Effects of the parametric interaction on the toplogical charge of acoustical vortices.

Acoustical vortices are one of the three kinds of phase singularity corresponding to screw dislocations of the wavefront. They are characterized by an helical phase winding up around their axis of propagation along which the phase is singular (undefined). This kind of waves possesses several interesting properties like robustness to wavefront distortion in heterogeneous media or non diffracting propagation due to their relation to Bessel beams. Here we are interested by their potential to transmit information and perform basic arithmetics. We experimentally show that parametric interaction has a double effect on such a beam. First of all, the classical effect of creation of frequencies corresponding to all linear combinations of the primary frequencies is recovered. This classical manifestation of the quadratic nonlinearity in fluids is not new but leads to interesting properties for the spatial information of acoustical vortices as it is possible to do some arithmetics with acoustical vortices. Indeed, it is observed that for a frequency generated by a linear combination of the primary frequencies, the topological charge (number of twists made by the wavefront for one wavelength) is obtained by the same linear combination applied to the topological charges of the primary frequencies. For instance, vortices with negative topological charge appear for a secondary beam at the frequency corresponding to the difference of two primary beams with a positive topological charge when the highest frequency corresponds to the lowest topological charge. This phenomenon is studied for frequencies without and with a common divisor. In the latter case, generated frequencies can be degenerated, i.e two different linear combinations give the same frequency. However there is no reason to have the same common divisor for the topological charge so that two waves at the same frequency but with two different charges are propagating colinearly. In this case, the topological charge can be determined using energetic arguments. Finally, the potential applications are briefly discussed. [ABSTRACT FROM AUTHOR]