Anderson localization of classical waves in weakly scattering metamaterials

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1、AndersonlocalizationofclassicalwavesinweaklyscatteringmetamaterialsAraA.Asatryan1,SergeyA.Gredeskul2,3,LindsayC.Botten1,MichaelA.Byrne1,ValentinD.Freilikher4,IlyaV.Shadrivov3,RossC.McPhedran5,andYuriS.Kivshar31DepartmentofMathematicalSciencesandCentreforUltrahigh-bandwidthDevicesforOpticalSystems(

2、CUDOS),UniversityofTechnology,Sydney,NSW2007,Australia2DepartmentofPhysics,BenGurionUniversityoftheNegev,BeerSheva,84105,Israel3NonlinearPhysicsCenterandCUDOS,AustralianNationalUniversity,Canberra,ACT0200,Australia4DepartmentofPhysics,Bar-IlanUniversity,Raman-Gan,52900,Israel5SchoolofPhysicsandCUD

3、OS,UniversityofSydney,Sydney,NSW2006,AustraliaWestudythepropagationandlocalizationofclassicalwavesinone-dimensionaldisorderedstruc-turescomposedofalternatinglayersofleft-andright-handedmaterials(mixedstacks)andcomparethemwithstructurescomposedofdifferentlayersofthesamematerial(homogeneousstacks).Fo

4、rweaklyscatteringlayers,wehavedevelopedaneffectiveanalyticalapproachandhavecalculatedthetransmissionlengthwithinawiderangeoftheinputparameters.Thisenablesustodescribe,inaunifiedway,thelocalizedandballisticregimesaswellasthecrossoverbetweenthem.Whenbothrefractiveindexandlayerthicknessofamixedstackare

5、random,thetransmissionlengthinthelong-waverangeofthelocalizedregimeexhibitsaquadraticpowerwavelengthdependencewithdif-ferentcoefficientsofproportionalityformixedandhomogeneousstacks.Moreover,thetransmissionlengthofamixedstackdiffersfromthereciprocaloftheLyapunovexponentofthecorrespondinginfinitestack.

6、Inboththeballisticregimeofamixedstackandinthenearlong-waveregionofahomogeneousstack,thetransmissionlengthofarealizationisastronglyfluctuatingquantity.Inthefarlong-wavepartoftheballisticregion,thehomogeneousstackbecomeseffectivelyuniformandthetransmissionlengthfluctuationsareweaker.Thecrossoverregionf

7、romthelocalizationtotheballisticregimeisrelativelynarrowforbothmixedandhomogeneousstacks.Inmixedstackswithonlyrefractive-indexdisorder,Andersonlocalizationatlongwavelengthsissubstantiallysup-pressed,withthelocali