结合非线性效应和线性干涉效应设计的全光半加器.pdf

文章编号2097-1842（2023）05-1186-09Design of all-optical half-adder based on nonlinear effect andlinear interference effectYANGJian-ye*，WURong，ZHANGHao-chen（School of Electronic and Information Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China）*Corresponding author，E-mail:Abstract:Anall-opticalhalf-adderisdesignedbycombiningthenonlineareffectandlinearinterferenceef-fectofphotoniccrystals.Bydividingthelightsourceintotwopartsequally,thehalfadderANDgateandXORgatearedesignedseparately.ThenonlineareffectisusedtorealizetheANDgatewithhighcontrast,andthelinearinterferenceeffectisusedtorealizetheXORlogic,sothattheoverallresponsespeedofthedeviceisimproved.Inthisdesignstructure,thedeviceonlyhasthresholdrequirementsforthesignallightsourcepower.Whenthesignalpowerisgreaterthan51.4mW/m2,ithasstableoutputandstronganti-inter-ferenceability.Thedesignedcontrastofthehalfaddercarryoutputportis20.69dB,andtheoutputportcon-trastis20.13dB.Thedatatransferrateis0.75Tbits/sandtheoccupiedareais623m2.Key words:all-opticalhalfadders;ringresonator;micro-cavity;opticallogics;linearinterferenceeffect结合非线性效应和线性干涉效应设计的全光半加器杨建业*，吴蓉，张皓辰（兰州交通大学电子与信息工程学院,甘肃兰州730070）摘要：结合光子晶体非线性效应和线性干涉效应设计了一种全光半加器。将光源平均分成两部分，对半加器的与门和异或门分开设计。利用非线性效应实现高对比度的与门；利用线性干涉效应实现异或逻辑，从而使器件整体响应速度更快。在这种设计结构下，器件对信号光源功率只有阈值要求，当信号功率大于 51.4mW/m2时输出稳定，抗干扰能力强。所设计的半加器进位输出端口对比度为 20.69dB，输出端口对比度为 20.13dB。数据传输速率为 0.75Tbits/s,占用面积 623m2。关 键 词：全光半加器；环形谐振腔；微腔；光逻辑；线性干涉效应中图分类号：TN256文献标志码：Adoi：10.37188/CO.EN.2022-0029收稿日期：2023-01-04；修订日期：2023-02-22基金项目：甘肃省自然科学基金(No.21JR7RA289)SupportedbyNaturalScienceFoundationofGansuProvince(No.21JR7RA289)第16卷第5期中国光学（中英文）Vol.16No.52023 年 9 月ChineseOpticsSept.20231IntroductionInrecentyears,duetothesignificantgrowthofcommunicationbandwidth,theneedforfasterpro-cessorsandopticalfibersystemsisbecomingmoreandmoreurgent.Theexistingsemiconductordevi-cesaffectedbyelectronicspeedisabouttoreachthebottleneck,andopticaldeviceshavehigh-speedpro-cessingcharacteristics,andarenotsusceptibletoele-ctromagneticnoise,sotheuseofopticaldevicesinthefutureisforeseeable1-3.All-opticallogicdevicesplayanimportantroleinopticalsignalprocessingsuchasaddressingandopticalcomputing4.Currently,all-opticallogicdevi-cesdesignedbasedonphotoniccrystalsarepopularamongdesignersfortheirsmallerfootprintandlowmanufacturingcost.Photoniccrystalisakindofar-tificialmaterialwithperiodicchangeofrefractiveindexinspace,whichhastwocharacteristics:photonbandgapandphotonlocality5-6.Aftertheintroduc-tionofdefectsinthecrystal7-8,lightwavetransmis-sioncanbeguided.Theresultingdefectivephoton-iccrystalsareusedinmanyopticaldevices,suchasfilters9-10,wavelengthdivisionmultiplexers11-12,op-ticalfibers13-14,beamsplitters15-16,andopticallogicdevices17-20.Thereareotherapplicationsofphoton-iccrystalswhichshouldbeaddressed，suchassen-sors21,solarcells22,photodetectors23,andetc.Manymethodscanbeusedtorealizeopticallogicdevicesby photonic crystals,such as multi-mode interfer-ence24,autocollimation transmission25 and