Lecture 7 Pumping & Populaon Inversion* Min Yan Op3cs and Photonics, KTH 15/04/16 1 * Some figures and texts belong to: O. Svelto, Principles of Lasers, 5th Ed., Springer. Reading • Principles of Lasers (5th Ed.): Chapter 6. • Skip: Quantum mechanical treatment in 6.4.1.1 • Squeeze: 6.3.3-6.3.5, 6.4.1-6.4.4. 15/04/16 2 Laser Pump Iin Iout Gain medium Mirror 1 Mirror 2 3 2 • Pump efficiency: ηp=Pm/Pp νp νmp • Pump rate: Rp, or dN2/dt 1 • Threshold pump power: P 0 th 15/04/16 3 Contents Content Time 1. Pumping varieties 10 ’ 2. Optical pumping (lamp) 20 ’ 2.1. Schemes; 2.2 ηp and Rp 3. Optical pumping (laser) 3.1. Schemes; 3.2 ηp and Rp 25 ’ 3.3. Pump threshold Pth 4. Electrical pumping 25 ’ Total: 80’ 15/04/16 4 Contents Content Time 1. Pumping varieties 10 ’ 2. Optical pumping (lamp) 20 ’ 2.1. Schemes; 2.2 ηp and Rp 3. Optical pumping (laser) 3.1. Schemes; 3.2 ηp and Rp 25 ’ 3.3. Pump threshold Pth 4. Electrical pumping 25 ’ Total: 80’ 15/04/16 5 Pumping varie3es • Opcal pumping (CW/pulsed) o Lamp: for solid-state/liquid lasers [broad absorp3on bands] o Laser: for solid-state/liquid/gas lasers [broad/narrow absorp3on bands/lines] • Electrical pumping (CW/RF/pulsed; for gas/semiconductor lasers) • X-ray pumping • E-beam pumping • Chemical pumping 15/04/16 6 Contents Content Time 1. Pumping varieties 10 ’ 2. Optical pumping (lamp) 20 ’ 2.1. Schemes; 2.2 ηp and Rp 3. Optical pumping (laser) 3.1. Schemes; 3.2 ηp and Rp 25 ’ 3.3. Pump threshold Pth 4. Electrical pumping 25 ’ Total: 80’ 15/04/16 7 Pumping: Lamp Lamp types • For pulsed lasers: Medium-to-high pressure (500~1500 Torr) Xe or Kr flashlamps • For CW lasers: High-pressure (1-8atm) Kr lamps • Ellipcal cylinder o Rod and lamp at foci o Specular reflec3on Rod radius: mm~cm Rod length: cm~<1m • Close-coupling o Close-pack o Diffusive reflecon ü More uniform 15/04/16 8 1 atm = 760 Torr Pumping: Lamps • Pp↑ ηp↓ • More uniform 15/04/16 9 Pump efficiency and pump rate Assump3on: uniform Rp 3 Pp 2 P r ν P p νmp t 1 Pa 0 Pm • Radiave efficiency • Transfer efficiency • Absorp3on efficiency • Power quantum efficiency 15/04/16 10 Pump efficiency, ηp Configuraon: Ellip3cal cylinder 15/04/16 11 Absorp3on efficiency, ηa Emission • Connuum ∝ J2 • Lines ∝ J Alexandrite Nd:YAG Absorp#on 3+ 15/04/16 • Nd:YAG: Nd in Y3Al5O12 crystal (host-independent) 12 3+ • Alexandrite: Cr in BeAl2O4 crystal (host-dependent) Contents Content Time 1. Pumping varieties 10 ’ 2. Optical pumping (lamp) 20 ’ 2.1. Schemes; 2.2 ηp and Rp 3. Optical pumping (laser) 3.1. Schemes; 3.2 ηp and Rp 25 ’ 3.3. Pump threshold Pth 4. Electrical pumping 25 ’ Total: 80’ 15/04/16 13 Laser pumping • Convenience: Efficient and high-power diode lasers widely available • Key examples: o Nd:YAG and “siblings” pumped by GaAs/AlGaAs QW-lasers (~800nm) o Yb:YAG, Nd:glass or Yb:Er:glass pumped by InGaAs/GaAs QW-lasers (950~980nm) o Alexandrite, Cr:LISAF pumped by GaInP/AlGaInP QW-lasers (640-680nm) o Tm:Ho:YAG laser pumped by AlGaAs QW-lasers (785nm) 808nm 15/04/16 14 Pumping diodes i ii i. Single-diode Beam:2x4µm2; P<100mW ii. Diode-array P≈2W iii. Diode-bar P=10-20W iv. Stacked-bars P=100W; emission bandwidth↑ iii iv 15/04/16 15 Pumping scheme • Longitudinal pumping Beam shaping • Transverse pumping Core ∅: 