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1 Sess 9, 9, ; di:.339/s97598 OPN ACCSS sess ISSN Aticle A Miiatue Pckels Cell with Nvel lectde Gemet Slbda J. Peticevic *, Pedja Mihailvic, ad Jva Raduvic Facult f lectical gieeig / Buleva Kalja Aleksada 73, Begad, Sebia; -Mails: pedjamih@gmail.cm (P.M.); aduvic@etf.s (J.R.) * Auth t whm cespdece shuld be addessed; -Mail: slbda@etf.s; Tel.: ; Fa: Received: Ma 9; i evised fm: 9 Jue 9 / Accepted: 6 Jul 9 / Published: 6 Jul 9 Abstact: This pape discusses imptat elemets f the Pckels sesig cell desig. A vel electde gemet is aaled i de t btai maimum sesitivit espse fm Pckels cstals (Bi GeO ). This eithe tasvesal tul lgitudial gemet, esults i electical field distibuti alg the sesig beam path that pvides high mdulati depth. Demstated pefmace level is i ageemet with theetical studies. Delta-sigma plaiati detecti methd allws high lieait f the detect tasfe fucti ad measuemet idepedet lase itesit vaiatis. Chael gai equaliati pcess ecessa f accuate delta-sigma maliati is pvided b a walk ff pism. Kewds: Pckels cell; electde gemet; delta-sigma; Bi GeO ; fibe ptic ses. Itducti Iceasig eed f electic pwe demads lage capacit f electic pwe sstems. Hece, tasmissi vltage iceases as well as the sies f vltage ad cuet tasfmes. Fibe-ptic sess have the ptetial t eplace vltage ad cuet tasfmes b ffeig seveal advatages: immuit t electmagetic itefeece, high damic age, cmpact desig, impssibilit f

2 Sess 9, eplsi ad wide badwidth [-4]. O the the had, i de t eplace eistig techlg, fibeptic sess maufactues must have lwe csts ad impve tempeatue cmpesati techiques. The piciple f the fibe-ptic cuet ses (FOCS) is t measue the magetic field caused b the sesed cuet usig Faada effect. The fibe-ptic vltage ses (FOVS) is based the Pckels effect ad measues electic field t calculate the vltage. Used tgethe the cstitute a electic pwe mete f supeme diagstics f electic pwe sstems [5]. It is a cmmecial beefit ad a techlgical simplificati t use the same ptical cstal f bth cuet ad vltage sesig. Ou cstal f chice is bismuth gemaium ide, Bi GeO (BGO). BGO is taspaet ve a wide wavelegth age ad is a lw-cst mateial eadil available withut ptical defects. BGO cstals have cubic smmet, space gup 3 ad ae withut biefigece but the pssess ptical activit. BGO shws Faada tati with a Vedet cstat f appimatel 7 ad/tm. Absece f biefigece is cucial f successful FOCS cstucti [6]. Sice BGO ehibits diamagetic ppeties Faada tati tempeatue cmpesati f FOCS ca be ealied [7]. This pape pesets cstucti ad calibati f a lw cst Pckels cell with a BGO cstal, small i dimesis ad ead t be icpated i plaimetic etisic fibe-ptic vltage sess. The electptical cefficiet f BGO is 4 [ - m/v ] 3.67, λ 633 m [8] ad that is sufficiet f FOVS cstucti. Additiall, malied tempeatue depedece f the BGO ptical activit is egative [9] ad ca be used t cmpesate f the tempeatue depedece f the Pckels effect i the cstal []. Ohtsuka ad Shimmua have ptimied legth ad cfiguati f electptic cstals t icease sesitivit []. Hweve, futhe impvemet ca be made b electde gemet that pvides ptimal electical field distibuti alg the light beam path eablig iceased mdulati depth. This pape ppses a vel, eithe tasvesal tul lgitudial, electde gemet that pvides bette sigal t ise ati f highe accuac measuemets.. Pckels Sesig Setup F the light suce we chse a mw, 63.8 m wavelegth He-Ne lase. A plaiig pism (PP) was placed i ft f the lase. This deceases the light beam iadiati but suppesses ise, sice plaiati fluctuatis ae cveted t light iadiati fluctuatis. A e de quate-wave plate fllws the plaiig pism with the fast ais at a 45º agle with espect t the plaie tasmissi aes. Ciculal plaied light impiges the Pckels cell ad becmes ellipticall plaied due t the electic field. The biefiget cstal (CaCO 3 ) with fast ad slw aes paallel t the maj ad mi aes f the efacti ellipse is placed behid the Pckels cell. It spatiall divides the lase beam it tw cmpets with mutuall thgal plaiatis. Iadiatis f bth beams deped the light suce itesit i the same wa. Usig this fact we ca calculate the etadace Φ that is t depedet the itesit f the light suce b diffeece-ve-sum methd. This ccept is illustated i Figue. Beam iadiatis ae measued usig tw segmets f a quadat phtdide (4QPD), fllwed b a dual tasimpedace (DUAL TIA) stages. Stages ae idetical, based dual peatial amplifie, havig the same tasimpedace gais.

