激光輻射損傷閾值與激光脈寬相互關(guān)系的模擬計(jì)算_英文_

1、第6卷 第3期1998年 6月Vol 6 N o 1June 1998光學(xué)精密工程OPT ICS AN D PREC ISION ENG INEER INGCalculationof Thresho Id D ependence of*Laser- induced Dam age upon Pulse DurationMAG uo-Bin(Sha ngha i In stitu te of Op tics a nd F ineM echa nics P. O. B ox 800- 211, Sha ngha i 201800)TAN W ei-H an(D epar tm ent of P h

2、y sic Sha nghai Un iversity, Sha nghai 201800)WANG Zhan-Shan(Cha ngchun In stitute of Op tics and F ine M echa nics P.O. Box 1024 Cha ng chun 130022)Abstract A theoretica l model is developed to describe the p rocess of laser-induced damage of dielectrics w ith u ltrasho rt p luses in w h ich the m

3、u lti pho ton ion ization, avalanche ion ization, electron-ion recomb ination, and the electron diffusion are taken into account. By assum ing aGaussian temporal shape of laser pulse some numerical results of the threshoId dependence on pulse duration are presented For pulse length longer than 10ps

4、the numerical resu lts agree w ell w ith the square-roo t relati on F or pulse length of subpicoseccnd, our model principally explain s the opposite experm ental resu lts of Du et al 's (A ppi Phys Lett. , 64, 3071(1994) and Stu art el al 's( Phys Rev Lett; 74, 2248( 1995) by prope rly choos

5、ing the criter ion of damageK ey words: L aser-induced damage Short laser pulse, Avalanche ion izationLa ser-induced dam age in otpically transparen t m ater ials has been stud ied extensively仁5since the laser w as inven ted in the 1960s. For laser pu lses Ion ger tha n a few tens of p-cosecond the

6、dam age m echanisn is w ell understood. T he bulk dam age of defect-free d - e lectrics in volves the heat ing of con duct ion band electr ons by the n cide nt laser field and tran sfer of th is e nergy to the lattice. During the c onven ti on a l heat depositi on, dielectrics are m elted and boiled

7、, then dam age occurs. B asedon num erous experim ental results, the fact that the dam age th resho ld depe nds on the laser pu lsew id th iswell estab lished A n em pirica l sca-6 ing law of the flue nee dam age th reshold for Ion ger pu lses(f > 10ps) is ge nerally accepted1 /2F th * f M eanwhi

8、le a theo reticalm odelw h ich p redicts th is square-root relation is also set-7, 8upF inancial suppo rted by the Sta teK ey Laborato ry of A pp lied Op ticsReceived October9 1997II 神真h性 reservedRevised wipt recced March 31, 1998Calcu ation of T h reshold Dependence of L ase廠 induced Dam age upon P

9、ulse Du ration25Howeve, laser- in du ced dam age by u ltrasho rt pu lses still rem ains as a challe nging research topic because subpicosecond high power laser pulses were not availab le before Asa result, the mechanism of dam age caused by subpicosecond pu lses is only p rm itive y understood Un ti

10、l the past years new tech n iq ues in u Itra short laser pulse ge ne ratio n and am plifica- tion, such as the chirped-pulse amplifica tion (CPA ), have enabled teraw att class laser system s p roduci ng subp icosec on dpulsesM ore m porta ntly, CPA allow s o ne to vary the pu lsew id th con tinuous

11、ly from fam to second to hundres of picosecond w ith a sin g le laser system. T h is offers a new set of convenien t opport uni ties to study laser- in duced dam age n a w ide range of laser pu lse w idths.9 In other aspect fu rther in crease in the peak pow er is availab le from a CPA system , bu t

12、 it is now lim ited by op tica l surface dam age due to the n tense short pu lses T herefo re laserin duced damage especially w ith short pu lses attracts mu ch n terests. In additio n, variou s p rospective applica ti ons from m aterials processing to b iom edica l tech no logies such as eye surg e

13、ry on ocular tissue als on eed tow ell un dersta nd the dam age m echa nism of these short laser pu lses and the th reshold depe ndence on pulse du rati onRecen tly, Du et al in vesti gated the laser- in duced dam age in fused silica employing 150 fsr 7 ns 780 nm laser pulses and found that the th r

