## Abstract

A general model is proposed to describe thermal-induced mode distortion in the step-index fiber (SIF) high power lasers. Two normalized parameters in the model are able to determine the mode characteristic in the heated SIFs completely. Shrinking of the mode fields and excitation of the high-order modes by the thermal-optic effect are investigated. A simplified power amplification model is used to describe the output power redistribution under various guiding modes. The results suggest that fiber with large mode area is more sensitive on the thermally induced mode distortion and hence is disadvantaged in keeping the beam quality in high power operation. The model is further applied to improve the power scaling analysis of Yb-doped fiber lasers. Here the thermal effect is considered to couple with the optical damage and the stimulated Raman scattering dynamically, whereas direct constraint from the thermal lens is relaxed. The resulting maximal output power is from 67kW to 97kW, depending on power fraction of the fundamental mode.

© 2013 OSA

Full Article |

PDF Article
### Equations (13)

Equations on this page are rendered with MathJax. Learn more.

(1)
$$\psi \text{'}\text{'}+\frac{1}{r}\psi \text{'}+\left({k}^{2}(n{(r)}^{2}-{n}_{eff}{}^{2})-\frac{{\nu}^{2}}{{r}^{2}}\right)\psi =0$$
(2)
$$n(r)=\{\begin{array}{cc}{n}_{co}+\frac{dn}{dT}({T}_{co}-{T}_{0})+\left(1-\frac{{r}^{2}}{{r}_{co}{}^{2}}\right)\frac{dn}{dT}\Delta {T}_{co}& r\le {r}_{co}\\ {n}_{cl}+\frac{dn}{dT}({T}_{co}-{T}_{0})-\left(2\mathrm{ln}\frac{r}{{r}_{co}}\right)\frac{dn}{dT}\Delta {T}_{co}& r>{r}_{co}\end{array}$$
(3)
$$\psi \text{'}\text{'}+\frac{1}{x}\psi \text{'}+\left(m(x)-{k}^{2}{r}_{co}{}^{2}({n}_{eff}{}^{2}-{n}_{cl}{}^{2})-\frac{{\nu}^{2}}{{x}^{2}}\right)f=0$$
(4)
$$m(x)=\{\begin{array}{cc}{V}^{2}+(1-{x}^{2}){Z}^{2}& x\le 1\\ -(2\mathrm{ln}x){Z}^{2}& x>1\end{array}$$
(5)
$$\{\begin{array}{l}V=k{r}_{co}\sqrt{{n}_{co}{}^{2}-{n}_{cl}{}^{2}}\\ Z=k{r}_{co}\sqrt{({n}_{co}+{n}_{cl})\frac{dn}{dT}\Delta {T}_{co}}\end{array}$$
(6)
$${\psi}_{in}\to {\displaystyle \sum _{k}{c}_{k}{\psi}_{k}}\Rightarrow {P}_{k}(0)=|{c}_{k}{|}^{2}{P}_{in}$$
(7)
$${P}_{k}(L)={P}_{k}(0){a}^{{\Gamma}_{k}}=|{c}_{k}{|}^{2}{a}^{{\Gamma}_{k}}\cdot {P}_{in}$$
(8)
$$G=\frac{{\displaystyle \sum {P}_{k}(L)}}{{\displaystyle \sum {P}_{k}(0)}}=\frac{{\displaystyle \sum |{c}_{k}{|}^{2}{a}^{{\Gamma}_{k}}}}{{\displaystyle \sum |{c}_{k}{|}^{2}}}$$
(9)
$${p}_{k}=\frac{{P}_{k}(L)}{{\displaystyle \sum {P}_{k}(L)}}=\frac{|{c}_{k}{|}^{2}{a}^{{\Gamma}_{k}}}{G{\displaystyle \sum |{c}_{k}{|}^{2}}}$$
(10)
$$\frac{{D}_{\text{mode}}}{{d}_{co}}=\sqrt{\frac{2}{Z}}$$
(11)
$$g(f({P}_{\mathrm{max}}^{condition-lens}))={P}_{\mathrm{max}}^{condition-lens}$$
(12)
$${P}_{\mathrm{max}}^{BQ}=\frac{{\eta}_{laser}}{{\eta}_{heat}}\frac{{Z}_{c}{}^{2}\kappa {\lambda}^{2}}{2{n}_{0}\pi \frac{dn}{dT}}\frac{L}{{r}_{co}{}^{2}}$$
(13)
$$\begin{array}{c}{P}_{\mathrm{max}}^{pump}={\eta}_{laser}{I}_{pump}\cdot \pi {r}_{cl}{}^{2}\cdot \pi N{A}^{2}\\ {P}_{\mathrm{max}}^{rupture}=\frac{{\eta}_{laser}}{{\eta}_{heat}}\frac{4\pi {R}_{m}}{1-{r}_{co}{}^{2}/(2{r}_{cl}{}^{2})}L\\ {P}_{\mathrm{max}}^{temp}=\frac{{\eta}_{laser}}{{\eta}_{heat}}\frac{4\pi \kappa ({T}_{\mathrm{max}}-{T}_{cooling})}{1+2\kappa /({r}_{cl}h)+2\mathrm{ln}({r}_{cl}/{r}_{co})}L\\ {P}_{\mathrm{max}}^{damage}={A}_{eff}{I}_{damage}\\ {P}_{\mathrm{max}}^{SRS}=\left(20.3-\mathrm{ln}\beta +\mathrm{ln}\frac{{A}_{eff}}{{g}_{R}{L}_{eff}}\right)\frac{{A}_{eff}}{{g}_{R}{L}_{eff}}G\\ {P}_{\mathrm{max}}^{lens}=\frac{{\eta}_{laser}}{{\eta}_{heat}}\frac{2\kappa {\lambda}^{2}}{{\Gamma}^{4}\pi {n}_{co}\frac{dn}{dT}}\frac{L}{{r}_{co}{}^{2}}\end{array}$$