Algorithm of Mie theory Calculation

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1、ProgressInElectromagneticsResearchSymposium2005,Hangzhou,China,August22-26691AlgorithmofNumericalCalculationonLorentzMieTheoryJianqiShenandXiaoshuCaiUniversityofShanghaiforScienceandTechnology,ChinaAbstractInthisworkanimprovedalgorithmispresented.Thequantitiesrelatedwiththescatteringcoefficientsar

2、ecalculatedbymeansofthedownwardorupwardrecurrencesofRiccati-Besselfunctionsrespectively,whichareprovedtobestable.Numericalcalculationshowsthatthealgorithmisefficient,reliableandrobustinawiderangeofparticlesizeandrefractiveindex.IntroductionTechniquesofparticlesizeanalysisbasedonlightscatteringhave

3、beendevelopedforseveraldecadesandhavebeenappliedinalotoffields.ThemeasurementsinvolvenumericalanalysisbasedonthescatteringtheoryforsphericalparticlesdevelopedbyMie[1].Itsmathematicalsolutionwasobtainedasaninfiniteseriesofterms.Thedevelopmentofcomputertechnologyhasmadeitfeasibletosumthesetermsnumer

4、ically,andtherehavebeenmanynumericalcomputationalstudiesofscatteringfunctions,mostofthosewerecontributedbyInfeld[2],Dave[3-5],Lentz[6],Wiscombe[7-8]andetc.However,thesituationisstillnotsosatisfying.TheMiescatteringshowsstrongvariationswithscatteringanglewhenthesizeoftheparticleislargecomparedtot

5、hewavelength.Forsomeapplications,itisdesirabletoevaluatethefieldofthescatteredradiationatmanyscatteringangles.Furthermore,whenoneisinterestedinscatteringpropertiesofapolydispersedparticlesystem,itisnecessarytocomputethescatteringlightforseveralhundredvaluesofparticlesizeforgoodreliability.Suchcom

6、putationaltaskscanbeverytediousandtimeconsuming.Therefore,thecomputationspeedshouldbeefficientandthealgorithmshouldbecapabletogiveaccurateandreliablesolutionforawiderangeofparticlesizeandrefractiveindex.Inthiswork,weproposeanefficientnumericalprocedureforcomputingtheMiescattering.Someexempli-fyingre

7、sultswillbepresented.ImprovedAlgorithmTheMiescatteringcoefficientsareusuallyexpressedas:ψ(α)ψ′(mα)−mψ′(α)ψ(mα)nnnnan=ζn(α)ψn′(mα)−mζn′(α)ψn(mα)(1)mψ(α)ψ′(mα)−ψ′(α)ψ(mα)b=nnnnnmζ(α)ψ′(mα)−ζ′(α)ψ(mα)nnnnwhichrequirethecalculatio