PHYS 534: Nanostructures and Nanotechnology II. Logistical details What we ve done so far What we re going to do: outline of the course

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1 PYS 534: Nanosucus and Nanochnology II Logscal dals Wha w v don so fa Wha w gong o do: ouln of h cous Logscs Pof. Douglas Nalson Offc: Spac Scncs Bldg., Rm. 39 Phon: x34 -mal: nalson@c.du Lcus: MWF 3: - 3:5 Poblm ss: mosly wly, handd ou Wdnsday du followng Wdnsday. 45% of gad Fs pap 5% Scond pap 5% Pacpaon 5% Cous wbpag: hp://

2 Mo logscs Tx: no spcfc x. Th wll b som wn lcu nos, as wll as handous basd on a numb of boos. Also a lag numb of paps. Goal: o ma you la abou h physcs of nanosucus and h cun and fuu ols n chnology, o h pon wh you a las now wha o consd and wh o loo fo mo nfomaon. Small class sz mans w can hav mo dscussons and lss pu lcung. Assgnmns wll nclud adngs of paps so ha w can al abou hm n class. Wha w v don so fa Rvw of condnsd ma physcs Band hoy lconc pops of bul solds Fn sz ffcs fo quanum sysms Physcal lconcs - ndusy dmands Smclasscal Quanum ffcs: Tunnlng, Landau-Bu Nanolconcs Nanoscal FTs Sngl lcon dvcs Molcula lconcs

3 Wha w v don so fa Magnsm and lconcs - ndusy dmands Domans Couplngs bwn magnsm and cun Nanomagnsm GMR, TMR, MRAM Wha w gong o do: Physcal opcs Phooncs Nanophooncs Connuum mchancs Mcolcomchancal sysms MMS Nanolcomchancal sysms NMS Flud mchancs Mco- and nanofludc dvcs Ingad nanosysms: nanobochnology, snsos Ovall hm: nw dvlopmns n manpulang ma a h nanoscal lad o vy xcng commcal and scnfc possbls. 3

4 Physcal opcs Rfsh abou &M fld popagaon and ffcs of nfacs: Bagg flcos, dlcc mos, opcal wavguds fbs Bascs of lass vanscn wavs, na-fld ffcs Imag fom ypphyscs GSU Imag fom FSU Phooncs Phooncs and opolconcs - ndusal nds Smconduco lass Rsonaos Infoms and opcal swchng Fgu fom Pay and Khan, Oxfod Unvsy Ma. Sc. hp:// 4

5 Phooncs Nanosucud phoonc maals: polym-basd mos and modulaos Fgus fom Wb al., Scnc 87, 45. Phooncs Phoonc band gap maals fo ngad phooncs Fgus fom Vlasov al., Nau 44, 89. 5

6 Phooncs: na-fld Na-fld + vanscn flds fo panng and magng wll blow h dffacon lm. Unv. of Kansas Bll Labs Phooncs: plasmons Sub-wavlngh mal nanopacls o mal sufac pans xhb plasmon sonancs. Ths lad o: maabl opcal pops local concnaons of lcc fld nnsy possbly fo conolld manpulaon of opcal ngy a small scals. xncon Ab. Uns nm nm 7 nm 5 nm Wavlngh nm 6 nm Co Radus nm Shll 6 nm Co Radus 5 nm Shll 6

7 Connuum mchancs Bascs of connuum lascy hoy Bndng of bams; oson of ods Whn should connuum hoy ba down? θx x MMS / NMS Commcal applcaon: accloms abags 7

8 MMS / NMS Commcal applcaon: gyoscops Physcs of opaon, dcon, and lmaons of sa of h a mcomchancal dvcs. MMS / NMS Commcal applcaon: opcal swchng 8

9 MMS / NMS Fundamnal scnc: Quanum focs Quanum lms on sonaos + dampng Tu quanum mchancs. Flud mchancs Dmnsonal analyss and scalng Basc flud mchancs Vscosy and lamna flow: Lf a low Rynolds numb 9

10 Mcofludc dvcs Combn mco / nanofabcaon capabls and fluds o conl flud flows on vy small lngh scals. Vy low Rynolds numbs xmly lamna flow. Kns al., Scnc 85, Mcofludc dvcs ydodynamcs allows manpulaon and confnmn of nanoscal quans of fluds. Kngh al., PRL 8,

11 Mcofludc dvcs Can ma valvs, pumps, c. usng lasoms and mcofabcaon. Rsul: Lab-on-a-chp capabls. Thosn al., Scnc 98, 58. Mcofludc dvcs Taayama al., Nau 4, 6 Caghad goup, Conll Mas possbl suds of ndvdual clls, song of clls, manpulaon of ndvdual macomolculs, c.

