Split-ring resonator

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]
Electric field (top) and magnetic field (bottom) of an electric-SRR under resonant electrical excitation. The magnetic response arises from the symmetry of the current loops. (Click for video)

A split-ring resonator (SRR) is an artificially produced structure common to metamaterials. Their purpose is to produce the desired magnetic susceptibility (magnetic response) in various types of metamaterials up to 200 terahertz. These media create the necessary strong magnetic coupling to an applied electromagnetic field, not otherwise available in conventional materials. For example, an effect such as negative permeability is produced with a periodic array of split ring resonators.[3]

A single cell SRR has a pair of enclosed loops with splits in them at opposite ends. The loops are made of nonmagnetic metal like copper and have a small gap between them. The loops can be concentric, or square, and gapped as needed. 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. The dimensions of the structure are small compared to the resonant wavelength. This results in low radiative losses, and very high quality factors.[3][4][5]

Background

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 transmission line metamaterials.[6] [7] [8] [9]

Characteristics

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.[3] [10]

SRR configuration

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.[11]

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 radii of 30 to 40 nanometers for success in the mid-range of the visible spectrum.[11] Microfabrication and nanofabrication techniques may utilize direct laser beam writing or electron beam lithography depending on the desired resolution.[11]

Various configurations

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][12]

Split-ring resonators (SRR) are one of the most common elements used to fabricate metamaterials.[13] Split-ring resonators are non-magnetic materials The first ones were usually fabricated from circuit board material to create metamaterials.[14]

Looking at the image directly to the right, it can be seen that at first a single SRR looked like an object with a two square perimeters, and each perimeter with small segment removed, which results in squared "C" shapes, on fiberglass, printed circuit board material.[13][14] In this type of configuration it is actually two concentric bands of non-magnetic conductor material.[13] There is one gap in each band placed 180° relative to each other.[13] The gap in each band gives it the distinctive "C" shape, rather than a totally circular or square shape.[13][14] 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 are added.[14] After processing, the boards are cut and assembled into an interlocking unit.[14] It is constructed into a periodic array with a large number of SRRs.[14]

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

Demonstrations

A periodic array of SRRs was used for the first demonstration of a negative index of refraction.[14] For this demonstration, square shaped SRRs, with the lined wire configurations, were fabricated into a periodic, arrayed, cell structure.[14] This is the substance of the metamaterial.[14] Then a metamaterial prism was cut from this material.[14] 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.[14]

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. In a later demonstration, 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.[14]

SRRs were first used to fabricate left-handed metamaterials for the microwave range,[14] and several years later for the terahertz range.[15] By 2007, experimental demonstration of this structure at microwave frequencies has been achieved by many groups.[16] In addition, SRRs have been used for research in acoustic metamaterials.[17] The arrayed SRRs and wires of the first Left-handed metamaterial were melded into alternating layers.[18] 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".[17] Another analysis showed Left Handed Material to be fabricated from inhomogeneous constituents, which yet results in a macroscopically homogeneous material.[17] SRRs had been used to focus a signal from a point source, increasing the transmission distance for near field waves.[17] 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).[14][17][18]

The resonance phenomena that occurs in this system is essential to achieving the desired effects.[16]

SRRs also exhibit resonant electric response in addition to their resonant magnetic response.[18] The response, when combined with an array of identical wires is averaged over the whole composite structure which results in effective values, including the refractive index.[19] 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.[20]

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.[20]

The Symmetrical-Ring Structure is another classic example. Described by the nomenclature these are two rectangular square D type configurations, exactly the same size, lying 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.[20]

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 lying 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.[20]

Another new metamaterial in 2005 was a coupled “S” shaped structure. There are two vertical "S" shaped structures, 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.[20][21]

Other types of split-ring resonators are the spiral resonator with 8 loops. broadside coupled split-ring resonator (BC-SRR). Two-layer multi spiral resonator (TL-MSR), the broad-side coupled spiral resonator with four turns, the open split-ring resonator (OSRR), and the open complementary split-ring resonator (OCSRR). Transmission line configurations include SRR-based CRLH (composite right-left-handed) transmission line and its equivalent compliment.[22]