14、eshold of dam age flue nee Fth , in-11 creases w ith the pu lse du rati on t asFth 1 f w henf < 1ps Sho rt afterw ards, Stua rt et al d id som e sim ilar experim ents in w h ich they m easured the dam age thresho lds for silica and calcium fluo ride at 1053 and 526nm for pu lse du rati on ranging

15、 from 270fs to 1 n s But the ir resu lts show ed that the th reshold of dam age flue nce still decreases w ith the pu lse du rati on w henf < 1 ps although it deviates from the square-roo t relation, w h ich is opposite to Du et al 's N ote tha t the dam age detection and defin ition s in the

16、ir expe rim ents are d ifferen t Du et a. detected the dam age through m easuri ng the p lasma em issio n from the sample and they defined dam agew hen considerab le plasm a em ission w asm easured Stuart et al detected the dam age w ith a N om arsk i scanniig electron m icroscope and they defined v

17、isible perm anent surface m odification on the sam ple as dam age The d ifferences are thought to resu lt in the ir d ifferen t th reshold dependence on pu lsedura tion t for t < psIn th is paper w e develop a theoretica l m odel to describe the p rocess of laser- induced dam age of d ielectr ics

18、 especially w ith u ltrasho rt pu lses in w h ich the m u ltipho ton ion ization avala nche ioni zatior, electr on-i on reccm b i natio n, and the electr on d iffu si on are take n into aG count By assu ming aG aussia n tem po ral shape o f laser pu Ise some nu merical resu lts of the th reshold dep

19、e ndence on pu lse du ratio n are p rese nted Fo r pu lse len gth bn ger tha n 10 ps the nu merical resu lts agree w ell w ith the square-root relation F or pulse len gths of subp icosec- ond, ourm ode l explains the opposite experim ental resu lts of Du et al 's and Stuarts et11al 's by pro

20、perly choosing the criterion of dam ageW e use the follow ing equation to descr ibe the temporal beh avior of the free electron density N edN e(t)dN e(t)2不=Z(E)Ne(t)+ (示)PI- VNe(t) - WJe(t)(1)w he neZ(E ) is the avala nche io ni zatio n coefficie nt, V= 1 /(Ne (t)fR), W= 1fD.fR andfD are the electro

21、n-i on recom b ination and electron diffu sion time respectively. These last tw o term s rep resent the electron lossesT he second term on the rgh t hand of eq (1) rep resents the free electron produc tion d - rectly by the pho tons of the laser rad iation In Du et al 's andStuartetal 's exp

22、erim ents the2 2power density of the laser radiation is in the order ofGW /cm TW /cm or higher, especially fo r u Itra shor t laser pu Ises A t th is m ag nitude the con tribu ti on of multiphot on ioni zati on is nonneg ligib le in the pro cesses of free electr on gen erati on. H ere w e use the fo

23、 llow i ng m u lti -5 pho ton ionization form uladN e(t)(n) n(Ndt )PI = Ne F (t)(2)(n)w here N is the active ion den sity, e is the n- phot on absorp tio n cross-sect ion, F is the photon flue nee den sity, respectively W e u se the m easured fou r-pho ton absorpti on cross- secti on(4)- 11483 5, 1l

24、 e = 2X 10 cm /sfor the 526 nm laser field.2A spo in ted above the pow er density of the laser rad iation is in the order of GW /cm 2TW /cm or h ighe r in Du et al 's and Stuar t et al 's experim ents thu s the applied electric fie ld is in the order of a few ten sofM V /cm and h igher expec

25、ially for ultra short laser pu Ises U nder such a high field electron sw illm akem ore than one collision du ring one period of the electric oscillation. A s a result the electric field is essentially a dc field to those high energy10 10 electron s . H ence w e take the sm ilar w ay used by Du et a-

26、lto descr be the avalanche3 dc2 21/2ioni zati on: first, w e use the re lati on sh ip E(k)= E (1+ k fc) corresp ond ing the optical dam age field to a dc b reakdow n fie ld, w he re w is the optical frequecny andfc is the electron collision time Second the avalanche ionization coefficient is express

27、ed in therms of ionization rate per un it len gth T w ith Z (E ) = T (E ) -vrif (, w here vrif * is the d rift velocity of electro ns. W hen the electric field is ashigh as a few M V /cm, the drift velocity of free electrons is saturated and independent of the laser electric field Vrift 2x 10 cm /s.

