Customized Design of Aperiodic Liquid Crystal Grating for Generation of Multiple Optical Patterns
Abstract
:1. Introduction
2. Theory and Methodology
2.1. Design Principle of LC Gratings Based on PB Phase
2.2. The Binary Particle Swarm Optimization Algorithm
3. Results and Discussion
3.1. LC Grating for Needle Beam
3.2. LC Grating for Linear Multi-Foci
3.3. LC Grating for Hollow Beam
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Number | Position (μm) | Number | Position (μm) | Number | Position (μm) | Number | Position (μm) | Number | Position (μm) | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Inner | Outer | Inner | Outer | Inner | Outer | Inner | Outer | Inner | Outer | |||||
1 | 0 | 2 | 19 | 28 | 30 | 37 | 47.5 | 49 | 55 | 64.5 | 69 | 73 | 85.5 | 86 |
2 | 2 | 2.5 | 20 | 30 | 31 | 38 | 49 | 50 | 56 | 69 | 70 | 74 | 86 | 87 |
3 | 2.5 | 4.5 | 21 | 31 | 34 | 39 | 50 | 51 | 57 | 70 | 70.5 | 75 | 87 | 88 |
4 | 4.5 | 6.5 | 22 | 34 | 35 | 40 | 51 | 51.5 | 58 | 70.5 | 72 | 76 | 88 | 88.5 |
5 | 6.5 | 12 | 23 | 35 | 37 | 41 | 51.5 | 52.5 | 59 | 72 | 72.5 | 77 | 88.5 | 89 |
6 | 12 | 12.5 | 24 | 37 | 37.5 | 42 | 52.5 | 53 | 60 | 72.5 | 73 | 78 | 89 | 90 |
7 | 12.5 | 14 | 25 | 37.5 | 38 | 43 | 53 | 53.5 | 61 | 73 | 73.5 | 79 | 90 | 90.5 |
8 | 14 | 14.5 | 26 | 38 | 38.5 | 44 | 53.5 | 55 | 62 | 73.5 | 75.5 | 80 | 90.5 | 92 |
9 | 14.5 | 15 | 27 | 38.5 | 39 | 45 | 55 | 57 | 63 | 75.5 | 76.5 | 81 | 92 | 94.5 |
10 | 15 | 15.5 | 28 | 39 | 39.5 | 46 | 57 | 57.5 | 64 | 76.5 | 79.5 | 82 | 94.5 | 96 |
11 | 15.5 | 19 | 29 | 39.5 | 40 | 47 | 57.5 | 59 | 65 | 79.5 | 80 | 83 | 96 | 97 |
12 | 19 | 21.5 | 30 | 40 | 40.5 | 48 | 59 | 59.5 | 66 | 80 | 81 | 84 | 97 | 97.5 |
13 | 21.5 | 22 | 31 | 40.5 | 41.5 | 49 | 59.5 | 61 | 67 | 81 | 81.5 | 85 | 97.5 | 99.5 |
14 | 22 | 22.5 | 32 | 41.5 | 42.5 | 50 | 61 | 61.5 | 68 | 81.5 | 82 | 86 | 99.5 | 100 |
15 | 22.5 | 25 | 33 | 42.5 | 43.5 | 51 | 61.5 | 63 | 69 | 82 | 83 | |||
16 | 25 | 25.5 | 34 | 43.5 | 44.5 | 52 | 63 | 63.5 | 70 | 83 | 83.5 | |||
17 | 25.5 | 26 | 35 | 44.5 | 47 | 53 | 63.5 | 64 | 71 | 83.5 | 84.5 | |||
18 | 26 | 28 | 36 | 47 | 47.5 | 54 | 64 | 64.5 | 72 | 84.5 | 85.5 |
Number | Position (μm) | Number | Position (μm) | Number | Position (μm) | Number | Position (μm) | Number | Position (μm) | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Inner | Outer | Inner | Outer | Inner | Outer | Inner | Outer | Inner | Outer | |||||
