基于二维光子晶体非线性效应的全光逻辑门.pdf

文章编号2097-1842（2024）02-0456-12All-optical logic gate based on nonlinear effects oftwo-dimensional photonic crystalsWURong，YANGJian-ye*，ZHANGHao-chen（School of Electronic and Information Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China）*Corresponding author，E-mail:Abstract:All-opticalXOR,NOTandtwo-inputANDlogicgatesaredesignedbasedonthenonlineareffectandlinearinterferenceeffectofphotoniccrystals.Thecomplexlogicexpressionsaredividedbyinversiontheorem,andall-opticalNORgateandfour-inputANDgatelogicdevicesaredesignedbycascadecombina-tion.Inthispaper,theFinite-DifferenceTime-Domain(FDTD)methodisusedforsimulation,andthecoup-lingcharacteristicsofnonlinearannularcavitiesareanalyzed.Then,theabovelogicdevicesaredesignedun-dertheconditionthatthesignalwavelengthis1.47m,andmoreinputdevicescanbedesignedbyexpand-ingtheinput.Theinfluenceofsignalpoweronthelogicfunctionofthefour-inputANDlogicdevicesisana-lyzed.Theresultsshowthatwhenthepowerofthesignallightsourceisbetween1.1W/m2and3.4W/m2,thelogicalcontrastratiooftheoutputisgreaterthan10dB.Theresponsetimeofthedesigneddeviceisonly1.6ps,theoccupiedareaissmall,andthedeviceiseasytoexpandandintegrate.Ithasgreatapplicationpro-spectinopticalprocessingsystemsandintegratedopticalpaths.Key words:ringresonator;microcavity;opticallogics;nonlineareffect基于二维光子晶体非线性效应的全光逻辑门吴蓉，杨建业*，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：基于光子晶体非线性效应和线性干涉效应设计了全光异或、非和与逻辑门。应用反演定理拆分较复杂逻辑表达式，通过级联组合设计了全光或非门和四输入与门逻辑器件。本文利用时域有限差分法进行仿真模拟计算，对非线性环形腔的耦合特性进行了分析，然后在信号波长为 1.47m 条件下设计了上述逻辑器件，且通过可扩展输入端可设计出更多输入的器件。分析了信号功率对四输入与逻辑器件逻辑功能的影响。结果表明信号光源功率在 1.1W/m2到3.4W/m2之间时，输出端的逻辑对比度均大于 10dB。所设计器件响应时间最短仅 1.6ps，占用面积小，易于扩展与集成，在光处理系统和集成光路中有较大应用前景。关 键 词：环形谐振腔；微腔；光逻辑；非线性效应中图分类号：TN256文献标志码：Adoi：10.37188/CO.EN-2023-0021收稿日期：2023-08-30；修订日期：2023-10-07基金项目：甘肃省自然科学基金（No.21JR7RA289）SupportedbyNaturalScienceFoundationofGansuProvince(No.21JR7RA289)第17卷第2期中国光学（中英文）Vol.17No.22024 年 3 月ChineseOpticsMar.20241IntroductionInrecentyears,thehumandemandforinform-ation has increased exponentially,necessitatingfasterdatatransmissioncapacityinthetransmissionnetwork,thereby also necessitating faster pro-cessorsandopticfibersystems.Theexistingsemi-conductordevicesareabouttoreachabottleneckbecauseoftheinfluenceofelectronicspeed,andop-ticaldeviceshavethecharacteristicsofhigh-speedprocessingandofnotbeingeasilyaffectedbyelec-tromagnetic noise,so the future use of opticaldevices is foreseeable1-2.Compared to traditionalelectronic devices,photonic crystal logic deviceshavelowerenergyconsumption.Throughresearchonthedesignandoptimizationofphotoniccrystallogicdevices,theirenergyconsumptioncanbefur-therreducedandmoreenergy-efficientinformationprocessingsystemscanbeachieved.Photoniccrys-tallogicdeviceshaveawiderangeofapplicationpotential,suchasphotoncomputing,photoncom-munication,quantumcomputing,etc.All-opticallogicdevicesareveryimportantinopticalsignalprocessing3.Inrecentyears,opticallogic devices4-5 have been implemented by someteamsforspatialcodingofopticalfields6-7,semi-conductoropticalamplifiers8-9,highlynonlinearop-tical fibers10,micro and nanoscale waveguides11,one-dimensionalmagnetizedInSbphotoniccrystalslayered topology12,Janus metastructures13 andphotoniccrystalstructures14-15.Atpresent,all-optic-al logic devices designed with photonic crystalstructure are more popular among designers withsmaller occupied area and manufacturing cost.Photoniccrystalisasyntheticmaterialinwhichsev-eralmaterialswithdifferentdielectricconstantsarearrangedaccordingtocertainrulesinspace,andhastwocharacteristics:photonicbandgapandphotoniclocal area,and a structure divisible into one,twoandthreedimensions16.Theintroductionofdefectsinto two-dimensional photonic crystals can