Fiber Laser Output Power

Fiber laser output power, optical and Stokes efficiency, efficiency beyond the quantum defect, the Rigrod optimum output coupling from gain and cavity loss, and the signal core's V number, mode count and mode-field diameter.

Model: Textbook approximation

Pump Power (W)Pump Wavelength (nm)Laser Wavelength (nm)Slope Efficiency (%)Threshold Pump Power (W)Small-Signal Single-Pass Gain (dB)Output Coupler Transmission (%)Internal Round-Trip Loss (dB)Signal Core Diameter (µm)Core NA

Output Power

78.40 W

η_s(P_pump − P_th): uses the entered slope efficiency and threshold, not the cavity model below

Optical-to-Optical Efficiency

78.4 %

P_out/P_pump

Stokes Efficiency

91.73 %

λ_p/λ_l, the quantum-defect limit

Efficiency Beyond Stokes

87.21 %

η_s/(λ_p/λ_l): losses other than the quantum defect

Optimum Output Coupling

51.5 %

Rigrod, at this gain and loss

Output at Your Coupler

61.9 % of optimum

1.378 vs 2.227 × P_sat

V Number at the Laser Wavelength

2.362

2πa·NA/λ_l

Guided Modes

single mode

only LP01 (2 polarizations)

LP01 Mode-Field Diameter

10.93 µm

Petermann II, exact step-index LP01

Single-Mode Cutoff Wavelength

1045 nm

LP11 cutoff 2πa·NA/2.405

Formulas

P_out = η_s·(P_pump − P_th) (your measured slope and threshold)

Stokes efficiency λ_p/λ_l; efficiency beyond Stokes = η_s/(λ_p/λ_l) ≤ 1

Rigrod: P/P_sat = (1 − R₂)√R₁ (g₀L + ln√(R₁R₂)) / ((√R₁ + √R₂)(1 − √(R₁R₂)))

R₂ = 1 − T, R₁ = 10^(−loss/10) (internal round-trip loss folded into the rear mirror), g₀L = gain/4.343

V = 2πa·NA/λ; single mode for V < 2.405 (LP11 cutoff); LP01 Petermann II diameter from the exact step-index mode

Rigrod (1965) treats a homogeneously broadened standing-wave laser with gain of any size, so it holds for high-gain fibre lasers where the low-gain rule T_opt = √(2g₀L·L_i) − L_i fails. The higher the gain, the less the output depends on the coupler: the 3.4 % Fresnel reflection of a cleaved end gives 55 % of the optimum output at 13 dB single-pass gain but 88 % at 30 dB, which is why high-power fibre lasers often use it as the output mirror. Gain saturation is that of a four-level system with g₀ fixed; reabsorption in Yb is not modelled.

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

Output from your slope and threshold. Optimum coupler from Rigrod's standing-wave model (four-level saturation, g₀ fixed), internal loss lumped into the rear mirror; output relative to the optimum. Core: weakly guiding step-index LP modes (Gloge), exact LP01 Petermann II diameter.

Gloge D. (1971). Weakly guiding fibers. Appl. Opt. 10, 2252. V number, LP mode cutoffs and the LP01 field. doi:10.1364/ao.10.002252
Rigrod W. W. (1965). Saturation effects in high-gain lasers. J. Appl. Phys. 36, 2487. Output power of a homogeneously broadened standing-wave laser against mirror reflectances. doi:10.1063/1.1714517
Zervas M. N., Codemard C. A. (2014). High Power Fiber Lasers: A Review. IEEE J. Sel. Top. Quantum Electron. 20(5), 219–241. Quantum defect and slope efficiency of Yb fibre lasers. doi:10.1109/JSTQE.2014.2321279

Report a problem