Fig. 1. Simplified model of fiber laser passing through focusing system

Fig. 2. Focusing properties varying with fundamental mode ratio when mixed modes are superimposed incoherently. (a) Average power density; (b) focus shift

Fig. 3. Focusing intensity distributions of incoherent superposition of two modes under different fundamental mode ratios. (a) α=0.3; (b) α=0.6; (c) α=0.9

Fig. 4. Power density of coherent superposition of two modes varying with fundamental mode ratio and phase difference. (a) Fundamental mode ratio; (b) phase difference

Fig. 5. Power density of coherent superposition of three modes varying with fundamental mode ratio and phase difference. (a) Fundamental mode ratio; (b) phase difference

Fig. 6. When the phase difference isπ, the focused spot of two modes of coherent superposition with different fundamental mode ratios. (a) α=0.1; (b) α=0.3; (c) α=0.7; (d) α=1.0

Fig. 7. When the phase difference is different, the focus shift in x direction varying with the fundamental mode ratio. (a) Superposition of two modes; (b) superposition of three modes

Fig. 8. When the fundamental mode ratio is different, the axial focus shift of the mixed modes varying with the phase difference. (a) LP₀₁ mode and LP₁₁ mode; (b) LP₀₁ mode, LP₁₁ mode, and LP₀₂ mode