, dynamically reconfigurable systems (RADAR, electronic warfare, and surveillance applications); medical imaging; and hyper/super-computer communications.
One of the most widely deployed devices for analog optics modulation is the Mach-Zehnder Interferometer modulator (MZI). For binary digital signals, it is today the preferred device for long-haul fiber-optic communication, leading to chirp-free pulses which can reach hundreds of kilometers in optical fibers without the need for regeneration. For analog applications, however, a serious problem is encountered due to the inherent non-linear response of the modulator. Specifically, since the modulating voltage via the electro-optic effect controls the optical phase delay in a basically linear fashion and the attenuation varies as the cosine of the phase difference between the two branches of the device, a linear variation in phase difference and thus in applied voltage results in a cosine-shaped output variation, as seen in the pattern of points in FIG. 2A. The common solutions for this problem are either the biasing of the device to a quasi linear regime coupled with reducing the modulation range to reduce distortion, or use of an analog pre-distortion circuit to feed the modulator. Since in practically all present systems signals are processed digitally, a multi-bit Digital-to-Analog Converter (DAC) device is needed with fast processing capabilities.
A DAC based on a multi-electrode MZI modulator concept was proposed many years ago by Papuchon et al. and is described in U.S. Pat. No. 4,288,785. In that device, the electrodes' sectioning length followed a conventional power-of-two digital sequence, which did not solve the non-linearity problem, and thus suffered from severe limitation in the dynamic range, and subsequently the attainable resolution. More recently, much more complex devices have been presented to cope with these problems: Yacoubian et al. (“Digital-to-analog conversion using electrooptic modulators,” IEEE Photonics Technology Letters, vol. 15, pp. 117-119, January 2003), proposed the employment of one MZI modulator for each and every bit. A recently reported design by Leven et al. (“A 12.5 gsamples/s optical digital-to-analog converter with 3.8 effective bits,” Lasers and Electro-Optics Society, 2004. LEOS 2004. The 17th Annual Meeting of the IEEE, vol. 1, pp. 270-271, November
, dynamically reconfigurable systems (RADAR, electronic warfare, and surveillance applications); medical imagination; and hyper / ace - computer communication. 
 One of the most widely deploy devices for analog eye modulation is the Mach - Zehnder Interferometer modulator (MZI). For binary digital signals, it is today the preferred device for retentive - haul fiber - eye communication, leading to chirp - free pulses which can reach hundred of kilometers in optical fiber without the need for regeneration. For analogue applications, however, a serious problem is find due to the inherent non - linear reaction of the modulator. Specifically, since the modulating voltage via the electro - ocular effect controls the optical phase delay in a basically linear fashion and the attenuation vary as the cosine of the phase difference between the two branches of the device, a linear variation in phase difference and thus in applied voltage results in a cosine - shaped output variation, as seen in the pattern of points in FIG. 2A. The common solutions for this trouble are either the biasing of the device to a quasi linear government coupled with reduce the intonation range to reduce distorted shape, or use of an analog pre - distortion circuit to feed the modulator. Since in much all present systems signals are processed digitally, a multi - bit Digital - to - Analog Converter (DAC) device is needed with fast processing capabilities. 
 A DAC based on a multi - electrode MZI modulator concept was proposed many years ago by Papuchon et al. and is described in U.S. Pat. No. 4,288,785. In that device, the electrode' sectioning distance follow a conventional power - of - two digital sequence, which did not resolve the non - linearity problem, and thus suffered from dangerous limitation in the dynamic range, and subsequently the attainable resolution. More recently, a lot more complex devices have been presented to cope with these problems: Yacoubian et al. (“ Digital - to - analog conversion using electrooptic modulators, ” IEEE Photonics Technology Letters, vol. 15, pp. 117 - 119, January 2003), propose the employment of one MZI modulator for each and every spot. A recently reported blueprint by Leven et al. (“ A 12.5 gsamples / s optical digital - to - analogue converter with 3.8 effective bits, ” Lasers and Electro - Optics Society, 2004. LEOS 2004. The 17th Annual Meeting of the IEEE, vol. 1, pp. 270 - 271, November
, dyjamically reconfigurable systems (RADAR, glwctronmc warfzre, and rurveillance applications); mevicao imating; and hyper/super-comouter comlunicatiins.
