Model of the multi-level laser
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1 Modl of th multilvl lsr Trih Dih Chi Fulty of Physis, Collg of turl Sis, oi tiol Uivrsity Tr Mh ug, Dih u Kho Fulty of Physis, Vih Uivrsity Astrt. Th lsr hrtristis dpd o th rgylvl digrm. A rsol rgylvl digrm is omputd to dsig optiml lsr with high ffiiy, oislss. W prst th modl of fivlvl lsr. Som lsr hrtristis suh s rltiv popultio ivrsio, pumpig thrshold, qutum ffiiy r ivstigtd. Th lvl lsr modl is possil prstd. I. Itrodutio Lvl digrm d lvl digrm sltio ply vry importt rol i th thory d i oprtio of lsr. A suitl lvl digrm sltio givs my dvtgs for lsr, suh s: high output, o itrfr, moohromti pump is ot dd. I this rtil, w propos lsr whih works o rgy lvl lsr. Th symols usd i this rtil: i: i th rgy lvl (i,,, i : Th umr of toms hvig i th rgy lvl i volum uit of tiv mdium. : Totl umr of toms i volum uit of tiv sust tkig prt i lsr kiti pross. : Proility of rditio trsitio du to idutio from (m lvl to ( lvl ( m. : Proility of orditio trsitio from (m lvl to ( lvl. ( m : Proility of trsitio from (m lvl to ( lvl du to othr rsos, suh s: utotrsitio, trsitio du to sttrig m : Asorptio proility of tom from si lvl (lvl to lvl m (F m osidrd s pumpig rt of lsr d m is proportiol to pumpig rgy. G i : i th lvl sttistil wight umr. : Popultio ivrsio sity tw lvls of lsr. α: Rltiv popultio ivrsio. h : Plk ostt. Q: Qulity of rsotor. G(:Rormliztio futio, spifi hrtristi of rditio or sorptio sptrum roig. : Light frquy tw lvl m d lvl ordig to Bohr xiom. It is prov tht th oditio to hv lsr rditio is: [] Grtio thrshold oditio: 9
2 h.q.g(.r 0 or: 0 α ( II. Thr lvl lsr d Fourlvl lsr For ovit ompriso, w itrodu th lultig rsults for thrlvl lsr d fourlvl lsr (Fig. d Fig.. II. Thrlvl lsr * Rltiv popultio ivrsio: g K ( g *So: [ K + (K ] + ( ( * Pumpig thrshold oditio: from ( d ( w hv: Fig.. ( ( ( Puttig: α.( + + K + (K g ( + α( ; K + (k ; + lds to: α + g ( α II. Fourlvl lsr * Rltiv popultio ivrsio: * Puttig: [ K + (K ] + ( + + ( + [ K + (K ] ( + + ( lds to pumpig thrshold: + ( + Fig.. ( ( ( ( (6 α + g (7 α 9
3 III. Fivlvl lsr III. Workig shm Th workig shm of fivrgy lvl lsr is show i Fig.. Lvl ( is th si lvl; lvls ( d ( r xitd lvls d hv rltiv lrg lvl wihs. Lvl (, ( d ( r vry los togthr. Lvl ( d ( r vry los togthr. Th lsr tivity is sd o th popultio ivrsio tw lvl ( d lvl (: g K g I Fig. w do ot show proilitis 9 suh s:,,,,,,, us << ;, << d it is otd tht: 0. ( Fig.., ( (,,,, III. Workig priipl Atoms i si lvl ( r pumpd to th xitd lvls ( d (. Lvls ( d ( hv quit lrg wih lvls so th pump is ot ssrily moohromti. Bus lvls ( d ( r ustl, toms sty thr for short tim, ftr tht th orditiv trsitios of toms from lvls ( d ( to lvl ( our (lvl ( is vry los to lvls ( d (, th trsitio proility from lvl ( to lvl ( is too smll, so w glt it. Lvl ( is osidrd s th suprstl lvl. Lvl ( is hos stisfyig th oditio: if trsitio of toms from lvls (, ( d ( to lvl ( (du to idutio d othr rdom rsos ours, ths toms will mov immditly to th si lvl ( (lvl ( is hos vry los to lvl (. Aftr tim itrvl w hv popultio ivrsio tw lvls ( d ( stisfyig th lsr grt ssry oditio. III. Workig oditio of fivrgy lvl lsr. Lvl ( is supr stl 0. Lvl ( is vry los to lvls ( d (:, >>,,,. Lvl ( is vry los to lvls (: >>,. III. Clultio for fivrgy lvl lsr Th lultio for lsr lvls is sd o th sttig up of quilirium qutios for h lvl tw th umr of toms (i volum uit of tiv mdium movig to th lvl (to irs th popultio d th umr of toms lvig th lvl (to drs th popultio. Usig (+ sig for toms whih irs th popultio d ( sig for toms whih drs th popultio, otig i th tom umr vritio i lvl (i, with fmilir symols, w hv th followig quilirium qutios: ( (
