/4/00 Dsign/Modling for Priodic Nno Structurs t for EMC/EMI Ji Chn Dprtmnt of ricl nd Computr Enginring Houston, TX, 7704 Outlin Introduction Composit Mtrils Dsign with Numricl Mixing-Lw FDTD dsign of Nno-scl FSS Stochstic nlysis Conclusions
/4/00 Introduction romgntic Comptibility /romgntic Intrfrnc http://n.wikipdi.org/wiki/romgntic_comptibility 3 Shilding NASA JSC Nnotub http://rsrch.jsc.ns.gov/binnilrsrchrport/pdf/eng-8.pdf http://www.ursi.org/procdings/procga05/pdf/e0.3(068).pdf 4
/4/00 3 nring Shilding Mtrils with Priodic Structurs tricl & Computr Engin 650nm Pitch 450nm lngth 00nm Arms 5 FSS nring Composit Mtrils with Numricl Mixing-Lw tricl & Computr Engin Mxwll-Grntt qution 6 q = = = N k k k k N k k k k f f ff 3 L L L L = ) ( / ) ( ) ( ) ( ) ( / ) ( ) ( ) ( 3 3 3 3 ff ff f
/4/00 Composit Mtrils with Numricl Mixing-Lw Priodic Composit Mtril 3D Priodicl Structur 7 Unit Elmnt Zmx FDM PBC Ymx PBC Voltg Voltg Voltg Voltg PBC PBC: priodic boundry condition PBC Xmx 8 Unit Elmnt 4
/4/00 Effct of Inclusion ricl Proprtis l =cm, =, r _ host = 3, = = rx _ inclusion ry _ inclusion rz _ inclusion 9 Effct of Inclusion ricl Proprtis l =cm, =, r _ host = 30, 3, = = 3 rx _ inclusion ry _ inclusion rz _ inclusion 0 5
/4/00 nring tricl & Computr Engin ricl Proprtis Vrsus Frquncy 6
/4/00 Cubic Inclusion Vf=0.764 3 Numricl Rsults Vrsus Frquncy = V ( V ) ff incl f host f 4 7
/4/00 Optimiztion for Multiphs Mixtur volum frctions 0.. spr: 4.4 nd 4.04 Conductivity : 0.0075 S/m nd.369 S/m 5 FDTD Modling 6 8
/4/00 Chllng in th Modling of IR FSSs PEC ssumption is not vlid ny mor Th mtl is highly frquncy- dpndnt now It hs both ngtiv prmittivity nd conductiv loss But ll of th trdition microwv dsigns r bsd on this ssumption. FDTD Modling for Priodic Structurs Lorntz-Drud Modl (gold) f b ( ) = ( ) ( ) ω ω ω r r r Ω k p fiω p = ω( ω j 0 ) Γ i= ( ωi ω ) jωγ i 7 8 k z. k 0 k x PBC Finit-Sizd romgntic Sourc z PBC Pln Wv Incidnc Pln wv incidnc. x. ( ) ( ) = ( ) ( ) x E x, H x E x, H x jk? z? Brut Forc. Finit Siz Sourc Incidnc Priodic boundry condition (PBC) cn b pplid for bov qution in both frquncy nd tim domins Finit siz sourc incidnc Assumption is no longr vlid In tim domin, Brut Forc FDTD simultion is ndd x 9
/4/00 ASM-FDTD Mthod n z Etot ( x n, y, t) z nth unit cll.... x x n=- n=- n=0 n= n= Spctrl domin trnsformtion of th finit siz sourc i i jkxn J % i ( x, y, kx ) = J ( x0, y0) δ ( x x0 n) δ ( y y0) ( ) i ( ) 0, 0 = % x n= π / J x y J k dkx Th fild in th 0th unit cll xcitd by this sourc cn b rprsntd s E π / ( x, yt, ) = tot π π E / ( kx, yt, ) dk 0 0 tot x Th 0 th unit cll spctrl domin solution E 0 tot ( kx, y, t) cn b obtind by FDTD simultion whn following PBC is pplid jkx E ( yt,, ) = E (0, yt, ) 0 0 tot tot Th fild in nth cll is found by E = π π / n 0 jkxn tot ( x n, y,) t Etot ( kx, y,) t dkx π / π π / 9 Numricl Exmpls dipol sourc 45 mm bov th structur dipol strip mm by 3 mm priodicity 5 mm in both dirctions fild smpld 90 mm undr th dipol sourc 0 0
/4/00 Diffrnt Modl Impcts On Th Finl Rsult Simultd trnsmission intnsity of n Au cross slot rry on th qurtz substrt (=650nm, L=500nm, W=0nm, thicknss=300nm nd substrt dilctric constnt is.36 Thr Prcticl Pttrns I: Stndrd Cs Simultd trnsmission intnsity of n Au cross slot rry on th qurtz substrt (=660nm, L=50nm, W=60nm, thicknss=0nm nd substrt dilctric constnt is.36
