ESSENCE - International Journal for Environmental Rehabilitation and Conservation Badoni et al./Vol. VI [2] 2015/148 - 154 Volume VI: No. 2 2015 [148 – 154] [ISSN 0975 - 6272] [www.essence-journal.com]

Metamaterials: Characteristics, Structures And Applications

Badoni, Anumeha; Belwal, Pravesh and Kumar, Nitin

Received: October 17, 2015  Accepted: November 05, 2015  Online: December 31, 2015

Abstract Introduction (MTM) is a metallic or As the light propagates through matter, substance whose properties conventional materials only react to the depend upon its inter atomic structure rather electric field, resulting in most common than on the composition of the atoms optical effects, including refraction, themselves. In this paper, overview of unique diffraction and imaging (Jackson, 1999). Five properties of MTMs is presented. Further decades ago Russian physicist victor discussion is held over MTM structures veselago pondered about whether magnetic based on their resonant characteristics field of light interacts with matter. Then he (Resonant and non resonant structure) and classify the materials based on their applications in various fields. The and permeability according to their sign superiority of non resonant structure over the (positive and negative).In electromagnetism resonant structure is also discussed in this electric permittivity and the magnetic paper. Applications of MTMs are characterized in three categories: guided permeability determine the propagation of wave application, radiated wave application electromagnetic waves in matter (Veselago, and Refracted wave applications. 1968), due to the fact that they are the only parameters of substance appear Keywords (MTM) | negative refractive index | split ring resonator | CRLH

Fig1: Classification of materials

in the dispersion equation. According to For Correspondence: veselago the materials in third quadrant Department of ECE, DIT University Dehradun, India shows the reverse properties than

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conventional materials and are named as left Snell’s law, Doppler effect, Vavilov- handed materials. Cerenkov radiation etc. Due to these unusual After more than thirty years, Pendry and properties, MTM can change the propagation Smith have developed a novel class of property of electromagnetic wave passing metallic structure based on thin wires and through it. Miniaturization in the size of the Split ring resonators (SRR) that are known as design component is possible as the structural metamaterials (Pendry et al., 1999; Smith et cell size of MTM is less than one-fourth of al., 2000 and Pendry et al.,1998). The the guided (Paul et al., 2013). To concept of MTM transmission line(TL) was understand why such materials are also called introduced for the first time in 2002 (Iyer and left hand materials, let us assume time Eleftheriades, 2002). Caloz and Smith given harmonic and plane wave variation for field their useful work on MTM TL. in maxwell’s equation . Unique Properties of Metamaterials E(x, y, z, t) = . (2) 𝑗𝑗𝑗𝑗𝑗𝑗 −𝑖𝑖𝑖𝑖 𝑟𝑟 Metamaterials are defined as artificial where wave 𝐸𝐸vector𝑒𝑒 k has been introduced, effectively homogeneous structures with Maxwell equation take the form unusual properties not readily available in k × E = - (3) nature. For an effectively homogeneous × = +𝜔𝜔𝜇𝜇𝑜𝑜 𝜇𝜇𝑟𝑟 𝐻𝐻 (4) structure the average cell size ‘p’ of a From the above𝑜𝑜 𝑟𝑟 equation and definition of structure should be much smaller than the 𝑘𝑘 𝐻𝐻 𝜔𝜔𝜀𝜀 𝜀𝜀 𝐸𝐸 cross product, one can immediately see that guided wavelength ‘λ ’. Averaged cell size g for >0 and >0 the vector E,H and should be at least small than quarter of k from a right𝑟𝑟 handed𝑟𝑟 triplet of vectors, and if guided wavelength[8]. Therefore the 𝜀𝜀 𝜇𝜇 <0 and <0 they from a left handed condition for effective homogeneity system. 𝜀𝜀𝑟𝑟 𝜇𝜇𝑟𝑟 p = λg/4 (1) Elementary Structure of Metamaterials For metamaterials with negative permittivity Metals at optical are and permeability, several names and characterized by its electric permittivity that terminologies have been suggested, such as varies with according to the Drude “left-handed” media (Veselago, 1968), media relation with negative refractive index (Iyer and 2 ( ) = 1 (5) Eleftheriades, 2002), “backward-wave ( + ) 𝜔𝜔𝑝𝑝 media” (Lindell et al. 2001); and “double- 2 𝑜𝑜 2 where𝜀𝜀 𝜔𝜔 ωp𝜀𝜀= �Ne−/me𝜔𝜔0𝜔𝜔 is 𝑖𝑖𝑖𝑖the� frequency negative (DNG)” metamaterials (Sanada et i.e. the frequency with which the collection al., 2003), to name a few. MTM shows of free (plasma) oscillates in the Negative permittivity and permeability which presence of an external driving field, where results in negative refractive index. Due to N= electron density, e = electron charge, m= negative index, it supports backward waves mass of electron, ϒ = rate at which the i.e. inside MTM, phase velocities and group amplitude of the plasma oscillation velocities are antiparallel. MTM shows decreases. reversal of some fundamental laws like

