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

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.