Two-dimensional analytic modeling of acoustic diffraction for ultrasonic beam steering by phased array transducers

Area of Science:

• Acousto-optics
• Ultrasonics
• Laser Material Processing

Background:

• Phased array ultrasonic transducers offer precise control over acoustic wave focal positions.
• This capability is crucial for applications in medical imaging, non-destructive testing, and advanced laser material processing via acousto-optic deflectors.
• Generating tilted wavefronts is key for deflecting laser beams with high precision.

Purpose of the Study:

• To develop a theoretical model for ultrasonic wave diffraction from phased array transducers into acousto-optic media.
• To derive a simple analytic expression for the ultrasonic displacement field distribution within the crystal.
• To validate the theoretical model against numerical simulation results.

Main Methods:

• Theoretical modeling of ultrasonic wave diffraction.
• Derivation of an analytic expression for the ultrasonic displacement field.
• Comparison with a numerical model based on the non-paraxial multi-Gaussian beam (NMGB) approach.

Main Results:

• A theoretical model for ultrasonic wave diffraction in acousto-optic media (e.g., TeO2) was successfully developed.
• A simple analytic expression was obtained for the ultrasonic displacement field distribution.
• The model's predictions showed good agreement with the results from the NMGB numerical model.

Conclusions:

• The presented theoretical model accurately describes ultrasonic wave diffraction from phased array transducers in acousto-optic crystals.
• The analytic expression provides an efficient way to predict the ultrasonic displacement field.
• This work validates the theoretical approach and supports its use in advanced acousto-optic applications.