Wave Propagation in Rectangular Waveguide Filled with Anisotropic Metamaterial
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1 IJCSI Ieiol Joul o Copue Sciece Issues Vol. 9 Issue 3 o 3 M ISS (Olie): Wve Popio i Recul Wveuide Filled wih Aisoopic Meeil edi Skli Dhou Bouchouich d Touik Auili cole iole diéieus de Tuis (o SYS COM) B.P: 37 e Belvédèe Tuis Tuisi Asc I his ppe ioous lsis o he Tsvese Opeo Mehod (TOM) ollowed he pplicio o he Gleki ehod is developed o sudi he popio i ecul el wveuide illed wih isoopic eeil. The wve equio d he dispesio elios o uided d evesce odes i he uide e oied d led. The hihe ode odes e eploied. The ueicl esuls e oied d coped o heoeicl pedicios. ueicl eples show he vlidi o his ehod. Aisoopic eeils oud ipo idusil pplicios such s ciculos isolos phse shies d es. Kewods: Gleki ehod ihe ode odes Recul wveuide wih isoopic eeil Tsvese opeo ehod.. Ioducio Doule eive eils (DG) wih eive peiivi d peeili ejo owi iees especill ecuse o hei phsicl popeies h e diee o hose o coveiol doule posiive eils (DPS). Veselo [] ws he is o sud heoeicll he DG eils. Diee specs o his clss o eeils hve ee sudied e i [-3]. Ieesi eues o he uided odes i wveuide illed wih wo pllel ples eils DPS d DG hve ee sudied i [4-8]. [9] d [] hve sudied he popio i wveuides o eeils. I his ppe we pese lsis o he popio i ecul el wveuides copleios illed wih isoopic eeil (Fi. ) usi he TOM ollowed he Gleki ehod. ueicl eples e ive eploii he hihe ode odes i hese pes o sucue. The esuls e coped o hose o coveiol doule posiive eils (DPS). MOT [] kes io ccou he spil disiuio o he peiivi d peeili o edi d heeoe discoiuiies o he le which is pplied o he svesl ield. This ehod is pplicle o vious sucues hooeeous o ihooeeous isoopic o isoopic. The coveece o cos popio o he sudied sucue is s. I is oied o 5 odes.. Alsis. The svese opeo ehod I ecul coodie sse we coside ellic ecul wveuide o widh d hih s show i iue copisi isoopic ediu chceied peiivi d elive peeili eso ive he equio () d (). o Fi. Coiuio o he ecul wveuide copleel illed wih isoopic eeil wih : ; () Copih (c) Ieiol Joul o Copue Sciece Issues. All Rihs Reseved.
2 IJCSI Ieiol Joul o Copue Sciece Issues Vol. 9 Issue 3 o 3 M ISS (Olie): Mwells equios e wie: () o jω. (3) o ω j. (4) Cosidei popio lo O we hve: Φ ( ) Φ ( ).ep( jk ) (5) wih Φ [ ] j. (6) Φ / : Repeses he svese copoes o he elecoeic ields ω is he ul equec d Z e especivel; he popio cos d he chceisic ipedce o ee spce. B eliii he loiudil copoes o elecoeic ields (3) d (4) c e wie []: Φ jη Φ (7) is he svese opeo deied : (8) wih : k / k [/ ] (9) / / We hve: / / k () () / k [/ ] () k / ] [ / k ω η j η d η η j (3) is he svesl opeo d is is djoi opeo. The loiudil copoes e eled o he svese ields : / / / k (4) / / / k (5) The ove eioed elios e vlid o solvi poles i ihooeeous edi uide wih isoopic o isoopic d dissipive. Ali he cse o isoopic eeils diols such s: (6) d (7) These codiios led o h. As esul he equio (7) ecoes jη (8) jη (9) Th is idepede o deivi he sse (8) d (9) wih espec o we oi wo decoupled equios i d. k η Φ Φ () wih η d η. () η I hese epessios: η () η (3) The decoupled equio wih k ecoes: (4) k O: k (5) wih k (6) (7) (8) Copih (c) Ieiol Joul o Copue Sciece Issues. All Rihs Reseved.
3 IJCSI Ieiol Joul o Copue Sciece Issues Vol. 9 Issue 3 o 3 M ISS (Olie): k (9) quio (4) is eievlue equio. u The decoposiio o he ields T o coplee sse povides eievlue. The es o svese ields sisi he oud codiios ( T o o o ) c e wie i he ollowi os π π cos.si π π si.cos (3) (3) We oe: π π si( ) cos( ) π π si( ) cos( ) (3) The sse o equios (5) c e wie k k. Applicio o he Gleki ehod (33) (34) We hve: ;. Oe c choose he ollowi es ucios π π si( ) cos( ) π π si( ) cos( ) (35) The ie poducs wih equio (33) d wih equio (34) he iei we oi ( ) ( O O) k [ ( ) ( O O) ( ) ( O O) ] dd [. dd ( ) ( O O) (36) ] dd k. dd (37) he c e wie i he ollowi i o. (38) G k. G B olisi we c esil id h: G G. We se:. (39) The sse (38) c e wie T k I T (4) I is he idei i. is sque i o ode ( ) wih : ue o odes; d e ul ues such s: ( ) ( ). The eievlues d he pope vecos o e especivel he popio cos d he coeicies o develope o he ield o he uide. Copih (c) Ieiol Joul o Copue Sciece Issues. All Rihs Reseved.