3 Sess 9, 9 53 Figue. Sesig setup. I de f this sesig sstem t achieve the desied accuac, it is equied that the detecti gais f tw beams be idetical. qualiati is accmplished b adjustig the paametes f the tasimpedace stages with bth cstals emved fm the beam path. Lss imbalace betwee the tw chaels afte sepaati f tw thgall plaied light beams is miimied b usig a highl biefiget CaCO 3 cstal istead f a plaiig pism ad makig the sepaate ptical paths paallel. This fact als eables the use f the quadat phtdide thus matchig ptelectic cvesi gais as much as pssible. 3. Pckels' Cell Cstucti ad Mdelig The task f the Pckels cell desig is t pvide maimum pssible etadace f the applied vltage. Retadace depeds the chice f elect-ptic cstal ad the gemet f the Pckels cell electdes. F eass stated i the itducti, we have selected a bismuth gemaium ide Bi GeO BGO cstal as the elect-ptic cstal. It has cubic smmet, space gup 3 ad it is withut biefigece, but pssesses ptical activit. The BGO cstal is cut paallel t the ( ) plae ad is mm thick. We assume that the ais is thgal t this plae ad that the light wave tavels alg the ais. I de t ptimie gemet f the Pckels cell electdes let us w cside a Pckels cell with eithe tasvese tul lgitudial cfiguati as displaed i Figue.

4 Sess 9, 9 53 Figue. Gemet f electdes. I such electde gemet the electical field ctais ad cmpets. Sice the pit gup f BGO is 3 electptic tes has the fm: 4 4 4, () ad ide ellipsid is: 4 4 () T fid efactive idices i plae we set. 4 (3) Rtati f ad aes aud the ais b 45º gives picipal idices f efacti ' ad ' : 4 cs 4 si 4 si 4 cs (4) 4 4 (5) (6)

5 Sess 9, (7) dφ ( ) d ( ) d λ (8) 3 4 λ Ad the ttal etadace is: Φ λ λ λ B B ( ) d 4 ( ) dl 4U AB A A. (9) Sice the BGO cstal is a liea medium, thee is a liea elatiship betwee vltages U AB ad measued vltage U: U AB MU, < M <. B itducig this liea elati i (9) e btais: MU U M 3 Φ 4 λ U () The BGO cstal pssesses fllwig imptat elect ptical ppeties at λ 633 m [8]:. 4 is m/v..55 Thee is up t 5% diffeece i these quatities betwee vaius cstal samples. Thus the half-wave vltage U is: λ U 5V () 3 4 ad it depeds the cstal tpe but is ivaiat the cstal sie ad shape f electdes. Fact M is depedet the electic field distibuti ad ca be ptimied b shapig the gemet f the electdes i such a fashi t maimie the scala pduct ude the itegal i equati 9. F each diffeet cstal legths thee is a ptimal gemet f electdes ad electdes efficiec ca be cmpaed usig fact M s we'll call it efficiec fact. Sice ptical activit pevets a icease f the cell sesitivit b iceasig the cstal sie [] we have chse a BGO cstal that is mm thick. The lwe limit f the cell css secti sie is set b the light beam used i this epeimet. F the Uiphase mdel P He-Ne lase used, beam waist diamete is w.63 mm ad beam diamete w at the sesig pit.5 m is: w w w, λ, w. 9mm F these dimesis paallel-plate capacit appimati is t valid ad istead f the stadad lgitudial mdulati gemet we eamied a gemet peseted i Figue. We have made a epeimetal pefmace cmpais betwee a cvetial lgitudial mdulati Pckels cell ad this vel asmmetic cfiguati.

