Laser spectroscopy. - Basic concepts and instrumentation - Wolfgang Demtröder. Nonlinear Optics Lab. Hanyang Univ. 2 nd enlarged edition

Transcription

1 Lsr spcroscopy - Bsc concps nd nsrumnon - nd nlrgd don Wolfgng Dmrödr Nonlnr Opcs L. Hnyng Unv.

2 . Inroducon Spcroscopy 분광학 : To nlyz h chrcrscs of EM rdon lgh nrcng wh mrs AsorponEmsson spcr Spcroscopc nfomons : Wvlngh : nrgy lvls of omc sysm Ln nnsy : rnson proly Nurl lnwdh : mn lfm of xcd ss Dopplr wdh : vlocy dsruon mprur Prssur rodnngshf : collsonnromc ponl ZmnSrk splng : mgnclcrc momns Spcroscopc chnqu : Snsvysoluon Opcl nsrumnon : lgh sourc, dcor, opcs Tchnqu : LnrNonlnr, Molculr m, Tm rsolvd, Fourr,... Nonlnr Opcs L. Hnyng Unv.

3 . Asorpon nd Emsson of Lgh. Cvy Mods Cuc cvy L, T Sonry rdon fld : suprposon of pln wvs E Ap xp [ωp k p r] p c.c. Boundry condon : sndng wvs cvy mods π k n, n, n3, n : posv ngrs L k π L n n n3.3. λ π k, λ ω c k L n n n3, ω πc L n n n3.4 Nonlnr Opcs L. Hnyng Unv.

4 Numr of mods wh frquncy m : Numr of ngr s n, n, n3 ssfyng h condon of c k ω ω m If L m rdus of sphr, c s lrg nough comprd o L, h numr of ngr s s roughly gvn y h volum of h ocn of sphr : nd kng no ccoun h EM wv hs wo possl polrzon componns A ê ê ê ê δ ; ê,ê k.5 N ω m π Lωm L ωm πc 3 π c Nonlnr Opcs L. Hnyng Unv.

5 Spcrl mod dnsy : n N L 3 ω 8πν ω dω dω or n ν dν dν.7 3 π c c n 3 xmpls vsl =5 nm, d GHz : 5 mcrowv = cm, d Hz : c X-ry = nm, d Hz : n d 3 n d m 3 n d m 3 m 3 Nonlnr Opcs L. Hnyng Unv.

6 . Thrml rdon nd Plnck s Lw In clsscl hrmodynmcs, ch mod would rprsn clsscl oscllor wh mn nrgy kt. Thrfor from.7, spcrl nrgy dnsy of h rdon fld s gvn y 8πν k ρνdν nννkt Tdν 3 c ylgh-jns lw I rgon.8 Plnck s rdon lw : Ech mod cn only m or sor nrgy n dscr mouns qhν, whch r ngr mulpls q of mnmum nrgy qunum hν phoon. In hrml qulrum, h pron of h ol nrgy no h dffrn mods s govrnd y h Mxwll-Bolzmnn dsruon : p q Z qhνhν.9 whr, Z q qh kt pron funcon. Nonlnr Opcs L. Hnyng Unv.

7 Mn nrgy pr mod W q qh kt h p q qh qh. h kt Z q Spcrl nrgy dnsy : mod dnsy mn nrgy pr mod 8 h d n d W d 3 h c kt Plnck s rdon lw.3 kt ylgh-jns h h kt Plnck Nonlnr Opcs L. Hnyng Unv.

8 .3 Asorpon, Inducd nd Sponnous Emsson In wo-lvl sysm, rnson prols pr scond for nducd sorpon, nducd msson, nd sponnous msson d d d d d d p p p spon B B ν.5 ν A.6.7 nducd sorpon smuldnducd msson sponnous msson whr, A, B, B : Ensn A, B coffcns Nonlnr Opcs L. Hnyng Unv.

9 lons wn h coffcns A hrml qulrum, h populon dsruon s gvn y h Bolzmnn dsruon N g Z whr, N : ol numr dnsy, g = J + : dgnrcy, nd E kt N.8 Sdy s soluon Z g E kt : pron funcon [ B A] N BN.9 usng h rlon, N N E E kt g g g g h kt g g A B B. B h kt B g g 8 3 c B h, A 3 8 h B 3 c h kt., Nonlnr Opcs L. Hnyng Unv.

10 Anlyss If g =g, B =B A Bh 3, whr n 8 c : numr dnsy of mod n 3 8h If n h, 3 c. : Th sponnous msson pr mod quls o h nducd msson. : Th ro of h nducd- o h sponnous-msson r n n rrry mod s qul o h numr of phoons n hs mod. B 3 8h B A 3 c : Smuld msson > sponnous msson A N [ ] g N N B AN N B[ ] N g N N B : If N g >N g populon nvrson Lsng!! Nonlnr Opcs L. Hnyng Unv.

