# Holographic Tailoring of Structured Light Field with Digital Device

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results and Discussion

#### 3.1. Precision of Holographic Tailoring

#### 3.2. Efficiency of Holographic Tailoring

#### 3.3. Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Generation of Pure Phase Holograms

## Appendix B. Generation of Binary Amplitude Holograms

## References

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**Figure 2.**An example of constructing CGH hologram, (

**a**–

**d**) are construction method for PP-CGH (where ${J}_{1}^{-1}$ is inverse of $1st$ Bessel function), (

**e**–

**h**) are construction method for BA-CGH and (

**d**,

**h**) are phase gray hologram and binary amplitude hologram of ${\mathrm{LG}}_{0}^{10}$, respectively.

**Figure 3.**Schematic diagram of PP-CGH and BA-CGH for generating structured light. (

**a**,

**b**) show that the input beam is modulated and diffracted into multiple orders for the binary amplitude hologram and phase gray hologram, respectively. (

**c**) shows the partially separated orders on the far-field pattern of binary amplitude or phase gray diffracted hologram of ${\mathrm{LG}}_{0}^{10}$ mode by illuminating a plane wavefront, while the intensity and phase of target beam are inserted in the upper left corner. (

**d**,

**e**) shows the reconstructed intensity and phase by extracting the +1st diffraction order for PP-CGH and BA-CGH, respectively.

**Figure 4.**Schematic of reconstructed vortex beam under discretized azimuthal phase. (

**a**) The phase sampling in a finite resolution $(40\times 40)$ phase diagram, (

**b**) the discretized azimuthal phase with different pixels, (

**c**) intensity of the vortex light field with different radii, where (

**d**,

**e**) are the intensity, phase and OAM spectrum of the reconstructed field. (

**b1**–

**e1**,

**b2**–

**e2**and

**b3**–

**e3**correspond to the optical field radius proportion of $25\%$, $50\%$ and $80\%$, respectively, relative to the computational aperture).

**Figure 5.**The complex amplitude correlation degree of vortex beam versus different TCs and different available pixel numbers for PP-CGH (

**a**) and BA-CGH (

**b**).

**Figure 6.**Tailored efficiency of holographic generation for vortex beams. (

**a**) Bar chart of tailoring efficiency for PP-CGH and BA-CGH methods, (

**b**) ratio of tailoring efficiencies of two methods, (

**c**) the ratio of target light field energy to energy within the computational aperture and (

**d**) extraction efficiency of target light field for PP-CGH and BA-CGH methods.

**Figure 7.**Schematic of tailoring of vortex beams ($\ell =10$) with PP-CGH and BA-CGH methods, (

**a**) energy of target is $100\%$, (

**b**–

**d**) and (

**e**–

**g**) are the modulated normalized light field distribution of input light, 0th order, and +1st order in the PP-CGH and BA-CGH method, respectively, while extraction efficiencies (inserted in upper right coner) of PP-CGH method and BA-CGH method are 30% and $11\%$, respectively.

Modulator | $\mathbf{Lc}\text{-}\mathbf{SLM}$ | DMD |
---|---|---|

Traits | Low refresh rate (50–500 Hz); polarization-sensitive; wavelength-sensitive; temperature-sensitive; relatively high efficiency(≤20%); expensive | High refresh rate (10 kHz–30 kHz); polarization-insensitive; wavelength-insensitive; temperature-insensitive; low efficiency(≤5%); relatively cheap |

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**MDPI and ACS Style**

Wan, Z.; Shi, Z.; Liu, Q.; Fu, X.
Holographic Tailoring of Structured Light Field with Digital Device. *Photonics* **2022**, *9*, 506.
https://doi.org/10.3390/photonics9070506

**AMA Style**

Wan Z, Shi Z, Liu Q, Fu X.
Holographic Tailoring of Structured Light Field with Digital Device. *Photonics*. 2022; 9(7):506.
https://doi.org/10.3390/photonics9070506

**Chicago/Turabian Style**

Wan, Zhensong, Zijian Shi, Qiang Liu, and Xing Fu.
2022. "Holographic Tailoring of Structured Light Field with Digital Device" *Photonics* 9, no. 7: 506.
https://doi.org/10.3390/photonics9070506