Pseudo angular momentum and topological charge conservation for nonlinear acoustical vortices

Area of Science:

• Acoustics and Optics
• Wave Physics
• Nonlinear Dynamics

Background:

• Acoustical vortices (AVs) are complex sound fields with phase singularities.
• Optical vortices (OVs) are light beams carrying orbital angular momentum.
• Understanding the relationship between AVs and OVs can reveal fundamental wave properties.

Purpose of the Study:

• To investigate the connection between acoustical vortices and optical vortices.
• To demonstrate that AVs and OVs exhibit similar characteristics when analyzed through the lens of pseudomomentum.
• To explore the implications of pseudomomentum in nonlinear acoustic phenomena.

Main Methods:

• Application of the pseudomomentum concept to acoustical vortices.
• Derivation of radiation stress and topological charge conservation laws using the pseudomomentum rule.
• Investigation in a weak nonlinear acoustic regime.

Main Results:

• Acoustical vortices and optical vortices share analogous properties under the pseudomomentum framework.
• The pseudomomentum rule successfully yields radiation stress and conservation of topological charge.
• Experimental verification of a linear increase in topological charge with harmonic order in nonlinear acoustics.

Conclusions:

• Pseudomomentum provides a unifying concept for understanding both acoustical and optical vortices.
• The study confirms the conservation of topological charge and its harmonic dependence in nonlinear acoustic wave propagation.
• Experimental results validate the theoretical predictions regarding pseudomomentum and topological charge in AVs.