guidethetransmissionoflightwaves.Ifthefrequencyofincidentlightiswithinthephotonicbandgap,thelightcanbetrappedinthephotoniccrystalstructure,andtheresultingdefectivephotoniccrystalsareap-pliedtomanyopticaldevices17,suchasfilters18,wavelength division multiplexers19-20,optical fib-ers21,beamsplitters22andopticallogicdevices23-24.Inadditiontosomephotoniccrystalapplicationsinneed of solving,such as sensors25,solar cells26,photodetectors27andsoon.Photoniccrystalscanbeusedtorealizeopticallogicdevicesbyavarietyofmethods,suchasmultimodeinterference28,autocol-limationtransmission29,nonlineareffectandlinearinterference,amongwhichtheopticallogicdevicesdesignedusinglinearinterferenceeffectandnonlin-ear effect are simple in structure and suitable forlarge-scaleintegration.Inordertoremovetheinter-ferencefrequencysignalandenhancethecouplingefficiencyoftheoutputend,afilterstructurecanbeaddedtotheoutputendtoselectthefrequencyoftheoutputlightwave.Commonlyusedstructuresin-cludemicrocavity structure and ring cavity struc-ture,andthefilteredfrequencycanbeadjustedbysettingtheradiusofthemediumcolumn.Thede-signers of the devices basic logic gate structuremakeuseoflinearinterferenceeffectsothatthede-signeddevice has a simple structure and fast re-sponse speed.Designing devices solely based onlinearinterferenceeffectsgenerallycannotachievehighefficiencyandhighcontrastoutput,sotheuseofnonlinearmaterialsisnecessary.In202029,Bou-aouinaMSet al.designedacommonlogicgateus-ingphotoniccrystalstructureonthebasisofdefectinterferenceandresonancecoupling.Thestructureofthegateiscomplexandthecontrastbetweennon,same or gate logic is too low.In 202230,TanayChattopadhyayet al.proposedaseriesoflogicgatesbased on complementary photonic crystal logicdevices.Theoverallareaofthedevicesislargeandthelogicalcontrastisnothigh.In202331,VadivuNSet al.proposedatriangularlatticetwo-dimension-alphotoniccrystalstructurebasedonthelinearin-第2期WURong,et al.:All-opticallogicgatebasedonnonlineareffectsof.457terferenceeffect.Thedesignedlogicgatestructureissimpleandworkswellinboththetransversemag-neticmode(TMM)andthetransverseelectricmode(TEM)polarizationmodes,butthephaseofthein-put signal needs to be controlled while operating,andthelogicalcontrastofthedeviceislow.In this paper,an all-optical logic gate withsimplestructure and high logical contrast is de-signedbycombiningnonlineareffectandlinearin-terferenceeffect.XOR,NOTandtwo-inputANDlogicgatesaredesignedinTEMpolarizationmode.Formorecomplexlogicexpressions,itconvertsin-to a cascaded combination of existing logic gatesthroughtheinversiontheorem.Thus,amorecom-plexornon-sumfour-inputANDgatelogicdeviceisrealized.The proposed device can also be de-signedasalogicgatewithmoreinputbyexpandingtheinput.2Theoreticalbasis2.1NonlineareffectAnonlinearringcavityisusedinthedevicestructuredesignedinthispaper.Whenthelightin-tensity of the output waveguide changes,the re-fractive index of the light-sensitive material willchangeandthecoupledlightwavewillchangeinconjunctiontherewith,sothatthewavelengththatcan be coupled by the nonlinear ring cavity willchange32-33.Therefractiveindexofmanynonlinearmaterialsdependsonthelightintensity,anditsre-fractiveindexnisexpressedasfollows:n=n0+n2I,（1）wheren0istheweak-fieldrefractiveindex,andtheproductfactorn2isthenonlinearrefractiveindex34.TheaboveformulashowsthattherefractiveindexofthenonlinearmaterialincreasesasaresultoftheincreaseofthelightintensityI.Assumingthatthefield is linearly polarized,the total polarization iscausedbysecond-andthird-ordernonlinearities:P=0(1)E+(2)EE+(3)EEE)P(1)+P(2)+P(3),（2）where(2)and(3)aresecond-andthird-ordernonlin-earpolarizability.Assumingthatthenonlinearma-terialhascrystalsymmetry,thesecond-ordermag-neticsusceptibilitycanbeignored,andthenonlin-earrefractiveindexn2canbeobtained:n2=3(3)4n20Z0,（3）whereZ0=376.7,isthefreespaceimpedance.Thephotonic