IJSER media (meta means beyond in Greek). Most researchers in

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1 Internatonal Journal of Scentfc & Engneerng Research, Volume 6, Issue 7, July ISSN A STUDY OF SIGNIFICANCE OF METAMATERIALS ON PHYSICS AND ENGINEERING Santosh Kumar Jha ABSTRACT The metamaterals are artfcally engneered structures wth unusual electromagnetc propertes. In ths paper, we revew the mplementaton of sotropc metamaterals that exhbt a negatve permttvty and a negatve permeablty, thus leadng to a negatve ndex of refracton. Specfcally, the paper focuses on transmsson lne metamaterals whch are planar structures comprsng a network of dstrbuted transmsson lnes loaded perodcally wth nductors L capactor C, n hgh pass confguraton. The perodc unt cell s much smaller than the wavelength, thus leadng to an effectve medum n whch the lumped loadng elements can be ether dscrete or prnted. Based on such negatve refractve ndex transmsson lne metamaterals, several fundamental propertes of physcal scences and engneerng based mcrowave devces havng broadband propertes are explaned. Key words Metamaterals, permttvty, permeablty, composte materals, negatve ndex materal, negatve refracton, lenses, mcrowave phase shfters, mcrowave broadband antenna and mcrowave balun. trace back to the let part of the 9th century when n 898 INTRODUCTION The metamaterals are artfcally engneered Jagdsh Chandra Bose [] conducted the frst mcrowave structures wth unusual electromagnetc propertes. The experment on twsted structures, geometres that were term metamaterals refers to artfcal meda wth essentally artfcal chral element by today's termnology. electromagnetc propertes that transcend those of natural In 94, Lndman [] worked an "artfcal" chral meda by meda (meta means beyond n Greek). Most researchers n ths feld restrcts metamaterals to be artfcally structured perodc meda n whch the perodcty s much less than the wavelength of the mpngng electromagnetc wave. The scatterng process can be macroscopcally characterzed by means of effectve materals parameters, such as a permttvty, a permeablty and a refractve ndex. Dr. Santosh Kumar Jha, Assstant Professor n ECE department, FET, Mody Unversty, Lakshmangarh, Rajasthan-333. E-mal: ersantoshjha@yahoo.co.n To the best of our knowledge, the frst attempt to embeddng many randomly orented small wre helces n a host medum. In 948, Kock [3] made lghtweght mcrowave lenses by arrangng conductng spheres, dsks and strps perodcally and effectvely talorng the effectve refractve ndex of the artfcal meda. Snce, the artfcal complex materals have been the subject of research for many nvestgators worldwde, so n recent years new concepts, n synthess and novel fabrcaton technques are employed. Fg.- gven below s sketches of a volumetrc metamateral syntheszed by embeddng varous nclusons n a host medum. explore the concept of artfcal metamaterals appears to 05

2 Internatonal Journal of Scentfc & Engneerng Research, Volume 6, Issue 7, July ISSN meda concepts. On the other hand, the EBG metamaterals nvolve dstances that are on the order of half a wavelength or more and are descrbed by the Bragg reflecton and other perodc meda concepts. Ths paper focuses on transmsson lne metamaterals, whch are planar structures consstng network of dstrbuted transmsson lnes loaded perodcally nductor L capactor C, n hgh pass confguraton. The perodc unt cell s much smaller then the wavelength, thus loadng to an effectve medum n whch the lumped loadng elements can be ether dscrete Fg.- : Generc sketch of a volumetrc metamateral or prnted. Based on such negatve refractve ndex syntheszed by embeddng varous nclusons transmsson lne metamaterals, several fundamental n a host medum. propertes of physcal scences and engneerng based In 967, Veselago [4] theoretcally nvestgated mcrowave devces havng broadband propertes are plane-wave propagaton n a materal whose permttvty explaned. and permeablty were assumed to be smultaneously Fundamental propertes explanng physcal scences: negatve. Smth, Schultz [5, 6] and ther group constructed such a composte medum for the mcrowave regme and demonstrated expermentally the presence of anomalous refracton n ths medum. Metamaterals are of dfferent types : It s well known that the response of a system to the presence of an electromagnetc feld s determned to a large extent by the propertes of the materals nvolved. We descrbe these propertes by defnng the macroscopc parameters permttvty and permeablty µ of these (a) (b) (c) SNG (Sngle negatve metamateral) DNG (Double negatve metamateral) EBG (Electromagnetc band gap metamateral) The SNG and DNG metamaterals nvolve materals. Ths allows for the classfcaton of a medum as follows. A medum wth both permttvty and permeablty greater than zero ( > 0, µ > 0) wll be desgnated a doublepostve (DPS) medum. nclusons and nterncluson dstances that are much smaller than a wavelength and, as a consequence, such meda can be descrbed by homogenzaton and effectve Most naturally occurrng meda fall under ths desgnaton. A medum wth permttvty less than zero and permeablty greater than zero ( < 0, µ > 0) wll be 05

