<p>The ability of structured light to reconstruct after partial obstruction, known as the self-healing phenomenon, has attracted considerable attention for applications in imaging, optical communication, and quantum technologies. While Bessel and Airy beams have been extensively studied, the self-healing behavior of Hermite–Gauss (HG) beams remains less well quantified. In this work, we systematically investigate the self-healing properties of six HG modes (HG<sub>01</sub>, HG<sub>10</sub>, HG<sub>11</sub>, HG<sub>12</sub>, HG<sub>21</sub>, HG<sub>22</sub>) under three classes of obstructions: circular disks, vertical strips, and rectangular fringes. Both intensity- and amplitude-based similarity measures are employed within the normalized self-healing degree (SHD) framework, providing a rigorous and comparable metric of recovery efficiency. Numerical simulations reveal that higher-order modes, particularly HG<sub>22</sub>, demonstrate superior resilience, achieving SHD values above 1.1 even for moderate obstructions, whereas lower-order modes exhibit incomplete recovery. Geometry–mode alignment effects are also observed, with HG<sub>11</sub> showing enhanced robustness under strip obstructions. Importantly, amplitude-based SHD is consistently lower than intensity-based SHD, confirming that apparent intensity recovery can overestimate robustness when phase fidelity is critical. These findings establish a comprehensive quantitative picture of HG self-healing and offer practical insights for designing resilient, structured beams in realistic optical environments.</p>

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Quantitative assessment of the self-healing phenomenon in Hermite–Gauss beams using intensity- and amplitude-based similarity metrics

  • Rafie Rafie Zadeh,
  • Abdollah Borhanifar,
  • Pari Amiri,
  • Yashar Azizian-Kalandaragh

摘要

The ability of structured light to reconstruct after partial obstruction, known as the self-healing phenomenon, has attracted considerable attention for applications in imaging, optical communication, and quantum technologies. While Bessel and Airy beams have been extensively studied, the self-healing behavior of Hermite–Gauss (HG) beams remains less well quantified. In this work, we systematically investigate the self-healing properties of six HG modes (HG01, HG10, HG11, HG12, HG21, HG22) under three classes of obstructions: circular disks, vertical strips, and rectangular fringes. Both intensity- and amplitude-based similarity measures are employed within the normalized self-healing degree (SHD) framework, providing a rigorous and comparable metric of recovery efficiency. Numerical simulations reveal that higher-order modes, particularly HG22, demonstrate superior resilience, achieving SHD values above 1.1 even for moderate obstructions, whereas lower-order modes exhibit incomplete recovery. Geometry–mode alignment effects are also observed, with HG11 showing enhanced robustness under strip obstructions. Importantly, amplitude-based SHD is consistently lower than intensity-based SHD, confirming that apparent intensity recovery can overestimate robustness when phase fidelity is critical. These findings establish a comprehensive quantitative picture of HG self-healing and offer practical insights for designing resilient, structured beams in realistic optical environments.