Yb Thin-Disk Laser

Yb:YAG thin-disk laser: quasi-three-level threshold inversion, multipass pump absorption with bleaching, threshold pump power, slope efficiency, output power and temperature rise through the disk.

Model: Textbook approximation

Disk, pump module and resonator

Disk thickness d (µm)Disk diameter (mm)Pump spot diameter (mm, top hat)Yb doping (at.%)Pump passes through the disk MLaser passes per round trip m (2: disk as end mirror)Incident pump power (W)Output coupler reflectanceOther loss per round trip (%)

Gain medium (defaults: Yb:YAG at 300 K, sources below; check them for your crystal)

Laser wavelength λ (nm)Pump wavelength λ_p (nm)Emission σ_e at λ (10⁻²⁰ cm²)Absorption σ_a at λ (10⁻²⁰ cm²)Absorption σ_ap at λ_p (10⁻²⁰ cm²)Emission σ_ep at λ_p (10⁻²⁰ cm²)Upper-level lifetime τ (ms)Heat fraction of the absorbed pumpThermal conductivity κ (W/(m K))

Threshold inversion β_th

9.117 %

transparency 6.250 %; pump bleaches at 77.55 %

Pump absorbed

94.83 %

16 passes at β_th; unpumped 96.51 %

Threshold pump power

41.68 W

0.5896 kW/cm² over the spot

Output power

103.0 W

slope 65.07 %; δ = 4.051 %

Ion density

13.80 × 10²⁰ cm⁻³

doping × 1.38 × 10²² Y sites/cm³

Absorbed pump intensity

2.683 kW/cm²

Temperature rise through the disk

37.05 K

η_h I_abs d/(2κ), heat sink and solder not included

Threshold: m d N(βσ_e − (1 − β)σ_a) = δ = −ln R_oc − ln(1 − loss). Pump absorption α_p = N(σ_ap − β(σ_ap + σ_ep)), clamped at β_th above threshold: η_abs = 1 − e^(−M α_p d).

P_th = h c N d β_th A/(λ_p τ η_abs); P_out = η_abs(λ_p/λ)(−ln R_oc/δ)(P − P_th) for a top-hat pump and mode of equal area. ΔT = η_h I_abs d/(2κ) for uniform heating with the back face cooled.

Defaults: cross sections at 300 K from Chanteloup et al. 2014, Table 1 (σ_a measured; σ_e from Fan 2007 and Brown 2005); τ = 0.951 ms (Sumida & Fan 1994, radiation trapping suppressed); heat fraction 1 − λ_p/λ = 0.087, Fan's thermal load with every excited ion extracted by the laser (Chénais et al. 2006, Eq. V.1; without lasing it is 1 − η_r λ_p/λ_f with λ_f 1007 nm, higher only when quenching makes the radiative efficiency η_r < 0.98); κ ≈ 6.3 W/(m K) for the 10 at.% default, between 7 W/(m K) measured on 8 at.% Yb:YAG (11 W/(m K) undoped; Chénais et al. 2006, §II) and 5.7 W/(m K) at 12 at.% (Körner et al. 2012, Table 4).

Output power versus incident pump power

Output power
This pump

Pump absorption versus number of passes

At the threshold inversion
Unpumped disk
This module

Temperature rise through the disk, above threshold

Front-to-back temperature rise

Model and references

Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers

Quasi-three-level rate equations with a top-hat pump and mode of equal area, inversion uniform through the disk and clamped above threshold; reabsorption and pump bleaching included, ASE and temperature-dependent cross-sections not. One-dimensional heat flow to the back face. Defaults: 300 K Yb:YAG cross sections (Chanteloup 2014 Table 1), τ 0.951 ms (Sumida & Fan), heat fraction 1 − λ_p/λ (lasing), κ 6.3 W/(m K) for 10 at.% Yb:YAG, between 7 at 8 at.% (Chénais 2006) and 5.7 at 12 at.% (Körner 2012); check them against your crystal.

Giesen A., Hügel H., Voss A., Wittig K., Brauch U., Opower H. (1994). Scalable concept for diode-pumped high-power solid-state lasers. Appl. Phys. B 58, 365–372. doi:10.1007/BF01081875
Fan T. Y., Byer R. L. (1987). Modeling and CW operation of a quasi-three-level 946 nm Nd:YAG laser. IEEE J. Quantum Electron. 23, 605–612. doi:10.1109/JQE.1987.1073371
Taira T., Tulloch W. M., Byer R. L. (1997). Modeling of quasi-three-level lasers and operation of cw Yb:YAG lasers. Appl. Opt. 36, 1867. doi:10.1364/AO.36.001867
DeLoach L. D., Payne S. A., Chase L. L. et al. (1993). Evaluation of absorption and emission properties of Yb³⁺ doped crystals for laser applications. IEEE J. Quantum Electron. 29, 1179. doi:10.1109/3.214504
Fan T. Y. (1993). Heat generation in Nd:YAG and Yb:YAG. IEEE J. Quantum Electron. 29, 1457–1459. doi:10.1109/3.234394
Sumida D. S., Fan T. Y. (1994). Effect of radiation trapping on fluorescence lifetime and emission cross section measurements in solid-state laser media. Opt. Lett. 19, 1343. Yb:YAG τ = 0.951 ms. doi:10.1364/OL.19.001343
Chénais S., Druon F., Forget S., Balembois F., Georges P. (2006). On thermal effects in solid-state lasers: the case of ytterbium-doped materials. Prog. Quantum Electron. 30, 89–153. Thermal load (Eq. V.1); κ 7 W/(m K) at 8 at.% Yb, 11 undoped (§II). arxiv.org
Chanteloup J.-C., Arzakantsyan M., Marrazzo S. (2014). Defining the optimal gradient doped Yb:YAG disk for room and low temperature diode pumped solid-state laser operations. High Power Laser Sci. Eng. 2, e35, Table 1. Cross sections at 940 and 1030 nm, 300 K. doi:10.1017/hpl.2014.38
Körner J., Vorholt C., Liebetrau H. et al. (2012). Measurement of temperature-dependent absorption and emission spectra of Yb:YAG, Yb:LuAG, and Yb:CaF₂ between 20 °C and 200 °C and predictions on their influence on laser performance. J. Opt. Soc. Am. B 29, 2493, Table 4: κ 5.7 W/(m K) at 12 at.% Yb. doi:10.1364/JOSAB.29.002493

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