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We propose a method for creating a three-dimensional (3D) shape-controllable focal spot array by combination of a two-dimensional (2D) pure-phase modulation grating and an additional axial shifting pure-phase modulation composed of four-quadrant phase distribution unit at the back aperture of a high numerical aperture (NA) objective. It is demonstrated that the one-dimensional (1D) grating designed by optimized algorithm of selected number of equally spaced arbitrary phase value in a single period could produce desired number of equally spaced diffraction spot with identical intensity. It is also shown that the 2D pure-phase grating designed with this method could generate 2D diffraction spot array. The number of the spots in the array along each of two dimensions depends solely on the number of divided area with different phase values of the dimension. We also show that, by combining the axial translation phase modulation at the back aperture, we can create 3D focal spot array at the focal volume of the high NA objective. Furthermore, the shape or intensity distribution of each focal spot in the 3D focal array can be manipulated by introducing spatially shifted multi vortex beams as the incident beam. These kinds of 3D shape-controllable focal spot array could be utilized in the fabrication of artificial metamaterials, in parallel optical micromanipulation and multifocal multiphoton microscopic imaging.

We present a method to generate multiple three-dimensional (3D) dark focal spots along the optical axis by focusing a cylindrical vector beam. The formation of uniform 3D dark spots is determined by optimizing three parameters of the pupil filter in the wavefront of the lens and the polarized state of the incident cylindrical vector beam. By adjusting the three parameters of the pupil filter, the number and position of dark spots can be controlled willingly, and the uniformity of dark spots can be adjusted by modulating the polarized state of the incident cylindrical vector beam. A single dark spot with uniform surrounding intensity is formed and double dark spots are also obtained with the proper parameters and can be separated with an equal distance away from the geometric focus. Moreover, multiple dark spots numbering up to six are formed along the optical axis. The size of each 3D dark spot is almost the same, and the central light intensity of the dark spots is nearly zero while the light intensity surrounding around is almost uniform. This work may find valuable application in particle trapping, microscopes, optical engineering, and so on.

A light beam propagating over an infinite anti-diffracting distance requires infinite power to preserve its shape. However, the fundamental barrier of finite power in free space has made the problem of diffraction insurmountable in recent decades. To overcome this limitation, we report an approach that employs the multiple energy oscillation mechanism, thereby permitting the creation of a light beam with an ultralong anti-diffracting distance in free space. A versatile optical pen is therefore developed to manipulate the number, amplitude, position and phase of energy oscillations for a focusing lens so that multiple energy oscillations can be realized. A light beam with a tunable number of energy oscillations is eventually generated in free space and propagates along a wavy trajectory. This work will enable the extension of non-diffractive light beams to an expanded realm and facilitate extensive developments in optics and other research fields, such as electronics and acoustics.

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