linearinterference,etc.Theopticallogicdevicesdesignedbyusinglinearinterferenceeffectandnonlinearef-fecthavesimplestructureandaresuitableforlarge-scaleintegration.Toachievesimpleall-opticallo-gicgate,designersoftenmakeuseoflinearinterfer-enceeffect,sothatthedesigneddeviceshavetheadvantages of simple structure and fast response.Whenthedesignedlogicdevicehasmultipleout-puts,itisnotpossibletoobtainhigh-efficiencyandhigh-contrastoutputsonlybymeansoflinearinter-ference,sotheuseofnonlinearmaterialsisneces-sary.Inordertoremovetheinterferencefrequencysignal and enhance the coupling efficiency of theoutputend,afilterstructurecanbeaddedtotheout-putendtoselectthefrequencyoftheoutputlightwave.Commonlyusedstructuresincludemicrocav-itystructure26andringcavitystructure27.Thefil-terfrequencycanbeadjustedbysettingtheradiusofthemediumcolumn.In202028,SaniMHet al.designedanall-opticalhalf-adderwithanoccupy-ingareaof249.75m2byusingnonlineareffects.Itslogicalcontrastishigh,thedelaytimeis3ps,andfourlevelsofinputpowerarerequiredtoreal-izethelogicfunction.In202129,ChattopadhyayTet al.proposedanall-opticalhalf-adderandfull-ad-derdataprocessingcircuitbasedonthenonlinearMach-Zehnderinterferometerswitch.Thestructureis easy to expand and the intensity of the lightsourceusedis10W/m2.In202230,SaadiKet al.implemented an all-optical half-adder logic gatebasedontheconceptoflinearinterferenceoflightwaves,withacompactstructureandasizeof17m12.2m.Theall-opticalhalf-adderdesignedinthispa-perisanewstructure.Itiscombiningnonlinearef-fectandlinearinterferenceeffect.Itcancontroltheoutputbyusingthepowerofthelightsourceandre-duce the dependence on the power of the lightsource.2Theoreticalbasis2.1NonlineareffectThestructuredesignedinthispaperusestwoidentical nonlinear ring cavities.When the inputlightintensitychanges,therefractiveindexofthenonlinearmaterialchanges,resultinginitsresonantwavelength changes31.The refractive indexes ofmanynonlinearmaterialsdependonthelightintens-ity,anditsrefractiveindexisexpressedasfollows:n=n0+n2I,（1）where,n0istheweak-fieldrefractiveindex,andtheproductfactorn2isthenonlinearrefractiveindex32,第5期YANGJian-ye,et al.:Designofall-opticalhalf-adderbasedonnonlineareffectand.1187indicating that the total refractive index increaseswiththeincreaseoflightintensityI.Assumingthatthefieldislinearlypolarized,thetotalpolarizationscausedbysecondandthirdordernonlinearitiesare:P=0(1)E+(2)EE+(3)EEE)P(1)+P(2)+P(3),（2）(2)and(3)aresecondandthirdordernonlinearpo-larizabilities.Assumingthatthenonlinearmaterialhascrystalsymmetry,thesecond-ordersusceptibil-itycanbeignored,sothenonlinearrefractiveindexn2is:n2=3(3)4n02Z0,（3）whereZ0=376.7,isthefreespaceimpedance.Thephotonic crystal has two kinds of structure:aircolumnandmediumcolumn.Theaircolumniseasytomanufactureandthemediumcolumnhasthead-vantageofstrongcoupling.Inthispaper,aphoton-iccrystalwithacubiclatticedielectriccolumnstru-ctureisdesignedwithlatticeconstanta=0.625mand filling factor r/a=0.18.The material of