demonstration, square shaped SRRs, with the lined wire configurations, were fabricated into a periodic, arrayed, cell structure.[7] This is the substance of the metamaterial.[7] Then a metamaterial prism was cut from this material.[7] The prism experiment demonstrated a negative index of refraction for the first time in the year 2000; the paper about the demonstration was submitted to the journal Science on January 8, 2001, accepted on February 22, 2001 and published on April 6, 2001.[7]

Just before this prism experiment, Pendry et al. was able to demonstrate that a three-dimensional array of intersecting thin wires could be used to create negative values of ε and that a periodic array of copper split-ring resonators could produce an effective negative μ. In 2000 Smith et al. were the first to successfully combine the two arrays and produce a LHM which had negative values of ε and μ for a band of frequencies in the GHz range.[7]

The resonance frequency is a key factor when using this periodic arrayed material.[8] At resonance the material delivers an effective magnetic permeability u of enhanced magnitude when coupled with the source electromagnetic field (and in this case the incident field).[8] The resonance frequency of the SRR depends on its intended geometrical parameters[8] derived during fabrication.

SRRs were first used to fabricate left-handed metamaterials for the microwave range,[7] and several years later for the terahertz range.[9] By 2007, experimental demonstration of this structure at microwave frequencies has been achieved by many groups.[8] In addition, SRRs have been used for research in acoustic metamaterials.[10] The arrayed SRRs and wires of the first Left-handed metamaterial were melded into alternating layers.[11] This concept and methodology was then applied to (dielectric) materials with optical resonances producing negative effective permittivity for certain frequency intervals resulting in "photonic bandgap frequencies".[10] Another analysis showed Left Handed Material to be fabricated from inhomogeneous constituents, which yet results in a macroscopically homogeneous material.[10] SRRs had been used to focus a signal from a point source, increasing the transmission distance for near field waves.[10] Furthermore, another analysis showed SRRs with a negative index of refraction capable of high-frequency magnetic response, which created an artificial magnetic device composed of non-magnetic materials (dielectric circuit board).[7][10][11]

A transmission medium composed of SRRs and wires could indeed be characterized by effective ε and µ whose real parts were both negative over a finite frequency band, as was the real part of the refractive index n. SRRs also exhibit resonant electric response in addition to their resonant magnetic response.[11] SRRs with wire elements have been constructed from repeated unit cells containing identical elements, such that the resulting medium can be considered homogeneous in the sense that the averaged electromagnetic response is averaged over the structure as a whole. A single SRR (cell) responds to electromagnetic fields in a manner analogous to a magnetic “atom,” exhibiting a resonant magnetic dipole response.[12] The original logic behind SRRs specifically, and metamaterials generally was to create a structure, which imitates an arrayed atomic structure only on a much larger scale.

Several types of SRR

In research based in metamaterials, and specifically negative refractive index, there are different types of split-ring resonators. Of the examples mentioned below most all of them have a gap in each ring. In other words, with a double ring structure, each ring has a gap.[13]

There is the 1-D Split-Ring Structure with two square rings, one inside the other. One set of cited "unit cell" dimensions would be an outer square of 2.62 mm and an inner square of 0.25 mm. 1-D structures such as this are easier to fabricate compared with constructing a rigid 2-D structure.[13]

The Symmetrical-Ring Structure is another classic example. Described by the nomenclature these are two rectangular square D type configurations, exactly the same size, laying flat, side by side, in the unit cell. Also these are not concentric. One set of cited dimensions are 2 mm on the shorter side, and 3.12 mm on the longer side. The gaps in each ring face each other, in the unit cell.[13]

The Omega Structure, as the nomenclature describes, has an Ω-shaped ring structure. There are two of these, standing vertical, side by side, instead of laying flat, in the unit cell. In 2005 these were considered to be a new type of metamaterial. One set of cited dimensions are annular parameters of R = 1.4 mm and r = 1 mm, and the straight edge is 3.33 mm.[13]

Another new metamaterial in 2005 was a coupled “S” shaped structure. There are two vertical "S" shaped structures, standing vertical, side by side, in a unit cell. There is no gap as in the ring structure, however there is a space between the top and middle parts of the S and space between the middle part and bottom part of the S. Furthermore, it still has the properties of having an electric plasma frequency and a magnetic resonant frequency.[13]

In the above section gapped "C" shaped rings have been described. There are also two of these per unit cell, one inside the other – a concentric configuration.

