Abstract
Vortex beams, characterized by a collimated wavefront with a phase dislocation at their principal axis, have found
practical applications to construct acoustic tweezers for particle
trapping and manipulation, or underwater communications.
However, the natural diffraction of the wavefront limits the
size of the vortex. This result in vortices whose bright core
is larger than the wavelength, limiting their use for practical
applications such as long-range underwater communications.
In this work, we synthesize a vortex beam of sub-wavelength
size at a distance beyond Rayleigh diffraction length using the
nonlinear mixing of two confocal, high-frequency and detuned
vortex beams of different topological charges. By using the
nonlinear mixing of two confocal vortices, it was generated a
low-frequency (1 kHz) focused vortex beam of integer topological
charge whose distance between magnitude maxima is about 18
times smaller than its wavelength at a distance about 3 times
the Rayleigh diffraction length. Sub-wavelength vortices emerge
as a result of the spatiotemporal interference of two primary
vortex beams due to the conservation of angular momentum
during nonlinear wave-mixing. This mechanism opens new paths
to design directive parametric antennas for vortex transceivers or
particle manipulation systems at scales well below the diffraction
limit.
