The generalized mean zone plate

Abstract

In this paper a generalized mean zone plate is proposed, which generates twin foci located at the positions satisfying the expression of the generalized mean, which includes the m-golden mean, precious mean, and so on. The generalized mean zone plate can be designed to generate twin foci with various position ratios. The diffraction properties of the generalized mean zone plates have been investigated with simulations and experiments. The results show that the ratio of the positions of the twin foci for the generalized mean zone plate can be designed with the selected zone plate parameters.

The Generation of Equal-Intensity and Multi-Focus Optical Vortices by a Composite Spiral Zone Plate

“…The rotating phase structure of optical vortices can be employed for manipulating the motion and rotation of particles. Accurate manipulation of microscopic particles can be achieved using optical vortices, such as optical rotation traps [9,10]. Additionally, applications of optical vortices in microscope imaging can provide higher resolution and better demonstration of fine Photonics 2024, 11, 466 2 of 11 structures and super-resolution microscope imaging can be accomplished by manipulating the phase and angular momentum of optical vortices [11][12][13].…”

Two pairs of twin foci with the golden mean generated by a modified Fibonacci zone plate

“…Another interesting way to generate twin foci with the golden mean is to implement a zone plate constructed by an m-bonacci sequence, which can have two foci with a position ratio related to the m-golden mean including the golden mean [26]. Moreover, generalized mean zone plates and kinoform generalized mean lenses are able to produce twin foci with the generalized mean including the golden mean [27,28]. Nevertheless, these zone plates based on the m-bonacci sequence cannot generate two pairs of twin foci with the golden mean.…”

An annular beam with segmented phase gradients generated by a modified spiral zone plate

“…Some methods have been proposed to generate optical vortices. For example, paraxial Laguerre-Gaussian laser beams carry a well-defined OAM [12]; a fabricated spiral phase plate with divided etching areas produces a doughnutshaped beam [13]; spiral zone plates and photon sieves with the binary phase structures generate the single optical vortex at the focal plane [14,15]; fractal zone plates are combined with spiral phase plates to produce a sequence of focused vortices along the propagation direction [5]; zone plates with helical phases provide the multiple optical vortices with equal intensity at the different planes [16][17][18]. In addition, an Laguerre-Gaussian mode with radial index p=0 appears as a ring of light whose radius R l depends on a topological charge l as = R w l 2 , l / where w is the beam's radius [19].…”

“…Furthermore, for an optical vortex created by dynamic holographic optical tweezers, R l obtained by averaging over angles and locating the radius of peak intensity scales linearly with the topological charge l [20]. However, the optical vortices produced by these methods [12][13][14][15][16][17][18][19][20] do not have the tailorable radii independent of ls and multiple OAM states at the defined focal plane. Recently, Sabatyan et al [21] proposed the radial phase shifted spiral zone plate, which is created by inserting a radial phase shift into the phase structure of a spiral zone plate and has the perfect vortex with a favorable radius, and found that the shifting parameter acts as a managing parameter for the vortex size.…”