Electromagnetic Wave Absorber with Isotropic and Anisotropic Metamaterials

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1 Ieaioal Joual of Maeials Sciece ad Applicaios 07; 6(6): hp:// doi: 0.648/j.ijsa ISSN: (Pi); ISSN: (Olie) Elecoageic Wave Absobe wih Isoopic ad Aisoopic Meaaeials Dog Yuxia School of Elecical ad Elecoic Egieeig, Noh Chia Elecic Powe Uivesiy, Beijig, Chia Eail addess: To cie his aicle: Dog Yuxia. Elecoageic Wave Absobe wih Isoopic ad Aisoopic Meaaeials. Ieaioal Joual of Maeials Sciece ad Applicaios. Vol. 6, No. 6, 07, pp doi: 0.648/j.ijsa Received: Novebe 0, 07; Acceped: Novebe, 07; Published: Decebe 6, 07 Absac: The absopio chaaceisics of he elecoageic wave popagaig hough oe diesioal syse wih he eaaeials ae sudied basig o he asfe aix ehod. The elaios bewee he absopiviy wih he fequecy of he icide wave ad he hickess of he eaaeials ae calculaed. The esuls show ha he absopiviy is abou 00% ea he esoa fequecy of he isoopic eaaeials. This eas ha he eaaeials ca be used as a aow bad absobe. The hickess of he eaaeials deeies he widh of he bad. Fuheoe he absopio chaaceisics of he ulilayes syse wih he isoopic ad aisoopic eaaeials ae sudied. The bad widh iceases wih he addiio of he laye ube. The absopio is depede o he polaizaio diecio of he icide elecoageic wave fo he aisoopic eaaeials. Thus he aisoopic eaaeials ca be used o be he polaizaio uable absobe. The laye ube ca also deeie he fequecy fo he axiu absopio as fo he ulilaye syse. Keywods: Absobe, Meaaeials, Mulilaye Syse, Polaizaio. Ioducio The eaaeials have aaced a gea deal of aeio fo boh heoeical ad expeieal sides i ece seveal decades. The eaaeials have he aificial sucue ad he elecoageic paaees ae depede o he esoa of he elecic ad he ageic field. I soe fequecy egio he effecive peiiviy ad he peeabiliy of he aeials ca be siulaeously egaive due o he peiodically posiioed scaeig elees. The aeials ae also called as he lef-haded aeials because he elecic field, he ageic field ad he wave veco fo a lef-haded elaio i he aeials. These edia exhibi a ube of uusual elecoageic popeies such as egaive efacive idex [] aplificaio of evaesce wave [], subwavelegh caviy esoao [3], zeo aveaged efacive idex bad gap [4] ec. Due o ha he ui esoace sucues of eaaeials ae usually aisoopic [], people becae ieesed i he aisoopic popeies ad evealed ay iiguig pheoea i diffee kids of aisoopic eaaeials [5-9]. Copaed wih he isoopic aeials, aisoopic aeials have oe feedo o cool he popagaio ad polaizaio of he elecoageic waves. People have show ha he popey of egaive efacio is o cofied o aeials wih egaive defiie peiiviy eso ad peeabiliy eso, bu ca be expeced o occue i ceai classes of uiaxially aisoopic edia. Reseach has show ha elecoageic wave polaizaios ca be aipulaed feely hough eflecios by aisoopic eaaeials [9, 0]. A sigle eaaeial plae ca seve as a badpass file, aspae wall, ad polaizaio covee ude illuiaio fo diffeely polaized waves []. A sudy of he quaizaio of he elecoageic field i aisoopic eaaeials has also bee pefoed; he ipu-oupu elaios of quaized adiaio have bee deived fo a sigle aisoopic eaaeial plae [, 3]. Soe uusual popeies fo he polaized phoo asiig hough a hee laye caviy coaiig aisoopic eaaeials ae sudies i Ref. [4]. Sice os poposed eaaeials ae eallic esoa sucues ad ely o sog esoaces, he absopio losses ae ieviable. The loss of he eaaeials ofe degades hei pefoace. Howeve, he loss becoes useful ad i could be sigificaly ehaced i pefec absobe. Sice is fis peseaio [5], eaaeial

