I'hysica B 17(~ (IC,iq2) 15~ 15<~ North Holland PHYSICA Exciton-polariton dispersion in ultrathin atomic cryocrystals* V.V. Rumyantscv and V.T. Shunvakov l~n('tsk IJh~,~i('o-l~'ctmi('al hlMilltl~<'. {ikrtlillitltl ~i('o,~l('#tlv ,'l ,~'('t('tl('('s..¢4fH14 IJom't~k. I '~,'.",A' t'~ccCi"ct_'d N /\ClgtlSl I~*',~l l hc local licld mclhod is tiscd to slud', the cxcilon pohirit(m dispcrsion in alOnlJc tlitralhin cl,,oc[',t,l:il', \n cxptc~.,l~,li her the liuld acting t)ll ;i separate tilt)ill t+l S, LLch it CtV',Ial iS <>t+taincd +~ ithin the ll{illlt-'~At)t k ilf ihc micro<,COl+iC appio~ich lhc lOtliid dispersion I+l~, ;tic ailalVsotl ill detail, in ptil-ticulnr, n c't+ncltlSit+tl is Itl~idc t+il the pt>s,,ibilil\ tel all additional Ii#hi ~a\'c existence in ll+c crystals considered. Thc optical propcrtics of crvocr\stals in the cx- ellen spectral region ;.ii-c lit>\\' studicd rather in- tensively Ill- In accordance with the solid-stale theory the uxciton IH:etimc determined hv the scattering mechanisms is o1 the order of I() ~: 1{I ~ s. However, under the ideal conditions al ~ct-x low temperatures there illtlV 12xist weakly attcnuatingexcitons whose lifetime is 2 3ordcrs of magnitude larger. Consider just the case when wc can neglect dissipation of the excitation -run- ning'" fronl site Io silo in the lattice of ;.ill ul- lrathin atomic cryocrystal. In this case thc effects of exciton-photon interaction and ..spatial disper- sion become well defincd. Whercas the dispersion of pohtritons in bulk samples has been studied in detail [2], in tile films whose width (U) is much less than the length of pohiriton wave, the problem is under discussion [3 I. In this report we are concerncd with a number o1 irisufficicrltlv known aspects of the problcnl. Thc most consistent and tit tile si.tnlc timc shnplc way of studying the optics of thin crystals is based on thc conccpt of tile local field accord- ing to which each ;.ttOlll being in the wiriablc field of the remaining atoms of the crystal external to it, becomes pohirized-the atomic dipolc me- • Originally submitted lor IJl-19, Brighton, bul not inchidcd in lhc proceedings for technical reasons. nlelll P is equal 1{~ #' X-A". luld ceils the Ilclct itscl[. Stt-ictly spc:.tking, lot muhi (1) is applicable lo crvocrvstals ~vith cot-rain reservations given. [he point is lhat tllc radius ~1 the electron excitation (R) in those Cl-Vstals amounts to several lattice coilstants which i,, equivalent to the sl;.itcnlelll that ill cr;ocl-\St;~lls there arc cxciton.,, o1 intermediate r:.lditlS [4 I. With this in mind x~c shall imply l.hal the polarizability parameters X,,. ,V. and the ics~> nancc frequency 1~'~ arc the rcnormalizcd olios X(W) =.V + WT'<(.\,, .V > (Wi< lt:l ~? Thc field acting on an atom of the crystal's ~\'th mtmohtvcr consists el +the licld created hv atom,, o[ the saint hirer and that iN' ncighl+ourin# lllOilol;.i_'¢ers. TIle C;.llcuhition <, done on the bcisis of Ewald's nleihod (whoso lwo-dimcnsitmal ~c'i sion was worked onl in rcf. fit +h<>,, thai the microficlds duo 1o neJghbouring 111onolai\,cr', tic- crease cxptmcntJall)with incre:.ising tile inter-- layer distallce 15]. if the laver width (U) is nluch htrgcr than the lattice constanl (1>) (i+c. 7V +. 1) ollc c;iil neglect the distorthnl of peripheral monohiyors and obtain lhc following compact formula for the local field /:": {IL.~21-452~,,~J2,,'$f15.00 © 19q2 Elscvicr Science Pubiishcrs B.V. All rights rcscrvcd