“…Actually, this binary pure-phase CDG with single period is essentially a kind of binary pure-phase filter. When the phase shift is not an integral multiple of π, the intensity distribution of its focused field along axial orientation will become asymmetric and the focal shift effect will appear even in a Debye approximation [22,23]. So, in this paper, the phase shift of the binary-phase CDG is constant, and it is always set as π.…”
Circular Dammann grating (CDG) under high numerical aperture (NA) focusing is described based on Richards-Wolf vectorial diffraction theory in this paper. Several CDGs are presented under the condition of NA=0.9 with the illumination of circularly polarized plane-wave laser beams. Numerical results show that the sizes of these circular patterns with equal-intensity are in the wavelength scale, and doughnut-shaped central spots and dark rings are in the subwavelength width. To verify this kind of CDG, a binary pure-phase three-order CDG is fabricated to produce a dark center pattern surrounded by three concentric bright rings. The corresponding intensity distribution of the pattern on the focal plane of a high-NA objective (NA=0.9) is measured, and the results agree well with theoretical simulations. This kind of CDG with annular patterns of equal-intensity in the wavelength scale should be highly interesting for its potential applications in optical trapping, stimulated emission depletion (STED) microscopy, and the study of singular optics, as well as annular array illumination.
“…Actually, this binary pure-phase CDG with single period is essentially a kind of binary pure-phase filter. When the phase shift is not an integral multiple of π, the intensity distribution of its focused field along axial orientation will become asymmetric and the focal shift effect will appear even in a Debye approximation [22,23]. So, in this paper, the phase shift of the binary-phase CDG is constant, and it is always set as π.…”
Circular Dammann grating (CDG) under high numerical aperture (NA) focusing is described based on Richards-Wolf vectorial diffraction theory in this paper. Several CDGs are presented under the condition of NA=0.9 with the illumination of circularly polarized plane-wave laser beams. Numerical results show that the sizes of these circular patterns with equal-intensity are in the wavelength scale, and doughnut-shaped central spots and dark rings are in the subwavelength width. To verify this kind of CDG, a binary pure-phase three-order CDG is fabricated to produce a dark center pattern surrounded by three concentric bright rings. The corresponding intensity distribution of the pattern on the focal plane of a high-NA objective (NA=0.9) is measured, and the results agree well with theoretical simulations. This kind of CDG with annular patterns of equal-intensity in the wavelength scale should be highly interesting for its potential applications in optical trapping, stimulated emission depletion (STED) microscopy, and the study of singular optics, as well as annular array illumination.
“…At present, the conventional methods represented by simulated annealing algorithm and genetic algorithm are the mainstream methods to design modulators. Such methods usually include the definition of fitness function, parameter scanning and other processes [13,[15][16][17][18], which are not only time-consuming and computational resourceconsuming, but also not adaptive.…”
The radially polarized beams are modulated by phase-type optical needle modulators can be tightly focused to create needle-like focused beams, which are called optical needles. The use of optical needles with different resolutions and focal depths as direct writing heads for laser direct lithography enables periodic, cross-scale processing of high aspect ratio micro-nano structures with different line widths. The design of the phase-type optical needle modulators is the key to obtain optical needles with different resolutions and focal depths. However, the existing conventional methods for designing phase-type optical needle modulators rely on the physical model for generating optical needles and the defined fitness function, which makes their design time long and not adaptive. Based on the deep learning, a novel phase-type optical needle modulator design (PONMD) approach is proposed in this paper. The results show that the PONMD method takes 0.5526ms to design a phase-type optical needle modulator, and the similarity between the designed and target values is 96.73%. Compared with the conventional methods, the time consumption is reduced by about 8 orders of magnitude, and the similarity is improved by 11.19%. The PONMD approach has the advantages of adaptability, more efficient, less timeconsuming, and less computational resource-consuming.
“…Yun et al [14] and Zhang et al [15] presented a method through solving the nonlinear equations, but this method requires an estimated value and cannot ensure that we obtain the global optimal solution. Yu et al [16] made use of the constraint simulation annealing algorithm and got good results, but the computational cost is large. In this work, we proposed an algorithm to design the ternary optical element based on rigorous vectorial diffraction theory.…”
We proposed a method to design a ternary optical element in order to achieve a needle of super-resolution longitudinally polarized beam with ultra-long depth of focus, and obtained a beam with a size of 0.3995λ and depth of focus of 12.83λ after focusing a ternary optical element modulated, radially polarized Bessel-Gaussian beam with an aplanatic lens of numerical aperture 0.95. The algorithm we used to design the ternary optical element is based on axial uniformity in the focal region, which allows rapid searching speeds and excellent performance. The ratio of pupil radius to the beam waist was set as 0.57, making the peak intensity of the incident beam occur at the rim of the lens aperture, which maximized the possible resolution of the focused beam.
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