3 Internatonal Journal of Scentfc & Engneerng Research, Volume 6, Issue 7, July ISSN desgnated an epslon-negatve (ENG) medum. In certan scatters from a DNG slab embedded n a medum have frequency regmes many plasmas exhbt ths characterstc. been derved. The geometry s shown n Fg.-3. For example, noble metals behave n ths manner n the nfrared (IR) and vsble frequency domans. A medum wth the permttvty greater than zero and permeablty Incdent wave less than zero ( > 0, µ < 0) wll be desgnated a munegatve (MNG) medum. In certan frequency regmes some gyrotropc materals exhbt ths characterstc. Artfcal materals have been constructed that also have DPS, ENG, and MNG propertes. A medum wth both the permttvty and permeablty less than zero ( < 0, µ < 0) Reflected wave Transmtted wave wll be desgnated a DNG medum. To date, ths class of Fg. 3 : Plane-wave scatterng from slab of thckness d. materals has only been demonstrated wth artfcal The slab has an nfnte extent n the transverse constructs. Ths medum classfcaton can be graphcally drectons; t has a thckness d n the drecton of llustrated as shown n Fg.-. propagaton of the ncdent plane wave. Let the medum ENG Materal DPS Materal before and after the slab be characterzed by, µ and the ( < 0, µ> 0) ( > 0, µ> 0) slab be characterzed by, µ. For a normally ncdent Plasmas plane wave, the reflecton and transmsson coeffcents for the slab are DNG Materal MNG Materal ( < 0, µ< 0) ( > 0, µ< 0) η η R = η + η e jkd jkd [( η η )/( η + η )] e Not found n nature, but physcally realzable Gyrotropc magnetc materals T 4η η = ( η + η ) e jkd jkd [( η η )/( η + η )] e () Fg. : Materal classfcatons. The reflecton and transmsson coeffcents where the wave number k = ω µ and wave assocated wth a normally ncdent plane wave that mpedance η = µ / for =,. For the case of 05

4 Internatonal Journal of Scentfc & Engneerng Research, Volume 6, Issue 7, July ISSN normal ncdence, f we consder a matched DNG medum, also become "negatve". Ths suggests that the refracton s one would have η = η so that R = 0 and T = jk d j k d e e + =. Negatve refracton : The phenomenon of negatve refracton s studed by consderng the scatterng of a wave that s oblquely ncdent on a DPS DNG nterface as shown n Fg.-4. anomalous, and the refracted angle s on the same sde of the nterface normal as the ncdent angle s. The wave and Poyntng vectors assocated wth ths oblque scatterng problem are also obtaned : k k nc reff = k = k ( cosθ zˆ + sn xˆ ) nc θnc ( cosθ zˆ + sn xˆ ) nc θnc Z (3) Incdent wave Reflected wave k trans = k ( cosθ zˆ + sn xˆ ) trans θtrans x Transmtted wave Transmtted n DGS medum wave n DPS medum Fg. 4 : Geometry of the scatterng of a wave oblquely ncdent upon a DPS-DNG nterface. Enforcng the electromagnetc boundary condtons at the nterface, one obtans the law of reflecton and Snell's Law from phase matchng : θreff = θnc & θtrans = sgn (n) sn n n snθ nc Mcroscopc and Macroscopc vews of Metamaterals : The substances postulated n [7] have not yet been found n nature and need to be fabrcated n the laboratory. Currently, they are realzed as an arrangement of metallzatons properly orented n space, yeldng metamaterals that are therefore ntrnscally nhomogeneous and mcroscopc. On the other hand, the metallzatons themselves as well as ther separatons are very small compared to the operatng wavelength. Callng upon the effectve medum theory, t s therefore legtmate to look for bulk propertes, n ths case a bulk permttvty and permeablty, that govern the macroscopc behavor of the medum. These two vews, the mcroscopc vew on one hand and the macroscopc vew on the other, are two aspects of the same problem that are connected by retreval () Note that f the ndex of refracton of a medum s negatve, then the refracted angle, accordng to Snell's law, should algorthm whch, from a set of parameters measured on the mcroscopc metamaterals, yeld the bulk propertes of the macroscopc metamaterals. Varous retreval algorthms 05

