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Agenda

2. E 3. E 2. 1. 3. E 1. Agenda. On post-it: Last class review-intensity dynamics, achieving population inversion Pumping the three-level system Even better? Four levels Can we achieve threshold? ASIDE: Problem set#6 due December 3 rd . ASIDE: Reading for next class: M.E. pp 310-315.

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Agenda

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  1. 2 E3 E2 1 3 E1 Agenda • On post-it: • Last class review-intensity dynamics, achieving population inversion • Pumping the three-level system • Even better? Four levels • Can we achieve threshold? ASIDE: Problem set#6 due December 3rd. ASIDE: Reading for next class: M.E. pp 310-315 If the pumping process to go from E1 to E3 is optical (i.e., an intense optical beam of frequency 31), what is the largest value of 22- 11 possible? M.E.: 300-304 M.E.: 304-306 M.E.: 306-308 Laser Optics – Phys460

  2. I I z L 0 2. Last class review • Cavity steady-state • Dynamics: I I I L 0 z’ z’+l Ignoring standing waves for the moment Laser Optics – Phys460

  3. 2 E3 Pump 1 E2 Fast decay 2 1 3 Laser transition 3 E1 Can < ? decay rate: 3 2 2. Review, cont. • Photon and population rate equations Still to be determined pumping process : spontaneous emission rate from 2 1 Not review: : decay rate from 2  1 Method for achieving population inversion – three-level system. Fast decay provides population inversion! Laser Optics – Phys460

  4. 2 E3 Pump 1 E2 very fast Fast decay 2 1 3 Laser transition 3 E1 3. Three-level system close to threshold “Problem set 6” bar indicates steady-state value If stimulated emission is negligible (close to threshold), steady-state is: Population inversion Laser Optics – Phys460

  5. 3. 3-level, cont. What power do we need to achieve population inversion? Pump quantum energy: Rate of energy pumped into system: Let the power/volume required to do this be: In steady-state: Minimum pump for population inversion for three-level system Laser Optics – Phys460

  6. 3. 3-level example: ruby laser Cr3+:Al2O3 Sapphire crystal Chromium ions N[Cr]=1.6E19cm-3 reflector E3 32=1E7s-1 E2 21=5E2s-1 694nm Xenon flash lamp (550nm) E1 Ruby rod (V=1cm3) M.E. 412-413 What is the minimum pump power required for population inversion? Laser Optics – Phys460

  7. T.H. Maiman T.H. Maiman, Nature, August 6, 1960 Laser Optics – Phys460

  8. 2 E3 E2 1 3 E1 2 E3 E2 very fast 1 3 E1 4 E0 4. Can we do better than the three level system? Pump 1 Fast decay 2 Laser transition 3 Fast decay 4 Laser Optics – Phys460

  9. 2 E3 E2 1 3 E1 4 E0 4. Four level system, cont. If stimulated emission is negligible (close to threshold), steady-state is: What is required to achieve population inversion for a 4-level system? Laser Optics – Phys460

  10. 2 E3 E2 1 3 E1 4 E0 4. 4-level example: neodynium YAG Nd+3 ions Yttrium aluminum garnet crystal (Y3Al5O12) 1064nm 21=2E3s-1 Laser Optics – Phys460

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