We describe a kind of true 3D array of focused vortices with tunable topological charge, called the 3D Dammann vortex array. This 3D Dammann vortex array is arranged into the structure of a true 3D lattice in the focal region of a focusing objective, and these focused vortices are located at each node of the 3D lattice. A scheme based on a Dammann vortex grating (DVG) and a mirror is proposed to provide a choice for changing the topological charge of the 3D Dammann vortex array. For experimental demonstration, a 5×5×5 Dammann vortex array is implemented by combining a 1×7 DVG, a 1×5 Dammann zone plate, and another 5×5 Dammann grating. The topological charge of this Dammann vortex array can be tuned (from -2 to +2 with an interval of +1) by moving and rotating the mirror to select different diffraction orders of the 1×7 DVG as the incident beam. Because of these attractive properties, this 3D Dammann vortex array should be of high interest for its potential applications in various areas, such as 3D simultaneous optical manipulation, 3D parallel vortex scanning microscope, and also parallel vortex information transmission.

We introduce the Dammann phase-encoding method into original distorted gratings and propose a modified distorted grating, called a distorted Dammann grating (DDG), to realize multiplane imaging of several tens of layers within the object field onto a single image plane. This property implies that the DDG makes it possible to achieve simultaneously high axial resolving power and large axial imaging range without scanning. This DDG should be of high interest for its potential applications in real-time three-dimensional optical imaging and tracking. Multiplane imaging of 7×7 object layers onto a single camera plane is experimentally demonstrated using a 7×7 DDG for an objective of NA=0.127.

Modal analysis of the reflective wideband grating with high efficiency of the negative first order in Littrow mounting is presented. The reflective grating consists of a highly reflective mirror and a transmission grating on the top. The modal analysis is carried out for TE polarization and it reveals that two modes are excited in the transmission grating. Using the two modes and ignoring the absorption of the mirror, a simple expression of diffraction efficiency of the reflective grating is derived and thus the grating depth to achieve high efficiency of the negative first order is obtained. The influence of duty cycle on the difference of effective indices of the two modes for different wavelengths is analyzed, which can explain the wideband behavior of reflective gratings. The modal analysis should be a useful tool for the design of high-efficiency wideband reflective gratings

We propose a new diffractive optical element, called a spiral Dammann zone plate (SDZP), to generate a series of dipole vortices along the optical axis in the focal region of a focusing objective. By combining this SDZP and another Dammann grating, we describe the generation of three-dimensional dipole vortex arrays in the focal volume of an objective. For experimental demonstration, a 1×5 SDZP with base charge of l=1 is fabricated by using lithography and wet-etching techniques, and a 1×5 coaxial dipole vortex array is achieved for an objective of NA=0.127. Furthermore, by combining the 1×5 SDZP and another 5×5 Dammann grating, a 5×5×5 dipole vortex array is also experimentally demonstrated. The results show that topological charges of these 5×5 vortex arrays on five coaxial planes could be tunable by selecting a vortex beam carrying different charge as the incident field.