n 1 = W 11 W 1a = n 2 2W 11 = W 1a = n b

Transcription

1 Deerminaion of he Er 3+ o Ho 3+ Energy Transfer Coefficien in (Er, Ho):YAG Russell M Kurz Physical Opics Corporaion, Elecro-Opics and Holography Division 0600 Gramercy Pl Bldg 100 Torrance, CA The coefficien describing energy ransfer from he firs excied level of rivalen erbium o he firs excied level of rivalen holmium in YAG was obained from measuremen of he relevan maerial parameers The value of his coefficien is necessary for esimaing he improvemen in Er:YAG and/or Ho:YAG lasing when he wo ions are co-doped in he same crysal This coefficien deermines he depopulaion efficiency of he lower level of he erbium 3-µm ransiiond he sensiizaion of he upper level of he -µm ransiion in holmium Our echnique for measuring he energy ransfer coefficien, by fluorescence decay measuremens in conjuncion wih compuer simulaions of he decay and rae equaion modeling, resuled i value of cm 3 s -1, implying ha he erbium holmium energy ransfer is srong enough o improve he room-emperaure holmium -µm laser We developed a mehod of deermining he Er 3+ Ho 3+ energy ransfer coefficien hrough calculaions based on he decay of fluorescence from specific levels of Er 3+ in Y 3 Al 5 O 1 (YAG) This mehod was validaed by applicaion o singly-doped Er:YAG The rae equaions of he relevan levels in (Er, Ho):YAG are = W 11 (1) n b = W 11 W 1a 1 () = W 1a n b b (3) = n b b W 1a where n j is he volume densiy of populaion in level j, j is he lifeime of ha level, level 1 is he firs excied level of Er 3+ (he I 13/ ), level is he second excied level (he I 15/ ), level a is he ground level of Ho 3+ (he 5 I 8 ), and level b is he firs excied level (he 5 I 7 ) The ion-ion ineracions are described by he coefficiens W 11 for wo ions in he Er 3+ I 13/ level and W 1a for one ion each in he Er 3+ I 13/ and he Ho 3+ 5 I 8 levels The values of W 11 and W 1a describe he srengh of he ion-ion ineracions and can be used o predic energy ransfer boh wihin Er 3+ and from Er 3+ o Ho 3+ The energy ransfers are made possible by near-resonan energy level ransfers wihin he maerials (Figure 1) The Er 3+ wo-ion energy ransfer is fully resonan, while he Er 3+ Ho 3+ energy ransfer is nearly resonan The difference beween he energy given up by he Er 3+ ion and he energy received by he Ho 3+ ion is ~1100 cm -1, 5 higher han he average roomemperaure phonon bu significanly below he maximum phonon energy suppored by he YAG Copyrigh 005 Direced Energy Professional Sociey (DEPS) This paper appeard in Solid Sae and Diode Laser Technology Review, and is available as an elecronic reprin wih permission of DEPS One prin or elecronic copy may be made for personal use only Sysemaic or muliple reproducion, disribuion o muliple locaions via elecronic or oher means, duplicaion of any maerial in his paper for a fee or for commercial purposes, or modificaion of he conen of he paper are prohibied SS1-1, ()

2 crysal marix Noneheless, he need o generae his phonon reduces he probabiliy of his ransiion, and we expec ha W 1a W 11 I 9/ I 9/ I 11/ I 11/ I 13/ I 13/ I 13/ 5 I 7 I 15/ I 15/ Er 3+ Er 3+ I 15/ Er 3+ Ho 3+ 5 I 8 Figure 1 The resonan energy ransfer in Er 3+ has a higher probabiliy han he near-resonan energy ransfer from Er 3+ Ho 3+ We began our sudy of ion-ion ineracion srenghs wih singly doped Er:YAG wih no Ho in he crysal In his case, boh and n b are 0, so only Eqs (1) and () are needed, and Eq () does no include he erm wih W 1a The iniial condiions for solving hese coupled equaions are (0) = 0 and (0) = cm -3 The iniial condiion on comes from he absorpion of a 300 mj Q-swiched pulse a 531 nm i 35-mm hick piece of 0% (a) Er:YAG Eq (1) can be rewrien o define an effecive lifeime for level : d = eff ; eff 1 W 11 (5) Eq (5) can be solved for W 11 : W 11 = eff eff The effecive lifeime asympoically approaches a consan value (Figure ) The coupled differenial equaions (1) and () can be solved numerically o mach eff a several imes he iniial lifeime Using he early and lae lifeime fis from Figure wih he modeled values of (6) SS1-

