Astigmatic Mode Conversion of Defective Hermite‐Gaussian Modes

Hermite–Gaussian (HG) and Laguerre–Gaussian (LG) modes are two fundamental modes in structured light, and astigmatic mode conversion between them has been extensively investigated. Conventional structured light manipulation generally treats complete HG eigenmodes as the fundamental degrees of freedom (DOFs), with beam control achieved through the superposition of multiple eigenmodes. However, HG modes inherently possess internal spatial DOFs, enabling direct manipulation of their constituent lobes without explicitly engineering multiple eigenmodes. In this work, we systematically investigate the astigmatic conversion of HG modes across diverse defect configurations and characterize the redistribution behavior of these localized defects in the LG basis via astigmatic conversion. Complementary defective modes are further introduced to elucidate the formation of the diverse spatial structures observed in the converted fields. Remarkably, column defective HG modes, prone to free‐space profile distortion, are converted to self‐similar rotationally propagating fields whose transverse profiles are preserved up to global scaling and rotation. These findings extend astigmatic mode conversion from complete eigenmodes to spatially defective HG states and provide new insight into the conversion and propagation dynamics of structured optical fields.