Controlling the diffraction properties of materials over a large area holds great promise for a wide range of optical applications. Laser-based techniques have emerged as a viable solution to address this need. Here, we present the diffraction properties of laser-induced self-organized structures, which consist of three interlaced grating-like structures: self-organized nanoparticles, self-organized cracks, and laser marking lines. Under normal incidence external illumination, the sample exhibits an asymmetric diffraction pattern. However, when the incidence angle is tilted, circular diffraction patterns are observed in the plane perpendicular to both the sample and the incidence plane. These phenomena are attributed to the combination effect of the diffraction gratings. To elucidate the underlying physics of multiple diffraction, we use rigorous coupled-wave analysis (RCWA) and grating equations written in direction cosine space, extended to account for the presence of three superimposed gratings. Exploiting the laser-induced diffraction properties of these samples may have great potential for various industrial implementations, including security, display, and design.