/4/00 Fiv Prcticl Pttrns II: Fcd Cntrd Cs Simultd trnsmission intnsity of n Au cross slot rry on th qurtz substrt (=660nm, L=500nm, W=70nm, thicknss=0nm nd substrt dilctric constnt is.36 3 Vrition quntifiction Composit mixturs hv inhrnt rndomnss Th homognizd EM proprty nds to b vlutd Sourcs of rndomnss includs -- mtril lctricl proprtis -- componnt gomtry 4
/4/00 Vrition quntifiction tchniqus Mont-Crlo (MC) : Simpl to implmnt, computtionlly xpnsiv Prturbtion: Limitd to smll fluctution Stochstic colloction mthod (SCM): Cn hndl lrg fluctutions, highly fficint, trnsforms th stochstic nlysis into sris of dtrministic simultions 5 r { ξρ n = ( } N { ξ n = ξ), ξ,..., ξ N } Introduction to SCM { ξ } N n n= Suppos w hv N rndom prmtrs r w us th bbrvition ξ = { ξ, ξ,..., ξ N } { } N n n ξ = ρ ( r ξ ) th prmtrs could b distributd ccording to joint PDF ch ξ n could b distributd indpndntly ccording to its probbility dnsity function (PDF) ρ ( ξ ) n n r N ρ ( ξ) = ρ n( ξn) n= Rliztion = output r from th dtrministic simultion tool for spcific choic of ξ = { ξ } N n n= f ( r ξ ) 6 3
/4/00 Introduction to SCM (cont.) On my b intrstd in sttistics of outputs vrg or xpctd vlu vrinc r r r E[ f ] = f( ξ ) ρξ ( ) dξ Γ [ ] Vr f = E[ f ] E[ f] r r r r r r = f ( ξ ) ρ ( ξ ) d ξ f ( ξ ) ρ ( ξ ) d ξ Γ Γ ( ) Γ r r r G( f( ξ )) ρξ ( ) dξ highr momnts 7 Intgrls of th typ r r r G( f( ξ )) ρξ ( ) dξ Γ Introduction to SCM (cont.) cnnot, in gnrl, b vlutd xctly Thus, ths intgrls r pproximtd using qudrtur rul Γ r r r Q r r G( f( ξ)) ρ( ξ) dξ = ωqρ( ξq) G(( f( ξq))) for som choic of qudrtur wights nd qudrtur points q= { } Q q q ω = r { } Q q q ξ = 8 4
/4/00 f ( r ξ ) 9 Introduction to SCM (cont.) To us such rul, on nds to know th simultion output r Q t ch of th qudrtur points { } ξ q q= -- for this purpos, on cn build polynomil pproximtion G% ( f( r ξ )) nd thn vlut tht pproximtion t th qudrtur points G( f( r ξ )) -- th simplst mns of doing r this is to us th st of Lgrng N intrpoltion polynomils { ( )} smpl Ls ξ corrsponding to th smpl points s= r N { } smpl r r r ξ s s= G( f( ξ)) ρ( ξ) dξ Γ Q N r smpl r r r = ωρξ q ( q) G(( f( ξq))) % = G( f ( ξ) ) G( f ( ξs) ) Ls( ξ) q = s= Nsmpl r Q r r = G( f( ξ )) ωρξ ( ) L ξ Thn w hv th pproximtion for th mn: N smpl r r r r Q r r E f f( ξ ) ρξ ( ) dξ f ( ξ) ωρξ ( ) L ξ [ ] = = s q q s( q) Γ s= q= ( ) s q q s q s= q= ' i Numricl xmpl =, σ = 0 r _ host host x y= z= μ l = l l.0 m, Mn vlus: EVF [ ] :5% E[ ] = 8, E[ σ ] = r_ inclusion inclusion Gol: Evluting th globl snsitivity of ffctiv prmittivity du to vrition in crtin mixing prmtrs Vrying prmtrs: inclusion rltiv prmittivity, inclusion conductivity nd volum frction; ll of which r ssumd to b Gussin vribls. 30 5
/4/00 Oprting Frquncy: 0 Hz Convrgnc Tst Vribl: inclusion prmittivity, hs ±30% vrinc round its mn vlu mn Stndrd dvition 3 Th Effct of Inclusion Rltiv Prmittivity Vrition = r 8 _ inclusion This cs involvs vrinc of 30% round th mn vlu = 8 r_ inclusion host c = r_ host j σ ω 0 3 6
/4/00 Th Effct of Inclusion Conductivity Vrition c = r _ inclusion j σ ω inclusion 0 This cs involvs vrinc of 30% round th mn vlu σ inclusion = 33 Th Effct of Volum Frction Vrition This cs involvs vrinc of 30% round th mn vlu % VF = 5% 34 7
/4/00 Th Effct of Volum Frction Vrition This cs involvs vrinc of 30% round th mn vlu % VF = 5% 35 Conclusion Nw FDTD mthods for priodic structurs Applictions includ FSS Mt-mtrils Nno-scl dvics Multi-lyr lyr priodic structurs t diffrnt priodicitis 36 8