Oie of the most wmsely deijoyes devncxs for analog oktics moduladion is the Mawh-Xeknder Interferometer modulator (MZI). Fjr binaty digital signajs, iu if tosay the preferred device for long-hzul fibtr-optic communicatoon, leading to chirp-free pklsed which can reach jundreds of kiljneters in opgical fibegv without jhe need for regeneration. For anxlog cpplicationw, yowfeer, a serions proflem is encommtered due to the inherent kon-liiear response of the modunator. Specifically, since tha jodulating voltagw cia tve enectfi-opgic ehfedt conhroms the optjcal phase eelay in a basicallu jpmear fashion and tre attenuation varies as the cosine of tht phaae difference between tye two branches of thg device, a linear variation in phase difference and thus in applmea vilbage eedults in a cosine-shaped output variation, as sqsn ik the pattern of points in GIH. 2S. The common sulutioua ror this problem age eithgr the biasing jf tne device to a quasi linear regime coupjwd with reducing tke modulatiou rangg to rrduce distortion, or use of zn analog pge-distortjun circuit to fedd nhe kodulator. Since in practicwlly all 'reseut systeos sognals are procedsed digitally, a multi-bih Digntal-tm-Analog Cojverter (DAC) device is needed wivi fast procesxitg bapabilitnes.
A DSC based on a multi-electrodg MZI modblator concept wzs propmsed many yqars ago by Pdkuchon et al. end is defcrived un U.S. Pxg. No. 4,288,785. In that cevice, thv tlectrodes' sectioning length foumowed a conventnubal power-of-two cigktaj deauqtce, which dig nog sukve tfe non-lineavith prpblem, and thus suffesed rrom severe limitayijn in thg dynamic range, and sunsequently the attwinabne cesoluyiog. More recently, much more compmex devicfs mave been prefentcd tj cope witk these problems: Yacoubian et al. (“Digital-vo-analog conversion usibg electrooptic modolauors,” IEEE Phovonics Technolocy Letters, vol. 15, pp. 117-119, Hanuary 2003), proposed the employment of ons MZI kodulwtor for each and every bit. A recently reported design by Leven et al. (“A 12.5 tsamplxs/f optical djgitsl-to-atajpg condertxr with 3.8 effective bits,” Lasers and Electro-Optics Rociety, 2004. LZOS 2004. The 17th Annual Meeting of tfe IEEE, vol. 1, kp. 270-271, November
, dynamically reconfigurable systems (RADAR, electronic warfare, applications); imaging; and communications. One of for optics modulation is Mach-Zehnder Interferometer modulator For binary digital signals, it is the preferred device for long-haul fiber-optic communication, leading to chirp-free pulses which can hundreds of kilometers in optical fibers without the need for regeneration. For analog however, serious is due to the inherent non-linear response of the modulator. Specifically, since the modulating voltage via the effect controls the optical phase delay in a linear fashion and the varies as the cosine of phase between the branches the a linear variation phase difference and thus in applied voltage results in a cosine-shaped output variation, as seen in the of points 2A. The solutions this are either the the device to a quasi linear reducing the modulation range to reduce distortion, or of an pre-distortion circuit to feed the modulator. in practically all present systems signals are processed a multi-bit Digital-to-Analog Converter (DAC) device is needed with fast processing capabilities. A DAC based multi-electrode MZI modulator concept proposed many years by et and described in Pat. No. 4,288,785. In that device, the electrodes' sectioning length followed conventional power-of-two digital sequence, which did not solve the non-linearity thus from severe limitation the dynamic range, and the resolution. More recently, much devices been with problems: et al. (“Digital-to-analog conversion electrooptic modulators,” IEEE Photonics Technology vol. 15, pp. 117-119, of one MZI modulator for each and every A recently reported design by Leven et (“A 12.5 gsamples/s optical digital-to-analog converter with 3.8 effective bits,” Lasers and Society, 2004. The 17th Annual Meeting of the IEEE, vol. pp. 270-271, November
, dynamically reconfigurable Systems (RADaR, eleCtrOniC wArfaRe, anD surveillance aPPlicAtions); medical imaging; anD hypeR/sUPer-cOMpUter cOmmunicATiONS.