Such media – millimeter-scale split-ring resonators and wires, in a periodic configuration – are known as negative index metamaterials (NIMs), and first applied at microwave frequencies on the order of 10 GHz.[14] Negative values of permeability u and permittivity ε occurred via the resonant capacitive-inductive response of the split-rings and the effective plasma response of the wire lattice determined by mutual inductance.[14] Negative refraction was demonstrated throughout all angles in two dimensions by direct observation of plane wave refraction through prism-shaped samples (segments) of such assemblies.[14]

Magnetic resonances for different SRR parameters and designs

The magnetic resonance of split-ring resonators (SRR) experimentally and numerically investigated.[15][16] The dependence of the geometrical parameters on the magnetic resonance frequency of SRR is studied. Further investigation is accomplished concerning the effect of lumped capacitors integrated to the SRR on the magnetic resonance frequency for tunable SRR designs.[15] Different resonator structures are shown to exhibit magnetic resonances at various frequencies depending on the number of rings and splits used in the resonators.[15][16]

Nonlinear properties of split-ring resonators

In 2008 an overview of the non-linear capabilities of the split-ring resonators was presented. Specifically, the properties of split-ring resonators (SRRs) loaded with high-Q capacitors and nonlinear varactors are theoretically analyzed and experimentally measured. Experimental demonstration shows that the resonance frequency fm of the nonlinear SRRs can be tuned by increasing the incident power.[17]

In addition, most of the research in the properties of the SRR had been in the linear regime. However, there has been some research into non-linear capabilities. Specifically, the researchers refer to SRR nonlinear tunability studies. To tune the magnetic responses of the SRRs, extra components or materials need to be introduced into the SRRs. Therefore other research into this area is lightly discussed.[17]

The extra components employed in prior research were: ferroelectric films are added to the substrate of the SRRs, low-doped semiconductors are photodoped within the slits of the SRR, ferrite rods are introduced to ambient the SRR unit cells, and varactors in microwave applications. Furthermore, tunable metamaterials, based on the nonlinear SRRs with varactors, have been tested experimentally in both transmission line form and bulk form.[17]

Towards 3D electromagnetic metamaterials in the THz range

First results of microfabrication of nearly 3D EM3 structures for the THz range[18]

NIM configurations utilizing non-SRR structures

Nanoscale cut-wire pairs

Experimentally obtained and characterized metamaterials based on nanoscale cut-wire pairs and plate pairs. Comparison with theory and subsequent retrieval shows that both options exhibit a frequency range with negative magnetic permeability. In contrast to other reports, however, a negative refractive index is not obtained from the cut-wire pairs or plate pairs alone that we have studied so far (2005).[19]

Specialized periodic metallic crosses

A bulk metamaterial with negative refractive index in the terahertz frequency range is presented and analyzed. The structure is composed of pairs of metallic crosses embedded in benzocyclobutene (BCB). The design is specifically chosen to provide a low-loss, free-standing material which operates under normal incidence and independently of the polarization of the incident radiation. These qualities allow the fabrication of 3D structures by mechanical stacking of multiple thin films.[20]

Metamaterial Swiss roll

Swiss roll is a type of optical, electromagnetic metamaterial that has negative refractive index. It is named for its resemblance to the confectionery Swiss roll: it consists of concentric cylinders of insulated metal.[21]

A large array of swiss rolls proved to be an effective design for a metamaterial lens; near-field imaging with magnetic wires. Pendry's Swiss roll could find applications in magnetic resonance imaging.[22][21]

