Twin equal-intensity foci with the same resolution generated by a modified precious mean zone plate

Tian Xia; Shaohua Tao; Shaohua Tao; Shubo Cheng; Shubo Cheng

doi:10.1364/JOSAA.392166

Journal of the Optical Society of America A
Vol. 37,
Issue 6,
pp. 1067-1074
(2020)
•https://doi.org/10.1364/JOSAA.392166

Twin equal-intensity foci with the same resolution generated by a modified precious mean zone plate

Tian Xia, Shaohua Tao, and Shubo Cheng

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Tian Xia, Shaohua Tao, and Shubo Cheng, "Twin equal-intensity foci with the same resolution generated by a modified precious mean zone plate," J. Opt. Soc. Am. A 37, 1067-1074 (2020)

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Abstract

A modified precious mean zone plate (MPMZP) is proposed to generate twin equal-intensity foci with the same resolution related to the precious mean. The MPMZP with a bigger copy number $C$ can generate two equal-intensity foci with approximately the same resolution. The energy efficiencies of twin foci generated by the MPMZP are approximately the same. Moreover, the MPMZP with a helical phase can generate twin vortices with the same diameter. In addition, it is proven numerically that the MPMZP beam and the spiral-phase MPMZP beam have the self-reconstruction property. The construction method of the MPMZP is illustrated in detail. Moreover, it is proven in the simulations and experiments that twin equal-intensity foci generated by the MPMZP have the same resolution, and the spiral-phase MPMZP can produce twin vortices with the same diameter. The proposed zone plate can be used for optical lithography in two planes at the same extent, and applied to rotate different particles in two planes at the same speed and generate two of the same clear images at two planes related to the precious mean.

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	Modified Precious Mean Numbers	Precious Mean Numbers
Initial seeds	$N_{0} = 1$	$N_{0} = 1$
	$N_{1} = 2$	$N_{1} = C + 1$
Iteration rule	$N_{S} = C \cdot N_{S - 1} + N_{S - 2}$ ( $S \geq 2$ )

	Modified Precious Mean Numbers	Precious Mean Numbers
Initial seeds	$t_{0} = {1}$	$t_{0} = {1}$
	$t_{1} = {1, 0}$	$t_{1} = {\underset{C}{\underset{⏟}{11 \dots 1}} 0}$
Iteration rule	$t_{S} = {\underset{C}{\underset{⏟}{t_{S - 1} t_{S - 1} \dots t_{S - 1}}} t_{S - 2}} (S \geq 2)$

	MPMZPs			GMZPs
$C$	$S$	Ratios	$φ_{C} - C + 1$	$S$	Ratios	$φ_{C}$
1	9	1.6184	1.6180	9	1.6184	1.6180
2	5	1.4146	1.4142	5	2.4150	2.4142
3	4	1.2975	1.3028	5	3.2110	3.3028
4	4	1.2346	1.2361	3	4.2538	4.2361
5	4	1.1926	1.1926	3	5.2162	5.1926
6	3	1.1616	1.1623	3	6.1622	6.1623
7	3	1.1396	1.1401	3	7.1400	7.1401
8	3	1.1228	1.1231	2	8.2757	8.1231
9	3	1.1095	1.1098	3	9.1098	9.1098
10	3	1.0990	1.0990	2	10.3265	10.0990

	Focus at $u = 37.01$ (µm)	Focus at $u = 42.99$ (µm)	Ratios
FWHM	28.75	25	1.1500
Sizes	66.25	56.25	1.1778

	Diameters of Vortices at $u = 37.01$ (µm)	Diameters of Vortices at $u = 42.99$ (µm)	Ratios
Spiral-phase MPMZP of $l = 3$	88.75	76.25	1.1639
Spiral-phase MPMZP of $l = 5$	131.25	113.75	1.1538

	Size of the Focal Spot or Vortex at $z = 320 m m$ (µm)	Size of the Focal Spot or Vortex at $z = 375 m m$ (µm)	Ratios
MPMZP	50	60	1.2000
Spiral-phase MPMZP of $l = 3$	75	90	1.2000
Spiral-phase MPMZP of $l = 5$	115	130	1.1304

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Journal of the Optical Society of America A