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By the drude relation it can see that when Classification of MTM Structure ϒ=0 and ω<ωp then value of ‘e’ is less than Resonance type MTM: Resonant structures zero i.e. the medium is characterized by are made of thin wires and/or split ring negative permittivity. Unfortunately for all resonator (Pendry et al., 1999). They are frequencies for which ω<ωp while ϒ is very narrow band or high loss structure due to large which is associated with losses(light their resonant characteristics. SRR and absorption) therefore negative permittivity complimentary split ring resonator (CSRR) was imaginary in past. falls in this category. Equivalent circuits for Pendry first proposed a thin metallic structure SRR and CSRR are given below (Baena et to overcome this limitation. The plasma al., 2005) frequency which depends on the density and mass of the collective electron motion is very low in that thin wire structure (Smith et al., 2000). This give rises to two effects, firstly, the effective electron mass is increased due to self inductance of the wire structure. Secondly, the effective electron density is apparently reduced. Thin metallic wires give negative permittivity when electric field is directed in the z-axis (Pendry et al., 1996). SRR shows negative permeability when its y axis is perpendicular to magnetic field. A Fig.(a).SRR with its equivalent circuit combined array of thin wires and split rings (b).CSRR with its equivalent circuit shows that simultaneously negative (Baena et al., 2005) permittivity and permeability are achieved. A variety of split ring resonators have been come into existence by researchers i.e. square split rings (Majid et al., 2008), omega split rings (Othman et al.,2009), S type structure (Patel and Kosta, 2014), R split rings (Reddy and Raghavan, 2015), single split rings (Nornikman et al., 2012), and many more. In 2003, a new category of CRLH resonant antenna comes into existence (Sanada et al., 2003). CRLH resonant antenna has several advantages over resonator type antenna. Different types of CRLH resonant antennas have been investigated with their specific

applications. Fig 2. (a) thin metallic wires (b) split ring resonators (Smith et al., 2000) 150

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Non resonant type MTM: Resonant β can be real and imaginary; when β is structure was lossy with narrow bandwidth, purely imaginary γ = α a stop band occurs in limited its applications. Non resonant the frequency range which shows the unique transmission line (TL) structures are made of characteristic of CRLH TL. The equivalent lumped inductors and capacitors, have low circuit of CRLH TL and its dispersion loss over a broad bandwidth under diagram in balanced condition is shown in appropriate matching conditions and fig. overcomes the limitation of resonant type MTM. Composite right and left handed transmission line (CRLH TL) falls in this category. CRLH is combination of left handed (LH) and right handed (RH) transmission line because in general a pure left hand structure is not possible due to

unavoidable right hand parasitic series (a) inductance and shunt capacitance effects. The propagation constant of a transmission line is given by γ = α + jβ =√Z’Y’ (6) where Z’ and Y’ are respectively the per unit length impedance and per unit length admittance. In the case of CRLH TL, Z’ and Y’ are defined as [24]

