Fig. 1. Gaussian beam array with M = 12, n = 2, R = 1.2 mm, w₀ = 0.24 mm: (a) Source plane spatial distribution; (b) source plane phase distribution; (c) light field distribution of synthetic vortex beam after 2 m transmission; (d) phase distribution of synthetic vortex beam after 2 m transmission; (e) light field distribution of standard 2nd order BG vortex beam; (f) phase distribution of standard 2nd order BG vortex beam. M = 12, n = 2, R = 1.2 mm, w₀ = 0.24 mm时的高斯光束阵列　(a)源平面空间分布; (b)源平面相位分布; (c)传输 2 m后合成涡旋光束强度分布; (d)传输2 m后合成涡旋光束相位分布; (e)标准2阶BG涡旋光束强度分布; (f)标准2阶BG涡旋光束相位分布

Fig. 2. Target plane at z = 10 m: (a) Light field distribution of coherent synthetic vortex beam; (b) phase distribution of coherent synthetic vortex beam; (c) light field distribution of spiral harmonic reconstruction light field; (d) phase distribution of spiral harmonic reconstruction light field. z = 10 m处相干合成涡旋光束的(a)强度分布和(b)光束相位分布; 螺旋谐波重建的(c)强度分布和(d)相位分布

Fig. 3. Coherent synthetic vortex beam spiral spectrum distribution and size (n = 1, z = 10 m, w₀ = 0.2 mm, R = 2.1 mm): (a) M = 8; (b) M = 12; (c) M = 16. 相干合成涡旋光束螺旋谱分布及大小(其中n = 1, z = 10 m, w₀ = 0.2 mm, R = 2.1 mm)　(a) M = 8; (b) M = 12; (c) M = 16

Fig. 4. Coherently synthesized BG vortex beam (n = 1, z = 10 m, w₀ = 0.2 mm, R = 2.1 mm): (a) M = 8, light intensity distribution; (b) M =16, light intensity distribution; (c) M = 8, phase distribution; (d) M = 16, phase distribution; (e) M = 8, spiral distribution; (f) M = 16, spiral distribution. 相干合成BG涡旋光束(n = 1, z = 10 m, w₀ = 0.2 mm, R = 2.1 mm)　(a) M = 8时强度分布; (b) M = 16时强度分布; (c) M = 8时相位分布; (d) M = 16时相位分布; (e) M = 8时螺旋谱分布; (f) M = 16时螺旋谱分布

Fig. 5. Variation trend of the spectral purity P_l of the different order synthetic vortex beams with the number of sub-beams M (w₀ = 0.2 mm, R = 2.1 mm, z = 10 m). 不同阶合成涡旋光束拓扑荷模式纯度P_l随子光束数量M的变化趋势(w₀ = 0.2 mm, R = 2.1 mm, z = 10 m)

Fig. 6. Coherently synthesized BG vortex beam (n = 1, z = 10 m, M = 12, R = 2.1 mm): (a) w₀ = 0.15 mm, light intensity distribution; (b) w₀ = 0.3 mm, light intensity distribution; (c) w₀ = 0.15 mm, phase distribution; (d) w₀ = 0.3 mm, phase distribution; (e) w₀ = 0.15 mm, spiral distribution; (f) w₀ = 0.3 mm, spiral distribution. 相干合成BG涡旋光束(n = 1, z = 10 m, M = 12, R = 2.1 mm)　(a) w₀ = 0.15 mm时强度分布; (b) w₀ = 0.3 mm时强度分布; (c) w₀ = 0.15 mm时相位分布; (d) w₀ = 0.3 mm时相位分布; (e) w₀ = 0.15 mm时螺旋谱分布; (f) w₀ = 0.3 mm时螺旋谱分布

Fig. 7. Variation trend of the spectral purity P_l of the different order synthetic vortex beams with sub beam waist radius w₀ (M = 12, R = 2.1 mm, z = 10 m). 不同阶合成涡旋光束拓扑荷模式纯度P_l随子光束束腰半径w₀的变化(M = 12, R = 2.1 mm, z = 10 m)

Fig. 8. Coherently synthesized BG vortex beam (n = 1, z = 10 m, M = 12, w₀ = 0.2 mm): (a) R = 1 mm, light intensity distribution; (b) R = 2.2 mm, light intensity distribution; (c) R = 1 mm, phase distribution; (d) R = 2.2 mm, phase distribution; (e) R = 1 mm, spiral distribution; (f) R = 2.2 mm, spiral distribution. 相干合成BG涡旋光束(n = 1, z = 10 m, M = 12, w₀ = 0.2 mm)　(a) R = 1 mm时强度分布; (b) R = 2.2 mm时强度分布; (c) R = 1 mm时相位分布; (d) R = 2.2 mm时相位分布; (e) R = 1 mm时螺旋谱分布; (f) R = 2.2 mm时螺旋谱分布

Fig. 9. Variation trend of the spectral purity P_l of the different order synthetic vortex beams with beam ring radius R (M = 12, w₀ = 0.2 mm, z = 10 m). 不同阶合成涡旋光束拓扑荷模式纯度P_l随组束环半径R的变化(M = 12, w₀ = 0.2 mm, z = 10 m)