Parametric acoustic array lensed by a gradient-index phononic crystal

Area of Science:

• Acoustics
• Materials Science
• Wave Physics

Background:

• Parametric acoustic arrays typically require large transducer sizes for directional beams.
• Collimating non-directional ultrasonic waves into a focused beam is challenging with small transducers.
• Phononic crystals offer unique acoustic manipulation properties.

Purpose of the Study:

• To theoretically investigate the use of a gradient-index phononic crystal (GRIN PC) lens for collimating ultrasonic waves.
• To optimize GRIN PC lens parameters for maximizing primary wave amplitude at a distance.
• To demonstrate the feasibility of generating a highly-directional low-frequency ultrasonic beam from a small transducer.

Main Methods:

• Modeling the acoustic lens as a GRIN PC with toroidal scatterers.
• Employing an optimization procedure to determine GRIN PC lens parameters.
• Solving the Westervelt equation numerically using the finite element method in the frequency domain.
• Utilizing the quasi-linear approximation to account for nonlinearity and attenuation.

Main Results:

• The GRIN PC lens effectively collimates primary ultrasonic waves into a highly-directional beam.
• Optimization successfully determined lens parameters for enhanced wave amplitude.
• Numerical simulations confirmed the generation of a directional low-frequency beam from a small ultrasonic transducer.
• The study validated the Westervelt equation's applicability for this system.

Conclusions:

• A simple GRIN PC lens can achieve high directivity for parametric ultrasonic arrays.
• This approach enables efficient generation of directional low-frequency beams from compact ultrasonic sources.
• The findings have implications for applications requiring focused ultrasound, such as medical imaging and therapy.