Lecture 7 Pumping & Popula on Inversion*
Min Yan Op cs 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 varie es
• Op cal pumping (CW/pulsed) o Lamp: for solid-state/liquid lasers [broad absorp on bands] o Laser: for solid-state/liquid/gas lasers [broad/narrow absorp on 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
• Ellip cal cylinder o Rod and lamp at foci o Specular reflec on Rod radius: mm~cm Rod length: cm~<1m • Close-coupling o Close-pack o Diffusive reflec on 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 Assump on: uniform Rp
3 Pp 2 P r ν P p νmp t 1 Pa 0 Pm
• Radia ve efficiency • Transfer efficiency • Absorp on efficiency • Power quantum efficiency 15/04/16 10 Pump efficiency, ηp
Configura on: Ellip cal cylinder
15/04/16 11 Absorp on efficiency, ηa
Emission
• Con nuum ∝ 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 Op cal 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,
Space-dependent lasing/pump beams: a ma er of calcula ng A
1. Diode (longitudinal) ηpd: ηp for diode pumping
Op mum: wp ≈w0
2. Diode (transverse) Op mum 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 ra (undoped cladding)
15/04/16 18 Threshold pump power, Pth Procedure:
Comment:
1. Diode (longitudinal)
• Can be 50% larger 2. Diode (transverse) than case 1
• Can be 10 mes 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 • Configura on: 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 Excita on mechanisms
• Collision of the first kind: o Or: electron-impact excita on Excited state: • Vibra onal o For single-species gas • Rota onal 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 excita on cross-sec on o Dependent on electron energy E, as σe2(E) • Nt: Total species popula on • Ne: Electron density • v: Electron velocity o Follow a distribu on func on f(E)
15/04/16 23 σe2
σ e2 ~ Eth
Eth E
Width of the curve is much broader compared to op cal excita on.
15/04/16 24 f(E): Electron energy distribu on
• v=v +v th dri v /v ≈0.01 Electric-field-induced velocity dri th Thermal velocity: random, temperature-dependent,
Te: Electron temp.
Te→ f(E) → vth →
15/04/16 25 Balance condi ons
Te is related to electrical field and pressure
• Energy-balance condi on: 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
• Ioniza on balance condi on: Ioniza on Electron-ion recombina on at tube walls
15/04/16 26 Scaling law of gas laser
Op mum Te (for achieving max Rp) can be obtained with various combina ons 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