12 Nanoscal flud manpulaon Pu scnc ssus, oo: No-slp condon a walls? Badown of connuous mdum pops n confnd goms? Nanobochnology Soong al., Scnc 9, 555 Combn op-down nanofabcaon N ws, SO poss wh bochmcal ools hsadn ags, F - ATPas bomolcula moo. Rsul: ATP-powd poplls.

13 Nanobochnology hp://golg.havad.du/banon/ndx.hm Usng afcal nanopos and snsv lccal masumns o do sngl-sand DNA and RNA squncng. Summay: W gong o loo a sval oh aas of chnology, and s wh h ably o manpula ma on h nm scal s ncasng ou capabls and undsandng. Ths nclud: Phooncs Mco-and nanomchancs Mcofludcs Nanobochnology Wll conclud wh som ovvw and pspcv on nanochnology. 3

14 Nx m: Rvw of physcal opcs Lgh a nfacs 4

15 Physcal opcs Maxwll s quaons and wavs Fou analyss and dspson Bounday condons and nfacs Toal nnal flcon vanscn wavs Mcoscopcs of mda: dspson Dffacon Th na-fld Maxwll s quaons no soucs µ µ Combnng hs qucly gvs wav quaons fo h flds: µ µ µ Rcall: A A A µ Fo unfom mda, µ µ

16 Wav quaons µ µ Ths a wav quaons. Fo unfom mda, h soluons conssn wh hs and Maxwll s quaons a plan wavs. L s sa n h lna wold, wh w blv n supposon. Thn w can ba down any gnal soluon no Fou componns: W can hn ansla dffnal opaons no algba: Pluggng no ou wav quaons, w s + µ + µ Phas vlocy and fld snghs + µ + µ Ths s h dspson laon, and lls us h phas vlocy of h wavs: µ v p In vacuum, c v p µ Can us Faaday s law o la and : µ ˆ µ µ µ Ths quany s calld h chaacsc admanc of a mdum. Dfn ndx of facon, n c v n p µ µ

17 Fld dcons unfom mda Gauss law: lcc fld s ansvs o dcon of popagaon. Smlaly, snc ~ magnc fld s also ansvs. lcc fld magnc fld Ths wav s lnaly polazd: lcc magnc fld s always ond along y-axs x-axs. Wav popagas n -z dcon. Complx vcos Fom ou noaon, you v alady gussd ha and a complx vcos, wh ach casan componn s complx, and h physcal fld s h al pa of h complx vco. Fo xampl, π / xx + y y ˆ ˆ So, a, h al pa of h fld pons along x. A π/, h fld pons along -y. On could w h al pa of hs as: cos ˆ x + sn yˆ x y Wh dffn magnuds x and y, hs s llpcally polazd lgh. 3

18 Supposon In lna mda, w can w a gnc fld confguaon as a supposon of plan wavs. Sang fom a gvn lcc fld a, and usng h pops of Fou ss, π * + 3, d 3/ Knowng dcon of popagaon, can hn pc ou Fou ms w ca abou, and fgu ou h fuu confguaon of h wav:, d π 3 3/ Goup vlocy and dspson Consd a gnc wav bul up fom componns hs way: ψ, A d 3 3 / π W wan o m-volv hs: 3 ψ, A d 3 / π Obvously, f s ndpndn of, hn h whol shap of ψ has jus bn anslad by a dsanc /. If dpnds on, and h wavpac s localzd aound som, w can Taylo xpand: + + v g 4