Split ring resonator research

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 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.[23] Research has also covered variations in magnetic resonances for different SRR configurations.[24][25][26] Research has continued into terahertz radiations with SRRs[27] Other related work fashioned metamaterial configurations with non-SRR structures. These can be constructed with materials such as periodic metallic crosses, or an ever widening concenteric ring structures known as Swiss rolls.[28][29][30][31] Permeability for only the red wavelength at 780 nm has been analyzed and along with other related work [32][33][34]

See also

References

  1. 1 2 Smith, D. R.; Padilla, WJ; Vier, DC; Nemat-Nasser, SC; Schultz, S (2000). "Composite Medium with Simultaneously Negative Permeability and Permittivity" (PDF). Physical Review Letters 84 (18): 4184–7. Bibcode:2000PhRvL..84.4184S. doi:10.1103/PhysRevLett.84.4184. PMID 10990641.
  2. ↑ Shelby, R. A.; Smith, D. R.; Nemat-Nasser, S. C.; Schultz, S. (2001). "Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial". Applied Physics Letters 78 (4): 489. Bibcode:2001ApPhL..78..489S. doi:10.1063/1.1343489.
  3. 1 2 3 Gay-Balmaz, Philippe; Martin, Olivier J. F. (2002). "Electromagnetic resonances in individual and coupled split-ring resonators" (free PDF download). Journal of Applied Physics 92 (5): 2929. Bibcode:2002JAP....92.2929G. doi:10.1063/1.1497452.
  4. ↑ Baena, J.D.; Bonache, J.; Martin, F.; Sillero, R.M.; Falcone, F.; Lopetegi, T.; Laso, M.A.G.; Garcia-Garcia, J.; et al. (2005). "Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines" (free PDF download). IEEE Transactions on Microwave Theory and Techniques 53 (4): 1451–1461. Bibcode:2005ITMTT..53.1451B. doi:10.1109/TMTT.2005.845211.
  5. ↑ Marqués, R.; Martel, J.; Mesa, F.; Medina, F. (2002). "Left-Handed-Media Simulation and Transmission of EM Waves in Subwavelength Split-Ring-Resonator-Loaded Metallic Waveguides" (free PDF download). Physical Review Letters 89 (18): 183901. Bibcode:2002PhRvL..89r3901M. doi:10.1103/PhysRevLett.89.183901. PMID 12398601.
  6. ↑ Naqui, Jordi; Durán-Sindreu, Miguel; Martín, Ferran (2011). "Novel Sensors Based on the Symmetry Properties of Split Ring Resonators (SRRs)". Sensors 11 (12): 7545–7553. doi:10.3390/s110807545. ISSN 1424-8220. PMC 3231717. PMID 22164031.
  7. ↑ Pendry, J.B.; Holden, A.J.; Robbins, D.J.; Stewart, W.J. (1999). "Magnetism from conductors and enhanced nonlinear phenomena". IEEE Transactions on Microwave Theory and Techniques 47 (11): 2075–2084. Bibcode:1999ITMTT..47.2075P. doi:10.1109/22.798002. ISSN 0018-9480.
  8. ↑ Smith, D.; Padilla, Willie; Vier, D.; Nemat-Nasser, S.; Schultz, S. (2000). "Composite Medium with Simultaneously Negative Permeability and Permittivity". Physical Review Letters 84 (18): 4184–4187. Bibcode:2000PhRvL..84.4184S. doi:10.1103/PhysRevLett.84.4184. ISSN 0031-9007. PMID 10990641.
  9. ↑ Shelby, R. A. (2001). "Experimental Verification of a Negative Index of Refraction". Science 292 (5514): 77–79. Bibcode:2001Sci...292...77S. doi:10.1126/science.1058847. ISSN 0036-8075. PMID 11292865.
  10. ↑ Pendry, John B.; AJ Holden; DJ Robbins; WJ Stewart (1999-02-03. Actually published in 1999-11). "Magnetism from Conductors, and Enhanced Non-Linear Phenomena" (Free PDF download. Cited by 2,136 articles. Alternate PDF here Nov. 1999). IEEE Trans. Microwave Theory Tech 47 (11): 2075–2084. Bibcode:1999ITMTT..47.2075P. doi:10.1109/22.798002. Retrieved 2009-12-10. Check date values in: |date= (help)
