A New Era of Exotic Electromagnetism

GENERAL ¨ ARTICLE A New Era of Exotic Electromagnetism K Porsezian and Ancemma Joseph Nature hasitsownlimitsand naturally-occurring materials exhibit restricted electromagnetic properties bound within those limits. However, mod- ern dayresearchers have developed arti¯cially structured materialcomposites,called `metamaterials', that possess signi¯cant potentialtopro- (left) K Porsezian works at vide electromagnetic properties that are quite the Department of Physics, unusual and are not found in nature. This ar- Pondicherry Central University, Puducherry, ticle is aimed atgivingan introductory review India. He is investigating of this class of `designer materials' and their su- solitons and modulation perior properties that are not present in their instability in nonlinear constituent components. optics, Bose-Einstein condensates, metamaterials, 1. Metamaterial { Advent photo-refractive materials, photonic crystal fibers and Metamaterials are arti¯cially constructed structures ex- also integrability aspects of hibiting unconventionalcharacteristics thathave never nonlinear partial differential been observed in nature before. This factgivesthem equations. their name `metamaterials' { materials beyond (natural) (right) Ancemma is working materials. Unlike naturalmedia,theseare materials towards her doctoral degree which derive their properties from their structure rather in Pondicherry University, Puducherry, India. Her thandirectlyfrom their composition as shown in Fig- primary research interests ure 1. Though the notion of metamaterials wasorigi- are based on studying the nally proposed in regard to the idea of a negative re- nonlinear pulse propagation fractive index, or negative-index materials (NIMs), to- through nonlinear periodic daythevarious interpretations of the term have led to structures and negative index materials. their versatile terminologies like double negative material(DNG), left-handed material(LHM),backward phase material(BPM), negative phase velocity (NPV)material, etc. The vital decisive factor responsible for theunusual be- havior of these materials is the e®ective negative refrac- Keywords tive index resulting from the negative realpart of the Metamaterial, negative refraction, left-handedness. RESONANCE ¨ February 2012 163 GENERAL ¨ ARTICLE Figure 1. Conventional and metamaterial composition. magnetic permeability and negative realpart of electric permittivity. The dielectric permittivity and magnetic permeability are the key factors responsible for all the electric and magnetic characteristics exposed by materials. While some materials possess negative permittivity (like for metals below their plasma frequency), no naturalmaterials are seen with negative permeability. Tracing back the history of metamaterialconcept,itwas the Soviet physicistVictorVeselago's genius which postulated the physicalpermissibility of materials possessing simultaneous negative permittivity and permeability back in the late 1960s. He hadenvisioned the unusual electrodynamics of double negative materials in his fa- mous seminalpaper in Soviet Physics Uspekhi. This pu- tative concept which laylatent for almost three decades got resurrected with the pioneering e®ort of John Pendry of ImperialCollege, London who proposed a blueprint It was the Soviet structure exhibiting simulataneous negative permeabil- physicist Victor ity and negative permittivity. Veselago’s genius which postulated the These materials, which are still in their infancy, have exposed a varietyof fascinating e®ects such as reversal physical permissibility of Snell's law, reversed Doppler e®ect, Cerenkov radi- of materials ation, sub-di®raction imaging, photon tunneling, back- possessing simul- ward wave antennas,phase combination, electrically taneous negative small resonators, and are expected to satisfy a multi- permittivity and tude of other requirements in complex environments. In permeability back in the next section, wepeepinto each of the intriguing and the late 1960s. exciting traits of metamaterials. 164 RESONANCE ¨February 2012 GENERAL ¨ ARTICLE 2. Metamaterial { UnusualTraits From the foundations of macroscopic 2.1 Left-handedness electrodynamics From the foundations of macroscopic electrodynamics given by J C Maxwell given by J C Maxwell (1831{1879 ), it iswell known (1831–1879), it is well that the propagation of electromagnetic waves in a known that the medium is determined by dielectric permittivitiy and propagation of magnetic permeability of the medium. Accordingly, the electromagnetic e®ective refractive index of a medium can be written as waves in a medium is n = p²¹.Now,asperVeselago's notion, if both ² and determined by ¹ take up negative values in a given wavelengthrange, dielectric permittivitiy we can write ¹ = ¹ ei¼ and ² = ² ei¼. Then one can j j j j and magnetic easily see thattherefractive index permeability of the medium. n = ² ¹ e2i¼ = ² ¹ pe2i¼ = ² ¹ : (1) j jj j j jj j ¡ j jj j This impliesp thattherepfractive index opf the medium with simultaneous negative ² and ¹ must be also negative. Now what could be the consequences of this fact? For a monochromatic plane wave, the Maxwell's equations can be written as ~k E~ = ! ¹H~ and ~k H~ = £ c £ ! ²E~ . ¡ c Interestingly, one canseethat, while for positive values of ² and ¹, E~ , H~ and ~k form a right-handed triplet, but for Veselago's case, they form the left-handed triplet. ~ c ~ ~ While Poynting vector S = 4¼ E B is always directed away from the source for both£ left and right-handed cases, the wave vector surprisingly takes uptwodirec- tions, `away from the source' for the right-handed and `towards the source' for the left-handed case. One can see this fact well depicted in Figure 2. Figure 2. (a) Right-handed media with H >0,P>0. (a) (b) (b) Left-handed media with H<0,P<0. RESONANCE ¨ February 2012 165 GENERAL ¨ ARTICLE Light that enters 2.2 Negative Refraction from an ordinary Astrikingfeatureof the negative index materialisthe medium to the reversalof one of the fundamentalprincipleof optics, metamaterial the Snell's law. Light thatentersfrom anordinary medium will medium to the metamaterial medium will undergo re- undergo refraction fraction opposite to that occuring in the conventional opposite to that ordinary medium. How could this be explained? Con- occuring in the sider the refraction phenomena occurring when a beam conventional travels from one medium into another. ordinary medium. Suppose if the two media areof positive index with ²>0 and ¹>0, then we will have anordinary refraction case. But for the case when the second mediumisof negative index with ²<0 and ¹<0, we have a beamgoing from anordinary medium into a negative medium. One should rememberherethat, for any case, the boundary conditions requiretangential components of E~ and H~ , and normalcomponents of D~ and B~ to be continuous at the interface, i.e., Et1 = Et2;Ht1 = Ht2; and ²1En1 = ²2En2;¹1Hn1 = ¹2Hn2: (2) Now, it is clearthat x and y components of the ¯eld are not changed at transition from medium 1 to 2, re- gardless of the signs of ² and ¹.Asfor the normal z components of the¯eld, they preserve their directions if ² and ¹ preserve their signs in both media.Otherwiseit is obvious that they change their directions and hence the negative refraction as shown in Figure 3. Figure 3. Negative refraction. 166 RESONANCE ¨February 2012 GENERAL ¨ ARTICLE 2.3 Reversed Doppler Shift An apparent change in the frequency of a Thinking of oneself standing atthecrossroads and hear- wave when there is a ing an approaching ambulance will immediately bring to our mind the `Doppler e®ect'. As the vehicle races to- relativemotion wards us, the pitch of the siren becomes higher, and between the observer as it recedes, it gets lowered. This well-known fact of and the source of an apparent change in the frequency of a wave when waves is termed as there is a relative motion between the observer and the Doppler effect. source of wavesistermedas Doppler e®ect. As the object emitting the wave approaches the observer,thein- tervals between the waves diminish; in other words, the radiation gets squeezed, resulting in increased frequency and a blue shift. As the object recedes away from the observer, the wave gets stretched leading to a red shift. Now how could this e®ect get reversed in metamaterials? The apparent frequency measured by the observer when the source is moving inside the medium at velocity v is !0 = °(! + ~k:v)with~k = n!=c: (3) j j 2 2 1=2 Taking up the relativistic factor ° =(1 v =c )¡ and ¡ considering emission along the direction of the motion of the source in the ordinary (n =1)ormetamaterial medium (n = 1), we get the apparent frequency to be ¡ c + v !0 = ! for right-handed medium; c v r ¡ c v and !0 = ¡ !; for left-handed medium: (4) c + v r Thus one canseethat the Doppler e®ects gets exactly reversed in a metamaterial medium due to the reversed phase vector. RESONANCE ¨ February 2012 167 GENERAL ¨ ARTICLE The original principle 2.4 Reversal of Fermat's Principle of Fermat states that a beam of light The originalprinciple of Fermatstates that a beamof chooses such an light chooses such an actualpath between two points which is the one traversed in the least time. It was actual path between further reformulated as the route chosen by the light two points which is to be of minimum optical length. However, in the case the one traversed in of metamaterial the term `minimum' (both for path or the least time. time) is not apt. Let us consider the case of light propagating between two points sayAand

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