  Controlling light propagation through complex media plays a significant role
in a wide range of applications ranging from astronomical observations to
microscopy. Although, several advances have been made based on adaptive optics,
optical phase conjugation and wavefront shaping, but many of these involve
challenges. Recently, controlling light propagation in complex media by simply
structuring light has shown promising capabilities. We present experimental and
numerical investigations of abruptly autofocusing of circular Airy derivative
beams (CADBs) in complex media. We find that up to a relatively high turbulence
strength, CADB possesses relatively good abrupt autofocusing, however,
efficiency and autofocusing position vary with the strength of turbulence.
Further, the spatial distortions in CADB caused by turbulence are quantified by
an overlap integral, which shows that CADB possesses reasonably good resilience
against the turbulence. The diffraction efficiency of CADB changes by a factor
of ~ 1.7 with increasing strength of turbulence from zero to high, indicating
good confinement of intensity at autofocusing. The focused beam spot size grows
gradually with increasing the strength of turbulence, specifically, it grows by
a factor of ~ 2 for a strong turbulence, indicating reasonably good focusing
abilities. The results of CADB are compared with a Gaussian beam, and find that
CADB possesses superior focusing abilities in turbulent media. We have carried
out a detailed analysis of these observations based on Zernike polynomials,
which reveals that different kinds of aberrations present in turbulent media
leads to distortions in the spatial structure as well as other properties of
CADBs. Our results can be used for various applications, such as in biomedical
treatment, seismology, optical tweezers and material processing.
