Introduction. 1. Radiation damping of SP oscillations.

Transcription

1 \\ Titl: On Sufa Plasmon Damping in Mtalli Nanopatils Authos: Amn Mlikyan and Hayk Minassian (Stat ngining Univsity of Amnia, Yvan, Amnia Commnts: 6 pags; -mail addss: physdp@sua.am Subj-lass: Msosopi Systms and Quantum Hall fft; Optis \\ Two possibl mhanisms of sufa plasmon (SP osillations damping in mtalli nanopatils (MNPs, not onntd with lton-phonon intation a invstigatd thotially: a th adiation damping of SP, b sonant oupling of SP osillations with ltoni tansitions in matix. It is shown that th adiation damping at is popotional to th numb of ltons in MNP and thfo this hannl of ngy outflow fom MNP boms ssntial fo lativly lag patils. Th invstigation of sond mhanism shows that th at of SP osillations ngy lakag fom MNP dos not dpnd on patil siz and is fully mind by th optial haatistis of th matix. It is dmonstatd that fo vy small MNPs of -5 nm siz, wh th stong D siz quantization fft suppsss th lton-phonon intation, th sonan oupling in tain ass povids an fftiv ngy outflow. \\ Intodution Th MNPs in tanant matis show tally sltiv optial absoption du to olltiv osillations and intband tansitions []. Th sufa plasmon (SP fquny of MNPs, unlik bulk sampls and films, falls into th visibl ang du to gomty of nanopatil and dilti poptis of matix [-7], and this impotant puliaity is of gat intst fo a ang of optial appliations [,8-]. Whn th SP sonan is wll spaatd fom oth tansitions, th ntal poblm in appliations is th bhavio of SP, i.. th damping and dphasing of plasma osillations. Although th a many obsvations of SP sonan in vaious MNPs [4,5], th mhanisms of SP osillations damping and dphasing a not ompltly studid thotially and idntifid xpimntally. Th basi damping mhanism is onntd with th lton-phonon intation posss. It has bn notd many tims howv [6,7], that suh posss in systms with stong D siz quantization a suppssd baus of kinmatial stitions imposd on th ngy-momntum onsvation laws. Indd, in MNPs of siz of -5 nm and lss th lton lvl aing is ompaabl o lag than th Dby ngy, and thfo th lton-phonon intation may bom infftiv. On th oth hand in sval xpimnts with suh small MNPs th absoption lin boadning has bn obsvd [7-9]. This mans that bsids th lton-phonon satting oth damping mhanisms should b disussd as wll in od to intpt th obsvd SP lin boadnings. In this pap w onsid th adiation damping mhanism and th SP osillation ngy sonan tansf to th matix. Both ths mhanisms a not onditiond by th lton-phonon intation, and thus thy a not suppssd by th siz quantization ffts.. Radiation damping of SP osillations. On of th possibl mhanism of das of osillation ngy in MNP is th mission of ltomagnti wavs - so alld adiation damping. To th bst of ou knowldg th adiation damping of SP osillations is onsidd in litatu only phnomnologially, that is th damping at is xpssd in tms of susptibility []. W popos fully miosopial alulation, whih fo hial MNPs allows to min th SP damping at dpndn on all paamts inluding th dilti onstant of matix. Th instant valu of SP osillation ngy W (N m v an b psntd as

2 ( N m d W, ( wh N is th numb of ltons, v is th instant amplitud of vloity of osillations with fquny, d is th dipol momnt of on lton, is its hag and m is th lton mass. Th Poynting vto of adiation fild is ( H 4π. Substituting fo and ε fo n w obtain th ngy losss p unit tim owing to mission of adiation in mdia with dilti onstant ε [] ε Compaing qs ( and ( with at quation fo W 4 (N d ε. ( w obtain W, ( ad ε N, (4 ad m wh ad is th adiation damping tim of SP osillations, p 4ππ m mins th plasma osillations fquny in bulk, n is th lton onntation. Th fquny is onntd with SP fquny of hial nanopatil mbddd in a matix with al pat of dilti onstant ε by th xpssion + ε (s []. Th xpssion (4 an b p also psntd in fom, whih dmonstats th volum dpndn of th damping at p ad ε 4 p R, (5 9 + ε wh R is th MNP adius. As it follows fom (4 and (5 th adiation damping at is popotional to th numb of ltons in MNP o its volum, thus, this hannl of SP damping plays an impotant ol fo lativly lag MNPs. In fat to hav a omplt dsiption of SP osillation damping poss w should inlud into q. ( also th tm oonding th lton-phonon mhanism whih will lad to th following fom of this quation ad + ph W. (6 Th most impotant fatu of q (4, that is th popotionality of th damping at to th numb of ltons in nanopatil, aiss du to ohnt osillations of many patils. Th additional asonings onfiming this dpndn an b psntd as follows. As th siz of nanopatil is muh small than th wavlngth oonding to SP adiation, th intation