11 .6 Trnson Prols Th nnss of spcrl lns dpnd on h populon dnsy of n h sorng or mng lvl nd lso on h rnson prols of h corrspondng rnsons. If h prols r known, h populon dnsy cn ond from ln nnsy msurmns..6. Lfms. Sponnous nd donlss Trnsons <Sponnous msson> Sponnous msson proly : Tol Sponnous msson proly : Th dcrs of h populon dnsy : dn d d spon p k Ak A A Nd, N N.38 A A k k Mn lfm : A.39 Nonlnr Opcs L. Hnyng Unv.

12 <collson-nducd rdonlss rnson> d coll coll pk vn B.4 k d <nducdsmuld msson> d nd pk k Bk[ N g gk Nk ].4 d <Effcv lfm> ff [ A k k B k k { N g g k N k } N B σ k v].43 Nonlnr Opcs L. Hnyng Unv.

13 .6. Smclsscl Dscrpon; Bsc Equons Smclsscl dscrpon : EM wv clssclly, Aom qunum mchnclly <EM wv> E Ecos kz.44 Spl vron of h EM fld cn nglcd whn.g. In h vsl rgon ~5 nm, d~.5 nm d E E cos A, A E.44 Nonlnr Opcs L. Hnyng Unv.

14 <Aom> Hmlonn opror of h om nrcng wh lgh fld cn wrn s sum of h unprurd Hmlonn of h fr om plus h pruron opror : H H V.45 Dpol pproxmon for h pruron opror : V p E p E cos.46 Tm-dpndn Schrodngr quon : H.47 k, E E Gnrl soluon : En r, cn un r n.48 For our wo-lvl sysm, E E r, u u.5 whr,, : m-dpndn proly mpluds Nonlnr Opcs L. Hnyng Unv.

15 Susung.5,.45 no.47, nd usng h rlon, H u n E n u n gvs u E u E Vu E Vu E.53 * Mulplcon wh u n n=,, nd spl ngron ; r - [ V - [ V whr, hs odd pry! V V V E E E E * uvud E u * D D u ru ] ] * ru d d E D dpol mrx lmn cf Expcon vlu of h dpol momn undr h nflunc of h EM fld, D * rd D * E E * D Nonlnr Opcs L. Hnyng Unv.

16 Nonlnr Opcs L. Hnyng Unv. Pu, A D E D frquncy.58.58

17 .6.3 Wk-Fld Approxmon Assum h fld mplud o suffcnly smll so h for m <Tmxmum nrcon m h populon of uppr lvl rmns smll comprd wh h of lowr lvl,.., From.58 wh h nl condon of =, =, cn nglcd rong-wv pproxmon, nd scond rm osclls fs nough o vnshd ou n m vrgd msurmn. Nonlnr Opcs L. Hnyng Unv.

18 Proly h h sysm s m n h uppr lvl : sn.6 A h rsonnc, vld n m,.6 or T D E.63 Nonlnr Opcs L. Hnyng Unv.

19 Nonlnr Opcs L. Hnyng Unv..6.4 Trnson Prols wh Brod-Bnd Excon d D d p sn d sn For rod-nd lgh sourc, cus s slowly vryng ovr h sorpon-ln profl ; D p.64.65, E D If S, Fg..8c

20 Ensn B coffcn From.65, wh consdrng h h vrgd componn of h squr of dpol momn for soropc rdon: p cos p 3 p z d d From.6 d d p p 3 D B.66 B k 3 u * ru k d.68 In gnrl, whn h lvl k nd r dgnrd wh h dgnrcs g k, g, rspcvly B k g gk D mk n 3 g 3 g m n S k S k : Ln Srngh Nonlnr Opcs L. Hnyng Unv.

21 .6.5 Phnomnologcl Incluson of Dcy Phnomn Dcy phnomn sponnous msson, collson-nducd rlxon cn rd y ddng phnomnologcl dcy rms o.58 s follows ; Wk-fld Approxmon : p,.7c Nonlnr Opcs L. Hnyng Unv.

22 Dsprson nd Asorpon D D * * Dcos.56 Afr kng h scond m drvv of.56 nd usng.7, h quon of moon for h dpol momn D undr h nflunc of rdon fld D D 4 [ cos sn].7 Assum clos-o-rsonnc condon nd wk dmpng :, D Dcos Dsn.73 D D, Dsprson Asorpon Nonlnr Opcs L. Hnyng Unv.

23 Nonlnr Opcs L. Hnyng Unv..6.6 Inrcon wh Srong Flds From.58, n h rong wv pproxmon : C C C C Gnrl soluons: whr,, C, C.76

24 Proly mplud : sn.78 whr, -floppng frquncy.8 cf frquncy : -floppng frquncy h rsonnc, Prols : sn.79 - sn.8 S, Fg..8 Nonlnr Opcs L. Hnyng Unv.

25 A h rsonnc, cos D E sn D E Afr h m, T D E.8.8 -puls.83 h populon proly of h nl sysm hs n nvrd ;,, Nonlnr Opcs L. Hnyng Unv.

26 Nonlnr Opcs L. Hnyng Unv. Now nclud h dmpng rms, ] [ sn.84.85, whr,, whr, -floppng frquncy :.86 S, Fg..9

27 Nonlnr Opcs L. Hnyng Unv. For h cs of Closd wo-lvl sysm,.87.87,, nd For h rsonnc cs,.88 Spcl cs, : mpossl h populon nvrson!!