2 Ieaioal Joual of Maeials Sciece ad Applicaios 07; 6(6): absobes have eceived cosideable aeio ad ay absobes have bee poposed [6-8]. A effecive ehod o boade he absopio badwidh is o ake he eaaeial uis esoae a seveal eighboig fequecies. Followig his desig saegy, polaizaio isesiive o polaizaio depede boadbad absobes have bee widely deosaed fo icowave o opical. Huag e al. [9] peseed he polaizaio depede boadbad absobe based o hee I-shaped esoaos. Ga e al. [0] obaied polaizaio isesiive widebad absobes by sackig uliple paes. Bu he eseach abou he elecoageic wave popagaig hough a ulilaye caviy is o sudied a pese. I is eaigful o sudy he absopio chaaceisics of he wave popagaio hough ulilaye sucues of aisoopic eaaeials. I his wok, we ae ieesed i he opical aisoopy ad he asissio popeies a a plaa ulilaye caviy wih a egaive peiiviy, whose wave chaaceisics have ye o be exaied. I his pape, a polaizaio uable absobe foed by aisoopic eaaeials is peseed. The absobe fequecy is able o be ued by eely chagig he polaizaio of he ligh. The uable echais oigiaes fo he vaiaio of he effecive legh of he absobe. This feaue akes he poposed sucue vey useful i aipulaig polaizaio of ligh ad deecig waves wih specific polaizaio.. Theoical Deivaio ad Calculaios I is a oal ehod o calculae he asfe of he elecoageic i oe diesioal ulilaye sucue o use he asfe aix ehod (TMM). Fo a oe diesioal N laye sucue, he elaive peiiviy eso ε ad elaive peeabiliy eso µ of he aisoopic ediu i each laye ae give by ad εx 0 0 ε εy ε z µ x 0 0 µ µ y µ z Fo isoopic eaial, he diagoal elees i he above aix ae he sae. Fo he Maxwell equaios we ca ge k ω µ k E + ε E ( ) c () () i (3) 4 E(,) = Eσeˆ σe σ = i kxx+ kyy+ kzσz ω wih E σ as he expasio coeiffecies, ad ê σ as he veco of he elecic field. / ( ) ( X x Y y Z z) (4) eˆ = X + Y + Z ˆ + ˆ + ˆ (5) σ σ σ σ σ σ σ The paaees i he above equaio ae defied as ( ) ( ) Xσ = ω c ε µ k µ k ω c ε µ k µ k µ k k y z x x z z y x x y x y z ( ) Yσ = µ x µ y kxkykz µ z kxk y ω c ε z µ y kx µ x k y ( ) Zσ = µ x µ z kxkykz µ y kxk z ω c ε y µ z kx µ x k z (8) We ca also ge he ageic field fo he Maxwell equaios as wih 4 ( ) ˆ i k x x k y y k z σz ω Eσhσe + + σ = H, (6) (7) = (9) hˆ σ = µ ( k eˆ σ ) (0) µ ω Hee µ 0 is he peeabiliy of he vacuu. The asfe aix ca be obaied by he bouday codiio of he elecoageic field. Fo he oe diesioal ulilaye sucue, he elecoageic wave i he -h laye ca be expessed as 0 4 ˆ E e σ i kxx+ kyy+ kzσ ( z z ) ω E e = σ ˆ H () σ = h σ wih { k, k k, k, k k,} = = as he udeeied z z z z3 z4 z3 coefficies, ê σ, ˆ ( h ) σ ad kz σ ae he eige veco of he elecic filed, he ageic field ad he wave veco i he -h laye. The value z - is he sa value of coodiae of he -h laye. Usig he bouday codiio, which is ha he ageial copoe of he elecic filed ad he ageic field ae equal i z=z -, we ge 4 4 ( ) ( ) ik ˆ ˆ ˆ ˆ zσ d Eσ eσ y = Eσ eσ ye () σ = σ = Hee d =z -z - is he hickess of he -h laye aeial. The above equaio ca also be wie i a aix foa as Hee k is he wave veco of he elecoageic wave