3 btwn ltons via adiation fild in th nanopatil an b dsibd by involving th ation fild [], i.. th fild atd by th patil at distans muh small than th wavlngth ( t &&& d ( t. (7 All th ltons ohntly osillat with th sam phas, so that th sultant fild ating on on of N & N >> ltons will b d & and th quation of motion of this lton taks th fom & N &&& d + d + d. (8 m In diving th xpssion (7 it was assumd, that th ation fild is muh lss than th quasilasti fo & d. Thus fom zo od quation d + d w stimat th ation fild and obtain & d, and th q. (8 taks th fom & N d & + d + d. (9 m It follows fom (9, that th adiation damping at is indd popotional to th total numb of osillating ltons N in MNP (s (4. Thus w hav an obvious manifstation of so alld supadian [], th fft, whih aiss du to intation of ltons via adiation fild whn th siz of a systm of adiating ltons is muh small than th wavlngth. It follows fom (5, that th adiation damping tim of nm diamt Au MNP mbddd in glass matix with ε 4 is appoximatly 4 s, whih is los to th lton laxation tim [4]. Th vaiation of diamt of MNP aound nm aoding to (4 will lad to th hang of ngy lakag at. Sin at this ang of sizs dos not ph dpnd on th siz, th masumnts will allow to distinguish th adiation damping mhanism of SP. It should b mntiond, that in as of lag patils th SP osillations an not b xitd, as th pntation dpth of th adiation in visibl gion is about 5 nm. It would b intsting to ay out th masumnts with lag MNPs at vy law tmpatus, whn th lton-phonon intation is substantially wak but th adiation damping at dominats du to th ubi dpndn on MNP siz and an xd th at of hating of th latti du to th ngy tansf fom ltons to phonons.. Rsonant oupling of SP osillations with matix. Th oth mhanism of th ngy outflow fom MNP is onditiond by th sonant oupling of SP osillations with th matix whih vals itslf whn th fquny of osillations is los to that of th lton tansitions in matix. H w onsid th as of so alld wak oupling, whn th matix absoption tum wih is vy lag [5], thn th SP osillation ngy ivsibly dass owing to th lakag into th matix. Consid a MNP loatd at th oigin of th fn fam. Th dipol momnt D t N d t D os of th osillating ltons in th nanopatil ats at point an ( ( t

4 wh v is th d of light in th v matix, is mind by (5, and th fild stngth amplitud has th fom altnating lti fild ( ( os ( t, ( D n ε ( D n [ ( ( χos t - χsin t - ] (, wh χ and χ a th fquny dpndnt al and imaginay pats of th matix susptibility oondingly. Thus th dilti onstant is ( ε ( + iε ( 4π χ ( + iχ (,, ( n is th unit vto in dition of adius vto []. This fild in its tun ats a polaization P ( P( R[ ( χ iχ ( xpi ( t + ] ( [ ] ε + th imaginay pat bing muh small than th al pat ε << ε. Th ngy absobd in matix p unit tim p unit volum avagd ov th osillation piod is &, ( ( P( χ ( ( Th total pow absobd will b th intgal of ( ov th matix volum P & ( 4π D ε ( ( d χ ( ( dv χ ( R, ( wh R is th adius of th MNP. As th ngy absobd by th matix is qual to th ngy loss du to th damping of osillations, i.., it follows fom ( and ( that χ ( 4π N W & W. (4 ε ( R m Finally, th damping at du to lakag of osillations ngy to th matix is ε( + s ε( p. (5 9 ε ( As th plasma fquny of nobl mtals is appoximatly th sam ( 6 ad/s [4], th damping at is mind mainly by th imaginay pat of dilti onstant of matix.

