In order to obtain a super-resolution non-diffraction beam, we propose a fast searching method to design a ternary optical element combined with the circularly polarized light. The optimized results show that a beam with a spot size of 0.356λ and depth of focus of 8.28λ can be achieved by focusing with an oil lens of numerical aperture NA = 1.4 and refractive index of oil n = 1.5. The analysis reveals that the spot size of transverse component is 0.273λ, indicating that the super-resolution effect mainly comes from the transverse component. The spot size inside the media can theoretically reach down to 0.273λ because the spot size inside the media is mainly determined by the transverse component.
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