3 304 Dog Yuxia: Elecoageic Wave Absobe wih Isoopic ad Aisoopic Meaaeials ( ) E E ( ) E E D ( ) DP = E3 E3 ( ) E4 E4 wih ad P D eˆ yˆ eˆ yˆ eˆ 3 yˆ eˆ 4 yˆ ˆ ˆ ˆ ˆ h xˆ h xˆ h3 xˆ h4 xˆ = ˆ ˆ ˆ ˆ h yˆ h yˆ h3 yˆ h4 yˆ eˆ xˆ eˆ xˆ eˆ 3 xˆ eˆ 4 xˆ e z ik d ikz d 0 e 0 0 = ikz3 d 0 0 e A las, he asfe aix ca be obaied as e z4 ik d (3) (4) (5) sp pp ps Bp M M M M = = A M M M M p A Bp M M M M A M M M M p A B s M M M M A M M M M 3 3 (0) () () The asissio coefficies fo diffee polaizaios ae especively ss sp Cs M 33 = = A M M M M Cp M 3 = = A M M M M pp p A Cp M A M M M M (3) (4) (5) (0) ( ) ( ) E + E + E (0) ( + ) ( + ) E E E (0) = D0 DPD DPD DPD D + M ( + ) = ( + ) E3 E3 E3 (0) ( + ) ( + ) E4 E4 E4 Hee 4 4 asfe aix M is defied as 0 + (6) M = D DPD D PD D PD D (7) We use A s, A p, B s, B p ad C s, C p o epese he icide, eflecio ad he asied wave of he elecic field apliude. Coside he elecoageic wave is icide fo he fis laye fo he lef side, he we have As Cs M M M3 M4Cs B s 0 M M M3 M 4 0 = M = (8) Ap Cp M3 M3 M33 M34Cp B p 0 M 4 M4 M43 M44 0 The eflecio ad asissio coefficies ae he expessed i es of he elees of he popagaio aix by achig he ageial field copoes a he exeal boudaies. Whe he asfe aix is block diagoal, he eflecio ad asissio aices becoe diagoal, eaig ha he wo odes ae he TE ad TM odes. If he icide wave is s/p polaizaio, he eflecio coefficies ss / pp ad sp / ps ae especively ss Bs M M M M = = A M M M M (9) ps C s M3 A M M M M p A (6) Accodig he defiiio of he absopio, he absopio A s fo he icide wave which is s polaizaio is s ss sp ss sp A = (7) The absopio A p fo he icide wave which is p polaizaio ca be obaied by p pp ps pp ps A = (8) 3. The Calculaio Resuls Fis we coside a sigle slab of isoopic eaaeials wih he hickess d ebedded i he dielecic backgoud (ai). Assuig he elecoageic wave which is liealy polaized alog x-diecio ad y-diecio avels alog he z diecio. We ake he values of he peiiviy ad peeabiliy as ( ) ( ) ωp 0 ε ω = ε + ω ω iγ ω ( ) ( ) ωp, 0, µ ω = µ + ω ω iγ ω e (9) (30) fo he isoopic eaaeial. Hee ωp, ω p, ae he plasa

4 Ieaioal Joual of Maeials Sciece ad Applicaios 07; 6(6): fequecy. γe, γ ae he dissipaio fequecy. ε ( ), µ ( ) ae he saic peiiviy ad peeabiliy. ε ( ω ) = µ ( ω) ae used o ake he ipedace achig. ωp = ωp, = π.5thz, ω0 = ω0, = π.0thz, γ γ π 0.THz ad ε ( ) µ ( ).0 = = ae used i he calculaio. The calculaed esul fo he elaio bewee he eal pa ad he iagiay pa of he elaive effecive peiiviy ad he peaeabiliy wih he fequecy is show i Figue. The esuls show ha he eal pa of he elaive effecive peiiviy chages fo he posiive value o he egaive value whe he fequecy is THz. A he sae ie he iagiay pa has he axiu value ad he elaive effecive peiiviy is esoa. The iagiay pa of he elaive effecive peiiviy deeies he dissipaio of he elecoageic wave i he aeial. Thus he absopio is he axial whe he fequecy is locaed i he esoa fequecy. Figue. The elaios bewee he eal pa ad he iagiay pa of he effecive elaive peiiviy wih he fequecy. Figue. (colo o lie) The elaios bewee he absopio wih he fequecy ad he hickess. Figue is he esul fo he absopio of a sigle laye isoopic eaaeial wih he fequecy ad he hickess of he eaaeial. The esul shows ha he fequecy has a esoa peak ad he badwidh is deeied by he hickess. As he iceasig of he hickess, he badwidh is bigge. These esuls ea ha we ca use a sigle laye of eaaeial o be he elecoageic wave file wih he adjusable badwidh. Fo he ulilaye syse wih he eaaeial, we ca sudy he effec of he ulilaye eflecio o he absopio of he elecoageic wave. Cosideig such a sadwiched hee layes syse, a laye of eaaeial is placed i wo adiioal aeial wih he elaive peiiviy ad he peaeabiliy as ε =.0, µ =.0. The hickess of each

