Solid State Laser Resonator
Nd:YAG-type rod laser: two-mirror stability and TEM₀₀ mode with the crystal in the cavity, threshold pump power, small-signal gain, Rigrod output power and slope efficiency.
g₁g₂
0.2725
g₁ = 1.000, g₂ = 0.2725; stable
TEM₀₀ waist w₀
173.7 µm
0.000 mm from the HR
TEM₀₀ spot in the rod
174.0 µm
Rod radius 1500 µm; spot on OC 332.7 µm
Effective cavity length
145.5 mm
L − l(1 − 1/n)
Round-trip loss δ
5.429 %
−ln(R_HR R_OC) + 2αl
Threshold pump power
7.325 W
Small-signal gain g₀l = 0.07412 at 20.00 W
Output power
9.093 W
I_sat = 2.899 kW/cm²
Slope efficiency
71.74 %
Quantum defect limit λₚ/λ = 75.94 %
Four-level rod pumped uniformly over its area A = πd²/4: g₀l = ηₚστPₚλₚ/(hcA), threshold Pₜₕ = δhcA/(2ηₚστλₚ), I_sat = hc/(λστ).
Rigrod output P = I_sat A (1 − R₂)√R₁′(g₀l + ln√(R₁′R₂))/((√R₁′ + √R₂)(1 − √(R₁′R₂))), R₁′ = R_HR e⁻²ᵅˡ; for small losses P ≈ I_sat A (T/2)(2g₀l/δ − 1).
TEM₀₀ mode: Kogelnik–Li with the crystal (against the HR) folded into the effective length L − l(1 − 1/n).
Output power versus absorbed pump power
- Output power
- Operating point
TEM₀₀ beam radius along the cavity (crystal against the HR at z = 0)
- TEM₀₀ radius w(z)
- Crystal (rod radius)
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
Four-level rod pumped uniformly over its cross-section with a multimode output filling it: P_th = δhcA/(2ηₚστλₚ), output from Rigrod's homogeneous plane-wave model. The TEM₀₀ mode is Kogelnik–Li with the crystal (against the HR) folded into the effective length L − l(1 − 1/n). No thermal lens, no ground-state absorption (not for quasi-three-level media such as Yb:YAG).
- Koechner W. (2006). Solid-State Laser Engineering, 6th ed., ch. 2–3. Springer. doi:10.1007/0-387-29338-8
- Svelto O. (2010). Principles of Lasers, 5th ed., ch. 6–7. Springer. doi:10.1007/978-1-4419-1302-9
- Rigrod W. W. (1965). Saturation effects in high-gain lasers. J. Appl. Phys. 36, 2487–2490. doi:10.1063/1.1714517
- Kogelnik H., Li T. (1966). Laser beams and resonators. Appl. Opt. 5, 1550–1567. doi:10.1364/ao.5.001550