28、 T he th ird, w e use the ex-12p ressi on forT (E ) de rived by T hor nber which is applicab le for all e lectric fie ld stre ng ths and essentia lw hen com par ing w ith Du etal 's a nd Stuart et al 's expe rim e nta I dataeEE iT(E )= exp -(3)'丿 Ui I e (1+ E /Ep)+ EkT2w here Ui is the i

29、oni zati on thresho ld of the vale nee ba nd electro n, Ep, EkT an dEi are the thresh- o ld fie lds for e lectro n to overccm e the decelerati on effects of pho non, them al and ioni zati on scattering, respectively.Sett ing aGussia n tem pora l shape of laser pu lsew ith peak pow er den sity P and

30、du rati on t one can determ ine the en ergy flue n ceFE , phot on flue nee den sity F , and the laser electric d cfie ld E and thu s the corresp on ding dc electric field E . Then from eqs (1), ( 2), an d( 3) one can calcu late the free electro n den sity Ne. A t the end the pu lse du rati on, ifN e

31、= N th , the free electron density corresponding to the sam p le dam ag this F E is the dam age th reshold In our calculation E i = 30M V /cm, EP = 3 2M V /cm, andEkT =001M V /cmare usedT hese param eters are take n from Ref 10( and referen ces there in)with U = eEl, w hereUis the ap-p ropr iate the

32、m al, phono n and ioni zati on en ergy; and I isthecorresp onding en ergyrelaxati onlen g th( lkT = b 5? , the atom ic spaci ng and l 30?).F igure 1 and 2 are tw o typical run s of evolu tion of free electron density N e for a 100fs2and a 1 ns, 526 nm laser pu lse(two-dotted dashed curve)of peak int

33、ensity 11. 7 TW /cm and227. 7 GW /cm in fused silica, respectively Fo r comparis on, w e separte the con tribu tions of avalanche ionization(do tted curve), and the mu ltipho ton ionization( dashed curve). W hen the electron losses due to diffu sion and recom b ination are included, the electron evo

34、lu tion( long- dashed curve) are also show n. Fo r h igh inten sity laser pu lses fie ld-i nduced m u lti phot on ion- izati on produce s the free e lectro ns which m ay result in fu rther ioni zati on due to collision therefo re it is no tn ecessary to in voke some arbitra ry nu mber of n itia l &q

35、uot;seed" electr on s N otetha t in F ig 1 m u ltipho ton ioni zati on produces a substa n tia l amount of free e lectr ons, w hich makes some nonneg ligible contribu tions to the sample damage In contrast avalanche ionization only p roduces a sm all amount of free e lectr on s dur i ng th is 1

36、00 fs pulse durati on if it is taken to be the only one sourceof free electron generation by setting the initia l electron den-10- 3sity N 0 = 10 cm . Bu t if m u ltipho t on ioni zati on produces e no ugh free e lectr ons, avala nche ion ization is m pro tant especia lly at the second half o f the

37、laser pu lsew hen the m u lti pho ton ioni zati on is saturated. T he e lectr on losses due to diffu sion and recomb i nati on are com p letely negligible hence itm akes no difference for the free electron evolutions w hether these losses are in cluded or not Fo r 1 ns pu lse du rati on( Fig 2), ava

38、la nche oni zati on domin ates the free e lectr on gen erati on, bu t con tribu tion ofm u lti phot on ioni zati on is n eg lig ib le except from provid in g the initia l electrons for avalanche ionization. Becausem ultipho ton ionization is strong ly in ten sity depe ndent the electr on p rodu cti

39、on take s p lace pr i ncpally at the peak of the pu lse It is necessary to point out tha t the electron losses are nonneg lig ible for th is 1 ns pu lsedura- tion; when they are included, the total electron density decreases about one order of magn-eudrime，：p 即50o oEo-卷切匚曲口匚20世山212010“IIIoDoF ig. 1

40、Calculated evolution of free electron density N e fo r a 100fs 526 nm laser pu lse (tw o-do t- ted dashed cu rve) of peak in ten sity 11. 72TW /cm n fused silica. Dotted curve only avalanche ionizat on is taken n to account by setti ng the n itia l electron density No = 1010 cm-3; dashed curve only

41、m ultipho ton ion iza- tion is taken in to account solid curve both avalanche and m u ltipho ton ion ization are taken into account W hen the loss term due to electron diffusion and recombination are inc luded, the evo lu tion of free electron density is identical to the solid curveFig 2 Calculated

