Encoding the Intensity and Phase Gradient of Light Beams with Arbitrary Shapes

Abstract

We present an approach for engineering the intensity trajectory and phase gradient of light beams with arbitrary shapes by estimating their parametric equations using Freeman chain code and by applying the fast Fourier transform. The analysis of the electric field distribution expected for a given curve allows the phase extraction over each local coordinate, generating a phase pattern to be displayed over a spatial light modulator. The intensity and phase gradient of eight different shapes is encoded during our experiments. The far field intensity profiles are captured and compared in shape to those designed, while the encoded phase is demonstrated by implementing a common path interference setup with a pair of beams from the spatial light modulator. The designed beams, initially drawn either by hand or generated with software, exhibit both the intensity and phase profiles encoded onto them.