Lecture 7 Pumping & Popula3on Inversion*

Transcription

1 Lecture 7 Pumping & Popula3on 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.

2 Reading Principles of Lasers (5th Ed.): Chapter 6. Skip: Quantum mechanical treatment in Squeeze: , /04/16 2

3 Laser Pump I in I out Mirror 1 Gain medium Mirror ν p ν mp 1 0 Pump efficiency: η p =P m /P p Pump rate: R p, or dn 2 /dt Threshold pump power: P th 15/04/16 3

4 Contents Content Time 1. Pumping varieties Optical pumping (lamp) 2.1. Schemes; 2.2 η p and R p 3. Optical pumping (laser) 3.1. Schemes; 3.2 η p and R p 3.3. Pump threshold P th Electrical pumping 25 Total: 80 15/04/16 4

5 Contents Content Time 1. Pumping varieties Optical pumping (lamp) Schemes; 2.2 η p and R p 3. Optical pumping (laser) 3.1. Schemes; 3.2 η p and R p Pump threshold P th 4. Electrical pumping 25 Total: 80 15/04/16 5

6 Pumping varie3es Op#cal 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

7 Contents Content Time 1. Pumping varieties Optical pumping (lamp) 2.1. Schemes; 2.2 η p and R p 3. Optical pumping (laser) 3.1. Schemes; 3.2 η p and R p 3.3. Pump threshold P th Electrical pumping 25 Total: 80 15/04/16 7

8 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 reflec3on Rod radius: mm~cm Rod length: cm~<1m Close-coupling o Close-pack o Diffusive reflec3on ü More uniform 15/04/ atm = 760 Torr

9 Pumping: Lamps P p η p More uniform 15/04/16 9

10 Pump efficiency and pump rate Assump3on: uniform R p P p 3 2 P r P t P a P m ν p ν mp 1 0 Radia3ve efficiency Transfer efficiency Absorp3on efficiency Power quantum efficiency 15/04/16 10

11 Pump efficiency, η p Configura3on: Ellip3cal cylinder 15/04/16 11

12 Absorp3on efficiency, η a Emission Con3nuum J 2 Lines J Alexandrite Nd:YAG Absorp#on 15/04/16 Nd:YAG: Nd 3+ in Y 3 Al 5 O 12 crystal (host-independent) 12 Alexandrite: Cr 3+ in BeAl 2 O 4 crystal (host-dependent)

13 Contents Content Time 1. Pumping varieties Optical pumping (lamp) 2.1. Schemes; 2.2 η p and R p 3. Optical pumping (laser) 3.1. Schemes; 3.2 η p and R p 3.3. Pump threshold P th Electrical pumping 25 Total: 80 15/04/16 13

14 Laser pumping Convenience: Efficient and high-power diode lasers widely available Key examples: o o o o Nd:YAG and siblings pumped by GaAs/AlGaAs QW-lasers (~800nm) Yb:YAG, Nd:glass or Yb:Er:glass pumped by InGaAs/GaAs QW-lasers (950~980nm) Alexandrite, Cr:LISAF pumped by GaInP/AlGaInP QW-lasers ( nm) Tm:Ho:YAG laser pumped by AlGaAs QW-lasers (785nm) 808nm 15/04/16 14

15 Pumping diodes i ii i. Single-diode Beam:2x4µm 2 ; 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

16 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

17 Pump efficiency Nd:YAG Lamp v.s. Diode: η a (6 ) and η pq (1.5 ) 15/04/16 17

18 Pump rate, <R p > For uniform R p Space-dependent lasing/pump beams: a mater of calcula3ng A 1. Diode (longitudinal) η pd : η p for diode pumping Op3mum: w p w 0 2. Diode (transverse) Op3mum a exists 3. Lamp η pl : η p for lamp pumping w 0 : Laser beam waist w p : pump beam waist a: radius of the ac3ve region Assump#on for cases 2 and 3: R p =const if r<a (doped region) R p =0 if r>a (undoped cladding) 15/04/16 18

19 Threshold pump power, P th Procedure: <N 2 > c <R p > c P th γ: logarithmic cavity loss σ e : effec3ve s3mulated emission cross-sec3on l: ac3ve medium length τ: upper-level life3me Comment: <N 2 > c differs for quasi-3-level system 1. Diode (longitudinal) 2. Diode (transverse) Can be 50% larger than case 1 3. Lamp Can be 10 3mes larger than case 2 High thermal load 15/04/16 19

20 Contents Content Time 1. Pumping varieties Optical pumping (lamp) 2.1. Schemes; 2.2 η p and R p 3. Optical pumping (laser) 3.1. Schemes; 3.2 η p and R p 3.3. Pump threshold P th Electrical pumping 25 Total: 80 15/04/16 20

21 Electrical pumping Applicability: Gas or semiconductor lasers Principle: Gas discharge Configura#on: o Longitudinal: Uniform pumping (glow discharge) o Transverse: small voltage (arc edges) Low-pressure mercury vapor discharge [Wikipedia] He Ne Ar Kr Xe N O 2 H 2 Source: Wikipedia 15/04/16 21

22 Excita3on mechanisms Collision of the first kind: o Or: electron-impact excita#on o For single-species gas o More common o Non-resonant o Prelude for 2 nd -kind collision Excited state: Vibra3onal Rota3onal Electronic Collision of the second kind: o Resonant o ΔE < kt such that probability is high 15/04/16 22

23 Pump rate σ e2 : Electronic excita3on cross-sec3on o Dependent on electron energy E, as σ e2 (E) N t : Total species popula3on N e : Electron density v: Electron velocity o Follow a distribu3on func3on f(e) 15/04/16 23

24 σ e2 σ e2 ~ E th E th E Width of the curve is much broader compared to op3cal excita3on. 15/04/16 24

25 f(e): Electron energy distribu3on v=v th +v driy v Electric-field-induced velocity driy /v th 0.01 Thermal velocity: random, temperature-dependent, <v> f(e): Maxwell-Boltzmann distribu#on T e : Electron temp. T e f(e) v th <v> He-Ne: f(e):maxwellian (mean electron energy of 10 ev); σ e2 : 1 1 S 2 1 S; 1 1 S 2 3 S transi3ons of He; High electron energy; inefficient 15/04/16 25

26 Balance condi3ons T e 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 T e is related to gas pressure and tube radius Ioniza#on balance condi#on: Ioniza3on Electron-ion recombina3on at tube walls 15/04/16 26

27 Scaling law of gas laser Op3mum T e (for achieving max R p ) can be obtained with various combina3ons of R, p and ε. Example: R p 15/04/16 27

28 Contents Content Time 1. Pumping varieties Optical pumping (lamp) 2.1. Schemes; 2.2 η p and R p 3. Optical pumping (laser) 3.1. Schemes; 3.2 η p and R p 3.3. Pump threshold P th Electrical pumping 25 Total: 80 15/04/16 28