The localization of fluorescent microspheres is often employed for drift correction and image registration in single molecule microscopy, and is commonly carried out by fitting a point spread function to the image of the given microsphere. The mismatch between the point spread function and the image of the microsphere, however, calls into question the suitability of this localization approach. ...

In this work, a non-integer order Airy equation involving Liouville differential operator is considered. Proposing an undetermined integral solution to the left fractional Airy differential equation, we utilize some basic fractional calculus tools to clarify the closed form. A similar suggestion to the right FADE, converts it into an equation in the Laplace domain. An illustration t...

We study numerically and demonstrate experimentally a novel type of singular optical beams formed by the phase imprinting of an optical vortex into the structure of the three-Airy beams. In contrast to a vortex-free product of three Airy beams, in this type of singular-Airy beam, the vortex in the beam axis causes a twist in the beam transverse intensity profile with propagation. Such a new typ...

The Airy theory of the rainbow is extended to polarized light. For both polarization directions a simple analytic expression is obtained for the intensity distribution as a function of the scattering angle in terms of the Airy function and its derivative. This approach is valid at least down to droplet diameters of 0.3 mm in visible light. The degree of polarization of the rainbow is less than ...

Researches on Airy beams have grown explosively since the first demonstration in 2007 due to the distinguishing properties of nondiffraction, transverse acceleration and self-healing. To date, a simple and compact approach for generating Airy beams in high quality and efficiency has remained challenging. Here, we propose and demonstrate a liquid crystal (LC) polarization Airy mask (PAM) feature...

Expressions for the average intensity of both phase-locked and non-phase-locked Airy array beams propagating through atmospheric turbulence are derived based on the extended Huygens–Fresnel principle. The evolution of the average intensity distribution of both phase-locked and non-phase-locked Airy array beams during propagation in atmospheric turbulence is examined by numerical examples and is...

Airy beam, a non-diffracting waveform, has peculiar properties of self-healing and self-acceleration. Due to such unique properties, the Airy beam finds many applications including curved plasma wave-guiding, micro-particle manipulation, optically mediated particle clearing, long distance communication, and nonlinear frequency conversion. However, many of these applications including laser mach...