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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.

Model: Textbook approximation

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

051015200510152025303540Absorbed pump power (W)Output power (W)
  • Output power
  • Operating point

TEM₀₀ beam radius along the cavity (crystal against the HR at z = 0)

5001.0k1.5k020406080100120140Position from the HR (mm)Beam radius (µm)
  • 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).

  1. Koechner W. (2006). Solid-State Laser Engineering, 6th ed., ch. 2–3. Springer. doi:10.1007/0-387-29338-8
  2. Svelto O. (2010). Principles of Lasers, 5th ed., ch. 6–7. Springer. doi:10.1007/978-1-4419-1302-9
  3. Rigrod W. W. (1965). Saturation effects in high-gain lasers. J. Appl. Phys. 36, 2487–2490. doi:10.1063/1.1714517
  4. Kogelnik H., Li T. (1966). Laser beams and resonators. Appl. Opt. 5, 1550–1567. doi:10.1364/ao.5.001550
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