5 306 Dog Yuxia: Elecoageic Wave Absobe wih Isoopic ad Aisoopic Meaaeials laye is ake as 0.0. The absopio of he elecoageic wave hough such a hee laye syse is show i Figue 3 as he dashed lie. The absopio of he elecoageic wave hough such a sigle laye syse wih he hickess 0.0 is also show i Figue 3 as he solid lie fo copaiso. The esuls show ha he absopio of he hee laye syse is bigge ha he sigle laye syse alhough ha he hickess of he eaaeial fo he wo kid of he sucue is he sae. This is because ha he ieface uli-eflecio of he ulilaye syse elage he absopio. We also plo he esul fo a peiodic ulilaye sucue wih he laye ube as N= as doed lie i Figue 3. The hickess of each laye fo a laye syse is ake as 0.0. The paaee of he adiioal aeial is he sae as he hee laye syse. Fo he plo we fid ha he badwidh fo a laye ube sucue is bigge he hee laye sucue. I eas ha he badwidh of he absopio is deeied by he laye ube. Figue 3. The elaios bewee he absopio wih he fequecy fo he sigle laye sucue (solid lie), he hee laye sucue (dashed lie) ad he uli-laye sucue (doed lie) coaiig he isoopic eaaeials. Figue 4. The elaios bewee he absopio wih he hickess of he eaaeial fo a sigle laye sucue wih he fequecy as f=.0thz (solid lie), f=.thz (dashed lie) ad f=.5thz (doed lie). We also sudy he elaio bewee he absopio wih he hickess of he isoopic eaaeial fo a sigle laye syse which is show i Figue 4. The plo give hee diffee cases wih he fequecy f=.0thz (solid lie), f=.thz (dashed lie) ad f=.5thz (doed lie). The absopio fo he elecoageic wave wih he fequecy.0thz which is he esoa fequecy is easie o achieve sauaio. Fo he aisoopic eaaeial, we sudy he absopio of he elecoageic wave i diffee polaizaio hough he sigle laye ad ulilaye sucue wih he aisoopic eaaeial. The followig paaees

6 Ieaioal Joual of Maeials Sciece ad Applicaios 07; 6(6): p, ω µ x ( ω ) = µ z ( ω) = ω + iγ ω p, ω µ y ( ω) ω + iγ ω (3) (3) ae ake fo aisoopic aeial. ε = ε = ε =, x y z ωp, = π.5thz, ad γ = π 0.THz ae used i he calculaio. The esuls fo he absopios As ad Ap ae show i Figue 5 as solid lie ad doed lie especively. The hickess is ake as 0.0 i he calculaio. The absopio Ap achieves he axiu value ea abou 0.4THz. Howeve he absopio achieves he axiu value ea abou.3thz. This is caused by he diffee peeabiliy. The absopio is depede o he polaizaio diecio of he icide elecoageic wave fo he aisoopic eaaeial. Thus we ca use he aisoopic eaaeial o be he polaizaio uable absobe. Figue 5. The elaios bewee he absopio fo he aisoopic eaaeial wih he fequecy fo elecoageic wave i he s polaizaio (solid lie) ad p polaizaio (doed lie). Figue 6. The elaios bewee he absopio fo he ulilaye aisoopic eaaeial (N=) wih he fequecy fo elecoageic wave i he s polaizaio (solid lie) ad p polaizaio (doed lie). Fo he ulilaye syse wih he aisoopic eaaeial, we ake he laye ube N= show i Figue 6. Cosideig he ulilaye syse like his, a laye of eaaeial is sepaaed by wo adiioal aeial wih he elaive peiiviy ad he peaeabiliy as ε =.0, µ =.0. The hickess of he adiioal aeial each laye is ake as 0.0 ad he sae as he aisoopic eaaeial. Fo he esul we fid ha he absopio fo he ulilaye syse

7 308 Dog Yuxia: Elecoageic Wave Absobe wih Isoopic ad Aisoopic Meaaeials is geae ha he sigle laye syse. A he sae ie he fequecy fo he axiu absopio is ovig. So he laye ube ca also deeie he fequecy fo he axiu absopio. 