19 5 Goup vlocy and dspson,, 3 3/ 3 3/ d A d A g p g g g g v v v v v v + ψ π π ψ So, h nvlop of h wav movs fowad a vlocy v g. Th ndvdual componns mov wh h phas vlocy. Oh vlocs: fon, sgnal, ngy. Poynng s hom and vco Sa fom Amp s law and do wh : J + No: Combnng and aangng, J + Pluggng n Faaday s law, J µ + Raangng, J µ Poynng vco magnc ngy dnsy lcc ngy dnsy S µ

20 6 ngy dnss valuang hs fo h plan wav cas, w hav o mmb ha s h al pas of h complx flds ha ma. In f spac, * + Ugly! If all w ca abou, hough, s h m-avag, * 4 Sam da fo magnc ngy dnsy: * 4 µ Tm avagd Poynng vco Can follow sam da: + + * * S Agan, loong jus a m avag, S * * + In f spac, ˆ µ So, ˆ S µ

21 ngy dnss and supposon Wha abou supposng wavs wh dffn wavvcos? Gnal ul: fo nonlna quans l ngy dnsy, nd o w down full xpsson fo al flds, hn squa o fnd ngy dnss. Fo lna mda, w g a b lucy, and h fnal answ nds up loong l: * 3 d 4 Tha s, w can fnd h ngy conn fo ach fquncy o wavvco, and add hm. Agan, hs s somhng of a lucy ba. Inacons wh mda Th pvous xpssons can b complcad whn alsc mda a nvolvd. W ll gno magnc mda, and assum µ µ. Ponal complcaons: Dlcc consan can dpnd on fquncy dspson. Dlcc consan can dpnd on dcon nso!. Dlcc consan can b complx conducos. Dlcc consan can b spaally vayng nfacs. 7

22 Complx dlcc funcon Rmmb, a complx jus mans ha polazaon dosn hav o b n phas wh h lcc fld. Th changng polazaon can a ngy fom h lcc fld, causng dampng. In gnal, D / + f τ τ dτ Fou ansfomng, D, / + f τ τ dτ Wng ' + '' * ' ', w s '' '' Kams-Kong laons I s possbl o us h analyc pops of whch com fom h causal dfnon of h dlcc funcon o la h al and magnay pas o ach oh. Th suls a: s Jacson, p. 3ff R I [ / ] [ / ] + P π P π I[ / ] ' R[ / ] ' d' d' W wll s sholy ha h magnay pa of s lad o conducvy and absopon. Thus, on can masu an absopon spcum and nf dlcc pops, and vc-vsa. 8

23 Rflcon and facon a nfacs n z Wan o a h gnal poblm of dsconnuy of dlcc pops. Wll fnd appopa bounday condons and a wo spcfc cass. Rflcon and facon a nfacs Incdn: ˆ µ x n Rflcd: ˆ µ Tansmd: Wavvco magnuds: ˆ µ µ µ 9

24 Bounday condons Th angnal componn of mus b connuous. Longudnal componn of B and h mus b connuous. Tangnal componn of mus b connuous fo qual µ. Longudnal componn of D mus b connuous. + n + n + n + n T wav a a sngl nfac +x Apply con. of ang. a x ; mus b u fo all y and z, ncludng ogn. n Ths lls us ha y y y. Snc, hs mmdaly gvs ha angl of ncdnc angl of flcon. Smlaly, on fnds sn θ snθ whch gvs Snll s law: Knowng hs lls us n snθ n + snθ

25 T wav a a sngl nfac Usng h ang. condon gvs a scond quaon, n cosθ n cosθ n cosθ n +x W now hav wo quaons, wo unnowns, and can fnd h flcd and ansmd ampluds n ms of h ncdn amplud: n cosθ n cosθ n cosθ + n cosθ n cosθ n cosθ + n cosθ Ths s an xampl of a Fsnl fomula. TM wav a a sngl nfac Can do sam hng fo cas wh polazaon s offs by 9 dgs. Can hn do any vson of polazaon by supposon. n +x Sppng o h sul, n cosθ n cosθ n cosθ + n cosθ n cosθ n cosθ + n cosθ No ha an abaly polazd ncdn wav can lad o a flcd wav fo xampl wh qu dffn polazaon. Rmmb hs.