thedielectriccolumnisSiwithrefractiveindexn=3.46.ThecharacteristicsofthenonlinearannularcavityareexploredthroughthestructureofFig.1(a)(coloronline),whereRisthenonlinearannularcavityandthenonlinearmaterialsetforthesquareshapedRinFig.1(a)isdopedglass,theradiusisthesameasthatofasilicondielectriccolumn,whichis0.18a.Theweakfieldrefractiveindexn0=1.4,andthenonlin-earKerrcoefficient(3)=1014m2/V2.TheGaussianlightsourceisincidentatINandoutputatportsO1,O2,andO3.Fig.1(b)(coloronline),showsthenor-malizedpowercurvesofthethreeoutputportswhenthelightsourceisinthebandof1.521.58m.Itcanbeseenthatthelightwavewithwavelengthof1.55mismainlyoutputfromtheO2andO3portsafter coupling through the ring cavity.Fig.2(coloronline)showstheinfluenceofthelightwavepowerontheoutputofFig.1(a).Thewavelengthofthelightsourceis1.55m,andtherefractiveindexofthenonlinearannularcavityisclosetoitslinearrefractive index when the light wave power is1.0Normalized power/(%)0.90.8IN(a)(b)RO1O2O30.70.60.50.40.30.21.521.531.541.55Wavelength/m1.561.571.580.10O1O2O3Fig.1Characteristicsofnonlinearannularcavity.(a)Structureofnonlinearannularcavity.(b)Normalizedpowerofoutputportinthebandof1.521.58m1.2(a)(b)O1O2O3O1O2O31.00.80.60.4Normalized power/(%)0.200100 200 300 400 500cT/m600 700 800 9001.21.00.80.60.4Normalized power/(%)0.200100 200 300 400 500cT/m600 700 800 900Fig.2Normalizedoutputportpowersat(a)lowpowerincidenceand(b)highpowerincidence1188中国光学（中英文）第16卷small33-34.ItcanbeseenfromFig.2(a)thatthelightwaveismainlyoutputfromO2andO3.Afterthein-creaseoflightwavepower,duetotheincreaseofrefractiveindexincrementofnonlinearannularcav-ity35,the coupling efficiency of light wave isgreatlyreduced.ItcanbeseenfromFig.2(b)thatlightwaveismainlyoutputfromO1terminal.2.2LinearinterferenceeffectWhen there is phase difference between twobeamsofthesamepath,therewillbeconstructiveordestructiveinterference.Whenthephasedifferenceis2m(m=0,1,2,3.),therewillbeconstructivein-terference,theoutputsignalwillbeenhanced.Whenthephasedifferenceis(2m+1),therewillbede-structiveinterference,theoutputsignalwillbeweak-ened.Fig.3(a)(coloronline)isanXORgatestruc-ture,whereAandBareinputterminalsandOisoutput36.Thewavelengthoftheusedsignallightsour-ceis1.542m.Whentheinputislogic01or10,theoutputislogic1,andwhentheinputis00or11,theoutputislogic0.Fig.3(b)(coloronline)showsthesteady-stateelectricfielddiagramwhenbothsignallightsourcesarelogical1,lightwavedestructivelyinterfereswitheachotherattheoutputport,andtheoutputis0whentheinputislogical11.(a)(b)ABOFig.3(a)XORgatestructure.(b)Steadystateelectricfielddiagramwheninputislogic113Designandoptimization3.1Structureandsimulationresultsofhalf-adderIn computer data processing,the addition ofbinarynumbersisoneofthemostbasicarithmeticoperations,which plays a crucial role in informa-tion processing.A half-adder can add two binarynumbers,withtwoinputsAandB,andtwooutputsSUM=AB,andCARRY=AB.Fig.4(coloronline)shows the structure of the half-adder designed