Fiber Amplifier Calculator
EDFA, YDFA, TDFA and HDFA signal gain, output power, residual pump and noise figure from pump power, fiber length, doping and cross-sections, with gain against pump and length.
Presets fill measured cross-sections (Er in alumino-germanosilicate, Barnes et al. 1991; Yb in aluminosilicate, Melkumov et al. 2004; Tm in Al/La silica, Agger & Povlsen 2006, signal at 1900 nm; Ho in silica, Le Gouët et al. 2020, signal at 2120 nm). They vary with the host glass by tens of percent: enter your fibre's own data where you have it.
Signal Gain
10.12 dB
full-inversion bound 10.4 dB
Output Signal
0.12 dBm
1.029 mW
Noise Figure
2.84 dB
signal–spontaneous limit, ≥ 3 dB at high gain
Residual Pump
195.6 mW
97.8 % of launched
Small-Signal Absorption
0.5906 dB/m
at the pump; 0.7644 dB/m at the signal
Signal Saturation Power
0.4592 mW
hνA/(Γ(σ_a + σ_e)τ)
Upper-State Fraction n₂
0.988 → 0.975
input → output end
Best Length (0–3L)
≥ 30.0 m
gain still rising at 3L: the pump is not used up
Model
n₂/N = Σ Γ_kσ_akφ_k / (1/τ + Σ Γ_k(σ_ak + σ_ek)φ_k), φ_k = P_k/(hν_kA)
dP_k/dz = Γ_k N (σ_ek n₂ − σ_ak n₁) P_k (n₁ = 1 − n₂), solved exactly (Saleh et al. 1990)
NF = (1 + 2n_ASE)/G, n_ASE = G ∫ Γσ_e N n₂(z)/G(z) dz
Full-inversion bound: G = 4.343·Γσ_e N L dB
Two-level, co-propagating pump and signal at one wavelength each, uniform intensity over the doped area. ASE is not fed back into the inversion, so above about 20–25 dB of gain the model overestimates it, as it does with ion clustering, excited-state absorption or a backward pump. Er pumped at 980 nm is a two-level system here because the pump level empties in microseconds.
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
Two-level rate equations solved exactly: co-propagating pump, no ASE self-saturation (it matters above about 20–25 dB), ESA or clustering. Preset cross-sections are measured (Er³⁺: Barnes et al. 1991, GeO₂–Al₂O₃–SiO₂; Yb³⁺: Melkumov et al. 2004, aluminosilicate; Tm³⁺: Agger & Povlsen 2006, Al/La silica, pumped in band at 1600 nm; Ho³⁺: Le Gouët et al. 2020, silica, pumped in band at 1908 nm, 2120 nm read from their Fig. 1 to ±0.1e-25 m²); edit them for a fibre.
- Giles C. R., Desurvire E. (1991). Modeling erbium-doped fiber amplifiers. J. Lightwave Technol. 9, 271. Two-level rate equations, eqs. (6)–(9), and the saturation power hνA/(Γ(σa + σe)τ). doi:10.1109/50.65886
- Saleh A. A. M., Jopson R. M., Evankow J. D., Aspell J. (1990). Modeling of gain in erbium-doped fiber amplifiers. IEEE Photon. Technol. Lett. 2, 714. Closed-form solution for co-propagating beams. doi:10.1109/68.60769
- Barnes W. L., Laming R. I., Tarbox E. J., Morkel P. R. (1991). Absorption and emission cross section of Er³⁺ doped silica fibers. IEEE J. Quantum Electron. 27, 1004–1010. Er preset (GeO₂–Al₂O₃–SiO₂). doi:10.1109/3.83335
- Melkumov M. A., Bufetov I. A., Kravtsov K. S., Shubin A. V., Dianov E. M. (2004). Lasing parameters of ytterbium-doped fibres doped with P₂O₅ and Al₂O₃. Quantum Electron. 34, 843–848; full report arXiv:1502.02885. Yb preset (aluminosilicate). arxiv.org
- Agger S. D., Povlsen J. H. (2006). Emission and absorption cross section of thulium doped silica fibers. Opt. Express 14, 50–57. Tm preset (Al/La silica, fibre Tm1): σ_a(1600) 3.5e-25 m², σ_e/σ_a 0.10 at 1600 nm, τ 650 µs; 1900 nm read from the vector data of Figs. 3–4. doi:10.1364/OPEX.14.000050
- Le Gouët J., Gustave F., Bourdon P., Robin T., Laurent A., Cadier B. (2020). Realization and simulation of high-power holmium doped fiber lasers for long-range transmission. Opt. Express 28, 22307; arXiv:2003.14188. Ho preset (silica): σ_a/σ_e(1908) 1.9/1.6e-25 m² from the text, τ 0.7 ms, fibre #1 N 3.7e25 m⁻³ and Γ 0.76; 2120 nm read from Fig. 1. doi:10.1364/OE.394011
- Desurvire E. (1994). Erbium-Doped Fiber Amplifiers: Principles and Applications, ch. 2. Wiley. Noise figure (1 + 2n_ASE)/G from the inversion profile.