Excellent web site with information on various methods and numerical codes for scattering by nonspherical particles:

Transcription

1 Lectue 5. Lght catteng and abopton by atmophec patcuate. at 3: Scatteng and abopton by nonpheca patce: Ray-tacng, T- Matx, and FDTD method. Objectve:. Type of nonpheca patce n the atmophee.. Ray-tacng method. 3. Outne of the T-Matx method. 4. Outne of the FDTD method. Requed Readng: L: 5.3, 5.4, 5.5 Advanced/Addtona Readng: Mhchenko, Hovene, and Tav (Ed.) Lght catteng by nonpheca patce. Academc e.. Exceent web te wth nfomaton on vaou method and numeca code fo catteng by nonpheca patce: Type of nonpheca patce n the atmophee. Reca Lectue 4 about popete of atmophec aeoo and ce cyta. Nonpheca aeoo: Dy at (e.g., dy ufate, ntate, ea-at) Dut Cabonaceou In contat to the pheca patce, the catteng popete of nonpheca patce ao depend on hape of the patce and t oentaton wth epect to the ncdent ght beam.

2 Fo nonpheca patce: Reca Lectue 4: In the fa-fed zone (.e., at the age dtance fom a patce), the outon of the vecto wave equaton can be obtaned a (eq.[4.] + = E E S S S S k kz k E E 4 3 ) exp( and fo the Stoke paamete (ee Eq.[4.5] = o o o V U Q I V U Q I 4 σ whee the phae matx = [5.] Oentaton of the patce: Aeoo patce have andom oentaton n pace, wheea the ce cyta ae often oented. Oentaton aveaged catteng phae functon and catteng co ecton ae σ σ = Θ d d )n, ( ), ( ) ( / [5.] σ σ = d d n ), ( / [5.3] whee ` and ` ae the oentaton ange of a nonpheca patce wth epect to ncdent ght beam.

3 . Ray-tacng method. Ray-tacng method (o geometca optc appoxmaton, o ay optc appoxmaton) an appoxmate method fo computng ght catteng by patce much age than a waveength (.e., the maet ze paamete about 8-). Bac pncpe: Ray-tacng method baed on the aumpton that the ncdent EM wave can be epeented a a coecton of ndependent paae ay. Ray tacng commony pefomed ung a Monte Cao appoach. Ray tacng cont of two pat: ) dffacton theoy fo the fowad catteng peak; ) ay tacng ung Fene efecton and tanmon fomua. Advantage: Ray-tacng method can be apped to any hape (pheca o non pheca) Lmtaton: Ray-tacng method an appoxmate by defnton; Lmted ange of ze paamete; Abobng patce eque peca teatment. Dffacton In geometc optc, ght may be teated a ay, except fo Faunhofe dffacton aound a patce. Babnet pncpe- dffacton patten the ame fom an apetue a fo opaque patce of ame ze. 3

4 Integate the fa fed contbuton of ncdent wave ove the apetue E E = exp( kr ) da Rλ Huygen pncpe each pont a ouce of ccua wave font. Fo phee (ccua apetue), the dffacton patten I A 4 I o x J ( x n Θ) ( Θ) = whee k = /λ, and J Bee functon. R k 4 x n Θ [5.4] [5.5] Exampe: catteng dagam fo dffacton by a ccua dk Dffacton peak n phae functon: wdth Θ ~/x, heght () ~x Ft zeo at x nθ = 3.83 and max at x nθ = 5.4 4

5 Fene efecton and tanmon Sne aw gve efacton ange θ t : n θ = m n θ t [5.6] Fene fomua fo poazed efecton amptude coeffcent: co θ m n θ = [5.7] co θ + m n θ m n θ m co θ = [5.8] m n θ + m co θ Refectvty and tanmon coeffcent fo ntenty: R =, R =, T R =, T = R [5.9] NOTE: Fo θ=, efecton m R = => efectvty nceae wth efactve m + ndex 5

6 Dffacton + efecton and efacton Fgue 5. A chematc epeentaton of the component of the phae functon fo andomy oented hexagona ce cyta (fom Lou, 99) 6

7 3. Outne of the T-Matx method. T-Matx method, TMM, enabe cacuaton of optca popete of patce wth otatonay ymmetc hape (uch a epod, ccua cynde, Chebyhev hape, etc.) NOTE: FORTRAN code of TMM openy avaabe at Bac pncpe: TMM baed on expandng the ncdent EM and catteed fed n vecto pheca wave functon. The T matx tanfom the expanon coeffcent of the ncdent fed nto thoe of catteed fed and, f known, can be ued to compute any catteng chaactetc of a nonpheca patce. The eement of the T matx ae ndependent of the ncdent and catteng fed and depend ony on the hape, ze paamete, and efactve ndex of the catteng patce and on t oentaton wth epect to the efeence fame. Advantage: TTM hghy accuate and computatonay fat Lmtaton: Lmted type of patce hape; Lmted ange of ze paamete (x< 3). 4. Outne of the FDTD method. Fnte Dffeence Tme Doman, FDTD, method enabe cacuaton of optca popete of patce of compcated geomete and compoton. Bac pncpe: FDTD ove the Maxwe cu equaton (ft two equaton n eq.[4.] ) n the tme-doman by ntoducng a fnte dffeence anaog. The pace contanng a catteng patce dcetzed by ung a gd meh. The extence of the patce epeented by agnng utabe eectomagnetc contant n tem of pemttvty, pemeabty and conductvty (dependng on patce popete) ove the gd pont. 7

8 Advantage: FDTD can be apped to patce havng any hape and compoton. Lmtaton: Known mpementaton pobem (fo ntance, tacang effect - due to eecton of Catean meh gd) Lmted ange of ze paamete (up to x =5-) Appcaton Ice cyta: Yang and Lou: FDTD fo ze paamete ~5 and ay-tacng (fo x >5) Dut patce: Mhchenko et a.: T-matx apped to a mxtue of epod Kaahnkova and Sokok (): DDA apped to SEM data of dut patce (ee Lectue 6) Soot aeoo: Mackowk et a.: modfed T-matx apped to facta-ke phee cute. 8

9 How to defne an equvaent phee: ze paamete kl 9