What are the traveling waves composing the Hermite-Gauss beams that make them structured wavefields?

Shadows of structured beams in lenslike media

The self-healing phenomenon of structured light beams has been comprehensively investigated for its important role in various applications including optical tweezing, superresolution imaging, and optical communication. However, for different structured beams, there are different explanations for the self-healing effect, and a unified theory has not yet been formed. Here we report both theoretically and experimentally a study of the self-healing effect of structured beams in lenslike media, this is, inhomogeneous lenslike media with a quadratic gradient index. By observing the appearance of a number of shadows of obstructed structured wave fields it has been demonstrated that their self-healing in inhomogeneous media are the result of superposition of fundamental traveling waves. We have found that self-healing of structured beams occurs in this medium and, interestingly enough, that the shadows created in the process present sinusoidal propagating characteristics as determined by the geometrical ray theory in lenslike media. This work provides what we believe to be a new inhomogenous environment to explain the self-healing effect and is expected to deepen understanding of the physical mechanism.

Effect of aberrations on the beam quality factor of Hermite-Gauss beams

The effect of aberrations on the beam quality factor (M2) of Hermite-Gauss (HG) beams is examined. Using the method of moments, we derive closed-form analytical expressions of M2 due to astigmatism and spherical aberration. Our analysis reveals that the radius of the HG beams plays a significant role in determining the effect of the aberrations on M2. For each aberration, we establish a critical width that separates the region where M2 changes infinitesimally from the region where it changes sharply. The analytical results are validated through numerical simulations.

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.