Binary Annular Phase Plate Used to Generate Hollow Focal Field

Fig. 5. R, M, S in focal plane versus NA. (a) R value for 4-ring; (b) R value for 5-ring; (c) S and M values for 4-ring; (d) S and M values for 5-ring

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Fig. 6. Light intensity distributions in axial direction for different ring structures. (a) 2-ring; (b) 3-ring; (c) 4-ring; (d) 5-ring; (e) 6-ring

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Fig. 7. R, M, S in axial direction versus NA. (a) R value for 4-ring; (b) R value for 5-ring; (c) S and M values for 4-ring; (d) S and M values for 5-ring

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Table 1. Radius of each ring when generating hollow focal field
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Table 1. Radius of each ring when generating hollow focal field
Number of rings Relation among normalized ring radii
2 2 $\begin{matrix} ρ_{1}^{2} \end{matrix}$ -1=0
3 2( $\begin{matrix} ρ_{1}^{2} \end{matrix}$ - $\begin{matrix} ρ_{2}^{2} \end{matrix}$ )+1=0
4 2( $\begin{matrix} ρ_{1}^{2} \end{matrix}$ - $\begin{matrix} ρ_{2}^{2} \end{matrix}$ + $\begin{matrix} ρ_{3}^{2} \end{matrix}$ )-1=0
5 2( $\begin{matrix} ρ_{1}^{2} \end{matrix}$ - $\begin{matrix} ρ_{2}^{2} \end{matrix}$ + $\begin{matrix} ρ_{3}^{2} \end{matrix}$ - $\begin{matrix} ρ_{4}^{2} \end{matrix}$ )+1=0
6 2( $\begin{matrix} ρ_{1}^{2} \end{matrix}$ - $\begin{matrix} ρ_{2}^{2} \end{matrix}$ + $\begin{matrix} ρ_{3}^{2} \end{matrix}$ - $\begin{matrix} ρ_{4}^{2} \end{matrix}$ + $\begin{matrix} ρ_{5}^{2} \end{matrix}$ )-1=0

Table 2. Optimized three-ring structure
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Table 2. Optimized three-ring structure
ρ₁ ρ₂ R /λ S M
0.35 0.789 5.649 0.065 0.208
0.69 0.988 2.92 0.098 0.288
0.01 0.707 2.845 0.108 0.287

Table 3. Optimized four-ring structure
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Table 3. Optimized four-ring structure
ρ₁ ρ₂ ρ₃ R /λ S M
0.6 0.73 0.82 2.88 0.07 0.12
0.58 0.69 0.80 2.84 0.07 0.12
0.57 0.70 0.816 2.88 0.065 0.12
0.55 0.65 0.787 2.84 0.07 0.11

Table 4. Optimized five-ring structure
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Table 4. Optimized five-ring structure
ρ₁ ρ₂ ρ₃ ρ₄ R /λ S M
0.36 0.68 0.72 0.828 5.52 0.05 0.15
0.54 0.64 0.76 0.98 3.01 0.060 0.11
0.55 0.66 0.77 0.98 3.01 0.059 0.10
0.56 0.67 0.78 0.98 2.91 0.064 0.11

Table 5. Optimized six-ring structure
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Table 5. Optimized six-ring structure
ρ₁ ρ₂ ρ₃ ρ₄ ρ₅ R /λ S M
0.40 0.41 0.60 0.73 0.83 2.91 0.066 0.10
0.39 0.40 0.58 0.69 0.80 2.81 0.066 0.10
0.49 0.50 0.60 0.71 0.81 2.91 0.071 0.11
0.50 0.51 0.61 0.73 0.82 2.91 0.071 0.11

Table 6. Ring radii and R, S, M values corresponding to Fig. 6
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Table 6. Ring radii and R, S, M values corresponding to Fig. 6
Number of rings ρ₁ ρ₂ ρ₃ ρ₄ ρ₅ R /λ S M
2 0.707 37.046 0.525 0.088
3 0.01 0.707 37.036 0.525 0.088
4 0.59 0.65 0.758 35.034 0.392 0.153
5 0.56 0.62 0.73 0.981 38.037 0.332 0.174
6 0.5 0.54 0.69 0.73 0.774 35.284 0.376 0.079

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Wei Wang, Jianguang Wu, Xutao Mo, Xianshan Huang. Binary Annular Phase Plate Used to Generate Hollow Focal Field[J]. Laser & Optoelectronics Progress, 2019, 56(7): 070501

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