  11. 1 2 3 Moser, H.O.; et al. (2005-07-08). "Electromagnetic metamaterials over the whole THz range – achievements and perspectives" (Free PDF download, click on link.). ELECTROMAGNETIC MATERIALS Proceedings of the Symposium R, ICMAT 2005 (World Scientific Publishing Co.): 18. doi:10.1142/9789812701718_0003. ISBN 978-981-256-411-5. Retrieved 2009-10-21.
  12. ↑ Shelby, R. A.; Smith D.R.; Shultz S.; Nemat-Nasser S.C. (2001). "Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial" (PDF). Applied Physics Letters 78 (4): 489. Bibcode:2001ApPhL..78..489S. doi:10.1063/1.1343489.
  13. 1 2 3 4 5 Lee, Yun-Shik (2008). Principles of Terahertz Science and Technology. Lecture Notes in Physics. New York: Springer-Verlag New York, LLC. pp. 1–3, 191. ISBN 978-0-387-09539-4.
  14. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Shelby, RA; Smith, DR; Schultz, S (2001). "Experimental Verification of a Negative Index of Refraction". Science 292 (5514): 77–9. Bibcode:2001Sci...292...77S. doi:10.1126/science.1058847. PMID 11292865.
  15. ↑ Yen, T. J.; et al. (2004). "Terahertz Magnetic Response from Artificial Materials". Science 303 (5663): 1494–1496. Bibcode:2004Sci...303.1494Y. doi:10.1126/science.1094025. PMID 15001772.
  16. 1 2 Kamil, Boratay Alici; Ekmel Özbay (2007-03-22). "Radiation properties of a split ring resonator and monopole composite" (PDF). Physica Status Solidi (b) 244 (4): 1192–1196. Bibcode:2007PSSBR.244.1192A. doi:10.1002/pssb.200674505. Retrieved 2009-09-17.
  17. 1 2 3 4 5 Movchan, A. B.; S. Guenneau (2004). "Split-ring resonators and localized modes" (PDF). Phys. Rev. B 70 (12): 125116. Bibcode:2004PhRvB..70l5116M. doi:10.1103/PhysRevB.70.125116. Retrieved 2009-08-27.
  18. 1 2 3 Katsarakis, N.; T. Koschny; M. Kafesaki; E. N. Economou; C. M. Soukoulis (2004-04-12). "Electric coupling to the magnetic resonance of split ring resonators" (PDF). Appl. Phys. Lett. (Crete,Greece and Ames,Iowa, USA: American Institute of Physics) 84 (15): 2943–2945. arXiv:cond-mat/0407369. Bibcode:2004ApPhL..84.2943K. doi:10.1063/1.1695439. Retrieved 2009-09-15.
  19. ↑ Smith, D. R.; J. J. Mock; A. F. Starr; D. Schurig (Received 4 July 2004; published 17 March 2005). "A gradient index metamaterial". Phys. Rev. E 71 (3): 036609. arXiv:physics/0407063. Bibcode:2005PhRvE..71c6609S. doi:10.1103/PhysRevE.71.036609. Check date values in: |date= (help)
  20. 1 2 3 4 5 Wu, B.-I.; W. Wang; J. Pacheco; X. Chen; T. Grzegorczyk; J. A. Kong (2005). "A Study of Using Metamaterials as Antenna Substrate to Enhance Gain" (PDF). Progress in Electromagnetics Research 51: 295–328. doi:10.2528/PIER04070701. Retrieved 2009-09-23.
  21. ↑ J. Lezec, Henri; Jennifer A. Dionne; Harry A. Atwater (2007-04-20). "Negative Refraction at Visible Frequencies" (PDF). Science 316 (5823): 430–2. Bibcode:2007Sci...316..430L. doi:10.1126/science.1139266. PMID 17379773. Retrieved 2009-10-06.
  22. ↑ Marta Gil, Francisco Aznar, Adolfo Velez, Miguel Duran-Sindreu, Jordi Selga, Gerard Siso, Jordi Bonache and Ferran Martin (2010). Electrically Small Resonators for Metamaterial and Microwave Circuit Design, Passive Microwave Components and Antennas, Vitaliy Zhurbenko (Ed.), ISBN 978-953-307-083-4, InTech, Available from: Electrically small resonators for metamaterial and microwave circuit design