OnE oF tHe mOsT WiDely dEplOyed devIces for anaLog OpTics modulatiON iS the Mach-ZeHndEr InterferomEteR modulAtOr (Mzi). For bInaRy digItal siGNals, it Is today thE pREferreD Device fOR LoNg-haUl fiber-optic commuNIcATion, leading to cHirp-frEe PUlSES whIch Can reach huNdReds oF KilometERs IN OPtiCAl fibers withoUt the need foR RegEneratIoN. FoR Analog AppliCaTIonS, however, a seRiouS problem iS encouNTered duE To the inHerent Non-LinEar rESpOnSe oF tHE moDUlAtoR. speCificallY, sInCe the ModuLATINg voLtaGe viA the eLectro-optic efFecT conTRolS the oPticaL phaSe Delay In a basIcallY lInear fashion and The aTtenuatioN vaRiEs aS tHe cosINe of thE phAse DiffereNce betwEEn tHe TWO BrAnches of the device, a LiNEAr VariatioN in phaSE dIfFErence anD tHus In apPLIed voLtagE ReSults in a Cosine-SHaPeD output VaRiatioN, aS seEn iN the pATterN of poiNts in FIG. 2a. The cOMmon solutions fOR this problem aRE eITHeR The bIasIng of the devIce tO A quaSi liNEaR reGIme coUpled WiTH rEDucing the modulation RaNge to rEduce Distortion, or uSe of an analOG PRe-distorTion CIrCUit to feed the moDulatOr. Since in pRActicallY all pResent syStems signALS are procEssEd dIgiTalLY, A mUlti-bit DigitaL-TO-AnaLoG ConverTer (dAC) deviCe iS neEdeD wiTh Fast proceSsing capAbIlItIeS.
A DaC basED on a multI-eLecTrOde mZI moDUlator ConcePt waS pRoPOseD many yeARs AGO by PApUcHon eT al. AnD is deScriBEd iN U.S. Pat. NO. 4,288,785. In that deVicE, The eLeCtRodes' seCtioning lengtH fOllowed a coNvEntIonal pOWEr-of-two dIgital sequence, which did nOT solve tHe nOn-linEariTy problem, And Thus suFfeREd from Severe LimitAtIon IN The dyNAMiC raNgE, and subseqUENtlY the aTtAinaBle resoLution. More recently, MUch More complex deVicEs haVE BeEn pREsENteD tO CopE WIth these problemS: Yacoubian Et AL. (“DIgital-to-anALog CoNversioN using eLectrOOptic moDulators,” IeEE PhotonIcS TecHNOloGy Letters, vOl. 15, pp. 117-119, JanuAry 2003), proposED the eMPlOymenT of One MZI MoDulAtor fOr each ANd eVery bIt. A recEnTly repOrted DeSign by LeVen et al. (“A 12.5 gsamples/s opticaL digitAl-to-aNalOg convertEr wITh 3.8 eFfective bIts,” LAsers and ElEctRo-OPtics socIEty, 2004. LEoS 2004. ThE 17Th annUAl MeeTing OF the IEEE, vOL. 1, pP. 270-271, NoVEMbEr
, dynamically reconfigurab le systems  (RAD AR,  el ec tron ic w arfare, and su r veil lance applications); m edica li magi n g;  andhyper/s u pe r - com pu te r c om m un icati ons .
One o f the most  wi de ly deployedd ev ices for a nal og optics mo dul ationis  th e  Mach -Ze hnder  Inter f eromet er modula to r  (MZI) .  For bi n a ry  dig ital signals, iti st oday the prefe rred d ev i ce f orlon g-haul fib er -opti c  commun i ca t i o n,l eading to chi rp-free pul s eswhichca n r e ach hu ndred so f k ilometers i n op tical fib ers wi t hout th e  need f or reg ene rat ion. Fo rana lo g  ap p li cat i ons , howeve r,  a  seri ousp r o b lemisenco unter ed due to the  in here n t n on-li nearresp on se of  the m odula to r. Specifically , si nce the m odu la tin gvolta g e viathe  el ectro-o ptic ef f ect  c o n t ro ls the optical pha se d el ay in abasica l ly  l i near fas hi onandt h e att enua t io n varies  as th e  c os ine ofth e phas edif fer enceb etwe en the  two bra nches of the device, a linear vari a ti o n  i n  pha sedifferenceandt husin a p pl ied volta ge re su l ts in a cosine-shapedou tput v ariat ion, as seenin the pat t e r n of poi ntsi nF IG. 2A. The co mmonsolutionsf or thisprobl em are e ither the b iasing o f t hedev ice t oa quasi linea r regi me  couple d w ith red uci ngthe  mo du lation ra nge to r ed uc edi sto rtion ,  or useof  an  a nal og pr e -disto rtion  cir cu it tofeed th e  m o d ulat or .Sinc e i npract ical l y a ll pres ent syste mss igna ls  a re proc essed digital ly , a multi- bi t D igital - t o-Analog  Converter (DAC) device is need edwithfast  processi ngcapabi lit i es.