1 | 0 | 1.5 | 23 | 20 | 20.5 | 45 | 37.5 | 38.5 | 67 | 58.5 | 59 | 89 | 78 | 78.5 |
2 | 1.5 | 2.5 | 24 | 20.5 | 21.5 | 46 | 38.5 | 39.5 | 68 | 59 | 59.5 | 90 | 78.5 | 80.5 |
3 | 2.5 | 3.5 | 25 | 21.5 | 22 | 47 | 39.5 | 40 | 69 | 59.5 | 61 | 91 | 80.5 | 82 |
4 | 3.5 | 5.5 | 26 | 22 | 24 | 48 | 40 | 40.5 | 70 | 61 | 61.5 | 92 | 82 | 83.5 |
5 | 5.5 | 6 | 27 | 24 | 24.5 | 49 | 40.5 | 41 | 71 | 61.5 | 62 | 93 | 83.5 | 84.5 |
6 | 6 | 6.5 | 28 | 24.5 | 25.5 | 50 | 41 | 41.5 | 72 | 62 | 62.5 | 94 | 84.5 | 86 |
7 | 6.5 | 7 | 29 | 25.5 | 26 | 51 | 41.5 | 42.5 | 73 | 62.5 | 63 | 95 | 86 | 87 |
8 | 7 | 8 | 30 | 26 | 26.5 | 52 | 42.5 | 43.5 | 74 | 63 | 67.5 | 96 | 87 | 88.5 |
9 | 8 | 8.5 | 31 | 26.5 | 28 | 53 | 43.5 | 45 | 75 | 67.5 | 68 | 97 | 88.5 | 89 |
10 | 8.5 | 9.5 | 32 | 28 | 29 | 54 | 45 | 46.5 | 76 | 68 | 68.5 | 98 | 89 | 92.5 |
11 | 9.5 | 10 | 33 | 29 | 30.5 | 55 | 46.5 | 48 | 77 | 68.5 | 69 | 99 | 92.5 | 93 |
12 | 10 | 11 | 34 | 30.5 | 31 | 56 | 48 | 49 | 78 | 69 | 70 | 100 | 93 | 94.5 |
13 | 11 | 12 | 35 | 31 | 32 | 57 | 49 | 49.5 | 79 | 70 | 70.5 | 101 | 94.5 | 95.5 |
14 | 12 | 12.5 | 36 | 32 | 32.5 | 58 | 49.5 | 50.5 | 80 | 70.5 | 72 | 102 | 95.5 | 96 |
15 | 12.5 | 13.5 | 37 | 32.5 | 33 | 59 | 50.5 | 52 | 81 | 72 | 72.5 | 103 | 96 | 96.5 |
16 | 13.5 | 16.5 | 38 | 33 | 33.5 | 60 | 52 | 53.5 | 82 | 72.5 | 74.5 | 104 | 96.5 | 97 |
17 | 16.5 | 17 | 39 | 33.5 | 34 | 61 | 53.5 | 55 | 83 | 74.5 | 75 | 105 | 97 | 97.5 |
18 | 17 | 17.5 | 40 | 34 | 34.5 | 62 | 55 | 55.5 | 84 | 75 | 75.5 | 106 | 97.5 | 98 |
19 | 17.5 | 18 | 41 | 34.5 | 35 | 63 | 55.5 | 56 | 85 | 75.5 | 76.5 | 107 | 98 | 98.5 |
20 | 18 | 18.5 | 42 | 35 | 36.5 | 64 | 56 | 57 | 86 | 76.5 | 77 | 108 | 98.5 | 99 |
21 | 18.5 | 19 | 43 | 36.5 | 37 | 65 | 57 | 57.5 | 87 | 77 | 77.5 | 109 | 99 | 100 |
22 | 19 | 20 | 44 | 37 | 37.5 | 66 | 57.5 | 58.5 | 88 | 77.5 | 78 |
Number | Position (μm) | Number | Position (μm) | Number | Position (μm) | Number | Position (μm) | Number | Position (μm) | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Inner | Outer | Inner | Outer | Inner | Outer | Inner | Outer | Inner | Outer | |||||
1 | 0 | 2 | 20 | 22 | 22.5 | 39 | 40 | 41.5 | 58 | 59 | 59.5 | 77 | 85 | 85.5 |
2 | 2 | 3 | 21 | 22.5 | 25.5 | 40 | 41.5 | 42 | 59 | 59.5 | 60.5 | 78 | 85.5 | 86 |
