U of A



  Natural vs. Artificial


  The NRI-TL

  The Superlens

  Invisibility and More!












Here is a brief summary of the advent of metamaterials and the ideas behind our Group's research. The included references are by no means exhaustive and are intended to serve only as a starting point for the interested reader. Any inquiries may be directed by E-mail to Dr. Ashwin K. Iyer.


The electromagnetic properties of materials are the collective, macroscopic effect of their response to electric and magnetic fields at the atomic or molecular level. This response is captured by parameters known as permittivity (ε) and permeability (μ). Several familiar optical properties are decided by these parameters - for example, a material's refractive index, n , is given by \sqrt(\epsilon*\mu). The term 'macroscopic' implies that these properties are apparent only when the material is viewed using wavelengths of light (λ) that are muchEffMedium longer than the spacing between atoms and molecules (d). For decades, researchers have attempted to synthesize such known material properties using artificial materials, or dielectrics. Any effort to engineer the intrinsic electromagnetic properties of a material requires access to its atoms or molecules, a degree of precision that, at first, appears to make the task prohibitively difficult. However, researchers in the artificial-dielectrics community recognized that the long-wavelength condition can be met at scales far more accessible than those of atoms and molecules; indeed, for sufficiently long wavelengths -- for example, those corresponding to RF/microwave frequencies -- artificial 'molecules' such as metallic or dielectric spheres, disks, or wires, could be fabricated with entirely practicable dimensions. Large, ordered arrays of these artificial particles would react to electric and magnetic fields much like the atoms and molecules of natural materials. These ideas led to the development of structures that, although they seemed different when viewed by the naked eye using visible light, displayed a response to light at RF/microwave frequencies nearly identical to that of conventional dielectrics [1, 2].


Several decades passed before it was realized that similar principles could be applied to realize materials with properties not available or not readily available in nature. These 'metamaterials' could be engineered to exhibit exotic negative values of μ and ε, as well as their most unusual product: a negative refractive index (NRI). The inspiration for the study of metamaterials was provided by the theoretical work of V. Veselago [3], who suggested that materials with a NRI supported waves that carried energy in the forward direction, but propagated backwards. This property came to be known as 'left-handedness', named after the peculiar orientation of the electric and magnetic fields describing these waves, and so NRI metamaterials are also often referred to as left-handed (LH).VeselagoPendry However, one of Veselago's most intriguing conclusions was that flat LH slabs acted as lenses by virtue of their NRI contrast with the surrounding medium. Further impetus to metamaterials research was lent by J. B. Pendry [4], who suggested that, if properly designed, such a lens could theoretically produce an infinitely fine, focused image of the source by restoring the amplitude of 'evanescent' waves that would otherwise decay in conventional materials. Indeed, this would be a 'superlens' capable of overcoming the classical diffraction limit and outperforming all conventional lenses. If superlenses could be practically realized, they would have several biomedical, microelectronics, and defense-related applications in subdiffraction microscopy, lithography, tomography, and sensing. These notions prompted several groups to pursue the realization of the first NRI metamaterial, and this seminal result was ultimately achieved in 2001 by researchers at the University of California at San Diego [5] using an assembly of wires interleaved with an array of split-ring resonators (SRRs). However, the wire/SRR structure suffered from narrow operating bandwidths and high losses, and thus, could not be designed to meet the strict subdiffraction-imaging conditions outlined in [4]; another solution was required.



The NRI transmission-line (NRI-TL) metamaterial is based on the well-known TL model for wave propagation, and models materials with μ < 0 and ε < 0 using a practical, planar TL network (e.g., a grid of microstrip TLs on a printed-circuit board), periodically loaded at short intervals by lumped (e.g., surface-mount chip) capacitors and inductors [6]. This work provided the first experimental demonstration of focusing by virtue of a NRI, and also showed that the NRI-TL metamaterial is inherently broadband and low-loss. Indeed, the first successful demonstration of subdiffraction imaging was also achieved using a planar NRI-TL metamaterial [7], and the properties of several other NRI metamaterials, including the Wire/SRR implementation and later plasmonic implementations at optical frequencies, could ultimately be explained by the NRI-TL concept [8, 9]. Aside from the demonstration of imaging phenomena, the NRI-TL metamaterial was also used to realize novel couplers providing very large coupling levels over extremely short distances, miniaturized power dividers and baluns, as well as leaky-wave antennas with the unique ability to frequency-scan from negative to positive angles through broadside.


In spite of the success of the planar NRI-TL metamaterial as a lens, it was understood that the applicability of the subdiffraction-imaging phenomenon to biomedicine, defense, and communications would require a three-dimensional, rather than planar, metamaterial superlens able to interact with electromagnetic fields in free space. Although there were many exciting efforts to build free-space metamaterials for subdiffraction imaging, they either did not possess a NRI, as required by Veselago and Pendry, or their narrowband, lossy nature rendered them unsuitable for the demonstration of subdiffraction imaging (see, for example, [10-12]). Based on the success of the NRI-TL metamaterial superlens in a planar environment, VNRITLa new type of NRI-TL metamaterial suitable for free-space subdiffraction imaging was developed, also at the University of Toronto. It was determined that such a metamaterial could be constructed by stacking planar NRI-TL metamaterial layers, which could be easily realized using standard lithographic processes and would also possess broadband, low-loss properties akin to those of the planar variety [13]. Indeed, this effort culminated in the first experimental demonstration of free-space subdiffraction imaging using a multilayer NRI-TL metamaterial superlens [14].



