Amplitude Modulation and Demodulation in Magnetized Quantum Plasma with SDDC

Transcription

1 IOSR Jourl o Applid Physis (IOSR-JAP) -ISSN: olu 8, Issu 6 r. (Nov. - D. 6), PP -8 Aplitud Modultio d Dodultio i Mgtizd Qutu Pls with SDDC N.Ydv, A. Agrwl *, S.Ghosh 3 Shool o Studis i Physis, ir Uivrsity, Ui - 65 (M.P.), Idi Abstrt: Aplitud odultio s wll s dodultio o ltrogti wv i trsvrsly gtizd qutu pls with stri dpdt diltri ostt is lyzd i dirt wv ubr rgios ovr wid rg o rrir ylotro rquy. Th osidrtio o qutu ts i odultio d dodultio is o pri iport or th ddig o w disios i ousto-ltri gtizd siodutor pls. It is oud tht qutu ts odiy th plitud odultio d dodultio prosss tivly. Nuril stits r d or -BTiO 3 rystl t 77K duly shid by pulsd.6 µ CO lsr.coplt bsorptio o th wv ts pl i ll th possibl wvlgth rgis wh th ylotro rquy ω bos rly qul to ω. Kywords: Aoustoltri t, Stri dpdt diltri ostt, Qutu ts. I. Itrodutio Motivtd by th xtsiv rsrhs i th ild o siodutor qutu pls ro th dirt rsrhrs, [-3] i prst ppr lytil ivstigtios r d or th plitud odultio d dodultio o ltrogti wv i tril with stri dpdt diltri ostt (SDDC) usig qutu hydrodyi odl (QHD). Aplitud odultio (AM) is odultio thiqu usd i ouitio pross i whih th plitud o high rquy rrir wv is hgd i ord with th ssg or iortio sigl. AM grtio ivolvs ixig o rrir d iortio sigl. Th odultio o ltrogti wv propgtig through pls is othig but th priodi vritios o th propgtio prtrs. Wh uodultd ltrogti wv propgts through pls diu with priodilly vryig prtrs, it gts odultd or dodultd i trs o plitud or rquy. This priodi vritio i th propgtio prtr hs b usd by ti-vryig hrg rrir dsity d ollisio rquy o pls. Modultio or dodultio o pup wv is th pross o hgig plitud or rquy or phs. I otrst to rquy odultio d phs odultio, AM thiqu ws th rlist or o odultio usd to trsit udio sigls. This typ o odultio wh utilizd to bst dvtg, its iiy ithr qul or xd tht o ll othr odultio prosss. I y oplx odultio shs, th phoo o odultio o ltrogti wv by ousti wv is vry usul i lrg ubr o pplitios ivolvig th trsissio, disply d prossig o iortio. A AM typ syst trsits th rrir d both sid bds with qul iiy. This is ot usd or xiu sipliity d ooy, prtiulrly t low outputs []. Th britio o so oustoltril dvis is bsd o th itrtio o ousti vibrtios d th obil rrirs. This itrtio givs usul iortio rgrdig th physil proprtis o th host diu. I th study o possibl itrtios i di whr wv utios o th ighborig prtils ovrlppd, qutu orrtios tht y b stitd by QHD odl o plss, plys iportt rol. Ths wv utio ovrlppig bos possibl oly wh th dbrogli wv lgth o th hrgd prtils bos oprbl to th disios o th pls syst. Thr is otibl itrst or qutu plss du to thir wid-rgig pplitios i ultr sll ltroi dvis [5-7]. Th its pup b ltrostritivly grts ousti wv withi th SDDC diu tht idus itrtio btw r hrg rrirs d th ousti phoos. This itrtio idus strog sp hrg ild tht odults th pup b. Thus, th pplid optil d grtd ousti wv i ltrostritiv odultor produ plitud odultio d dodultio t t ousti wv rquy. Svrl rports o odultio i siodutor plss hs b rportd by ubr o worrs [8-]. Ni d his oworrs [] rportd th plitud odultio d dodultio o ltrogti wv i prs o hot rrirs