Efficient realization of on-demand functional ultrasonic fields based on prolate spheroidal wave functions from...

Area of Science:

• Acoustics
• Wave Physics
• Signal Processing

Background:

• Traditional ultrasonic field design often relies on time reversal in whole-space.
• Practical applications require flexible ultrasonic field generation within bounded, finite regions.

Purpose of the Study:

• To propose and validate a novel method for generating arbitrary ultrasonic fields in finite regions.
• To utilize prolate spheroidal wave functions for precise acoustic field control.

Main Methods:

• Employing prolate spheroidal wave functions, a complete set of band-limited and orthogonal functions.
• Reconstructing these functions efficiently using the sampling theorem.
• Numerical simulation to validate the generation of standing wave and focusing fields.

Main Results:

• Successfully simulated ultrasound standing wave fields with controlled nodal distributions (e.g., 6 and 2 nodes) in a finite range.
• Demonstrated the generation of ultrasound focusing fields with three distinct focal spots (mainlobe sizes λ, 0.5λ, 0.35λ).
• Achieved super-oscillation focusing with controlled side lobes approximately 3λ from the central spot.

Conclusions:

• Prolate spheroidal wave functions provide an effective tool for arbitrary ultrasonic field generation in finite regions.
• The proposed method offers significant potential for applications in acoustic tweezing, ultrasonic imaging, and medical treatment.
• This approach enhances control and flexibility in designing complex acoustic fields.