3 | 3 | 4 | 22 | 25.5 | 27 | 41 | 42 | 43 | 60 | 60.5 | 61.5 | 79 | 86 | 86.5 |
4 | 4 | 4.5 | 23 | 27 | 27.5 | 42 | 43 | 43.5 | 61 | 61.5 | 62 | 80 | 86.5 | 88 |
5 | 4.5 | 5.5 | 24 | 27.5 | 28 | 43 | 43.5 | 45 | 62 | 62 | 63 | 81 | 88 | 89.5 |
6 | 5.5 | 6 | 25 | 28 | 30 | 44 | 45 | 45.5 | 63 | 63 | 64.5 | 82 | 89.5 | 90 |
7 | 6 | 8 | 26 | 30 | 30.5 | 45 | 45.5 | 46.5 | 64 | 64.5 | 65.5 | 83 | 90 | 91 |
8 | 8 | 8.5 | 27 | 30.5 | 31 | 46 | 46.5 | 47.5 | 65 | 65.5 | 67 | 84 | 91 | 91.5 |
9 | 8.5 | 9.5 | 28 | 31 | 31.5 | 47 | 47.5 | 49.5 | 66 | 67 | 68 | 85 | 91.5 | 92 |
10 | 9.5 | 10 | 29 | 31.5 | 32 | 48 | 49.5 | 50 | 67 | 68 | 70.5 | 86 | 92 | 92.5 |
11 | 10 | 11 | 30 | 32 | 33 | 49 | 50 | 50.5 | 68 | 70.5 | 71 | 87 | 92.5 | 93 |
12 | 11 | 11.5 | 31 | 33 | 34.5 | 50 | 50.5 | 51 | 69 | 71 | 72.5 | 88 | 93 | 93.5 |
13 | 11.5 | 13.5 | 32 | 34.5 | 35 | 51 | 51 | 52 | 70 | 72.5 | 73.5 | 89 | 93.5 | 95 |
14 | 13.5 | 15.5 | 33 | 35 | 35.5 | 52 | 52 | 53.5 | 71 | 73.5 | 75 | 90 | 95 | 95.5 |
15 | 15.5 | 16 | 34 | 35.5 | 36.5 | 53 | 53.5 | 55.5 | 72 | 75 | 76 | 91 | 95.5 | 97.5 |
16 | 16 | 16.5 | 35 | 36.5 | 38.5 | 54 | 55.5 | 56 | 73 | 76 | 76.5 | 92 | 97.5 | 99 |
17 | 16.5 | 20 | 36 | 38.5 | 39 | 55 | 56 | 57.5 | 74 | 76.5 | 77.5 | 93 | 99 | 100 |
18 | 20 | 21 | 37 | 39 | 39.5 | 56 | 57.5 | 58.5 | 75 | 77.5 | 84 | |||
19 | 21 | 22 | 38 | 39.5 | 40 | 57 | 58.5 | 59 | 76 | 84 | 85 |
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Liu, C.; Guo, Z.; Wu, J.; Yuan, D.; Zhou, G.; Tang, B.; Ye, H. Customized Design of Aperiodic Liquid Crystal Grating for Generation of Multiple Optical Patterns. Crystals 2023, 13, 300. https://doi.org/10.3390/cryst13020300
Liu C, Guo Z, Wu J, Yuan D, Zhou G, Tang B, Ye H. Customized Design of Aperiodic Liquid Crystal Grating for Generation of Multiple Optical Patterns. Crystals. 2023; 13(2):300. https://doi.org/10.3390/cryst13020300
Chicago/Turabian StyleLiu, Chen, Zhenghao Guo, Jun Wu, Dong Yuan, Guofu Zhou, Biao Tang, and Huapeng Ye. 2023. "Customized Design of Aperiodic Liquid Crystal Grating for Generation of Multiple Optical Patterns" Crystals 13, no. 2: 300. https://doi.org/10.3390/cryst13020300
APA StyleLiu, C., Guo, Z., Wu, J., Yuan, D., Zhou, G., Tang, B., & Ye, H. (2023). Customized Design of Aperiodic Liquid Crystal Grating for Generation of Multiple Optical Patterns. Crystals, 13(2), 300. https://doi.org/10.3390/cryst13020300