3 populaion densiy in he relevan levels, Eq (6) yields values of cm 3 s -1 for W 11 a a concenraion of 30% and cm 3 s -1 for W 11 a a concenraion of 0% Figure Fluorescence from level of singly-doped Er:YAG wih aomic doping levels of 30% and 0% demonsrae he prediced nonlineariies For (Er, Ho):YAG, Eqs (1)-() were all used The criical equaion for deermining W 1a is Eq () A sufficienly long imes (Figure 3 demonsraes ha imes > ms are sufficien) he decay of level 1 is conrolled by he las wo erms Then (7) 1+ W 1a 1 1 eff 1 Since is he populaion of he ground level ( 5 I 8 ) of he Ho 3+ ion, i is effecively consan wih ime The Ho doping concenraion ill doubly-doped ess was 15%, for a populaion densiy = cm -3 The fluorescence from level 1 ( I 13/ ) of Er 3+ is shown in Figure 3 The known fluorescence lifeimes of Er:YAG a 30% and 0% concenraions, ogeher wih Eq (7), resul i value of cm 3 s -1 for W 1a a boh concenraion levels SS1-3

4 (c) (d) Figure 3 Fluorescence from level 1 of (30% Er, 15% Ho):YAG and (0% Er, 15% Ho):YAG shows ha he Er Ho energy ransfer has nearly linearized he fluorescence decay from he firs excied level when compared o he singly-doped 30% Er:YAG (c) and 0% Er:YAG (d) Noe ha he value of W 1a does no vary wih Er concenraion, indicaing ha i depends more heavily on Ho concenraion Inuiively, and by he assumpions inheren in he radiional rae equaion model, he srengh of an ion-ion ineracion should no depend on concenraion The value of W 11, however, depends srongly on Er concenraion The experimens by which we deermined his parameer were designed o eliminae any effecs, such as hole burning and reabsorpion, ha affec he lifeime measuremen I is clear, herefore, ha he lifeime variaion wih concenraion is a real effec This can be explained by recognizing ha one of he assumpions made in deriving he rae equaion model is ha inroducing he dopan (Er) ino he hos (YAG) does no affec any parameers of he hos, including is local crysal field Since he SS1-

5 dopan concenraion in hese experimens was so high, i is likely ha his assumpion does no hold, and he lifeime is affeced by he concenraion To validae his predicion, we measured lifeimes of he I 13/ level of Er:YAG for Er concenraions of 1%, 10%, 167%, 30%, 333%, 0%, 50%, and 60% Based on hese measuremens, we propose a hird-order equaion for he lifeime of his level: 1 ( x) = x 0097x x 3, (8) valid for concenraions from 1% o 60% Eq (8) resuls in lifeimes measured in milliseconds for inpus of concenraion (x) in % Likewise, we have modeled he lifeime of he I 11/ level as ( x) = x 00300x x 3 (9) wih lifeimes measured in microseconds These wo lifeime equaions are graphed in Figure Lifeime (ms) Lifeime (µs) Er Concenraion (%) Er Concenraion (%) Figure The lifeimes of he Er 3+ I 13/ and I 11/ levels vary significanly wih concenraion Lines represen he hird-order approximaions while dos are measuremens In conclusion, we have developed a simple mehod for calculaing he srengh of ion-ion ineracions based on rae equaions and lifeime measuremens This echnique was used o deermine he Er Er I 13/ cross-relaxaion srengh a wo Er concenraions in singly-doped Er:YAG, and he Er Ho ion-ion inerchange srengh for wo Er concenraions of (Er, Ho):YAG The value of W 11, he Er Er cross-relaxaion parameer, was found o be cm 3 s -1 for 30% Er:YAG and cm 3 s -1 for 0% Er:YAG The value of W 1a, he Er Ho ion-ion ineracion srengh, was calculaed as cm 3 s -1 for boh (30% Er, 15% Ho):YAG and (0% Er, 15% Ho):YAG The Er Ho ineracion was sufficien o reduce he lifeime of he Er 3+ I 13/ level by ~0%, bu no nearly enough o unblock he 9-µm Er ransiion from he I 11/ o he I 13/ level I is sufficien, however, o ac as a pump for he Ho 3+ -µm ransiion from he 5 I 7 o he 5 I 8 level Acknowledgmens: These experimens were performed a he USC Cener for Laser Sudies under he direcion of Prof Milon Birnbaum, applying measuremend noise-reducion echniques developed by Jason Machan while a he Cener The auhor graefully acknowledges heir assisance SS1-5