i gtizd diusiv siodutor plss usig hydrodyi odl. Ydv d Ghosh [3] hv obsrvd th plitud odultio d dodultio i stri dpdt diusiv siodutors. Th diusio o rrirs shows th strog ilu o th olirity o high obility III- opouds siodutor. Th siodutor thology is grlly bsd o th high obility o xitd hrg rrirs through diusio prosss. Th odultio o lsr b produd du to rti pls t i siodutor ws rportd by S d Kw []. Rtly, xtsiv studis with qutu orrtio o prtri itrtios d logitudil phoo Plso DOI:.979/ Pg

2 Aplitud Modultio d Dodultio i Mgtizd Qutu Pls with SDDC itrtios hv b rportd [5-6]. Th opt o plitud odultio d dodultio i siodutor pls hs rportd by y rsrhrs but th study o suh pross i qutu pls systs ss to b thortilly uxplord. H, ispird by th bov sttus i th prst ppr, uthors studid qutu ts o plitud odultio d dodultio o ltrogti wv i SDDC tril. For th study o qutu t i suh pross, uthor usd QHD odl whih is brig odl dvlopd or qutu pls through th piorig wors o Mrdi d Hss [7]. II. Thortil Forultio Authors hv usd th QHD odl to gt th obtiv stblishd i itrodutio stio. Authors hv osidrd hoogous -typ rystl (-BTiO 3 ) or th thortil orultio o plitud odultd lsr b. Th diu is irsd i stti gti ild B poitig log z-xis tht is orl to th propgtio vtor o prtrilly grtd ousti wv log x-xis ;. Hr, w hv ssud xpi xt dpdy o th ild qutitis. Th low-rquy prturbtios r ssud to b du to th ousti wv, produd by ousti polriztio i th rystl. Th ltro otrtio osillts t th ousti wv rquy du to th SDDC ild ssoitd with th ousti d is th pup wv rquy. Th trsvrs urrt dsitis produd t rquy wv. Th pup wv th givs ris to trsvrs urrt dsity t th rquis whr r ow s irst ordr sid bd urrt dsitis. Ths sid bd urrt dsitis produ sid bd ltri ild vtors d this wy th pup wv gts odultd. I th subsqut lysis th sid bds will b rprstd by th suixs ±, whr + stds or th od propgtig with th rquy d stds or od. Th qutio o otio or x t u, is osidrd i ordr to id th prturbd urrt dsity i SDDC rystl whih dsribs th ltti vibrtio d is giv by, * u u C g () t x x whr d C r th ss dsity d th lsti ostt rsptivly, is th diltri ostt wh th stri is zro d g is ouplig ostt is giv by DOI:.979/ Pg g. Th * ovr qutity rprsts its oplx 3 ougt. Th sp hrg ild is dtrid by th Poisso qutio s * g u () x x whr lst tr o RHS rprsts th SDDC otributio. To oput th prturbtio urrt dsity i - typ SDDC rystl usig qutios () d (), o obtis th prturbd rrir otrtio s u A g (3) g is th I whih is th ousti spd i th rystl ltti giv by C d A C disiolss ouplig oiit du to SDDC. Th osilltory ltro luid vloity i prs o th pup ltri ild s wll s tht du to th sid bd ods giv blow t whr, ostt b obtid by usig th ltro otu trsr qutio o th QHD odl whih is x B P x 3 P is th Fri prssur i whih Fri vloity 3 d Fri tprturt. B x BT () with Boltz

