Accelerating and Airy beams are of great interest in a variety of applications as they remain diffraction free while experiencing a transverse quadratic shift along propagation, transporting intensity in the transverse plane over a straight line and describing an overall parabolic trajectory in space. This work presents optical fields that transport intensity in the transverse plane over a continuum of directions arranged over a semi-circle, creating transverse intensity fluxes with a variety of shapes. We construct these beams via a superposition of a nondiffracting beam with a strong carrier wave that reproduces phase variations of the former field over the resultant intensity distribution, generating profiles with a finite and well defined propagation period. The on-demand light patterns presented here are expected to find diverse applications as Airy beams and nondiffracting beams have previously found.
We put forth an analytical approach to the engineering of quasinondiffracting beams based on a relationship between the circular Radon transform and two-dimensional functions with annular support in Fourier space.
In this work we explore extensions of the well-known tomographic imaging process to gradient-index media within
the geometrical optics regime. We propose a generalized Radon transform that relates a linear weak-absorption
profile to the change of intensity due to a varying wavefront.