Autofocusing and self-healing of partially blocked circular Airy derivative beams

We numerically and experimentally study the autofocusing and self-healing of partially blocked circular Airy derivative beams (CADBs). The CADB consists of multiple rings, and partial blocking of CADB with different kinds is achieved by using symmetric and asymmetric binary amplitude masks, enabling blocking of inner/outer rings and sectorially. The CADB blocked with different types possesses the ability to autofocus, however, the required propagation distance for abrupt autofocusing vary with the amount and types of blocking. The abrupt autofocusing is quantified by a maximum k-value, and how fast it changes around the autofocusing distance ($z_{af}$). In particular, CADB blocked with inner rings (first/two/three) exhibits an abrupt autofocusing, as the k-value sharply increases [decreases] just before [after] $z_{af}$. The maximum k-value always occurs at $z_{af}$, which decreases as the number of blocked inner rings increases. For CADB blocked with outer rings, the k-value gradually changes around $z_{af}$, indicating a lack of abrupt autofocusing. The value of $z_{af}$ increases with the number of blocked outer rings. This suggests that although outer rings contain low intensities, these play an important role in autofocusing. A sectorially blocked CADB possesses an abrupt autofocusing, and maximum k-value depends on the amount of blocking. The CADB blocked with different types possesses good self-healing abilities, where blocked parts reappear as a result of redistribution of intensity. The maximum self-healing occurs at $z_{af}$, where an overlap integral approaches a maximum value. Finally, we have compared ideal CADB and partially blocked CADB having the same radii, and found that an ideal CADB possesses better abrupt autofocusing. We have found a good agreement between the numerical simulations and experimental results.