# Generating Convergent Laguerre-Gaussian Beams Based on an Arrayed Convex Spiral Phaser Fabricated by 3D Printing

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## Abstract

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## 1. Introduction

## 2. Structure Design, Fabrication and Topography Measurement

#### 2.1. Design and Fabrication

_{0}represents the refractive index of the surrounding medium, and n the refractive index of the material for constructing the structure mentioned above, and λ the wavelength of incident light beams, and l the TC. Among them, l is generally an integer. If H is not an integer corresponding to the wavelength, the phase of incident beams at each phase step will be discontinuous, so as to destroy the circular intensity distribution of the transmitted light [39,40,41,42]. We set the central wavelength at ~650 nm, where the refractive index of Nanoscribe IP-Dip is 1.545 and the l being 5, and then the parameter H = 5.963 μm can be calculated. The value of the key parameters are shown in Table 1:

#### 2.2. Topography Measurement

## 3. Experimental Measurement

## 4. Discussion

_{0}the beam waist radius of the Gaussian beam, and z the transmission distance, and k the wave number [46].

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Parameter configuration: r being the curvature radius of the upper surface of the convex spiral phaser and D the diameter of the bottom circle and H the height of the cut surface and d the height of the base.

**Figure 4.**Measured overall morphology of the sample fabricated. (

**a**) Two-dimensional topography, and (

**b**) three-dimensional topography.

**Figure 5.**Appearance of a CSPA with a period of 25 μm. (

**a**) Two-dimensional topography and (

**b**) three-dimensional topography and both the surface profiles indicating the height or depth by (

**c**) and the featured horizontal size by (

**d**).

**Figure 6.**The CSPA with a 30 μm period. (

**a**) Two-dimensional topography and (

**b**) three-dimensional topography and both the surface profiles indicating the height or depth by (

**c**) and the featured horizontal size by (

**d**).

**Figure 10.**(

**a**) Schematic diagram of the distance between CASP and the light field detection plane. The light intensity distribution of a center wavelength in the range of 635–671 nm laser beams, when the distance d is: (

**b**) 200 μm, (

**c**) 300 μm, (

**d**) 380 μm, (

**e**) 400 μm, (

**f**) 500 μm, (

**g**) 600 μm, (

**h**) 3000 μm, and (

**i**) 10,000 μm, respectively.

**Figure 11.**The three-dimension light intensity distribution of the laser beams with a center wavelength in the range of 635–671 nm, when the distance is: (

**a**) 300 μm, (

**b**) 400 μm, (

**c**) 600 μm, and (

**d**) 2500 μm, respectively. The scan and enlarged view of the annular LG beam at the focus, when the distance is: (

**e**) 300 μm, (

**f**) 400 μm, (

**g**) 600 μm, and (

**h**) 2500 μm, respectively.

**Figure 12.**The light intensity distribution of the laser beams with a center wavelength in the range of 501–561 nm, when the distance is: (

**a**) 300 μm, (

**c**) 390 μm, (

**e**) 500 μm, and (

**g**) 10,000 μm, respectively. The light intensity distribution of the laser beams with a center wavelength in the range of 430–473 nm, when the distance is: (

**b**) 300 μm, (

**d**) 380 μm, (

**f**) 500 μm, and (

**h**) 10,000 μm, respectively.

**Figure 13.**The three-dimension light intensity distribution of the laser beams with a center wavelength in the range of 501–561 nm, when the distance is: (

**a**) 300 μm, (

**c**) 390 μm, (

**e**) 450 μm, and (

**g**) 3000 μm, respectively. The light intensity distribution of the laser beam with a center wavelength in the range of 430–473 nm, when the distance is: (

**b**) 300 μm, (

**d**) 380 μm, (

**f**) 440 μm, and (

**h**) 3000 μm, respectively.

Parameter | Value (μm) |
---|---|

r | 200 |

R | 20 |

d | 2 |

H | 5.963 |

Rp | Rv | Rz | Ra | Rq | Rsk | Rku | RΔq | RSm | |
---|---|---|---|---|---|---|---|---|---|

Seg.1 | 0.09 μm | 0.10 μm | 0.19 μm | 4.17 μm | 4.17 μm | 1.0002 | 1.0005 | 0.1922 | 0.00 μm |

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## Share and Cite

**MDPI and ACS Style**

Liu, C.; Hu, C.; Wei, D.; Chen, M.; Shi, J.; Wang, H.; Xie, C.; Zhang, X.
Generating Convergent Laguerre-Gaussian Beams Based on an Arrayed Convex Spiral Phaser Fabricated by 3D Printing. *Micromachines* **2020**, *11*, 771.
https://doi.org/10.3390/mi11080771

**AMA Style**

Liu C, Hu C, Wei D, Chen M, Shi J, Wang H, Xie C, Zhang X.
Generating Convergent Laguerre-Gaussian Beams Based on an Arrayed Convex Spiral Phaser Fabricated by 3D Printing. *Micromachines*. 2020; 11(8):771.
https://doi.org/10.3390/mi11080771

**Chicago/Turabian Style**

Liu, Chang, Chai Hu, Dong Wei, Mingce Chen, Jiashuo Shi, Haiwei Wang, Changsheng Xie, and Xinyu Zhang.
2020. "Generating Convergent Laguerre-Gaussian Beams Based on an Arrayed Convex Spiral Phaser Fabricated by 3D Printing" *Micromachines* 11, no. 8: 771.
https://doi.org/10.3390/mi11080771