26 Pcn polazaon Suppos w hav wo wavs of sam amplud ha dff n fquncy by som small amoun, Ω. Th lcc fld a som fxd poson fom h supposon of h wo loos l: y +Ω ˆ ˆ yˆ + zˆ + z Ω Th polazaon a hs poson loos l s vayng n m a a fquncy Ω. A vy slow dco wll s an avag of all polazaons, and s oupu would b ndsngushabl fom on llumnad by unpolazd lgh. Now suppos ampluds of wo fquncy componns dff slghly. Pcn polazaon and Sos paams + p p + Ω yˆ + zˆ + p + p If you hn abou a slow y-polazd dco and h nnsy ss, you fnd ha s quvaln o an unpolazd wav conanng h facon -p /+p of h ngy, whl h polazd wav conans p/+p of h ngy. Colloqually, h wav has a faconal polazaon of p/+p n h y-dcon. Usful quans: Sos paams assumng x-d. popagaon I Q U V µ µ y y + z * R yz µ * Im y z µ z Q + U + V Facon of polazd lgh I

27 Toal nnal flcon Runng o wavs a nfacs, s cla fom Snll s law ha somhng wd happns whn n snθ > n. Th sul s oal nnal flcon; cos θ bcoms puly magnay. Th flcd amplud s qual o h ncdn amplud consvaon of ngy. Th flcd wav pcs up a phas shf, hough, ha dpnds on h dcon of polazaon. Fo T wavs, Fo TM wavs, n sn θ n xp an n sn θ n n sn θ n xp an n n sn θ xp φ T xp φ TM vanscn wavs Th M flds ha xnd ou no h scond maal a an xampl of an vanscn wav. Th x-componn of h wavvco n mdum s x n θ n κ c sn W pcd h physcally asonabl posv oo, so ha h flds dcay xponnally movng no mdum. No: h wav n mdum acually popagas n h y-dcon, so h s no dsspaon h. Loo a avg. Poynng vco T cas: * * + S ẑ ˆ µ yy κx zˆ y y κx yxˆ κyˆ µ S yy κx xp κx yˆ No avag ngy flux no mdum! Plug n numbs fo vsbl lgh 5 nm wavlngh, n.5, n, θ 6 dgs gvs ~ 6 nm. 3

28 Wavguds Toal nnal flcon s h physcs ha pms on o ma opcal wavguds.g. opcal fbs. Th a wo basc appoachs o analyzng opcal wavgud sucus: Ray opcs hows ou nnsy and phas nfomaon, bu can b mahmacally smpl and valng somms Wav-fld mhod acually solv Maxwll s quaons, png ac of all bounday condons A coupl of gnal pons: n.5 n Wavguds n.5 n Ray opcs pcu Bcaus of laal bouncs, longudnal popagaon of ngy, sgnals, c. s ypcally slow han jus c/n. Wav fld pcu Soluon o bounday valu poblm lads o wll-dfnd mods ha a naually ohogonal. Tha s, n a complly lna mdum, a wavgud wll only pass adaon of pacula wavlnghs; fuhmo, populang on mod dos no affc popagaon n h oh mods. Wav fld pcu Flds fom hs mods xnd ousd h oal nnal flcon nfac. Placng wo wavguds n clos poxmy can caus mxng - complly analogous o ou wo on quanum wlls fom las sms. Ral opcal fbs can b vy complcad: bfngn; dspsv; lossy; c. 4

29 Loss Wha do w man by loss? W ll s a spcfc cas n a mnu. Gnal da: M wav dos wo on somhng, and ha ngy s los fom h M wav. Manfss slf as a complx ndx of facon. Rmmb, n µ µ Suppos h s a dampd chagd mpuy bound by a hamonc ponal ha nacs wh h M wav: m [&& + γ& + ], Can solv fo h polazaon, assumng N of hs p un volum: N P γ m Loss Dlcc consan s hn: P N + + m γ Can a squa oo of hs, and loo a al and magnay pas of n /c o fnd h absopon coffcn. Ral and magnay pas of dlcc consan loo l: R[] Im[] 5