200µm Nd:YAG slab Op3cal fiber Water Gold-coated glass 10W CW 15/04/16 16 Pump efficiency Nd:YAG • Lamp v.s. Diode: ηa (6×) and ηpq (1.5 ×) 15/04/16 17 For uniform R Pump rate, <Rp> p Space-dependent lasing/pump beams: a maer of calculang A 1. Diode (longitudinal) ηpd: ηp for diode pumping Opmum: wp ≈w0 2. Diode (transverse) Opmum a exists 3. Lamp ηpl: ηp for lamp pumping w0: Laser beam waist Assump#on for cases 2 and 3: wp: pump beam waist • Rp=const if r<a (doped region) a: radius of the ac3ve region • Rp=0 if r>a (undoped cladding) 15/04/16 18 Threshold pump power, Pth Procedure: <N2>c → <Rp>c → Pth γ: logarithmic cavity loss σe: effec3ve s3mulated emission cross-secon l: ac3ve medium length τ: upper-level lifeme Comment: <N2>c differs for quasi-3-level system 1. Diode (longitudinal) • Can be 50% larger 2. Diode (transverse) than case 1 • Can be 10 3mes larger 3. Lamp than case 2 • High thermal load 15/04/16 19 Contents Content Time 1. Pumping varieties 10 ’ 2. Optical pumping (lamp) 20 ’ 2.1. Schemes; 2.2 ηp and Rp 3. Optical pumping (laser) 3.1. Schemes; 3.2 ηp and Rp 25 ’ 3.3. Pump threshold Pth 4. Electrical pumping 25 ’ Total: 80’ 15/04/16 20 Electrical pumping • Applicability: Gas or semiconductor lasers • Principle: Gas discharge • Configuraon: o Longitudinal: Uniform pumping (glow discharge) o Transverse: small voltage (arc discharge @ edges) Low-pressure mercury vapor discharge [Wikipedia] He Ne Ar Kr Xe N O2 H2 Source: Wikipedia 15/04/16 21 Excitaon mechanisms • Collision of the first kind: o Or: electron-impact excitaon Excited state: • Vibraonal o For single-species gas • Rotaonal o More common • Electronic o Non-resonant o Prelude for 2nd-kind collision • Collision of the second kind: o Resonant o ΔE < kT such that probability is high 15/04/16 22 Pump rate • σe2: Electronic excitaon cross-secon o Dependent on electron energy E, as σe2(E) • Nt: Total species populaon • Ne: Electron density • v: Electron velocity o Follow a distribu3on func3on f(E) 15/04/16 23 σe2 σ e2 ~ Eth Eth E Width of the curve is much broader compared to op3cal excitaon. 15/04/16 24 f(E): Electron energy distribu3on • v=v +v th dri v /v ≈0.01 Electric-field-induced velocity dri th Thermal velocity: random, temperature-dependent, <v> • f(E): Maxwell-Boltzmann distribu#on Te: Electron temp. Te→ f(E) → vth → <v> He-Ne: • f(E):Maxwellian (mean electron energy of 10 eV); 1 1 1 3 • σe2: 1 S→2 S; 1 S→2 S transi3ons of He; • High electron energy; inefficient 15/04/16 25 Balance condi3ons Te is related to electrical field and pressure • Energy-balance condion: Energy loss by electron collisions = Energy supplied to electrons by E field • Momentum-balance condi#on: Momentum should be conserved with a collision Te is related to gas pressure and tube radius • Ionizaon balance condion: Ionizaon Electron-ion recombinaon at tube walls 15/04/16 26 Scaling law of gas laser Opmum Te (for achieving max Rp) can be obtained with various combinaons of R, p and ε. Example: R↓ → p↑ → ↑ 15/04/16 27 Contents Content Time 1. Pumping varieties 10 ’ 2. Optical pumping (lamp) 20 ’ 2.1. Schemes; 2.2 ηp and Rp 3. Optical pumping (laser) 3.1. Schemes; 3.2 ηp and Rp 25 ’ 3.3. Pump threshold Pth 4. Electrical pumping 25 ’ Total: 80’ 15/04/16 28 .