Analogs of quantum Hall effect edge states in photonic crystals

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1、AnalogsofquantumHalleffectedgestatesinphotoniccrystalsS.Raghu∗andF.D.M.HaldaneDepartmentofPhysics,PrincetonUniversity,PrincetonNJ08544-0708(Dated:February25,2006)“Photoniccrystals”builtwithtime-reversal-symmetry-breakingFaraday-effectmediacanexhibit“chiral”edgemodesthatpropagateunid

2、irectionallyalongboundariesacrosswhichtheFaradayaxisreverses.ThesemodesarepreciseanalogsoftheelectronicedgestatesofquantumHalleffect(QHE)systems,andarealsoimmunetobackscatteringandlocalizationbydisorder.The“Berrycurvature”ofthephotonicbandsplaysaroleanalogoustothatofthemagneticfield

3、intheQHE.Explicitcalculationsdemonstratingtheexistenceofsuchunidirectionally-propagatingphotonicedgestatesarepresented.I.INTRODUCTIONtheBerrycurvature,the“semiclassical”descriptionoftheaccelerationofwavepacketsinmediawithspatialin-homogeneityoflengthscaleslargecomparedtotheunder-T

4、hecontroloftheflowoflightusingphotonicband-gaplyinglatticespacingisincompleteifitisnottakeninto(PBG)materialshasreceivedconsiderableattentionover71account.RecentlyOnodaetal.havepointedouttherolethepastdecade.Moreover,thepotentialforusingarti-ofBerrycurvatureinphotoniccrystalswithou

5、tinver-ficiallystructured“metamaterials”,suchastherecently2sionsymmetry;whiletheseauthorscharacterizethisasadiscovered“left-handedmedia”,hasshownconsiderable“Halleffectoflight”,theHalleffectinelectronicsystemstechnologicalpromise.Inthepast,significantprogressisassociatedwithbrokentime

6、-reversalsymmetryratherhasbeenachievedinthefieldofphotonicsbymakingusethanbrokenspatialinversionsymmetry,andwehavere-ofanalogieswithelectronicsystems.Forinstance,the8centlydiscussedsomeoftheat-first-sight-surprisingef-typicalPBGmaterial,asystemwithaspatiallyvary-fectsthatbrokentime-

7、reversalsymmetrycouldproduceingandperiodicdielectricfunction,wasmotivatedbyinphotonicsystems.thewellknownphysicsofelectronicBlochstates;theInthepresenceofnon-vanishingBerrycurvature,thedielectricscatteringoflightinperiodicmediapresentsusual“semiclassical”expressionforthegroupveloc

8、itythesameformalsolutionsasthosef