Universal understanding of self-healing and transformation of complex structured beams based on eigenmode superposition

The self-healing property of laser beams with special spatial structures is of great interest. We take the Hermite-Gaussian (HG) eigenmode as an example, theoretically and experimentally investigating the self-healing and transformation characteristics of complex structured beams composed of incoherent or coherent superposition of multiple eigenmodes. It is found that a partially blocked single HG mode can recover the original structure or transfer to a lower order distribution in the far field. When the obstacle retains one pair of edged bright spots of the HG mode in each direction of two symmetry axes, the beam structure information (number of knot lines) along each axis can be restored. Otherwise, it will transfer to the corresponding low-order mode or multi-interference fringes in the far field, according to the interval of the two most-edged remaining spots. It is proved that the above effect is induced by the diffraction and interference results of the partially retained light field. This principle is also applicable to other scale-invariant structured beams such as Laguerre-Gauss (LG) beams. The self-healing and transformation characteristics of multi-eigenmode composed beams with specially customized structures can be intuitively investigated based on eigenmode superposition theory. It is found that the HG mode incoherently composed structured beams have a stronger ability to recover themselves in the far field after occlusion. These investigations can expand the applications of optical lattice structures of laser communication, atom optical capture, and optical imaging.