′ ′ 1 (b) ( ) = j ′ (7) Fig 4. (a) Equivalent circuit model of 𝑅𝑅 𝑍𝑍′ 𝜔𝜔 �𝜔𝜔𝐿𝐿 ′ − 𝜔𝜔𝐶𝐶1𝐿𝐿 � ( ) = ′ (8) CRLH (b) dispersion diagram in balance condition Therefore𝑌𝑌 𝜔𝜔 𝑗𝑗 �the𝜔𝜔𝐶𝐶 dispersion𝑅𝑅 − 𝜔𝜔𝐿𝐿𝐿𝐿 � relation for a homogeneous CRLH TL is Balanced condition of CRLH TL is achieved when series and shunt resonance are equal. ( ) = Under balanced condition the propagation ′ ′ 2 ′ ′ 1 𝛽𝛽(𝜔𝜔) + 2 ′ ′ ′ + ′ (9) constant reduces to the simpler expression 𝐿𝐿𝑅𝑅 𝐶𝐶𝑅𝑅 � 𝑅𝑅 𝑅𝑅 𝜔𝜔 𝐿𝐿𝐿𝐿 𝐶𝐶𝐿𝐿 𝐿𝐿𝐿𝐿 𝐶𝐶𝐿𝐿 1 𝑆𝑆Where𝜔𝜔 𝜔𝜔 𝐿𝐿( 𝐶𝐶) − � � = + = ′ ′ (10) ′ ′ 𝑆𝑆 𝜔𝜔 1 1 𝛽𝛽 𝛽𝛽𝑅𝑅 𝛽𝛽𝐿𝐿 𝜔𝜔�𝐿𝐿𝑅𝑅 𝐶𝐶𝑅𝑅 − 1 < 1 = min , 𝜔𝜔�𝐿𝐿𝐿𝐿 𝐶𝐶𝐿𝐿 ′ ′ ′ ′ • Superiority of Non- resonant Structure ⎧ = − 𝑖𝑖𝑖𝑖 𝜔𝜔 𝜔𝜔𝑟𝑟 � � over Resonant Structure: The structure ⎪ �𝐿𝐿𝑅𝑅 𝐶𝐶𝐿𝐿 �𝐿𝐿𝐿𝐿 𝐶𝐶𝑅𝑅 1 1 made of resonating element generally does +1 > 2 = max , ⎨ ′ ′ ′ ′ not constitute a good transmission medium ⎪ 𝑟𝑟 ⎪ 𝑖𝑖𝑖𝑖 𝜔𝜔 𝜔𝜔 ��𝐿𝐿𝑅𝑅 𝐶𝐶𝐿𝐿 �𝐿𝐿𝐿𝐿 𝐶𝐶𝑅𝑅 � for a modulated signal because of the quality ⎩ factor intrinsically associated with each 151

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resonator (Collin, 1992). In 2002, to and can therefore be used as an antenna. overcome this limitation a new approach of Leaky wave antenna and resonant type transmission line is being introduced. CRLH TL comes in this category. Because of their non-resonant nature, TL Refracted Wave Application: In refracted MTMs can be designed to exhibit wave applications some examples are planar simultaneously low loss and broad distributed negative lens, microwave surface bandwidth, where low loss is achieved by a etc. A 2-D LH TL circuit using LC balanced design and broad bandwidth can be lumped-element components has been directly controlled by its LC parameters. implemented and its NRI focusing property Another advantage of TL MTM structures is has been shown experimentally by an NRI that they can be engineered in planar slab lens (Lai et al., 2004). configurations, compatible with modern Conclusion microwave integrated circuits (MICs). Metamaterials have become an extremely Finally, TL MTM structures can benefit from exciting research area. The unique the efficient and well-established TL theory electromagnetic properties of MTMs attract for the efficient design of microwave considerable attention of research. Non applications. resonant structures who are recently Application of MTM discovered have several advantages over the MTMs have many microwave applications previous structures with having many which may be classified in three applications in the field of microwaves. categories:guided wave, radiated wave and Many other fascinating discoveries and refracted wave application. applications are waiting for us to explore Guided Wave Applications: In guided wave with the complete degree of freedom to applications may be 1D or 2D CRLH TL. control over material properties. Electromagnetic energy remains confined in References the metal and dielectric media constituting Jackson, J. D. (1999): “Classical the components. Some 1D guided wave Electromagnetics”, John Wiley & Sons, applications are dual band components, New York, 3rd edn. quarter wavelength transmission line and Veselago, V. G. (1968): “The stubs,passive components(quadrature hybrid electrodynamics of substances with and Wilkinson power divider),nonlinear simultaneously negative values of ε and components,couplers etc. μ,”Sov. Phys. Uspekhi. 10(4): 509-514. Radiated Wave Application: Radiated- "Metamaterials”:Andrew Houck, Dave wave applications cover several types of Kong,Matt Reynolds, Peter Eckley,J. novel antennas and reflectors, which may be Kong, Ike Chuang, Joe Jacobson. 1D or 2D, passive or active, and static or dynamically tuned. If a MTM structure is Pendry, J. B.; Holden, A. J.; Robbins, D. J. open to free space and support a fast wave and Stewart, W. J. (1999): “Magnetism mode called a leaky wave mode, it radiates from conductors and enhanced nonlinear phenomena,” IEEE Trans. 152

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