Binary Annular Phase Plate Used to Generate Hollow Focal Field

Wei Wang; Jianguang Wu; Xutao Mo; Xianshan Huang

doi:10.3788/LOP56.070501

Journals >Laser & Optoelectronics Progress >Volume 56 >Issue 7 >Page 070501 > Article

Laser & Optoelectronics Progress
Vol. 56, Issue 7, 070501 (2019)

Binary Annular Phase Plate Used to Generate Hollow Focal Field

Wei Wang^*, Jianguang Wu, Xutao Mo, and Xianshan Huang

Author Affiliations

School of Mathematics and Physics, Anhui University of Technology, Maanshan, Anhui 243032, China

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DOI: 10.3788/LOP56.070501 Cite this Article Set citation alerts

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 Copy Citation Text

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Fig. 1. Schematic for calculation of focal field

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Fig. 2. Light intensity distribution in focal plane for two-ring structure

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Fig. 3. Light intensity distributions in focal plane for three-ring structure. (a) R=5.65λ; (b) R=2.85λ

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

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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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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 1. Radius of each ring when generating hollow focal field

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 2. Optimized three-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 3. Optimized four-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 4. Optimized five-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 5. Optimized six-ring structure

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

Table 6. Ring radii and R, S, M values corresponding to Fig. 6

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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