crystal has two kinds of structure:aircolumnandmediumcolumn.Theaircolumniseasytomanufacture,andthemediumcolumnhasthead-vantageofstrongcoupling.Allthedesignsinthispaperadoptthephotoniccrystalwithacubiclatticedielectric column structure.The lattice constanta=0.54m and the filling factor r/a=0.18are set.ThematerialofdielectriccolumnisSi,andthere-fractiveindexnis3.46.ThecharacteristicsofthenonlinearringcavitycanbeunderstoodthroughthestudyoftheoutputcharacteristicsofthestructureinFigure1(a)(coloronline),whereRisanonlinearringcavityandthematerialisdopedglass,whoseweak-field refractive index n0=1.4and nonlinearKerr coefficient(3)=1014 m2/V2,the radius of thedielectric column is 0.18a.35-36 The structure inFigure 1 was simulated and analyzed using theFDTDmethod.TheGaussianlightsourcewasin-cidentontheINportontherightsideofthestruc-ture,andthenormalizedpowercurveoftheoutputportofthelightsourceintheband1.421.52mwasshowninFigure1(b)(coloronline).Itcanbeseen that the light wave with a wavelength of1.47mwillnotbeoutputfromtheO1andO2portsaftercouplingthroughtheringcavity.Figure2(col-or online)shows the influence of the light wavepowerontheoutputofFigure1(a)structure.Setthewavelengthoflightsourceto1.47m.Whenthepoweroftheincidentlightsourceislow,therefract-ive index of the nonlinear ring cavity does notchangemuch.ItcanbeseenfromthenormalizedpowercurveinFigure2(c)thatonlysmallpowerlightwavesareoutputfromO1andO2ports.Whenthepoweroftheincidentlightsourceincreases,the458中国光学（中英文）第17卷couplingcharacteristicsofthenonlinearringcavitychangebecauseofthelargeincrementoftherefract-ive index of the nonlinear ring cavity.As can beseenfromFigure2(d),lightwavesareoutputfromO1 and O2ports.The waveband coupled by thestructureofFigure1(a)andoutputfromtheINportcanbecontrolledbyadjustingparameters.Whenthelatticeconstant or medium column radius is in-creased,the overall image will be redshifted(in-creasingin wavelength);likewise,when it is de-creased,theimagewillbeblueshifted(decreasinginwavelength).INO2(a)(b)O1R1.2Normalized power1.00.80.60.40.201.421.431.441.451.461.47Wavelength/m1.481.491.501.511.52O1O2Fig.1Characteristicsofnonlinearringcavityanditsoutputateachportinthe1.421.52mband.(a)Structureand(b)nor-malizedpowerofoutputport0.9(a)(c)(d)(b)0.80.70.6Normalized powerNormalized power0.50.40.30.20.10200400600800O1O2O1O2ct/m1 0000200400600800ct/m1 00001.00.80.60.40.20Fig.2Steady-stateelectricfielddiagramsandnormalizedpowersofoutputportswhenincidentlightsourcehasdifferentpowers.(a)Electricfielddiagramatlowpower,(b)electricfielddiagramathighpower,(c)outputpoweratlowpower,and(d)outputpowerathighpower2.2LinearinterferenceeffectWhenthereisaphasedifferencebetweentwobeamsoflightinthesamepath,therewillbecon-structive interference or destructive interference.When the phase difference is 2m(m=0,1,2,3,),theoutputsignalisenhancedbecauseofcon-第2期WURong,et al.:All-opticallogicgatebasedonnonlineareffectsof.459structiveinterferencebetweenlightwaves;whenthephase difference is(2m+1),the output signal isweakenedbecauseofdestructiveinterference34.Inthedesignofall-opticallogicdevices,thephasedif-ferencecanbegeneratedbetweentheinputsignalsby introducing optical path difference,so as toachieve the purpose of destructive interference.Figure3showstheXORgatestructuredesignedinthispaper,withI1andI2asinputterminalsandOUTas output terminal.The wavelength of the signallightsourceissetas1.47mandthepowerasPin.ThefunctionoftheXORgateisthatwhentheinputislogic01or10,theoutputislogic1,andwhentheinputis00or11,theoutputislogic0.IntheXORgatestructure,thedistancebetweensignalI1andsignalI2totheoutputportOUTwaveguideis2a,andthephasedifferenceisgeneratedwhenthetwosignalspropagatetotheoutputwaveguide.TheFDTDmethodwasusedtosimulatethestructureinFigure3,andtheresultswereshowninFigure4(coloronline).Figure4(a)andFigure4(d)showthesteady-stateelectricfielddiagramsandthenormal-izedpowercurvesattheoutputendofOUTwhentheinputlogicis01.Whenthelightsourceisincid-entfromI2,partofthelightwavewillbereflectedback,part