Fig. 1. Scheme of the launch of LMA fiber laser.

Fig. 2. Comparison between the analytic and simulated results when z=1  km and Cn2=1×10−15  m−2/3.

Fig. 3. Irradiance distribution of fiber modes. (a) LP01; (b) LP11.

Fig. 4. Irradiance distribution at z=5  km. (a) Near-field intensity with ALP11=0. (b) Near-field intensity with ALP11=0.3, Δϕ=π/4. (c) Far-field intensity with ALP11=0. (d) Far-field intensity with ALP11=0.3, Δϕ=π/4.

Fig. 5. Normalized intensity distribution.(a) ALP11=0.1, z=5  km. (b) ALP11=0.1, Δϕ=π/4. (c) ALP11=0.2, z=5  km. (d) ALP11=0.2, Δϕ=π/4. (e) ALP11=0.3, z=5  km. (f) ALP11=0.3, Δϕ=π/4. (g) Δϕ=π/4, z=5  km.

Fig. 6. PIB as a function of relative phase and HOM content ALP11. (a) z=5  km. (b) Δϕ=0.

Fig. 7. PIB as a function of Δϕ.

Fig. 8. Example of phase screen used in numerical simulation. (a) Cn2=5×10−16  m−2/3. (b) Cn2=1×10−15  m−2/3.

Fig. 9. Irradiance distribution at z=5  km. (a) Without HOM content. (b) ALP11=0.3, Δϕ=π/4.

Fig. 10. Normalized intensity distribution. (a) ALP11=0.2, Δϕ=π/2. (b) ALP11=0.2.

Fig. 11. PIB as a function of HOM content ALP11.

Fig. 12. PIB as a function of turbulence strength.

Fig. 13. SI as a function of turbulence strength.

Fig. 14. PIB as a function of Δϕ. (a) Cn2=1×10−16  m−2/3. (b) Cn2=5×10−16  m−2/3. (c) Cn2=1×10−15  m−2/3.