5 Internatonal Journal of Scentfc & Engneerng Research, Volume 6, Issue 7, July ISSN have been publshed n the lterature [8 0], all wth the where negatve values occur. Hence, t s of lttle surprse same purpose of establshng the connecton between the metallzatons and the consttutve parameters of the that the desgn and optmzaton of the geometry of the rngs have been an actve area of research. effectve medum. In the next secton, we shall brefly descrbe both ponts of vew to ascertan how these metamaterals are realzed and how they are modeled. Mcroscopc Vew : Rods and Rngs as Buldng Blocks of Metamaterals: Current mplementatons of metamaterals rely on 'nfnte" rods and splt-rng resonators (SRRs) to acheve a negatve permttvty and a negatve permeablty, respectvely. The rngs can take varous shapes, some of whch wll be detaled n the forthcomng sectons. The rngs are the buldng blocks to acheve an effectve frequency-dspersve permeablty, whch has been shown to obey the frequency dspersve Lorentz model [3] llustrated n Fg.- 5a,b. µ r = f mp f f mo (4) f + Y mo m f / π where the subscrpt r refers to relatve values, Ym s the magnetc dampng factor, and fmo and fmp are the magnetc resonant and plasma frequences, respectvely, wth fmo < fmp. It s seen that for frequences between fmo and fmp the permeablty assumes negatve values. The shape of the rngs, ther effectve rad, the wdth of ther metallzatons, and many other factors drectly translate nto ther propertes and govern ther resonant and plasma frequences, whch are drectly related to the bandwdth Fg. 5a,b : Permttvty, permeablty, and assocated sotropc ndex of refracton for a medum characterzed by a Drude model and a Lorentz model. Propertes on Engneerng : In conventonal postve-refractve-ndex (PRI) transmsson-lnes (TLs), the phase lags n the drecton of postve group velocty, mplyng that the phase ncurred s negatve. It therefore follows that phase compensaton can be acheved at a gven frequency by cascadng a secton of a 05

6 Internatonal Journal of Scentfc & Engneerng Research, Volume 6, Issue 7, July ISSN negatve-refractve-ndex lne (.e., a backward-wave lne) wth a secton of a postve refractve-ndex lne to synthesze postve, negatve, or zero transmsson phase at a short physcal length. The structure of Fg.-6 can be rearranged to form a seres of symmetrc metamateral unt cells, as proposed n [,]. Such a unt cell s shown n Fg.- 7. It s nothng but a transmsson lne of characterstc mpedance Z0, perodcally loaded wth seres capactors C0 and shunt nductors L0. A representatve dsperson dagram for typcal host transmsson-lne and loadng parameters s shown n Fg.- 8. Fg. 8 : The dsperson dagram for the perodc structure wth typcal lne and loadng parameters. The edges of the stop band are desgnated by fc and fc. The metamateral phase-shftng lnes can then be Fg.-6 : A phase-compensatng structure based on a conventonal transmsson lne and a backward-wave lne. constructed by cascadng a seres of these unt cells. The edges of the stop band, fc and fc n Fg.-8 are determned at the seres resonance between the nductance of the transmsson lne secton and the loadng capactor, CO, and the shunt resonance between the capactance of the transmsson-lne secton and the loadng nductance, L0, respectvely. Alternatvely, these are the frequences at Fg. 7 : A unt cell of a metamateral phase-shftng lne comprsng a host transmsson-lne, perodcally loaded wth seres capactors and shunt nductors. whch the effectve permeablty, µn (ω), and the effectve permttvty, N(ω), vansh : N(ω) = 0, µn (ω) = 0. Broadband Balun : Baluns are partcularly useful; devces for feedng two-wre antennas, where balanced currents on each 05

7 Internatonal Journal of Scentfc & Engneerng Research, Volume 6, Issue 7, July ISSN branch are necessary to mantan symmetrcal radaton band, whch follows drectly from the fact that the phase patterns wth a gven polarzaton. Two-wre antennas have nput ports that are closely spaced, therefore, ther feedng structures should be chosen to accommodate ths requrement. A broadband NRI-TL balun that meets these requrements s shown n Fg. 9a and 9b. characterstcs of the +900 and 900 lnes match very closely. The flat dfferental output phase has a 800 ± 00 bandwdth of.6 GHz, from.7 GHz to.33 GHz. For comparson, a dstrbuted-transmsson-lne Wlknson balun (TL-balun), employng 700 and 900 lnes nstead of the +900 and 900 metamateral lnes, was also smulated, fabrcated, and measured at f0 =.5 GHz. The dfferental output phase of the transmsson-lne balun s also shown n Fg.- 0b. It can be observed that the phase response of the transmsson-lne balun was lnear wth frequency, wth a slope equal to the dfference between the Fg.-9a : A photograph of the fabrcated NRI-TL balun n phase slopes of the 700 and 900 transmsson lnes. mcrostrp. Fg. 9b : The archtecture of the NRI-TL balun. It conssts of a Wlknson power dvder, followed by a +900 metamateral phase-shftng lne along the bottom branch. Fg.- 0a shows excellent solaton for the devce, as well as an equal power splt between the two output ports. Fg.-0a : The measured and smulated solaton (S3) and through (S and S3) magntude responses of the NRI-TL balun. Fg.-0b shows the measured and smulated dfferental output phase of the NRI-TL balun, wth excellent agreement between the two. It can be observed that the dfferental output phase remans flat for a wde frequency 05

