Method to define non-diffracting optical beams mimicking the shape of simple plane curves

We theoretically and experimentally demonstrate a method to define non-diffracting beams with different geometries. Our findings constitute an alternative to current methods for finding non-diffracting beams, which rely on the solution of the wave equation in a given coordinate system that has a limited number of possibilities or uses a complicated and time-consuming optimization algorithm. Therefore, the method is easier to follow, because it does not require optimization and allows one to obtain non-diffracting beams mimicking the geometry of simple plane curves. The method could find applications in manipulation of matter with optical waves, such as colloidal and living particles, and in quantum, nonlinear, and atom optics.