## Abstract

We show by numerical modeling that saturation of the population inversion reduces the stimulated thermal Rayleigh gain relative to the laser gain in large mode area fiber amplifiers. We show how to exploit this effect to raise mode instability thresholds by a substantial factor. We also demonstrate that when suppression of stimulated Brillouin scattering and the population saturation effect are both taken into account, counter-pumped amplifiers have higher mode instability thresholds than co-pumped amplifiers for fully Yb^{3+} doped cores, and confined doping can further raise the thresholds.

© 2013 OSA

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### Equations (9)

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(1)
$${n}_{u}\left(x,y\right)=\frac{{I}_{p}{\sigma}_{p}^{a}/h{\nu}_{p}+{I}_{s}\left(x,y\right){\sigma}_{s}^{a}/h{\nu}_{s}}{{I}_{p}\left({\sigma}_{p}^{a}+{\sigma}_{p}^{e}\right)/h{\nu}_{p}+{I}_{s}\left(x,y\right)\left({\sigma}_{s}^{a}+{\sigma}_{s}^{e}\right)/h{\nu}_{s}+1/\tau}.$$
(2)
$$Q\left(x,y\right)={N}_{Yb}\left(x,y\right)\left[\frac{{\nu}_{p}-{\nu}_{s}}{{\nu}_{p}}\right]\left[{\sigma}_{p}^{a}-\left({\sigma}_{p}^{a}+{\sigma}_{p}^{e}\right){n}_{u}\left(x,y\right)\right]{I}_{p},$$
(3)
$$\frac{\partial {P}_{11}\left(z\right)}{\partial z}=\left[{g}_{11}+{g}_{01}\chi {P}_{01}\left(z\right)\right]{P}_{11}\left(z\right)={g}_{\text{net}}{P}_{11}\left(z\right).$$
(4)
$${\chi}^{\prime}=\frac{{g}_{\text{comp}}-{g}_{s}}{{g}_{s}{P}_{s}}=\frac{{g}_{\text{strs}}}{{g}_{s}{P}_{s}}$$
(5)
$${P}_{\text{thres}}{L}_{\text{eff}}={\int}_{0}^{L}{P}_{s}\left(z\right)dz.$$
(6)
$$\frac{{g}_{B}}{\gamma}\frac{{P}_{\text{thres}}{L}_{\text{eff}}}{{A}_{\text{eff}}}>17,$$
(7)
$$\gamma >\frac{{g}_{B}{P}_{\text{thres}}{L}_{\text{eff}}}{17{A}_{\text{eff}}}.$$
(8)
$$\gamma =\frac{{P}_{\text{thres}}{L}_{\text{eff}}}{400\hspace{0.17em}\text{W}\cdot \text{m}}.$$
(9)
$${P}_{\text{thres}}={P}_{\text{ref}}\frac{\text{log}\left({P}_{\text{start}}/10\right)}{\text{log}\left({10}^{-16}/10\right)}$$