Construction and application of knotted acoustic fields with intensity maxima

Knots have always played an important role in the life sciences because of their complex topology. Some previous investigations have shown that an optical field can be modulated into knot structures, and a knotted trap formed by light beams has also been demonstrated. Very recently, it has also been demonstrated that an acoustic vortex field with phase singularities can be tied into a knotted structure. However, for knotted tweezers, we need to use the relative maximum points of the amplitude distribution to construct the knotted field (although it is still not known how to create such a knotted line acoustic field) which is beneficial for particle trapping into knotted shapes. In this work we propose a method to generate acoustic fields with knotted intensity maxima in three dimensions. Based on the finite element method and angular spectrum theory, we prove that both Hopf link and trefoil knot lines in acoustic fields can be generated by the designed holograms. Furthermore, under particle tracking simulation in the time domain, we demonstrate that the knotted line acoustic fields can be used to capture particles into different topologies in three dimensions.