42、evolution of free electron density N e for a 1ns 526 nm laser pu lse( tw o-do tted dashed curve) of peak intensity 27 7 GW / cm in fused silica Dotted curve onlyavalanche onization is taken into setting the in itia l electron density3cm- ; short-dashed curve only maccountN 0 =wo10u ltipho tonionizat

43、ion is taken nto account; solid curve both avalanche and m u ltipho ton ion ization are taken into account long-dashed curv e all the p rocesses of electron p roduction and losses due to electron diffusion and recombi- nat bn a re inc ludedCalcu ation of T h reshold Dependence of L ase廠 induced Dam

44、age upon Pulse Du ration#Calcu ation of T h reshold Dependence of L ase廠 induced Dam age upon Pulse Du ration#9V42<)14 China Academic Journal Kkctmnic Publishing I IfMJg All nghtJ； reserved, http7Calcu ation of T h reshold Dependence of L ase廠 induced Dam age upon Pulse Du ration27Laer pulseidtn

45、t ipsF ig. 3 Calculated thresholds of dam age fluences F th versus laser pulsew idth t for differen t dam age condiations N th. Dotted curve only avalanche ion ization is taken into ac- coun t other th ree curves all pro cess are include. Details for shorter pulse length see text2210 cm3w hen avalan

46、cheF g. 3 shows the calcu lated th resholds of dam age flue ncesF th versus laser pu lsew id th t for d ifferen t dam age conditions N th . Fo r pu ls- es bn ger tha n 10 ps the dam age thresholds all increa se w ith t according to Fth * f , the w ell-k nown scalin g. While for shorte r pu Ises the

47、dam age thresho lds vary w ith the pu lse duration m uch diffe rently. Fo r sam ll dam age con-18- 3d ition( N 也=io cm ), the th reshold deviates from the square-roo t relation, bu t it still decreases w ith pu lse du rati on w he n t< 10 ps (th ick solid line). T h is is alm ost dentical toiithe

48、 experim ental results ofStuart et al F or22- 3bigger dam age condition( N th = io cm ), the th reshold in creasesw ith pulse du rati on w hen t < 2 ps( dashed line). T his is sm ilar to the ex-10perim ental results of Du et al T hese results nvoke us to conjecture that the free electron density

49、corresponding to D u et al 'sdam - age is sm aller than that of Stuart et aJ 's Recalling their experim ents Du et a. defined the considerable p lasm a em ission as the sam p ledam age, and Stuar t et a. defined the v isib le perm anent m od ifica tion to surface obse rvablew ith a N omarski

50、 m icroscope as the sam ple damage In fact, con siderab le plasm a em issio n can bem easu red on I y whe n the sam ple is strong ly dam aged N everthelss su rfacem od ification can be observed w ith a h igh resolution m icro scope even only w he n sligh t dam age occurs In addiation, for pulse du r

51、atio n sig ni fica n tly shorter than the tim e scale for electron energy transfer to the lattice ( here subpicosecond pu lse length is th is situa ti on), con du ct ion -ba nd electr on s ga in en ergy from the laser field m uch faster tha n they transfe r to the lattice. T he actual dam age occurs

52、 afte r the pu lse h as pa ssed,w hen thisin situ,e lectr on en ergy is coup led into the lattice. Du et a. m easu red the plasm a em issi onth isw ay, ou r ca-thus h igher electro n den sity and hence h igher dam age flue nee are n eeded Incu lati on p rin ci pally exp lains the two opposite exper

53、m e ntal resu lts- Asa reference the th reshold versus pu lse dura tion forN th =ionization is ony taken into account is also show n in F ig. 3w ith a dotted curve Becausecon- tribu tions by m u ltiphoton ionization are not included, the dam age thresho ld n creasesw ith the pu lsew idth m ore quick

54、ly Du et a. 's experim ental result is close to th is curve but d iffer- ent from the curve ofwh ich all electron generation processes are included, as shown above T h is m ea ns that m u ltiphoto n ioni zati on alm ost makes no con tribu tio n to the free e lectr on gen e ration, w h ich can n

55、ot be exp lained by ou r prese nt modelIn con elusion our calcu lati ons show that in the process of free e lectro n product ion, the con tr ib u ti on s of electr on-ion recomb in a ti on and e lectr on d iffu si on are small for Ion g er pulse w id th, and they are comp letely neglig ible for shorte r pu lsew idth. T he avalanche ionization dom in ates the free e lectr on producti on in the w ho l