3 Aplitud Modultio d Dodultio i Mgtizd Qutu Pls with SDDC Hr, th subsript stds or, + d ods. Th bov qutio dsribs th ltro otio udr th ilu o th ltri ilds ssoitd with th pup d sid bd ods i whih is th tiv ss o th ltro d is th phoologil ltro ollisio rquy. stds or prturbd d uprturbd ltro dsity. I th bov rltio, th pup gti ild is gltd by ssuig tht th ltro pls rquy o th diu is o th ordr o pup rquy. By lirizig qutio (), th vloity opots r obtid s, x y i ' i p ' ' with. i p d rprsts th ilusio o qutu t i th itrtio pross. 8 T B I qutios (5) d (6) B is th ylotro rquy d p rquy. Th totl trsvrs urrt dsity i th diu is giv by, J totl xpi x t (5) (6) is th pls (7) whr, xpi x t rprsts th urrt grtd du to th itrtio o th pup with ousti wv. Usig qutios (5), (6) d (7) i th grl wv qutio, x totl totl J totl (8) t t xp i x i opriso to, w obtid th whr is th prbility o th diu d gltig ollowig xprssios or odultio idis, i uc A i i p i whih g. By rtioliztio o bov qutio, o obtis th rl prt o odultiol idis s, ' uc A p It b irrd ro th bov qutio tht qutu ts ppr i th prtr ' (9) () ' d SDDC otributio otid i A d ply sigiit rol i didig th gituds o th odultio idis i siodutor pls. III. Rsult Ad Disussio I this stio w lyz th bov xprssio () to disuss th plitud odultio/dodultio du to ousto-ltri itrtio with d without qutu t i th prs o SDDC i trils with high diltri ostt. To gt so uril ppritio, w us th ollowig prtrs o -BTiO 3 siodutor rystl ssud to b duly irrditd by.6 µ pulsd CO lsr t 77K:..5, 5 s, L s,.6 s s s, 3 g 3 T 77. DOI:.979/ Pg

4 + / ( ) + / ( ) / ( ) / + ( ) Aplitud Modultio d Dodultio i Mgtizd Qutu Pls with SDDC xprssio () or th odultio idx i th SDDC tril with d without qutu t b lyzd or two dirt wv ubr rgis viz., (i) d (ii) (i) Wh : Th vritio o d with th pplid gti ild r dpitd i igurs d.it bos y b irrd ro igurs tht wh o pplis w gti ild, th ylotro rquy sllr th th rrir rquy, th both th ods r i phs with pup wv, whih xhibits odultio pross. At prtiulr vlu o gti ild wh th odultio idis o both th ods bo zro d oplt bsorptio o wvs ts pl o gltig th ollisio tr i qutio (). O urthr irsig th ylotro rquy both sid bd go out o phs. Ths out o phs sid bds th itrt with th pup wv udr this oditio to produ dodultd ousti wv. W olud tht dodultio pross b obsrvd i th rgi with i prs d bs o qutu tr. It lso b s tht th odultio idx o th ius od is lwys grtr th tht o th plus od. with qutu t 5 with qutu t with out qutu t with out qutu t ( 3 )s - Figur. ritio o odultio idx o plus od (wh ) with gti ild with d without qutu ts. ( 3 s - ) Figur. ritio o odultio idx o ius od (wh ) with gti ild with d without qutu ts. (ii) Wh : Th vritio o d with th pplid gti ild r dpitd i igurs 3 d. I this wv ubr rgi th bhvior o odultio idis or plus d ius ods r (s show i igurs 3 d ) opposit i tur. I th s wv ubr rgi th plitud o th plus od is positiv udr th oditio. H udr this rgi o ylotro rquy, th plitud o plus od is i phs with th pup wv. This sid bd th itrts with th wv to produ odultd ousti wv. Howvr, wh th rrir rquy bos rly qul to th ylotro rquy, oplt bsorptio o wvs ts pl o gltig th ollisio tr i qutio (). I th rg did s, th odultio idis o plus od is gtiv. This out o phs sid bd wvs th gi itrt with th pup to produ dodultd wv whih xhibits dodultio pross. Fro igur w s tht i this wv ubr rgi th plitud o th ius od is gtiv udr th oditio d out o phs with pup wv. This sid bd th itrts with th wv to produ dodultd ousti wv. DOI:.979/ Pg

