  The self-healing property of laser beams is of great interest. And a laser
beam with spatial structures is also widely concerned due to its important
applications in lots of areas. We theoretically and experimentally investigate
the self-healing and transformation characteristics of obstructed structured
beams composed by incoherent or coherent superposition of multiple
Hermite-Gaussian (HG) modes. We reveal that partially obstructed single HG mode
can recover itself or transfer to a lower order in the far-field. When the
obstacle retains one pair of edged bright spots of HG mode in each direction of
its two symmetry axes, the beam structure information (number of knot lines)
along each axis can be restored. Otherwise, it will be transferred to the
corresponding low-order HG mode or multi interference fringes in the far-field,
according to the interval of the two most edged remaining spots on each axis.
It's 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 multi-eigenmodes composed beams with special customized
optical structures. Then the self-healing and transformation characteristics of
the partially obstructed HG modes composed structured beams are investigated.
It's found that the HG modes incoherently composed structured beams have a
strong 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.
