Zero order synthetic hologram with a sinusoidal phase carrier for generation of multiple beams

We discuss a phase synthetic hologram, for encoding arbitrary complex fields, whose design is based on a sinusoidal phase grating with a spatially modulated phase depth. An important feature of the hologram is that it encodes the complex field at the zero diffraction order of the carrier grating. The smoothness of this sinusoidal carrier grating facilitates the implementation of the hologram with a pixelated spatial light modulator. We take advantage of the hologram reconstruction at the zero-diffraction order for the simultaneous generation of a collection of complex beams.