5 + / ( 3 ) + / ( ) - / ( 3 ) - / ( ) Aplitud Modultio d Dodultio i Mgtizd Qutu Pls with SDDC with qutu t with qutu t with out qutu t with out qutu t ( 3 )s - Figur 3. ritio o odultio idx o plus od (wh ) with gti ild with d without qutu ts ( 3 )s - Figur. ritio o odultio idx o ius od (wh ) with gti ild with d without qutu ts. Wh th rrir rquy bos rly qul to th ylotro rquy, oplt bsorptio o wvs ts pl o gltig th ollisio tr i qutio (). A slight tuig i th rg did s t this rso oditio drss th idis bruptly to zro d xhibits odultio pross. Thus, or prtiulr gti ild i o gts odultio o plus sid bd od th ius sid bd od bos dodultd d vi-vrs. It is vry sitig rsult. I. Colusios Fro th bov disussio th odultio d dodultio o th M wv by th ousti wv b sily hivd by usig tril with high diltri ostt. It is oud tht qutu t plys sigiit rol i didig th prtr rg d sltig th sid bd od, whih will b odultd by th bov tiod itrtio. Th qutu orrtio tr ltrs th rsult vorbly. It lwys irss th vlu o odultio/dodultio idis or both th ods roud.thus i prs o qutu tr th tril with stri dpdt diltri ostt ors itrstig diu or th purpos o ivstigtios o dirt odultiol itrtios d o hops to op pottil xpritl tool or rgy trsissio d solid stt digostis i rystls with high diltri ostt. Rrs []. F. Hss, L.G. Gri, J. Godrt d G. Mrdi, Qutu io-ousti wv, 3, Phys. Plss, (), 3, []. P. K. Shul d S. Ali, Dust ousti wvs i qutu plss Phys. Plss,, 5, 5-3. [3]. A.P. Mishr d A.R Chowdhury, Modultio o dust ousti wvs with qutu orrtio, Phys. Plss 3, 6, []. R. Sghvi d S. Ghosh, Aplitud Modultio d Dodultio o ltrogti Wvs i Mgtizd with Stri- Dpdt Diltri Costt, Mtril, Phys. Stt. Sol. 8, 99, 35. [5]. Art Shr, Nilsh Ni, N. Ydv d S. Ghosh, t o Dsity Grdit o Logitudil Phoo-Plso [6]. Itrtios i Colloids Ld Siodutor Qutu Plss, Itrtiol J. o Adv. Rs. i Physil Si.,, 9-7. [7]. Ar P. Mishr d P. K. Shul., Aplitud odultio o ltro pls osilltios i ds ltro-hol pls, Phys. o Plss,, 7, 83. [8]. S. Ghosh, Swti Duby, d R. shpl, Qutu t o prtri pliitio hrtristis i pizoltri siodutors, Phys. Ltt. A, 375,, 3-7. [9]. S.S. Mthur,d MS. Sgoo, Ultrsoi odultio o irowvs i pizoltri siodutors, Cdi J. o Phys., 5,973, []. C.N. Lshor Dvis,Modultiol istbility o iit plitud Alv wv, Phys. o Fluids, 9, 976, 587. []. A. Nogi, KP. Mhswri d MS. Sodh, Modultiol istbility i optilly strid gto-tiv siodutors, J. o th Optil Soity o Ari B,, 99, []. S. Ghosh d M.P. Rishi, Aousto-opti odultio i gtisd diusiv siodutors, urop Physil J. D:Atoi, Molulr, Optil d Pls Physis, 9,, 3-3. [3]. Nilsh Ni, Swti Duby d S. Ghosh, Aplitud Modultio d Dodultio o ltrogti Wv i Mgtisd ousto-opti diusiv siodutor plss, Optis d Lsr Thology,,, []. S. Ghosh d Nishhhl Ydv, Aplitud Modultio d Dodultio i Stri Dpdt Diusiv siodutors, At Physi Poloi A,, 7. [5]. A. S, d P. Kw, Rsot bsorptio thod o lsr odultio, Jourl o Physis D: Applid Physis, 6, 973,9. [6]. S. Ghosh, Swti Duby, d R. shpl, Qutu t o prtri pliitio hrtristis i pizoltri siodutors Phys. Ltt. A, 375,, 3-7. [7]. Art Shr, Nilsh Ni, N. Ydv d S. Ghosh, Logitudil phoo-plso itrtio i qutu siodutor plss with o-prtiiptig olioids, Itrtiol Jourl o Physis d Mthtil Sis, (), 3, 5-5. [8]. G. Mrdi d F. Hss, Sl-osistt luid odl or qutu ltro gs, Phys. Rv. B, 6,, DOI:.979/ Pg