Beam Shaping Method Based on Combined Gratings

Zhongsheng Zhai; Yi Zhang; Qinghua Lü; Xuanze Wang; Wei Feng; Zhi Xiong

doi:10.3788/CJL202249.1305001

Chinese Journal of Lasers, Volume. 49, Issue 13, 1305001(2022)

Beam Shaping Method Based on Combined Gratings

Zhongsheng Zhai^1、*, Yi Zhang¹, Qinghua Lü², Xuanze Wang¹, Wei Feng¹, and Zhi Xiong¹

¹Hubei Key Laboratory of Modern Manufacturing Quantity Engineering, School of Mechanical Engineering, Hubei University of Technology, Wuhan 430068, Hubei, China

²School of Science, Hubei University of Technology, Wuhan 430068, Hubei, China

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Figures & Tables(13)

Fig. 1. Schematic of experimental equipment

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Fig. 2. Schematics of shaping for different holograms. (a) Black hologram; (b) mask with external blazed grating (EBG); (c) mask with EBG and internal gradient grating (IGG)

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$Diffraction diagram of external grating$

Fig. 3. Diffraction diagram of external grating

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Fig. 4. Binary gratings with different gray levels. (a) h₁＝38; (b) h₂＝127; (c) h₃＝166

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Fig. 5. Intensity proportion of 0 order changed with gray level

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Fig. 6. Phase distribution. (a) Internal gradient binary grating; (b) gray profile of gradient binary grating

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$Schematic of orthogonal grating and diffraction. (a) Orthogonal grating hologram; (b) gradient orthogonal grating hologram; (c) schematic of orthogonal grating diffraction$

Fig. 7. Schematic of orthogonal grating and diffraction. (a) Orthogonal grating hologram; (b) gradient orthogonal grating hologram; (c) schematic of orthogonal grating diffraction

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Fig. 8. Phase holograms generated by four kinds of methods. (a) GS; (b) EBG-only; (c) EBG＋IGBG; (d) EBG＋IGOG

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Table 1. Comparison of diffraction efficiency of external gratings

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Table 1. Comparison of diffraction efficiency of external gratings

Grating	Formula of m-order diffraction efficiency
Sinusoidal grating	$η_{s ， m} ＝ J_{m}^{2} (\frac{q}{2})$ , where J is the Bessel function and q is the amplitude
Binary grating	$η_{b ， m} ＝ {sinc}^{2} (\frac{m π}{2})$
Blazed grating	$η_{g}_{， m} ＝ {sinc}^{2} (\frac{m π}{g})$ ，where g is the number of steps

Table 2. Shaping results for flattop hexagon with different methods
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Table 2. Shaping results for flattop hexagon with different methods
Method Shaping result
d＝1 mm d＝2 mm d＝3 mm d＝4 mm
GS
EBG-only
EBG＋IGBG
EBG＋IGOG

Table 3. Profile curves of shaping results with different methods
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Table 3. Profile curves of shaping results with different methods
Method Profile curve
d＝1 mm d＝2 mm d＝3 mm d＝4 mm
GS
EBG-only
EBG＋IGBG
EBG＋IGOG

Table 4. Energy efficiency of four shaping methods
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Table 4. Energy efficiency of four shaping methods
Shaping method Energy efficiency /%
d＝1 mm d＝2 mm d＝3 mm d＝4 mm
EBG＋IGBG 3.42 12.35 25.97 42.90
EBG＋IGOG 3.71 12.99 26.90 43.71
EBG-only 4.06 14.09 28.70 46.49
GS 72.10 70.63 68.93 68.62

Table 5. Beam nonuniformity of four shaping methods
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Table 5. Beam nonuniformity of four shaping methods
Shaping method Beam nonuniformity /%
d＝1 mm d＝2 mm d＝3 mm d＝4 mm
EBG＋IGBG 3.59 2.21 2.12 4.71
EBG＋IGOG 3.72 3.61 3.50 5.26
EBG-only 4.71 4.35 4.17 9.94
GS 19.57 18.97 12.79 21.50

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Zhongsheng Zhai, Yi Zhang, Qinghua Lü, Xuanze Wang, Wei Feng, Zhi Xiong. Beam Shaping Method Based on Combined Gratings[J]. Chinese Journal of Lasers, 2022, 49(13): 1305001

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