6 Sess 9, Sigal Pcessig Sigal pcessig is accmplished alg the lies f the blck diagam shw i Figue 3. Fllwig discussis elates t this diagam. Ifmati the measued high vltage is peset i the tw lw pwe phtcuets cmig fm tw quadats f the e biased fu quadat phtdide (QPD). These phtcuets ae amplified ad cveted t vltage b smmetical tasimpedace stages. Opeatial amplifies used i these stages ae muted the same PCB at the ptical setup ed. Resultig vltages ae fed t tw aalg t digital cvetes (ADC) iside a SiLabs C85F64 micctlle (MCU). Cvetes peate at ksps with 6 bits f esluti ad ste acquied wavefms i a bad mem. Mem is gaied as tiple buffes. Data tasfes take place simultaeusl with data acquisiti pcess via USB iteface. This eables data acquisiti f ewe sigal peids while lde peids ae tasfeed t the PC f pcessig. The micctlle is cected t a RS3 t USB cvete (INTRFAC USB) that pvides a USB lik t the PC i the fm f the vitual COM pt. USB pwe suppl (5 V DC) is cveted t ± V DC used t pwe peatial amplifies i tasimpedace stages ad the aalg cmpets. This fucti is accmplished b the POWR SUPPLY blck. Figue 3. Blck diagam f the sigal pcessig cicuit. Of paticula imptace is the phase lcked lp (PLL) blck used t lck the ADC sample ate t pwe lie fequec. This is ecessa sice fequec lckig f the samplig ate elimiates leakage ad picket fecig i the fequec dmai. PLL is cstucted usig a vltage ctlled scillat (VCO) as a fequec geeat ad multiplicati ati is detemied b cutig the umbe f high fequec pulses i e sigal peid ( ms). The VCO iput is adjusted usig a DA cvete t establish the equied multiplicati. Oce this ati is established, the MCU checks the metied cut ad detemies its ate f chage, i de t aticipate et accuate values f VCO iput. This pcess is ctiuus, ad is used t hld the PLL i the lcked state. Gais f tasimpedace stages ae pgammable, case gai settig is accmplished usig digital ptetimetes f tasimpedaces ad fie gai ctl is accmplished usig ADC calibati. Gai ctls ae ecessa i de t equalie gais (slpes f the light t vltage tasfe fuctis) f the tw idepedet sesig chaels i delta-sigma maliati methd.

7 Sess 9, The PC ctls eecuti f all steps i the algithm b cmmads set via a USB lik t the bad MCU. MCU eecutes cmmads ad espds with data steams ctaiig wavefms f sampled values. The sigal pcessig algithm is peseted i Figue 4. Iitial ctl steps establish acquisiti ate, umbe f samples pe peid, umbe f peids pe fame ad statig the PLL blck. The PLL the us util it lcks, ad futhe steps ae itduced t check the PLL stabilit ad jitte. Oce the ecessa cditis f accuate sesig ae established, the PLL is left ude the ctl as descibed t maitai it i the lcked state. The, the light suce is switched ff ad ffsets i tasimpedace stages ae elimiated b applig cmpesati vltages t passive iputs f peatial amplifies. Tasimpedaces f TIAs ae the set t accmplish equal DC espse (case gai ctl) f bth chaels. The ADC fie gai ctl is used t equalie DC espses belw level f detecti (agula e f mdeg). This eds the calibati pcedue ad chaels ae w csideed t be bth equalied ad calibated t the ecessa degee f accuac. Figue 4. Sigal pcessig algithm.

8 Sess 9, Thee fllws a ctiuus lp csistig f fame acquisiti, pcessig, filteig ad esult calculati. The PC istucts the MCU t acquie a ew fame, check f cmpleti flag, ad etieves the fame t the iteal PC mem. The fame is the pcessed t deal with ADC utput fmats ad discete Fuie tasfm (DFT) is the calculated. Opeatis take place i basebad, e fequec bi is 5 H wide, thee beig a ttal f bis pe wavefm f a kh sample ate. DFT btaied i this wa is filteed b emvig all fequec cmpets apat fm the base fequec ad is evese pcessed usig ivese discete Fuie tasfm (IDFT) t btai filteed time dmai wavefms. These wavefms ae the displaed f bsevati pupses. Results ae calculated usig the magitudes f bth chaels base fequec DFT bis ad a ms value is btaied fm them. These ms values ae used as iputs i delta sigma equati ad the esultig agle is displaed the scee. 5. peimetal Results With chaels gais equalied, aes f the biefiget cstal aliged f the maimum espse ad i the case whe etadace is much smalle tha ptical activit, utput sigal vltages U / f the tasimpedace stages ae: U kγ si ρ ( ) ρ / ±Φ () whee Γ is the beam iadiati, ρ is the ptical activit ad k is a cstat that mdels ptical lsses ad ptelectic cvesi efficiec [-3]. The diffeece ve sum espse is: U U si ρ M si ρ R Δ / Σ Φ U cu U U ρ U ρ (3) Calibati f the Pckels cell was pefmed epeimetall, b measuig the espse R Δ/Σ btaied fm Δ/Σ sesig methd, as descibed abve. The magitude f the AC ecitati the cstal electdes was vaied b meas f the auttasfme ad measued with the vltmete cected t a PC usig a seial pt. The fm f the measuemet scee ca be see i Figue 5 tgethe with esults btaied f a ecitati vltage f 7.5 V (amplitude). The gee ad mageta sigals epeset utput vltages f the tasimpedace stages (left ais). The white sigal epesets the espse R (ight ais, deted Theta the scee). All sigals ae fuctis f time deted b the Time ais i [s]. Hamics diagam displas fequec ctet f the espse sigal (digital filte implemets a cut ff abve H). Numeic displas peset mea espse value MAN R (.353 deg), espse (RMS R) calculated fm the fequec bi at 5 H, ad espse (R) value calculated fm the wavefm, als i degees. Lwe pat f the scee ctais fuctis f ctllig the electic sigal pcessig cicuit ecessa t implemet gai equaliati.