inthispaper.Thewavelengthofthecontinuouslightsourceis1.542mandthepoweris66.4mW/m2.AfterthelightsourceentersfromportsAandB,itwillbedividedintotwopartsandpropagatealongtwopathsatthesametime.Inordertoensurethatthelightsourcecanenterthetwopathsequally,thetwosilicondielectriccolumnsatthecouplingpointDC1andDC2areadjustedandtheradiusrissetto0.1584mtoenhancethelightcouplingtotherightwaveguide.AfterthelightsourceentersfromportA,most of the light waves along the waveguideW1andW2willbeoutputalongtheinputportBafterresonance.The same is true for the light wavesalongportB,sotheinfluenceonthetwooutputter-minalsisweakenedandthedevicehasbetterper-formance.Therearetwononlinearringcavitiesontheleftsideofthehalf-adderstructure.Whenthereisnosignaloronlyonesignalinput,theinputpowerislow.Ascanbeseenfromtheresultsofthestruc-ture in Fig.5(a)(coloronline),when the CARRYporthasonlyasmallpowerinput,theoutputpowerisalsosmall.Whenthetwoinputsarebothlogical1,theopticalpathdifferencebetweenthetwoin-putsignalsattheCARRYoutputendisthesame.Duetothepresenceofconstructiveinterference,theopticalinputpowerattheCARRYportincreases,andtheincreaseofthepowerwillgreatlychange第5期YANGJian-ye,et al.:Designofall-opticalhalf-adderbasedonnonlineareffectand.1189therefractiveindexofthenonlinearmaterial,andthelightwavewillbeoutputfromtheCARRYend.Ontherightsideofthestructure,byadjustingtheopticalpathdifferencebetweenthetwoinputsig-nalsattheSUMoutputport,whentheinputis11,thetwosignalsdestructiveinterferenceattheSUMoutput port presents,and there is only light waveoutputofverysmallpower.Whentheinputis01or10,theSUMporthasahighpoweroutput,andtheXORlogicisrealized.Fig.5(coloronline)showsthe normalized power curves of the CARRY andSUMoutputportsaftersignalinput.Thedevicehasahighlogicalcontrast.ThecontrastoftheCARRYportisashighas20.93dBandthatoftheSUMportis13.17dB.ADC1BCARRYRW1W2DC2SUMFig.4Half-adderstructure0.40.30.20.1001 0002 000cT/mNormalized power/(%)0.30.20.1001 0002 000cT/mNormalized power/(%)0.30.20.1001 0002 000cT/mNormalized power/(%)CARRYSUMCARRYSUMCARRYSUM(a)(b)(c)Fig.5Half-addernormalizedpoweroutputcurve.(a)Inputislogical01.(b)Inputislogical10.(c)Inputislogical113.2Structureoftheoptimizedhalf-adderandthesimulationresultsTheabovehalf-adderstructurehashighcon-trast,butlowoutputpowerandsmalloutputpowerdifferencebetweenlogic0and1.Afteranalysis,itisfoundthattherearetworeasons:oneisthatwhenthetwosignalsareinput,therectangularwaveguideleadstoexcessivereflection;theotheristhatasthesignalenters the output waveguide without coup-lingstructure,andthecouplingefficiencyislow.Inordertoincreasetheoutputefficiencyoflogic1ofCARRY and SUM ports,a micro-cavity couplingstructureisaddedtotheoutputport,andadielectriccolumnisaddedtotherectangularwaveguidetore-ducetheloss,andtheSUMoutputportisadjusted.Thestructureoftheimprovedhalf-adderisshowninFig.6(coloronline),MC1and MC2aretwo mi-crocavitystructureswithamediumcolumnradiusof0.1584 m in the middle.After optimizing thestructureofthehalf-adder,thepowerofthesignallight source is adjusted to 169.9 mW/m2.Fig.7(coloronline)shows the steady-state diagram