Nonlinear metamaterials

EM field shielding by non-linear metamaterials

It is well known that over certain frequencies, typical metals can reflect electromagnetic (EM) fields and can thus be used as electromagnetic shielding materials. However, conventional linear LHMs cannot be used to shield electromagnetic fields. This is drastically modified when nonlinearity of the magnetic response is taken into account, creating a controllable shielding effect in LHMs, accompanied by a parametric reflection.[23]

SRR microwave nonlinear tunable metamaterial

Fabrication and experimental studies of the properties of the first nonlinear tunable metamaterial operating at microwave frequencies. Such a metamaterial was fabricated by modifying the properties of SRRs and introducing varactor diodes in each SRR element of the composite structure such that the whole structure becomes dynamically tunable by varying the amplitude of the propagating electromagnetic waves. In particular, the power dependent transmission of the left-handed and magnetic metamaterials at higher powers is demonstrated, as was suggested earlier theoretically and selective generation of higher harmonics.[24]

SRR microwave nonlinear magnetic metamaterials

The fabrication and experimental studies of the properties of the nonlinear tunable magnetic metamaterial operating at microwave frequencies. Such metamaterials are fabricated by modifying the properties of SRRs and introducing varactor diodes in each SRR element of the composite structure such that the whole structure becomes dynamically tunable by varying the amplitude of the propagating electromagnetic waves. In particular, we demonstrate the power-dependent transmission of the magnetic metamaterials at higher powers, as was suggested earlier theoretically, and we realize experimentally the nonlinearity-dependent enhancement or suppression of the transmission in dynamically tunable magnetic metamaterial.[25]

SRR microwave nonlinear electric metamaterials

A new type of nonlinear metamaterials, is proposed and designed, exhibiting a resonant electric response at microwave frequencies. By introducing a varactor diode as a nonlinear element within each resonator, we are able to shift the frequency of the electric mode stop band by changing the incident power without affecting the magnetic response. These elements could be combined with the previously developed nonlinear magnetic metamaterials in order to create negative index media with a control over both electric and magnetic nonlinearities.[26]

Given that the nonlinear shift in resonance results in a very strong nonlinear magnetic response for SRRs, we take a similar approach to the design of nonlinear electric resonators, in order to obtain a strong nonlinear electric response. [26]

Sub-diffraction limit for non-linear metamaterial lens

By covering a thin flat nonlinear lens on the sources, the sub-diffraction-limit observation can be achieved by measuring either the near-field distribution or the far-field radiation of the sources at the harmonic frequencies and calculating the IFT to obtain the sub-wavelength imaging. The higher order harmonics are used, the higher resolution is obtained.[27]

Non-linear electric metamaterial

A new type of nonlinear metamaterial is designed, and analyzed with a dominant negative electric response. Introducing nonlinearity into the electric response makes it tunable while leaving the magnetic response unchanged. It is expected that our results would constitute the building blocks of a complete nonlinear negative index metamaterial containing both nonlinear and tunable electric and magnetic elements, which can be engineered independently.[28]

Controllable magnetic response at optical frequencies

Negative permeability material for red light

Desired permeability achieved in one wavelength of the visible spectrum at 780 nm.[29]

Controllable permeability across visible spectrum

Coupled nanostrips demonstrate control of magnetic responses across the visible spectrum.[30]

Magnetic response at telecommunication and visible frequencies

At telecommunication or visible frequencies the desired magnetic response, negative permeability (μeff < 0) does not occur in natural materials. One stated technological challenge in November 2005 was to achieve μeff < 0 and this would be accomplished with an adapted SRR/wire metamaterial. Prior research had established that the SRR/wire metamaterials were used in the first demonstrations of μeff < 0 at microwave frequencies. By November 2004 magnetic resonance was demonstrated at 100 THz (3 μm wavelength), which is an increase of more than 4 orders of magnitude within four years.[31]

See also

Electromagnetic interactions

References

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