Fig 1.
Schematic diagrams of the designed elements and the design process of the QSGSZPs.
(a) Structure of the SZPs. (b) – (d) Design workflow for the proposed QSGSZPs: (b) the continuous transmittance profile of the GaborSZPs, (c) the partitioning of the profile into discrete square cells, and (d) the final binary structure of the QSGSZPs after the binarization operation.
Fig 2.
The comparison of the simulated diffraction performance.
(a) – (c) The normalized intensity distributions for the SZPs, GaborSZPs, and QSGSZPs at the focal plane, respectively. The x and y axes represent the spatial coordinates, and the color bar indicates the normalized intensity. (d) – (f) The corresponding spiral phase distributions corresponding to (a) – (c). The color bar indicates the phase value in radians. (g) – (i) The cross-sectional diffraction intensity distributions along the propagation from z = 10 mm to z = 250 mm corresponding to (a) – (c). The x-axis represents the propagation distance z, and the y-axis represents the radial distance from the optical axis.
Fig 3.
The axial simulated diffraction intensity of the yellow dashed line in Figs 2 (g) –2(i).
The x-axis represents the propagation distance z and the y-axis represents the normalized diffraction intensity on the optical axis.
Fig 4.
Simulation study on the effect of the square size S on the performance of the QSGSZPs.
(a) – (c) Normalized intensity distributions at the focal plane for S = 2.5 μm × 2.5 μm, 5 μm × 5 μm and 10 μm × 10 μm, respectively. (d) – (f) The cross-sectional diffraction intensity of the QSGSZPs along the propagation from z = 10 mm to z = 250 mm corresponding to (a) – (c).
Fig 5.
Simulated intensity distributions of complex vortices generated by the QSGSZPs with different topological charges (l1, l2).
(a) – (l) The topological charges of the QSGSZPs are as follows: (l1 = 2, l2 = 0), (l1 = 2, l2 = 1), (l1 = 2, l2 = 2), (l1 = 2, l2 = 3), (l1 = 2, l2 = 4), (l1 = 2, l2 = 5), (l1 = 2, l2 = −1), (l1 = 2, l2 = −2), (l1 = 2, l2 = −3), (l1 = 2, l2 = −4), (l1 = 2, l2 = −5), and (l1 = 2, l2 = −6), respectively.The parameters l1 is fixed at 2 while l2 is varied.
Fig 6.
Simulated phase distributions corresponding to the intensity patterns shown in Fig 5.
(a) – (l) The topological charges of the QSGSZPs are as follows: (l1 = 2, l2 = 0), (l1 = 2, l2 = 1), (l1 = 2, l2 = 2), (l1 = 2, l2 = 3), (l1 = 2, l2 = 4), (l1 = 2, l2 = 5), (l1 = 2, l2 = −1), (l1 = 2, l2 = −2), (l1 = 2, l2 = −3), (l1 = 2, l2 = −4), (l1 = 2, l2 = −5), and (l1 = 2, l2 = −6), respectively. The topological charges accumulated along the black and red circles correspond to the minimum and maximum values of l1 and l2, respectively.
Fig 7.
Simulated edge-enhanced imaging performance.
A comparative analysis of the imaging produced by the FZPs (Figs 7 (a1) – (d1) and (a2) – (d2)), SZPs (Figs 7 (a3) – (d3) and (a4) – (d4)), and QSGSZPs (Figs 7 (a5) – (d5) and (a6) – (d6)) under various aperture shapes. For each aperture shape (semicircular, triangular, rectangular, circular), the images show the intensity distribution at the position of first-order (f) and third-order (f/3) focal planes.
Fig 8.
Simulation of optical communication multiplexing and demultiplexing.
(a, d) Simulated carrier multiplexing patterns for the SZPs and QSGSZPs, respectively. The x and y axes represent spatial coordinates in the beam cross-section. (b, c, e, f) Demultiplexing patterns after a forked grating, shown in 3D (height represents intensity) and 2D (color represents intensity) views for the SZPs and QSGSZPs, respectively.
Fig 9.
Fabrication process and experimental setup.
(a) Design pattern of the QSGSZPs. (b) Experimental microscopy image of the fabricated sample on a quartz substrate. The scale bar indicates the spatial scale. (c) Enlarged experimental view of the area in the black rectangle in (b), showing the fine binary square structure. (d) Schematic of the experimental setup. The optical path, from left to right, consists of a laser, a beam expander, a diaphragm, the QSGSZPs, a CCD camera, and a computer.
Fig 10.
Experimental validation of high-order diffraction suppression.
(a) – (d) The recorded intensity distributions of the SZPs and the QSGSZPs at the position of f and f/3, respectively. The x and y axes correspond to the pixel coordinates of the CCD, representing spatial position in the image plane. (e) The intensity distributions of the red dotted lines corresponding to (a) – (d).
Fig 11.
Experimental results of complex vortex generation.
Recorded intensity distributions for the QSGSZPs with varying topological charges (l1, l2), corresponding to the simulations in Fig 5. (a) – (l) The topological charges of the QSGSZPs are as follows: (l1 = 2, l2 = 0), (l1 = 2, l2 = 1), (l1 = 2, l2 = 2), (l1 = 2, l2 = 3), (l1 = 2, l2 = 4), (l1 = 2, l2 = 5), (l1 = 2, l2 = −1), (l1 = 2, l2 = −2), (l1 = 2, l2 = −3), (l1 = 2, l2 = −4), (l1 = 2, l2 = −5), and (l1 = 2, l2 = −6), respectively. The parameters l1 is fixed at 2 while l2 is varied.
Fig 12.
Experimental characterization of the topological charge.
(a) – (c) Experimental interference patterns obtained after passing the vortex beams with topological charges of l = 2, = 4 and 6 through a cylindrical lens, respectively. (d) shows the intensity distribution along the red dashed line path between points A and B corresponding to (a) – (c). The positions of the dark fringes correspond to the purple dashed circles, and the number of these circles corresponds to the topological charge.