Spatial light structuring using a combination of multiple orthogonal orbital angular momentum beams with complex coefficients

Analogous to time signals that can be composed of multiple frequency functions, we use uniquely structured orthogonal spatial modes to create different beam shapes. We tailor the spatial structure by judiciously choosing a weighted combination of multiple modal states within an orthogonal orbital angular momentum (OAM) basis set, creating desired beam intensity "shapes." The weights of the OAM beams to be combined forms a Fourier pair with the spatial intensity distribution in the azimuthal direction of the resultant beam. As an example, we simulate and experimentally create various beam shapes by designing the weights of the combined OAM beams. We also find that 6× higher localized power, as compared to traditional beam combining, could be achieved by coherently combining nine orthogonal OAM beams.