Magneto-optical-isolators-with-flat-top-responses-

Availableonlineat–FundamentalsandApplications17(2015)15–21Magneto-opticalisolatorswithflat-topresponsesbasedonone-dimensionalmagneto-photoniccrystalsHongmingFeia,b,∗,JianjiaWua,b,YibiaoYanga,b,XinLiua,b,ZhihuiChena,baKeyLaboratoryofAdvancedTransducersandIntelligentControlSystem,TaiyuanUniversityofTechnology,MinistryofEducation,Taiyuan030024,ChinabCollegeofPhysicsandOptoelectronics,TaiyuanUniversityofTechnology,Taiyuan030024,ChinaReceived22July2015;receivedinrevisedform24September2015;accepted14October2015Availableonline28October2015AbstractWeproposetwocompositestructuresbasedonaone-dimensionalmagneto-photoniccrystalbasicstructureandemploythe4×4transfermatrixtoinvestigatetheirtransmissionproperties.Onecompositestructurewithtotalthicknessof15.09machievesflat-topwidthof3.5nmandpossessesFaradayrotationangleandtransmittancewavingat45–53.50◦and98.75–99.73%,respectively.Theothercompositestructurewiththetotalthicknessof22.71mmakestheflat-topwidthto2.5nm,andintheareaofthisbandwidth,Faradayrotationangleandtransmittancefluctuatefrom45◦to48.55◦and99.61%to99.87%,respectively.Moreover,bothofthemarethinenoughandshowacceptabletransmissionbandwidths.Thesetwostructurescanefficientlyreducethesizeofopticalisolatorsandthusapplyingtotheachievementoftheintegrateddevices.©2015ElsevierB.V.Allrightsreserved.Keywords:Flat-topresponse;Magneto-photoniccrystal;Magneto-opticalisolator;4×4transfermatrix1.IntroductionOpticalisolatorsarecriticalcomponentsinopticalcommunicationsystems,whichareusedtoeliminateunwantedback-reflectionsthattypicallycreateinstabilitiessuchasfrequencyshifts,modehopandamplitudemodulation.Asthewidelyusedopticalisolatorinourdailylife,themagneto-opticalisolator(MOI)consistsoftwolinearpolarizerswithpolarizationaxesoffsetequalto45◦andaFaradayrotationmaterialinsertedbetweenthem.Generally,bulkmagneto-opticalmaterialisbeingusedasFaradayrotationmaterial.However,thebulkmagneto-opticalmaterialhascommonlyalengthontheorderoffewmillimeters[1].Thisinducesalargesizeoftheopticalisolatorssothatitisnotsuitablefortheapplicationintheintegrateddevices.Ontheotherhand,one-dimensional(1-D)magneto-photoniccrystal(MPC)film,aPC[2–8]containsmagneticsubstances,possessesthesecharacteristicsofhightransmittanceandalargeFaradayrotationduetothemultipleinterferencesoflightwithinthemagneticdefectlayers.InoueandFujiifoundthatmultilayerfilmscomposedof∗Correspondingauthorat:TaiyuanUniversityofTechnology,CollegeofPhysicsandOptoelectronics,No.79,YingzeWestStreet,Taiyuan030024,China.Tel.:[phone].E-mailaddress:[e-mail](H.Fei).©2015ElsevierB.V.Allrightsreserved.16H.Feietal./PhotonicsandNanostructures–FundamentalsandApplications17(2015)15–21Fig.1.Thepropagationoflightinone-dimensionalmagneto-photoniccrystal.magneto-opticalanddielectricmaterialsexhibitgreatFaradayrotationeffect[9].Katoetal.,reportedthatwhenthe1-DMPCisoperatedatmulticavity(double-andtriple-cavity),veryhightransmittancereaching100%andverylargeFaradayrotationof45◦canberealizedsimultaneously[10].Subsequently,Katoetal.fabricatedexperimentallya1-DMPC,andconfirmedtheoreticalcalculationandthemeasuredvaluefortheFaradayrotationwereincloseagreement[11].Afterthis,Scientistshavemadealotofworktofindtheoptimizationof1-DMPCstructures[12–20].Theintroductionof1-DMPCfilmasFaradayrotationmaterialcanefficientlyreducethesizeoftheMOI,butconventionalMPCinevitablysufferfromnarrowbandwidths[13–18].Thatis,MPCisolatorcanworknormallyonlyatthecentralwavelength.Oncethesestructuresencounterinstabilitiesinducedbywavelengthortemperaturefluctuations,theywillloseeffectiveness.Wenotethat,Levyandco-workersintroducedtheuseofmultiplemagneticgarnet(Ce:YIG)defectquarter-wavephase-shiftsasameansforattainingatheflat-topresponse[21].Theflat-topresponsecouldbeyieldedbyadjustinginterdefectspacing.Zamanietal.morerecentlyproposedanddemonstratedseveralnovelMPCstructureswithflat-topresponses[22].Inthebestcase,theyhaveachieveda19.42m-thickperfectMOIwiththeflat-topwidthof7.2nm.Thesestructurescaneffectivelyovercomethelimitationofnarrowbandwidths.However,theysimultaneouslysufferfromnewshortcomingssuchasmorelayersorlargerfluctuationofFaradayrotationangleintransmissionbandwidth.Asweknow,Faradayrotationrequiresthatthemagnetizationbealongthedirectionofpropagation.Itsrotationawayfromthelongitudinaldirectionintroducesnewoff-diagonalcomponentsinthedielectricpermittivitytensor,thenresultsintheFaradayrotation.Inthispaper,weproposenewstructuresandintroducetherotationofmagnetizationinordertoavoidthesedefectsmentionedabove.First,weproposeanewbasicstructure,andbasedonthebasicstructure,weobtaintwocompositestructureswithflat-topresponses.Then,bytuningtheappliedmagneticfield,wegetperfectMOIswhichtheFaradayrotationangleθF=45◦andthetransmittanceT≈100%.2.TheoryTodescribethepropagationoflightin1-DMPC,4×4transfermatrixmethodcanbeapplied.ThelinearlypolarizedTMlight(E//X),havingaplanewaveforexp[i(kz−ωt)]withwavenumberkandangularfrequencyω,entersperpendic