Generation of V-point polarization singularity array by Dammann gratings

Dammann gratings conceived earlier are designed using iterative procedures to produce equal intensity light spots. In this paper, we show a novel method to design a Dammann grating by solving optimization problem. We solve the optimization problem by a grid search method with resolution determined by fabrication capabilities. The grid-search method utilizes a cost function to find the phase transition points in the unit cell of a Dammann grating, thereby maximizing the throughput. Since the goal in previously designed gratings is to produce required intensity pattern, other parameters of light such as phase and polarization were not expected to maintain any structure in the diffraction pattern and were considered as free parameters during design. We observe that the element preserves the topological features of the incident light in each of its diffracted orders. We show that Dammann grating when illuminated by a V-point polarization singularity of different Poincaré–Hopf index values, produces multiple beam-lets each containing same polarization distribution as that of the incident V-point. The experimentally obtained array structures are in concordance with the simulations.