Table 2 Parameters used for the simulation in Fig. 3

\({\mathrm{Yb}}^{3+}\) ion density \(n_{\mathrm{Yb}} = n_{e}+n_{g}\)

\(1.1\times 10^{26}~/{\mathrm{m}}^{3}\)

Loss rate \(\alpha _{\mathrm{loss}}\)

\(6.3\times 10^{-3}~/{\mathrm{m}}\)

Excited state lifetime \(\tau _{{\mathrm{Yb}}^{3+}}\)

\(0.8~{\mathrm{ms}}\)

Effective fiber core area \(A_{\mathrm{fiber}}\)

\(1.2\times 10^{-10}~{\mathrm{m}}^{2}\)

Time step δt

\(0.8~\mu{\mathrm{s}}\)

Time limit \(t_{\mathrm{limit}}\)

\(0.8~{\mathrm{ms}}\)

Length step δL

\(2~{\mathrm{mm}}\)

Fiber length \(L_{\mathrm{fiber}}\)

\(10~{\mathrm{m}}\)

ASE bandwidth per channel \(\Delta \lambda _{\mathrm{ASE}}\)

\(6.6~{\mathrm{nm}}\)

ASE wavelength range

864–\(1194~{\mathrm{nm}}\)

ASE channels

51

Pump spectrum channels

5

Seed power \(P_{S}\)

\(0.2~{\mathrm{W}}\)

Pump power \(P_{P}\)

\(13~{\mathrm{W}}\)

Seed input efficiency \(\varepsilon _{S}\)

30%

Pump input efficiency \(\varepsilon _{P}\)

80%

Return loss \(\varepsilon _{r}\)

0%