of the light wave will be output fromthe OUT port with a power of 0.442Pin,and theotherpartwillbeoutputfromtheI1port.Thesameis true when the input is 10,but because of theasymmetricstructure,theoutputpoweris0.503Pin.Figure4(c)showsthesteady-stateelectricfielddia-gramwhenbothsignallightsourcesarelogic1.Thephasedifferencebetweenthetwolightwavesattheoutputportis(2m+1),andthetwoinputsig-nals generate destructive interference.The outputpower at the OUT port is only 0.012Pin,and theoutputis0whentheinputislogic11.I1I2OUTFig.3XORgatestructure0.6(a)(b)(c)(d)(e)(f)0.50.40.30.20.1010020030040050060000.040.030.020.010Normalized powerct/m0.60.50.40.30.20.101002003004005006000Normalized powerNormalized powerct/m0100200300400500600ct/mFig.4Steady-stateelectricfielddiagramsandnormalizedpowercurveswheninputlogicis01,10and11respectively.(a)(c)areelectricfielddiagramswheninputlogicis(a)01,(b)10,and(c)11;(d)(f)arenormalizedpowercurveswheninputlogicis(d)01,(e)10,and(f)11460中国光学（中英文）第17卷LogicContrast(CR)isanimportantmeasureofdeviceperformancebycalculatingtheratiooftheminimum output power P1 of the logic 1 to themaximumoutputpowerP0ofthelogic0.Thecal-culationformulais:CR=10log(P1/P0).（4）A1=ATheminimumoutputpowerofXORgatelogic1is0.442Pin,themaximumoutputpoweroflogic0 is 0.012Pin,and the calculated CR is 15.7dB.Theresponsetimeofthelogicgateis0.25psandthedatatransferrateis4Tbits/s.TheXORgatelo-gicstructurecanalsobechangedintoanonlogicalgate,forexample,theinputI1oftheXORgateinFigure3isfixedasalogic1,sothattheXORgatebecomesaNOTgatewiththeinputI2,andthecalculatedCRis16.2dB.3Simulationanddiscussionoflogicgate3.1Two-inputANDlogicgateOut of the basic logic gates,AND,OR,andNOT,implementationoftheNOTgatehasthusfarbeendiscussedinthispaper.Thissectionusesnon-lineareffectstodesignatwo-inputANDgate,asshowninFigure5.TheORgateonlyneedsthein-put signal to be structurally symmetrical,whichmeansthattheopticalpathdifferenceisthesame.For example,in the structures of Figure 5 andFigure 6(color online),the two input signals I1andI2atthepositionoftheboxexhibitconstructiveinterferencewith each other,which can be con-sideredastheimplementationofORlogic.Ontheleftsideofthetwo-inputANDgatestructure,Risanonlinearannularcavity,andtheO1portistheout-putendoftheANDgate.Toreducereflection,asil-icon dielectric column is added at the right-anglewaveguide.IfthestructureofFigure5issimulatedusing the FDTD method,with a light source sig-nal of 1.47m continuous wave,and power of1.06W/m2,asshowninFigure6.Whenthereisnosignaloronlyonesignalinput,thentherefract-iveindexofthenonlinearmaterialdoesnotchangemuch,whichisnotenoughtochangethecharacter-istics of the nonlinear ring cavity.Therefore,theoutput power at the O1port is very small at only0.0168Pin.Becauseofthesymmetricalstructureofthedevice,theoutputpoweroftheO2andO3portsisthesame,soonlytheO2curveisplottedinthenormalized power curve.When the input is logic11,theopticalpathdifferencebetweenthetwoin-putsignalsisthesame,andthereisaconstructiveinterferenceintheO1waveguide.Becauseofthein-creaseinpower,thecouplingcharacteristicsofthenonlinear ring cavity change.Most of the lightwavescanbeoutputfromtheO1port,withanout-putpowerof1.0440Pin.TheCRofthedeviceis17.9dB,the response time of the logic gate is0.67ps,andthedatatransferrateis1.5Tbits/s.Thepowerofthelightsourcesignalhasasignificantim-pactonthelogicalfunctionofthedevice.Forex-ample,inlogicdevices,whenthelightsourcesig-nalpowerissmall,eveniftheinputisalllogic1,itcannot change the characteristi