4 Lvl (: (8 Lvl (: (9 Lvl (: ( + (0 Lvl (: ( + + ( + ( Th totl umr of toms of tiv mdium tkig prt th lsr kiti pross is ostt: ost ( Lvls ( d ( stisfy Boltzm distriutio: xp( ( At sttiory stts w hv: i 0 (i,,,, ( Usig sttiory oditio (, from (8, (9 d (0 w oti: ( + + ( + 0 ( otig tht: m, m, from ( d ( w hv: So: + + k K + O th othr hd, from (8, (9, (, ( d (6 o hs: + + ( From (7 d (8 w hv th formul for rltiv popultio ivrsio: [ K + (k ] 9 (7 (8 ( + (9 + + ( + + ( + + ( + + ( + I ordr to oti th xprssio for pump thrshold, w itrodu th offiit β: β (β > 0 (0 Puttig: + Lds to: β + ; β ( + β Whr is pump rt offiit of toms from th si lvl ( to uppr lvl ( d (. With th ottios: [ K + (k ]
5 ( + + ( + ( β + β + ( + + ( + + β + β w oti th pump limit xprssio lik tht of thrlvl d fourlvl lsr: α + g ( α Filly, w fid th xprssio for qutum ffiiy η of fivlvl lsr (qutum ffiiy is th rtio tw th rgy of grtd lsr ry d th pump rgy: η From ( w hv: ( + η + ( ( (β + (β + ( ( + ( III. Evlutio d disussio Exprssio (9 shows tht wh som smll trsitios r gltd, th rltiv popultio ivrsio sity dpds oly o, d,. Th dp of ( / o F is showd i Fig.. Fig. shows tht thr is limit of rltiv ( / popultio ivrsio. This limit quls. i I physil sid, it ms tht lthough my toms r pumpd to lvl (, thr lwys xist idutio rditios whih ld to th rlxtio of lvl (. ot tht i prti ( / dpds ot oly o F ut lso o xtrl ftors suh s, thrml odutivity or mhil durility of high tiv mdium dp of pump limit g(. O α is showd i Fig. If α oms lrg, pump limit lso oms lrg. Formul ( shows tht to sv rgy, w hos th followig ss:. lrg. But this us th followig ostls: lvl ( is quit fr from lvl ( (whih do ot stisfy th workig oditio, low produtivity., >>, : It ms tht lvls ( d ( r vry los togthr. This is rlizl i prti g Fig. Fig. F α
6 ot tht from (9, if puttig 0 w oti (6. So tht fourrgy lvl lsr is oly spil s of fivrgy lvl lsr. Fivlvl lsr hs two dvtgs:. Rduig osidrly th diffrtio so tht th grtd lsr rys r highly moohromti.. ot rquirig too moohromti pump light. This will lrify i Stio 6. III.6 lvl lsr Th shm of lvl lsr is plottd i Fig.6. Lvls,, 6,, r xitd. Lvl is th si lvl. Th workig of th lsr is sd o lvl (, ( ( (or rti p, q stisfyig popultio ivrsio oditio (oditio (. Doig th lultio work lik tht of fivlvl lsr lds to th followig rsult (for lsr whos workig is sd o lvls ( d (. ( ( ( ( [ K + (K ] Fig. 6 k k ( + k + + ( + + ( + k k lvl lsr hs quit lrg pump light sptrum wihs, dpdig o th umr of lvl. Th dft of lvl lsr usully is its ffiiy is lowr th tht of thrlvl or fourlvl lsr. Rfrs [] L.V. Trsov, Lsr physis, Mir. Rulishr, Mosow, 98. [] A. Yriv, Qutum ltrois, Joh Wily & Sos, I, w York,97,. [] M.O. Slly, gtsoy, Ts.. Wlthr, Dymi Cotrol of Miromsr d Lsr Emmisso From Driv ThrLvl Atoms, Opt, Comum,, (79 9, 996. [] Clud Rullir (Ed., Fmtosod lsr Rulss, sprigrvrgg Brli, 998. [] R.. Ptll,.E.Puthoff, Fudmtls of qutum ltrois, Joh Wily & Sos, I, w York,
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