Although much of the activity in metamaterials today is focused on the NRI property, several other types of metamaterials exist. For example, there has been a great deal of theoretical work suggesting that metamaterial 'shells' possessing either ε < 0 or μ < 0 could be used to affect the radiation characteristics of small antennas [15], and that metamaterials with ε and μ values close to zero could be used to 'cloak' nearby objects or 'tunnel' fields through small apertures [16, 17]. Transformation-optics techniques have been used to show that inhomogeneous and/or anisotropic metamaterials can be designed as 'hyperlenses' to magnify subdiffraction patterns so that they may be observed in the far-field by conventional microscopes (see, for example, [18] and [19]) or, most famously, as 'invisibility cloaks' to render objects invisible by bending light around them through a process of continuous refraction [20], without any reflection. The NRI-TL metamaterial, which achieves desired electromagnetic properties easily and precisely through the use of established TL techniques, may be useful for the application of several of these intriguing theories.


[1] W. E. Kock, "Metallic delay lenses," Bell Syst. Tech. J., vol. 27, pp. 58-82, Jan. 1948.

[2] R. E. Collin, Field Theory of Guided Waves, 2nd ed., Wiley-IEEE Press, Toronto, 1990.

[3] V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp, vol. 10, no. 4, pp. 509--514, Jan.-Feb. 1968.

[4] J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett., vol. 85, no. 18, pp. 3966-3969, Oct. 2000.

[5] R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science, vol. 292, pp. 77-79, Apr. 2001.

[6] G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, "Planar negative refractive index media using periodically L-C loaded transmission lines," IEEE Trans. Microwave Theory Tech., vol. 50, no. 12, pp. 2702-2712, Dec. 2002.

[7] A. Grbic and G. V. Eleftheriades, "Overcoming the diffraction limit with a planar left-handed transmission-line lens," Phys. Rev. Lett., vol. 92, p. 117403, Mar. 2004.

[8] G. V. Eleftheriades, O. Siddiqui, and A. K. Iyer, "Transmission line models for negative refractive index media and associated implementations without excess resonators," IEEE Microwave Wireless Components Lett., vol. 13,  no. 2, pp. 51-53, February 2003.

[9] A. Alù and N. Engheta, "Optical nanotransmission lines: synthesis of planar left-handed metamaterials in the infrared and visible regimes," J. Opt. Soc. Am. B, vol. 23, pp. 571-583, 2006.

[10] N. Fang, H. Lee, C. Sun, and X. Zhang, "Sub-diffraction-limited optical imaging with a silver superlens," Science, vol. 308., no. 5721, pp. 534-537, 2005.

[11] F. Mesa, M. J. Freire, R. Marqués, J.D. Baena, "Three-dimensional superresolution in metamaterial slab lenses: Experiment and theory," Phys. Rev. B, vol. 72, p. 235117, 2005.

[12] K. Aydin, I. Bulu, and E. Ozbay, "Focusing of electromagnetic waves by a left-handed metamaterial flat lens," Opt. Express, vol. 12, no. 22, pp. 8753-8759, 2005.

[13] A. K. Iyer and G. V. Eleftheriades, "A multilayer negative-refractive-index transmission-line (NRI-TL) metamaterial free-space lens at X-Band," IEEE Trans. Antennas Propagat., vol. 55, no. 10, pp. 2746-2753, Oct. 2007.

[14] A. K. Iyer and G. V. Eleftheriades, "Free-space imaging beyond the diffraction limit using a Veselago-Pendry transmission-line metamaterial superlens," IEEE Trans. Antennas Propagat., vol. 57, no. 6, pp. 1720-1727, June 2009.

[15] R. W. Ziolkowski and A. Erentok, "At and below the Chu limit: passive and active broad bandwidth metamaterial-based electrically small antennas," IET Microwave Antennas Propagat., vol. 1, no. 1, pp. 116-128, 2007.

[16] A. Alù and N. Engheta, "Plasmonic materials in transparency and cloaking problems: mechanism, robustness, and physical insights," Opt. Express, vol. 15, no. 6, pp. 3318-3332, 2007.

[17] M. Silveirinha and N. Engheta, "Tunneling of electromagnetic energy through subwavelength channels and bends using epsilon-near-zero materials," Phys. Rev. Lett., vol. 97, p. 157403, 2006.

[18] A. Salandrino and N. Engheta, "Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations," Phys. Rev. B, vol. 74, p. 075103, Aug. 2006.

[19] Z. Jacob, L. Alekseyev, and E. Narimanov, "Optical Hyperlens: Far-field imaging beyond the diffraction limit," Opt. Express, vol. 14, pp. 8247-8256, Sept. 2006.

[20] D. Schurig, J. J. Mock, B. J. Justice, S. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science, vol. 314, no. 5801, pp. 977-980, Nov. 2006.




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