11/13/ LASER Physics. Light Amplification and Inversion. Outline: Biomedical Optics LASER. Atomic Energy States: 2 Level System

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1 /3/8 Outlne: omedcal Optcs. SE Physcs ompute sssted lncal Medcne Medcal Faculty Mannhem Hedelbeg Unvesty TheodoKutzeUe Mannhem, Gemany Smon Hubetus, M.Sc. smon.hubetus@medma.unhedelbeg.de ectue asc Optcs. ectue SE Physcs ght mplcaton and Inveson esonato 3. ectue SE Popetes and Systems. ectue Tssue Inteactons I 5. ectue Tssue Inteactons II 6. ectue omedcal pplcatons Wednesday, 9..8, 3pm House, evel, ectue Hall Smon HubetusI Slde /3 I /3/8 SE ght mplcaton by Stmulated Emsson o adaton % mo 9 % mo mos: optcal esonato actve medum SE lght ght mplcaton and Inveson hgh powe lash lamp lght souce: enegy pump Smon HubetusI Slde 3/3 I /3/8 Smon HubetusI Slde /3 I /3/8 ght mplcaton tomc Enegy States: evel System souce: P.W. Mlonn, J.H. Elbely. ases. Wley 988 eeambetaw " # " $e%& " $ lght absopton depends on: electonc enegy states o the atoms band stuctue o the molecules otaton / vbaton a: absopton coecent g: optcal gan coecent g a absopton: g < amplcaton: g > oltzmann dstbuton n themal equlbum occupaton numbe: *+e %, oltzmann acto: 3. / e %,./ <5 elatve occupaton numbe deence: 6 %3 at themal equlbum: the hghe the enegy gap, the lowe the occupaton numbe 73 themal equlbum: w < Smon HubetusI Slde 5/3 I /3/8 Smon HubetusI Slde 6/3 I /3/8

2 /3/8 mplyng Medum Stmulated and Spontaneous Pocesses n themal equlbum: e < g n the SE medum: Inveson: e > g I, w ge eg eg couplng o an atom to a monochomatc lght wave couplng to the dvng eld: stmulated absopton couplng to the dvng eld: stmulated emsson coheent n phase, equency and polasaton ncoheent pocess: spontaneous emsson ndependent o dvng eld tanston pobabltes àensten coecents lght amplyng meda ae OT n themal equlbum * 8 e % :%:3 ;.> * 9 > T < H IJ KG 89 E M IJ M P 98 P 89 KQE E G 89 E spontaneous emsson stmulated absopton/emsson equal electc pemttvty speed o lght educed Planck s constant EF G 89 matx element o dpole opeato QM Smon HubetusI Slde 7/3 I /3/8 Smon HubetusI Slde 8/3 I /3/8 vng ght Feld I,w S TU hgh pumpng ecency: hgh onesonant dvng eld hgh absopton cosssecton Statonay condton d * dw level system V 89 6 " P 89 6 " P 98 V 98 V d* 9 dw XV 98* 9 YV 89 * 8 YH 89 * 8 d* 8 dw V 98* 9 XV 89 * 8 XH 89 * 8 ** 9 Y* 8 ** 8 XO* 9 * Z X * 5YK V [ H 89 < no statonay nveson possble n level system Occupaton umbe eence Themodynamc Equlbum e < g I, w P 98 P 89 KQE GE 89 E ot n Themodynamc Equlbum stmulated absopton / emsson o amplcaton e g Equal ate o stmulated absopton and emsson Inveson OT possble n a level system Smon HubetusI Slde 9/3 I /3/8 Smon HubetusI Slde /3 I /3/8 3 evel System evel System pump E p, p Fast nonadatve tanston ase tanston * \ ] ^ ** 9 Y* 8 d* 9 dw XV 9\* 9 YH 89 * 8 d* 8 dw V 9\* 9 YV 98 * 9 XV 89 * 8 XH 89 * 8 ` ^O * Z * ab%c ab7a7c statonay nveson possble n 3level system when V \ g ut: Inecent pump E p, p E, Fast nonadatve tanston ase tanston Fast nonadatve tanston * 9 * \ ] Y* 8 d* 9 dw d* 8 dw V YV 98 * 9 XV 89 * 8 XH 89 YH 8@ * 8 ` ab ^O* Z * ab7a7c37c statonay nveson s guaanteed n level system and ecent Smon HubetusI Slde /3 I /3/8 Smon HubetusI Slde /3 I /3/8

3 /3/8 Optcal Gan esonato Smon HubetusI Slde 3/3 I /3/8 Smon HubetusI Slde /3 I /3/8 Ideal esonato ealstc Stuaton actve medum n, gan optcal axs Poblem slght msaangement o mos optcal axs ssumptons. % electon no losses. peectly lat and paallel mos no scatteng 3. unom dstbuton o gan coecent. unom dstbuton o the eactve ndex themal lensng eect 5. electomagnetc modes not aected by SE medum Smon HubetusI Slde 5/3 I /3/8 Smon HubetusI Slde 6/3 I /3/8 ay Popagaton ay Popagaton Matx otaton lght popagaton: decton along optcal axs ^ paaxal ays optcal axs wave vecto epesentaton: decton & length n each pont decton: enegy low nomal to wave ont length: ntensty. dsplacement z Matx otaton optcal axs. slope z column vecto Smon HubetusI Slde 7/3 I /3/8 dz d j k # lm l tnop]p Smon HubetusI Slde 8/3 I /3/8 3

4 /3/8 ay Popagaton Matx otaton Sgn onventon: Slope z z + z z z z z z z z z d z tanq dz z z z zz z z z d > Þ < Þ > < Smon HubetusI Slde 9/3 I /3/8 Smon HubetusI Slde /3 I /3/8 Thn ens Equaton ay Popagaton: Thn ens ocal length : ocusng paallel ncdent lght object dstance g & mage dstance b Thn ens Equaton /g + /b / d d + d d Matx otaton / Smon HubetusI Slde /3 I /3/8 Smon HubetusI Slde /3 I /3/8 ay Popagaton: Sphecal Mo a Multple Optcal Elements open path d + thn lens lght ay decton ay matx? Matx otaton / d / / matxmultplcaton: lne x column d d / Smon HubetusI Slde 3/3 I /3/8 Smon HubetusI Slde /3 I /3/8

5 /3/8 5 Smon HubetusI Slde 5/3 I /3/8 esonato Stablty I / / Smon HubetusI Slde 6/3 I /3/8 esonato Stablty II + ate ound tps: Smon HubetusI Slde 7/3 I /3/8 esonato Stablty III +, nte, o *^q stablty condtons: ay onvegence teon ate ound tps Smon HubetusI Slde 8/3 I /3/8 Stablty teon + g g g: paametes o esonato g g stablty cteon: Smon HubetusI Slde 9/3 I /3/8 esonato Stablty: Examples g g 3 3 Mos too a away onvex Mos Smon HubetusI Slde 3/3 I /3/8 epetton ght mplcaton and Inveson eeambet aw oltzmann acto n equlbum Statonay nveson not possble n level, possble n 3level W p > and guaanteed n level system esonato no deal esonato: mssaangement o mos matx notaton o lght path o vacuum, thn lens, sphecal mo stablty cteon ay matx o combnaton o elements d / / thn lens sphecal mo g g 3 3 stablty cteon vacuum

6 /3/8 ext ectue 3. SE Popetes and Systems Smon HubetusI Slde 3/3 I /3/8 6