[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 bfpoX,:   
ZhigangChenandAllenTaflove uD[T l  
DepartmentofElectricalandComputerEngineering,NorthwesternUniversity,Evanston,Illinois60208 6$zd2N?  
VadimBackman  -rT#Wi  
DepartmentofBiomedicalEngineering,NorthwesternUniversity,Evanston,Illinois60208 \'|t>|zhp  
ReceivedDecember4,2002 _::ssnG3jT  
Finite-differencetime-domainnumericalexperimentsandsupportinganalysesdemonstratethatthespectral KuL+~  
dependenceofthetotalscatteringcrosssectionsofrandomlyinhomogeneousdielectricspheresofsizesin QjYw^[o  
theresonantrangecloselyresemblethoseoftheirhomogeneouscounterpartsthathaveavolume-averaged mX?t|:[b  
refractiveindex.Thisresultholdsevenfortheextremecaseinwhichtherefractiveindexwithinaninho- <'BsQHI  
mogeneousspherevariesrandomlyovertherange1.0–2.0.(C)2003OpticalSocietyofAmerica JxEz1~WK &  
OCIScodes: 290.5850,290.0290. ,p!IFS`  
W1ndb:  
Lf%}\0:  
Thephysicalbasisandphenomenologyoflight .'h^  
500–1000nmfortworangesofrandomlyassigned bQ&%6'ck  
scatteringbyparticlesintheresonantrangeareof 'MNCJ;A@V  
refractiveindex,1.45–1.55and1.0–2.0,separately, g`tV^b")  
8 s?4nR:ZC}  
interestinavarietyofscienceandengineering Md8<IFi9]Q  
usingapseudouniformrandom-numbergenerator. ->7zVAX  
1,2 {.DY\;Q  
Itiswellknownthatscatteringbyho- WMWUP ZsGS  
Figure1illustratestypicalassignmentsoftheran- +oHbAPs8  
disciplines. nK
I?Sc  
mogeneousorlayeredspheresthatcompriseisotropic %|>D{q6C  
domlydistributedrefractiveindexalongacutthrough 8U7dd[  
dielectricscanbeanalyzedbyMietheoryandits Y^;izM}  
thecenteroftheparticleforcases1[Fig.1(a)]and2 ;>F1?5P{  
2,3
4]-7S l,  
However,becausemostparticlesofin- yJ6g{#X4K<  
extensions. xVN!w\0  
[Fig.1(b)].Notethatgroupingsofadjacentrandom ]v?jfy  
teresthaveneithersphericalshapesnorhomogeneous {kb7u5-  
refractiveindicescreatecompositeinternalinhomo- | h+vdE8  
compositions,theirscatteringpropertiescannotbe 6Ypc]ym=J  
geneitieswitheffectivelengthscalesthatvaryovera \+0l#t$  
obtainedanalytically. 7@m+y  
widerange,asillustratedbythearrows. zJ:%iL@  
InthisLetterwereporttheapplicationofa koE]\B2A6  
Figure2(a)graphstheFDTD-calculatedTSCS(in %%)y4>I  
4 |ZXz&Xor  
to x"cB8bZ!$  
finite-differencetime-domain(FDTD)method wM3m'# xJ  
unitsofsquaremeters)versuswavelengthfor10ran- ! CJ*zZ*  
investigatetherolethatrandomdielectricinhomo- sYvlf0  
domsequencesofrefractiveindexrangingfrom1.45to 7KJ0>0~Et  
geneitiesplayinlightscatteringbyresonantspheres. iM9^.  
1.55forcase1,thefine-grainedinhomogeneity.The Z%=A[`5]  
Previously,theFDTDshowedpromiseincalculation ?IoA;GBg  
filledcirclesrepresenttheresultsoftheFDTDsimu- W5~!)Ec  
ofscatteringbyrealisticparticlesbecauseofitsability |WfL'_?$  
lationsfordistinctsetsofrandominhomogeneitiesat "/2kf)l{4  
tomodelcomplexsurfaceshapesandinternalstruc- lvNi/jk  
30wavelengthsfrom500to1000nm.Inaddition, WT3g31  
5,6  Vo%Z|  
InthisLetterwealsoreportanapproxi- u,N<U t  
tures. @ `mke4>_  
Fig.2(a)showstheresultsoftwofiner-frequency- c++q5bg@)  
mateanalysisthatsupportsournumericalfindings. <
s$T7Zk  
resolutionFDTDsimulationsat30wavelengths >
$)~B4  
FirstweverifiedourFDTDcodebycomputing <aI}+  
from750to800nmandat30wavelengthsfrom qZv@ULluc  
thescatteringpatternofhomogeneousspheresand #hMkajG  
850to900nmforasinglesetofrandominhomo- zE?dQD^OD  
comparingtheresultswithMietheory.AGaussian w ykaf  
geneities.Forcomparison,thedottedcurveshows v"o@q2f_  
pulsewavesourcewasimposedonthesimulation wjgFe]  
thecorrespondingMiedatafora 5-mm homogeneous UnEgsfN  
grid,andthescattered-fieldfrequencyresponsewas k`5K&  
spherewith n 1.5 (thevolumeaverageofthe ` K0PLxSv  
extractedbymeansofadiscreteFouriertransform L=M'QJl9  
randomrefractiveindicesoftheFDTDruns).From 5r~hs6H  
4 bD|VT  
The M-q5Jfm  
runconcurrentlywiththeFDTDtimestepping. D(&WEmm\B  
Fig.2(a)weseethattheTSCSofeachrandomly whrDw1>(  
7 cRNVqMpg  
perfectlymatchedlayerabsorbingboundarycondition 'op_GW  
inhomogeneousparticleasafunctionofwavelength 3f~znO  
wasusedinoursimulationstoterminatethecomputa- dO,;k+  
hasanoscillatorypatternthatcloselyresembles ^\Q%V
TM  
5-mm inhomogeneous :Gx5vo  
tionallattice.Weconstructeda )%f]P<kq6  
thatofitsvolume-averagedMiecounterpart.The WN#2<XjG  
sphericaldielectricparticlewithinaFDTDspace {))Cb9'  
primarydifferenceisthattheFDTD-modeled i->G{_gH  
latticethathadauniformcubiccellsizeof25nmon j'hWhLax  
spherelacksthehigh-frequencyripplestructure W )Ps2  
a side. Two cases of random inhomogeneity within 3TS:H1n  
calculatedbyuseoftheMieseries.Basedonour F2EX7Crj  
theparticlewerestudied.Incase1weassigneda >l=^3B,j  
numericalexperimentswithextremelyfinefrequency *Tr{a_{~C  
uniformlydistributed,fine-grained,randomvalueof T7O)  
resolution,webelievethatthisdiscrepancyarisesfrom qElPYN*wF  
permittivitytoeachlatticecellwithinthesphere(cor- A4b+:MQ*OX  
thestaircasingofthespheresurfacewithintheFDTD 25 nm).Incase2weassigned mG0_&'"YIG  
relationlength, L w*o2lg9  
spacegrid,whichreducesthesurface-waveeffects >&F:/   
c `>)pqI%L[g  
a u .. ;cp||uO  
BglbQ'6p  

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