4 IJCSI Ieiol Joul o Copue Sciece Issues Vol. 9 Issue 3 o 3 M ISS (Olie): Siulio Resuls 3. Wveuide o. Coside o. el sque wveuide: side [] copleel illed wih eeil. k/k Wveuide o. Coside o. el ecul wveuide: 35 d 5 [] copleel illed wih eeil. k/k Féquece () () Féquece ().5 ().5 k/k.5 k/k Féquece ().5 () Féquece () () k/k k/k Féquece () (c) Fi. Dispesio cuves o he uide o. : () ep uide; () uide illed wih isoopic eeil whee (c) uide illed wih isoopic eeil whee Féquece () (c) Fi. 3 Dispesio cuves Guide o.: () ep uide () uide illed wih isoopic eeil whee (c) uide illed wih isoopic eeil whee. Copih (c) Ieiol Joul o Copue Sciece Issues. All Rihs Reseved.
5 IJCSI Ieiol Joul o Copue Sciece Issues Vol. 9 Issue 3 o 3 M ISS (Olie): O he oe hd we oice h hee is sped i he uides copleel illed wih eeil (DG) isoopic. O he ohe hd he cuo equecies o isoopic eeil uides che ove he se uide vcuu. Ao he piculiies o his isoopic eil he ckwd d owd wves c oh pope elow he cuo equec i he uide. The ueicl esuls oied i his ppe e ee wih he eeeces [] d [5] which vlides ou ueicl clculios. 4. Coclusios Wih he olis o he TOM we peseed ioous sud o popio i hooeeous isoopic edi usi he eso chce o he peeili d peiivi. Wih he pplicio o he Gleki ehod we hve sudied he evesce d popi odes i ecul uides illed wih isoopic o isoopic eeil. Copisos o uides coii coveiol dielecic e eploied. The dves o he echiques used i his ppe lies i he pope licl oulio o he pole sudied o he oe hd d he speed o coveece o he ohe. This pe o eils kow s eeil is widel used d eeded idusies d ioio echolo especill i icowve d RF devices such s pch es he es wveuides esoos ciculos isolos phse shies... TOM oes s coveece o he popio cos. This shows he eeciveess o ou ueicl odel. As such he oulio o he svese opeo could e useul ool o icowve eiees. Reeeces [] V. G. Veselo "The elecodics o susces wih siuleousl eive vlues o peiivi d peeili" Sov. Phs. Usp Vol. pp [] F. Y. Me Q. Wu d. W. i "Tsissio chceisics o wve odes i ecul wveuide illed wih isoopic eeil" Appl. Phs. A (9) 94 pp [3] K. Sikv "Modl lsis o he icowve equec espose d coposie ih-/le-hded opeio o ecul wveuide loded wih doule posiive d doule eive eils" Ieiol Joul o RF d Micowve Copue Aided ieei 7 (7) pp [4] A. Alu d. he "Guided odes i wveuide illed wih pi o sile eive (SG) doule-eive (DG) d/o doule-posiive (DPS) les" I Ts. Micowve Theo Tech. Vol. 5 pp [5] S. J. Bolic d Z. Sipus "Wveuide iiuiio usi uiil eive peeili eeil" I Tscios o Aes d Popio 53 (5) pp. 9. [6] C. M. Kowe "e-hded eil isoop eec o uided wve elecoeic ields Joul o Applied Phsics" 99 (6) [7] Y. S. Xu "Wve popio i ecul wveuide illed wih sile eive eeil sl" lecoics ees 39 (3) pp [8] D. Zh d J. M "The popio d cuo equecies o he ecul ellic wveuide pill illed wih eeil ulile sls" PIR M Poess I lecoeics Resech M Vol. 9 pp [9] K.. Chop S. Ku J. Joseph d K. Sih "Advces i Phooic d Micowve Techoloies Bsed o eive Phse Veloci Meils d Reled Topics - A Quliive Biliophic Review o he Ye 6 : P II" Iveis Joul o Sciece & Techolo Vol 4 o. 3 pp [] G. Zhe d. R "ih sissio lo sl wveuide wih coe o isoopic eeil" Opik - Ieiol Joul o ih d leco Opics (Sepee 8) 9 () pp [] J. W. To R. Adijo d. Budd "Geel Wveuide Poles Sudies Tsvese Opeo Mehod" I Tscios o Meics Vol. 3 o. 3 pp M 995. edi SAKI ws o i Medeie Tuisi i 966. e eceived he Mse Deee i Telecouicios o he Me--Vllée Uivesi Pis Fce i d he Ph.D. deee i Telecouicios o he iol School o ieei o Tuis (IT) Tuisi i 9. Acull he is Assis Poesso i Telecouicios he Uivesi o Ges Tuisi. is esech ieess iclude he popio i isoopic ediu ueicl ehod i elecoeic eeil es. Dhou BOUCOUICA ws o i Medeie Tuisi i 978. e eceived he M.A. deee i elecoics (hih equec sses o couicio) o he uivesi o Me-l-Vllée Pis Fce i 6. I he eceived he Ph.D. deee i elecoics o he Uivesi o Fçois Relis Tous Fce. e is cuel Poesso o elecoics eieei wih he Isiu Supieu d Ioique Medeie Tuisi. Whee his esech ivolves RF d icowves. is ield o iees is he desi o hid d pssive icowve cicuis es d hei pplicios i wieless couicios d wieless powe sissio. Touik AGUII ws o i Tiis Tuisi. e eceived his Dip. I. i lecicl ieei d Ph.D. i Telecouicios o ISA Fce. e is woki s Poesso cole iole d Iéieus de Tuis (IT). is esech civiies iclude elecoeic icowve cicuis odeli d lsis o scei d popio pheoe i ee spce. Copih (c) Ieiol Joul o Copue Sciece Issues. All Rihs Reseved.
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