9 Sess 9, Figue 5. Measuemet scee f ecitati vltage f 7.5 V.,6 Figue 6. Calibati gaph.,5 Nvel gemet R Δ/Σ [ad],4,3, Cvetial gemet,, 5 5 Vltage U [V] Ou epeimets shw that cefficiet M f mm thick cstal is highe f the gemet shw i Figue. F bth cfiguatis the efficiec fact M ca be btaied fm Figue 6 usig a liea fit f the epeimetal data. F the case f asmmetic electdes, c is [V - ]. Sice ptical tat pwe at λ 63.8 m is 8 /mm, the ptical activit ρ 36. Theefe efficiec fact M is.537. F the case f cvetial lgitudial electde cfiguati, c is [V - ], theefe the M is Cclusi A ew Pckels cell electde gemet has bee ivestigated i de t icease the mdulati depth ad decease cell dimesis. The mathematical mdel peseted shws that mdulati depth depeds t l electptical ppeties f the cstal, but als the electdes psiti ad shape. This depedece is me sigificat at lwe cstal thickess t beam diamete ati. The same

10 Sess 9, mathematical mdel is applicable f cmpais f vaius electde cfiguatis usig the efficiec fact M. A vel gemet Pckels cell, mm thick ad with 6 4 mm css secti, was cstucted ad epeimetall cmpaed with a stadad lgitudial Pckels cell f the same dimesis. Pcedue f tw chaels gai equaliati, cucial f lase itesit ad plaiati fluctuati suppessi, i Δ/Σ maliati methd is descibed i detail. Accuate sigal pcessig i fequec dmai is accmplished b dedicated PLL cicuit that establishes fied elatiship betwee samplig ad sigal fequec. This vel gemet f electdes iceases the slpe f the tasfe fucti b.7-fld. Refeeces ad Ntes. Ulme,.A. A high-accuac ptical cuet tasduce f electic pwe sstems. I T. Pwe Delive. 99, 5, Sawa, T.; Kusawa. K.; Kamiishi, T.; Ykta, T. Develpmet f ptical istumet tasfmes. I T. Pwe Delive. 99, 5, Wag, Z.P.; Zhag, S.Q.; Zhag, L.B. Recet advaces i ptical cuet-sesig techiques. Sess Actuat. A. 995, 5, Lauesse, I.J.; Kema, C.G.A.; Rutges, W.R.; va de We, A.H. Applicatis f ptical cuet ad vltage sess. Sess Actuat. A 989, 7, Li, Y.; Li, C.; Yshi, T. Optical electic-pwe-sesig sstem usig Faada ad Pckels cells. Appl. Opt., 4, Tab, W.J.; Che, F.S. lectmagetic ppagati thugh mateials pssessig bth Faada tati ad Biefigece: peimets with Yttebium Othfeite. J. Appl. Phs. 969, 4, Madde, W.I.; Michie, W.C.; Cude, A.; Niewcas, P.; McDald, J.R.; Advic, I. Tempeatue cmpesati f ptical cuet sess. Opt. g. 999, 38, Webe, M.J. Hadbk f Optical Mateials, CRC Pess LLC: Bca Rat, FL, USA, Mihailvic, P.; Peticevic, S.; Stakvic, S.; Raduvic, J. Tempeatue depedece f the Bi GeO ptical activit. Opt. Mat. 8, 3, Lpe-Higuea, J.M. Hadbk f Optical Fibe Sesig Techlg, Wile & Ss, Ltd.: West Susse, glad, ; pp Ohtsuka, M.; Shimmua, T. Ifluece f ptical tat pwe ptical vltage ses usig BGO cstal. lect. Cmmu. Jp. 994, 77, 3.. Cude, A.; McDald, J.R.; Advic, I. Optical cstal based devices f cuet ad vltage measuemet. I T. Pwe Delive. 995,, Li, C.; Yshi, T. Simultaeus measuemet f cuet ad vltage b use f e bismuth gemaate cstal. Appl. Opt., 4, b the auths; licesee Mlecula Divesit Pesevati Iteatial, Basel, Switelad. This aticle is a pe-access aticle distibuted ude the tems ad cditis f the Ceative Cmms Attibuti licese (