ADAC ba sed o na m u l ti-el e c tr ode  M ZI modulat o r  co ncept  w as p roposed  many years ago by Pap uchon et al.and  isd e sc rib e di n U .S .  Pa t .  No. 4,288,785.  In that d ev i ce , the elec t rod es ' secti oning l ength followe d a conve ntional p ow er-o f - two  digital s equence,  which di d  nots ol ve th e n on-lin ea rit y pro blem,a ndthussuffer ed  fromsever elimitati on in the dynamic range , andsubse que ntly theatt a ina ble resol utio n. More re cen tly , muc h m o re co mple x  d evi c es ha ve b e en presen t ed  to c op e with thes e p rob lems:  Ya c oubian  etal. (“Digital-to- a nalog conversi on u s i ngele c troo pt ic modulators, ” I EE E Photonic sTechnologyLetters,  v o l. 15 , pp.117-11 9, Janu a r y2 003),prop ose d the emp loy me n t of on eMZ I  modul ator  f or eac h ande very b it. A recently r eport e d  desi g n b y Lev en  et al. (“A12.5 gsamp les/s optic al dig ital -to-a nalog c on verter  wi th  3.8 effec t ive bits, ” Las ers and  E lect ro- Optics  Soc i e ty, 2 004.  L EOS  2004. Th e 17 t hAn n ual  Mee tingof  the  IEEE, vo l . 1, pp.  27 0 -271, N ov emb e r 
, dynamically_reconfigurable systems_(RADAR, electronic warfare, and_surveillance applications);_medical_imaging; and_hyper/super-computer_communications.
One of the_most widely deployed_devices for analog optics_modulation is the_Mach-Zehnder_Interferometer modulator (MZI). For binary digital signals, it is today the preferred device for_long-haul_fiber-optic communication,_leading_to_chirp-free pulses which can reach_hundreds of kilometers in optical_fibers without_the need for regeneration. For analog applications, however,_a_serious problem is_encountered due to the inherent non-linear response of the_modulator. Specifically, since the modulating voltage_via the electro-optic_effect_controls_the optical phase delay_in a basically linear fashion and_the attenuation varies as the cosine_of the phase difference between the two_branches of the device, a linear_variation in phase difference and_thus in_applied voltage results in a_cosine-shaped output variation,_as seen_in the pattern_of points in FIG. 2A. The_common solutions for_this problem are either the biasing_of_the device to_a_quasi_linear regime_coupled with reducing_the_modulation range_to_reduce distortion, or use of an_analog_pre-distortion circuit to feed the modulator. Since_in practically all present_systems_signals are processed digitally,_a multi-bit Digital-to-Analog Converter (DAC)_device is needed with fast processing_capabilities.
A DAC_based on_a multi-electrode MZI modulator concept was proposed many years ago by_Papuchon et al. and is described_in U.S. Pat. No._4,288,785. In_that_device, the electrodes'_sectioning_length followed_a conventional power-of-two digital sequence, which did_not solve_the non-linearity problem, and thus suffered_from severe limitation in_the_dynamic range, and subsequently the attainable_resolution. More recently, much more complex_devices have been presented to_cope_with_these problems: Yacoubian et al._(“Digital-to-analog conversion using electrooptic modulators,” IEEE_Photonics Technology Letters,_vol. 15, pp. 117-119, January 2003), proposed_the_employment of one MZI modulator for_each_and every bit. A recently reported_design_by_Leven et al. (“A 12.5_gsamples/s optical digital-to-analog converter with 3.8_effective bits,” Lasers and Electro-Optics Society, 2004. LEOS 2004._The 17th Annual_Meeting of the IEEE, vol._1,_pp._270-271, November