  23. ↑ Smith DR, et al. (2000-05-01). "Composite Medium with Simultaneously Negative Permeability and Permittivity" (PDF). Physical Review Letters 84 (18): 4184–7. Bibcode:2000PhRvL..84.4184S. doi:10.1103/PhysRevLett.84.4184. PMID 10990641. Archived from the original (Free PDF download) on May 1, 2000. Retrieved 2009-12-07.
  24. ↑ Aydin, Koray; Irfan Bulu; Kaan Guven; Maria Kafesaki; Costas M Soukoulis; Ekmel Ozbay (2005-08-08). "Investigation of magnetic resonances for different SRR parameters and designs" (PDF). New Journal of Physics 7 (168): 1–15. Bibcode:2005NJPh....7..168A. doi:10.1088/1367-2630/7/1/168. Retrieved 2009-09-20.
  25. ↑ Prati, Prati (2004-02-20). "Crossover Between the Cell Size and the Wavelength of the Incident Radiation in a Metamaterial" (PDF). Microwave and Optical Technology Letters 40 (4): 269–272. doi:10.1002/mop.11349.
  26. ↑ Wang, Bingnan; Jiangfeng Zhou; Thomas Koschny; Costas M. Soukoulis (2008-09-24). "Nonlinear properties of split-ring resonators" (PDF). Optics Express 16 (20): 16058–. arXiv:0809.4045. Bibcode:2008OExpr..1616058W. doi:10.1364/OE.16.016058. PMID 18825245. Retrieved 2009-10-25.
  27. ↑ Casse BD, et al. (2007). "Towards 3D Electromagnetic Metamaterials in the THz Range" (PDF). Synchronotron Radiation Instrumentation Ninth international conference (American Institute of Physics): 1462. Archived from the original (PDF) on March 6, 2012. Retrieved 2009-12-04.
  28. ↑ Dolling, G.; et al. (2005-12-01). "Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials" (Free PDf download). Optics Letters 30 (23): 3198–3200. arXiv:physics/0507045. Bibcode:2005OptL...30.3198D. doi:10.1364/OL.30.003198. PMID 16342719. Retrieved 2009-10-31.
  29. ↑ Paul, Oliver; et al. (2008-04-28). "Negative index bulk metamaterial at terahertz frequencies" (Free PDF download). Optics Express (OSA) 16 (9): 6736–44. Bibcode:2008OExpr..16.6736P. doi:10.1364/OE.16.006736. PMID 18545376. Retrieved 2009-11-01.
  30. ↑ Pendry, J., "New electromagnetic materials emphasize the negative," Physics World, 1–5, 2001
  31. ↑ Wiltshire, M. C. K.; Hajnal, J; Pendry, J; Edwards, D; Stevens, C (2003-04-07). "Metamaterial endoscope for magnetic field transfer: near field imaging with magnetic wires" (Free PDF download). Opt Express 11 (7): 709–15. Bibcode:2003OExpr..11..709W. doi:10.1364/OE.11.000709. PMID 19461782. Retrieved 2009-11-02.
  32. ↑ Yuan, Hsiao-Kuan; et al. (2007-02-05). "A negative permeability material at red light". Optics Express 15 (3): 1076–83. arXiv:physics/0610118. Bibcode:2007OExpr..15.1076Y. doi:10.1364/OE.15.001076. PMID 19532335. Retrieved 2009-10-21.
  33. ↑ Cai, Wenshan; Chettiar, UK; Yuan, HK; De Silva, VC; Kildishev, AV; Drachev, VP; Shalaev, VM (2007). "Metamagnetics with rainbow colors". Optics Express 15 (6): 3333–3341. Bibcode:2007OExpr..15.3333C. doi:10.1364/OE.15.003333. PMID 19532574. Retrieved 2009-10-21.
  34. ↑ Enkrich, C.; et al. (2005-07-25). "Magnetic Metamaterials at Telecommunication and Visible Frequencies". Phys. Rev. Lett. 95 (20): 203901. arXiv:cond-mat/0504774. Bibcode:2005PhRvL..95t3901E. doi:10.1103/PhysRevLett.95.203901. PMID 16384056.

External links

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

Further reading

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. doi:10.1364/OE.18.003952. PMID 20389408. 

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