8 Internatonal Journal of Scentfc & Engneerng Research, Volume 6, Issue 7, July ISSN balun exhbted more than double the bandwdth, compared to a lumped element mplementaton usng lowpass/hgh-pass lnes, whch typcally exhbted a bandwdth of 3% [3]. Ths can be attrbuted to the fact that the low-pass lne has a lnear phase response, whle the response of the hgh-pass lne has a varyng slope wth frequency. Thus, the shapes of the phase responses of the two lnes dd not match resultng n a more narrowband dfferental output phase. REFERENCES :. J.C. Bose, "On the rotaton of plane of polarzaton of electrc waves by a twsted structure", Proc. Roy, Fg.-0b: The measured and smulated dfferental phase comparson between the NRI-TL balun and Soc., vol. 63, pp. 46 5, 898. the transmsson lne balun.. I.V. Lndell, A.H. Shvola, and J. Kurkjarv, "Karl F. Lndman: The last Hertzan, and a Harbnger of electromagnetc chralty", IEEE Antennas Propag. Mag., vol. 34, no. 3, pp. 4 30, 99. Snce the gradent of the resultng phase characterstc was qute steep, ths rendered the output dfferental phase response of the transmsson-lne balun narrowband. Thus the transmsson-lne balun exhbted a measured dfferental phase bandwdth of only %, from.4 GHz to.58 GHz, compared to 77% exhbted by the NRI-TL balun. In addton, the transmsson-lne balun occuped an area of 33.5 cm, compared to 8.5 cm for the NRI-TL balun. Thus, the NRI-TL balun was more compact, occupyng only 55% of the area that the conventonal transmsson-lne balun occuped. Furthermore, the NRI-TL 3. W.E. Kock, "Metallc delay lenses", Bell Sys. Tech. J., vol. 7, pp. 58 8, V.G. Veselango, "The electrodynamcs of substances wth smultaneously negatve values of and µ." Sov. Phys. Uspekh, vol. 0, no. 4, pp , 968. [Usp. Fz. Nauk, vol. 9, pp , 967]. 5. D.R. Smth, W.J. Padlla, D.C. Ver, S.C. Nemat- Nasser, and S. Schultz, "Composte medum wth smultaneously negatve permeablty and permttvty", Phys. Rev. Lett., vol. 84, no. 8, pp , May

9 Internatonal Journal of Scentfc & Engneerng Research, Volume 6, Issue 7, July ISSN R.A. Shelby, D.R. Smth and S. Schultz,. G.V. Eleftherades, A.K. Iyer, and P.C. Kremer, "Expermental verfcaton of a negatve ndex of refracton," Scence, vol. 9, no. 554, pp , 6, Apr V. Veselago, "The electrodynamcs of substrates wth smultaneously negatve values of and µ," Sav. Phy. USPEKHI, vol. 0, pp , Jan/Feb D.R. Smth, S. Shultz, P. Markos, and C.M. Soukouls, "Determnaton of effectve permttvty and permeablty of metamaterals from reflecton and transmsson coeffcents", Phys. Rev. B, vol. "Planar Negatve Refractve Index Meda Usng Perodcally L-C Loaded Transmsson Lnes", IEEE Transactons on Mcrowave Theory and Technques, MTT-50,, December 00, pp M.A. Antonades and G.V. Eleftherades, "Compact, Lnear, Lead/Lag Metamateral Phase Shfters for Broadband Applcatons", IEEE Antennas and Wreless Propagaton Letters,, 7, July 003, pp H.S. Nag, "Mnnature Lumped Element , pp. 9504, 00. Wlknson Dvder", IEEE Internatonal 9. R.W. Zolkowsk, "Desgn, fabrcaton, and testng Symposum on Mcrowave Theory and of double negatve metamaterals", IEEE Trans. Technques,, June 003, pp Antennas Propag., vol. 5, pp , July X. Chen, T.M. Grzegorczyk, B.I. Wu, J. Pacheco Jr., and J.A. Kong, "Robust method to retreve the consttutve effectve parameters of metamaterals", Phys. Rev. E. vol. 70, 06608,