5 In oth wods, th stong th absoption at SP fquny th fast th damping of osillations. W an xpss in tms of th absoption offiint α of matix at SP fquny s s ( + ε( α(, (6 9 ε ( wh is th d of light in vauum. Fo xampl, if w hav fom (6 s α( s, and fo α( ~ m and mo this damping mhanism boms impotant. Thus, in as of sonant oupling th optial haatistis of th matix fully min th SP osillations ngy lakag at fom MNP. ε.conlusion Thus w hav onsidd two possibl mhanisms of th SP osillations damping in MNP, whih a not onntd with lton-phonon intation and an play main ol und th onditions of stong-siz quantization. Th impotant diffn btwn thm is that th adiation damping at manifsts volum dpndn, whas th damping at of th sonant oupling mhanism dpnds only on th optial haatistis of matix. This diffn will allow to distinguish xpimntally th ontibution of ah of thm into th nt damping at. Whil fo vy small MNPs with siz -5 nm and lss th adiation damping mhanism boms infftiv (s q. (4, instad th a ass whn th sonan oupling povids fftiv ngy outflow. Rfns. U.Kibig, M.Vollm, Optial Poptis of Mtal Clusts, Sping V.Yannopapas, A.Modinos, N.Stfanou, Phys.Rv. B 6, 559(999. A.Dllafio, F.Mata, F.A.Biva, Phys.Rv. B 6, 6(. 4. J.P.Wiloxon, J..Matin, P.Povnio, Joun. of Chm. Phys. 5, 998( 5. T.Vatanyan, J.Bosbah, F.Stitz, F.Tag, Appl.Phys. B, Lass and Optis, B 7, 9(. 6. N.Dl Fatti, F.Vall`, ibid, S.Kumml, K.Anda, P.-G.Rinhad,, ibid, p K.Knipp, H. Knipp, I. Itzkan, t al.j. Phys.:Condns. Matt4( R597-R64,PII: S ( R.F.Hagland J., L. Yang, R.H.Magud III, J..Wittig, K.Bk, R.A. Zuh, Opt.Ltt. 8, 7(99.. J.Takahaa, S.Yamagishi, H.Taki, A.Moomoto, T.Kobayashi, Opt.Ltt., 475 (997.. M.Quintn, A.Litn, J.R.Knn, F.R.Aussngg, Opt.Ltt., (998.. O.Mati, R.Möll (ds., Phonons and Loal Pobs, NATO ASI Sis, S.: Appl. Si., (Kluw T.Shalkhamm, Chm. Monthly 9, 67 ( Spial issu: Appl.Phys. B, Lass and Optis, B 7, 9(.

6 5.G.V.Hatland, in Fmtohmisty and Fmtobiology: Ultafast Dynamis in Molula Sin, A.Douhal and J. Santamaia, ditos, p.6, (Wold Sintifi, Singapo, 6. M.Nisoli, S.Stagia, and D Silvsti t al, Phys. Rv. Ltt. 76, n.8, 575 ( J.P.Wiloxon, J..Matin, and P.Povnio, Joun. Chm. Phys., 5, n., 998( 8..Cottanin, J.Lm`, M.Gaudy t al, Phys. Rv. B6, 579 (. 9. K.Chattj, S.Bannj, and D.Chakavoty, Phys. Rv. B66, 854-(.A.Wokaun, J.P.Godon, P.F.Liao. Phys. Rv. Ltt. 48, 957(98. A. von Hippl, Diltis and Wavs, (Nw Yok, John Wily and Sons,954.. L.D. Landau and.m. Lifshits, Th Classial Thoy of Filds, (Nw Yok, Pgamon,97. R.H.Dik, Phys. Rv., 89, 49( J.Bass t al., Numial Data and Funtional Rlationships in Sin and Thnology, Landolt-Bonstin Nw Sis, Goup III, Vol. 5, Pt. b (Sping-Vlag, Blin, G.W.Robinson, R.P.Fosh, J. Chm. Phys. 7, 96(96; 8, 87(96