ofelectricfieldwhentheinputsignallogicis01,10and11respectively.Fig.8(coloronline)showstheABSUMCARRYDC1MC1MC2DC2Fig.6Optimizedhalf-adderstructure1190中国光学（中英文）第16卷normalizedpowercurveoftheoutputportsafterthestructureimprovement.Itcanbeseenthatthenor-malizedoutputpowersofthelogic1ofCARRYandSUMportshavebeengreatlyimproved.Table1showstheimprovedperformanceparametersofthehalf-adder.Thedesignedstructurehasadatatrans-missionrateof0.75Tbits/sandoccupiesanareaof623 m2.The above parameters of our proposedstructurearelistedinTable2andcomparedwithsomepreviousstructures.Tab.1 The output parameters of the latter half-adderInput（Normalizedpower）Output（Normalizedpower）ABCARRYSUM017.91030.512107.81030.505110.9264.9104Tab.2 Summarized features of proposed structure andprevious worksWorksSUMcontrast(dB)CARRYcontrast(dB)Bitrate(Tbps)Footprint(m2)Ref189.308.224.55138Ref198.409.296.67192Ref205.645.291.25130Thiswork20.1320.690.756233.3Influenceoflightsourcepowerondeviceper-formanceThestabilityofthedeviceisaproblemthatweareveryconcernedabout.Forthenonlineardevice,ahigherpowerofthelightsourceisdesired.Thestableoutputofthepowerofthelightsourceisre-latedtowhetherthecorrectlogicoutputcanbeob-tained.In this paper,the input light source is di-videdintotwoparts,sothatANDgateandXORgatecanbedesignedseparately.Thenonlinearef-fectplaysacrucialroleinthedesignoftheANDgate,whiletheinfluenceontheXORgateisverysmall,so the requirement for the light source isgreatlyreduced.InFig9(coloronline),theinflu-enceofthepowerofthelightsourceontheoutputofthe device under different logic inputs is ana-lyzed,whichcanbeobtainedfromFig9(a).Whenthepowerofthesignallightsourceisgreaterthan51.4mW/m2,thereisabettercontrastoftheANDgateandahighernormalizedoutputpower.AscanbeseenfromFig.9(b),theoutputofXORgateisextremelystableandbasicallydoesnotchangewiththepowerofthelightsource,whichisacharacter-isticofthedesignbasedonlinearinterferenceef-fect.The power of the signal light source can be(a)(b)(c)Fig.7Steadystatediagramofhalf-adderelectricfield.(a)Inputislogical01.(b)Inputislogical10.(c)Inputislogical11Normalized power/(%)0.60.50.40.30.20.1001 0003 0002 000cT/mNormalized power/(%)0.60.50.40.30.20.100.60.70.80.91.00.50.40.30.20.10Normalized power/(%)01 0002 0003 000cT/m01 0003 0002 000cT/mCARRYSUMCARRYSUMCARRYSUM(a)(b)(c)Fig.8Normalizedpoweroutputcurve.(a)Inputislogical01.(b)Inputislogical10.(c)Inputislogical11第5期YANGJian-ye,et al.:Designofall-opticalhalf-adderbasedonnonlineareffectand.1191roughlydividedintotwophases.Whenthepowerislessthan51.4mW/m2,thedevicecannotwork,andwhenthepowerisgreaterthan51.4mW/m2,thedevicehasbetterlogicfunction.1.21.00.80.60.40200400600800 1 000mW/m21 2001 4000200400600800 1 000mW/m21 200 1 4000.200.60.50.40.30.20.10Normalized power/(%)Normalized power/(%)011011011011(a)(b)Fig.9Influenceoflightsourcepoweronoutput.(a)ImpactonCARRYoutput.(b)ImpactonSUMoutput4ConclusionThispaperpresentsanddesignsaone-bitall-opticalhalf-adderwhichcombinesnonlineareffectandlinearinterferenceeffect.Therearetwononlin-earcircularcavitiesinthestructure,whicharecon-