4. Coclusio The absopio popeies of he oe diesioal sucue wih he eaaeial ae calculaed basig o he asfe aix ehod. The absopio is appoachig he axiu value, 00% whe he feuquecy of he icide wave is ea he esoa fequecy fo he sigle laye isoopic eaaeials. The badwidh of he icide wave becoes lage whe he hickess iceases. This eas ha he sigle laye eaaeials ca be used as he elecoageic wave aow bad absobe ad he badwidh ca be coolled by he hickess of he eaaeials. The ieface effec akes he absopio lage fo he hee laye sucue wih he eaaeial ad he adiioal aeial. The easo is ha iceasig he ube of he laye ake he hickess of he sucue lage, hus he badwidh of he absopio is bigge. Fo he syse wih he aisoopic eaaeial, we sudy he absopio of he elecoageic wave i diffee polaizaio. The absopio is diffee fo diffee polaizaio which is caused by he diffee peeabiliy. The absopio is depede o he polaizaio diecio of he icide elecoageic wave fo he aisoopic eaaeial. Thus we ca use he aisoopic eaaeial o be he polaizaio uable absobe. The laye ube ca also deeie he fequecy fo he axiu absopio. Iceasig he laye ube he absopio chages wih he fequecy. Ackowledgees This wok was suppoed by he Fudaeal Reseach Fuds fo he Ceal Uivesiies ude Ga No. 05MS0. Refeeces [] D. R. Sih, W. J. Padilla, D. C. Vie, S. C. Nea-Nasse, ad S. Schulz, Coposie Mediu wih Siulaeously Negaive Peeabiliy ad Peiiviy, Phys. Rev. Le (000) [] L. F. She, S. L. He ad S. S. Xiao, Sabiliy ad qualiy faco of a oe-diesioal subwavelegh caviy esoao coaiig a lef-haded aeial, Phys. Rev. B 69 5 (004) [3] J. Li, L. Zhou, C. T. Cha, P. Sheg, Phooic Bad Gap fo a Sack of Posiive ad Negaive Idex Maeials, Phys. Rev. Le (003) [4] D. R. Sih ad D. Schuig, Elecoageic Wave Popagaio i Media wih Idefiie Peiiviy ad Peeabiliy Tesos, Phys. Rev. Le (003) [5] L. Zhou, C. T. Cha, ad P. Sheg, Aisoopy ad oblique oal asissio a a plaa egaive-idex ieface, Phys. Rev. B (003) [6] S. Su, X. Huag, ad L. Zhou, Two-diesioal coplee phooic gaps fo layeed peiodic sucues coaiig aisoopic lef-haded eaaeials, Phys. Rev. E (007) [7] L. Hu ad S. T. Chui, Chaaceisics of elecoageic wave popagaio i uiaxially aisoopic lef-haded aeials, Phys. Rev. B 66, (00) [8] Q. Cheg ad T. J. Cui, Elecoageic ieacios bewee a lie souce ad aisoopic biaxial edia wih paially egaive cosiuive paaees, J. of Appl. Phys. 98, (005) [9] J. Hao ad L. Zhou, Elecoageic wave scaeigs by aisoopic eaaeials: Geealized 4 4 asfe-aix ehod, Phys. Rev. B (008) [0] J. Hao, M. Qiu ad L. Zhou, Maipulae ligh polaizaios wih eaaeials: Fo icowave o visible, Fo. Phys. 5(3), 9 (00) [] H. F. Ma, W. X. Tag, Q. Cheg ad T. J. Cui, A sigle eaaeial plae as badpass file, aspae wall, ad polaizaio covee coolled by polaizaiopl. Phys. Le (04) [] Y. Dog, X. Zhag, Quau-opical ipu oupu elaios ad eaglee disillaio by aisoopic plaa ulilayes, J. Op (0) [3] Y. Dog, C. Liu, Elecoageic field quaizaio ad ipu-oupu elaio fo aisoopic ageodielecic eaaeial, Chi. Phys. B (05) [4] Y. Dog, J. You, Popagaio of polaized phoos hough a caviy wih a aisoopic eaaeial, Fo. Phys., 406 (06) [5] N. I. Lady, S. Sajuyigbe, J. J. Mock, D. R. Sih, W. J. Padilla, Pefec Meaaeial Absobe, Phys. Rev. Le. 00, 0740 (008) [6] C. M. Was, X. L. Liu, W. J. Padilla, Meaaeial Elecoageic Wave Absobes,Advaced Maeials, 4 (3): OP98 (0) [7] H. Tao e al., A eaaeial absobe fo he eahez egie: Desig, fabicaio ad chaaceizaio, Op. Exp., vol. 6, o. 0, pp (008) [8] X. Liu, T. Sa, A. F. Sa, ad W. J. Padilla, Ifaed spaial ad fequecy selecive eaaeial wih ea-uiy absobace, Phys. Rev. Le., vol. 04, (00) [9] L. Huag e al., Expeieal deosaio of eahez eaaeial absobes wih a boad ad fla high absopio bad, Op. Le., vol. 37, o., pp (0) [0] J. Ga, Y. Ma, S. Saha, A. Khalid, ad D. R. S. Cuig, Polaizaio isesiive, boadbad eahez eaaeial absobe, Op. Le., vol. 36, o. 7, pp (0)