[数值]4[FDTD][Taflove-2003]Equivalent volume-averaged lights cattering behavior of randomly...

Equivalent volume-averaged lights cattering behavior of randomly inhomogeneous dielectric spheresi n the resonant range l.?R
7f  
ZhigangChenandAllenTaflove DHJh.Y@H  
DepartmentofElectricalandComputerEngineering,NorthwesternUniversity,Evanston,Illinois60208 agN`) F!  
VadimBackman l=[<gPE  
DepartmentofBiomedicalEngineering,NorthwesternUniversity,Evanston,Illinois60208 {n=)<w  
ReceivedDecember4,2002 &C<B=
T"I  
Finite-differencetime-domainnumericalexperimentsandsupportinganalysesdemonstratethatthespectral 8l0%:6XbI  
dependenceofthetotalscatteringcrosssectionsofrandomlyinhomogeneousdielectricspheresofsizesin
.G#S*L  
theresonantrangecloselyresemblethoseoftheirhomogeneouscounterpartsthathaveavolume-averaged EX7cjQsml  
refractiveindex.Thisresultholdsevenfortheextremecaseinwhichtherefractiveindexwithinaninho- a-,!K  
mogeneousspherevariesrandomlyovertherange1.0–2.0.(C)2003OpticalSocietyofAmerica d {a^  
OCIScodes: 290.5850,290.0290. &96I4su  
V=BF"S;-'
 
>Qz#;HI
 
Thephysicalbasisandphenomenologyoflight wX" 6 S:  
500–1000nmfortworangesofrandomlyassigned 1Dg\\aUk  
scatteringbyparticlesintheresonantrangeareof "d>{hP  
refractiveindex,1.45–1.55and1.0–2.0,separately, |j$&W;yC  
8 z,[4BM  
interestinavarietyofscienceandengineering /pZLt)=P  
usingapseudouniformrandom-numbergenerator. G*ZHLLO4S\  
1,2 F`3c uL[N  
Itiswellknownthatscatteringbyho- i2/:' i  
Figure1illustratestypicalassignmentsoftheran- s
={AdQ  
disciplines. c%
r?tKG6  
mogeneousorlayeredspheresthatcompriseisotropic 0#KDvCBJ  
domlydistributedrefractiveindexalongacutthrough (X@JlAfB  
dielectricscanbeanalyzedbyMietheoryandits ~cVFCM  
thecenteroftheparticleforcases1[Fig.1(a)]and2 7OYNH0EH  
2,3 Ey=
(B'A~  
However,becausemostparticlesofin- M2_sxibI  
extensions. Z!60n{T79c  
[Fig.1(b)].Notethatgroupingsofadjacentrandom ]
d}Z2I'  
teresthaveneithersphericalshapesnorhomogeneous Xy:'f".M~\  
refractiveindicescreatecompositeinternalinhomo- mnu4XE#|  
compositions,theirscatteringpropertiescannotbe }x`W+r  
geneitieswitheffectivelengthscalesthatvaryovera  ;?1H&  
obtainedanalytically. pHEhB9_A!  
widerange,asillustratedbythearrows. NduvfA4  
InthisLetterwereporttheapplicationofa ")"VQ|$y  
Figure2(a)graphstheFDTD-calculatedTSCS(in kXA o+l  
4 8i=J(5=  
to 3'8B rK  
finite-differencetime-domain(FDTD)method kMAQHpDD  
unitsofsquaremeters)versuswavelengthfor10ran- b"t95qlL  
investigatetherolethatrandomdielectricinhomo- 3:X3n\z  
domsequencesofrefractiveindexrangingfrom1.45to q [Rqy !,  
geneitiesplayinlightscatteringbyresonantspheres. -bu.Ar-#;h  
1.55forcase1,thefine-grainedinhomogeneity.The X90
VJb]  
Previously,theFDTDshowedpromiseincalculation gEbe6!; q3  
filledcirclesrepresenttheresultsoftheFDTDsimu- ehl){Dd^  
ofscatteringbyrealisticparticlesbecauseofitsability :2{6Pa(eg  
lationsfordistinctsetsofrandominhomogeneitiesat e)LRD&Q  
tomodelcomplexsurfaceshapesandinternalstruc- {$)zC*l  
30wavelengthsfrom500to1000nm.Inaddition, ,J"6(nk  
5,6 2i*-ET  
InthisLetterwealsoreportanapproxi- \RyOexNZ  
tures. :t-a;Q;  
Fig.2(a)showstheresultsoftwofiner-frequency- vF0#]  
mateanalysisthatsupportsournumericalfindings. ;BUJ5  
resolutionFDTDsimulationsat30wavelengths E8zga)  
FirstweverifiedourFDTDcodebycomputing Ol6jx%Je`  
from750to800nmandat30wavelengthsfrom Z;=G5O uvQ  
thescatteringpatternofhomogeneousspheresand [U
Ro#  
850to900nmforasinglesetofrandominhomo- YwyP+Sr\  
comparingtheresultswithMietheory.AGaussian \:-#,( .V  
geneities.Forcomparison,thedottedcurveshows >{p&_u.r-  
pulsewavesourcewasimposedonthesimulation E1usxF)  
thecorrespondingMiedatafora 5-mm homogeneous :jB~rhZ~  
grid,andthescattered-fieldfrequencyresponsewas ?*|AcMw5
 
spherewith n 1.5 (thevolumeaverageofthe im|( 4f  
extractedbymeansofadiscreteFouriertransform #\[h.4i  
randomrefractiveindicesoftheFDTDruns).From ,3&XV%1  
4 >Lx,<sE  
The [X]yj  
runconcurrentlywiththeFDTDtimestepping. IL`X}=L_  
Fig.2(a)weseethattheTSCSofeachrandomly C']TO/2q
 
7 R7}=k)U?d@  
perfectlymatchedlayerabsorbingboundarycondition %yX?4T;b  
inhomogeneousparticleasafunctionofwavelength O|=5+X  
wasusedinoursimulationstoterminatethecomputa- x1</%y5ev  
hasanoscillatorypatternthatcloselyresembles 5A oKlJrY  
5-mm inhomogeneous Md(AqaA  
tionallattice.Weconstructeda AM  cHR=/  
thatofitsvolume-averagedMiecounterpart.The P&"8R  
sphericaldielectricparticlewithinaFDTDspace 7Vd"k;:X  
primarydifferenceisthattheFDTD-modeled ;= ^kTb`X  
latticethathadauniformcubiccellsizeof25nmon iz!E1(z(  
spherelacksthehigh-frequencyripplestructure {I0b%>r=  
a side. Two cases of random inhomogeneity within 6&_"dg"  
calculatedbyuseoftheMieseries.Basedonour g*?)o!_*  
theparticlewerestudied.Incase1weassigneda sS(t }$  
numericalexperimentswithextremelyfinefrequency VI7f}  
uniformlydistributed,fine-grained,randomvalueof xDU>y  
resolution,webelievethatthisdiscrepancyarisesfrom $mOVo'2  
permittivitytoeachlatticecellwithinthesphere(cor- (? j $n?p  
thestaircasingofthespheresurfacewithintheFDTD 25 nm).Incase2weassigned nXPl\|pXt  
relationlength, L 8+Sa$R  
spacegrid,whichreducesthesurface-waveeffects ^F2OTz4n  
c (T:OZmEO.  
a u .. a3D''Ra  
?=,4{(/)  

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