High-order pseudo-Gaussian scalar acoustical beams

Area of Science:

• Acoustics and Wave Physics
• Computational Electromagnetics
• Mathematical Physics

Background:

• The scalar Helmholtz equation governs wave propagation, crucial for understanding acoustic and electromagnetic phenomena.
• Tightly focused beams are essential in applications like acoustic tweezers and advanced imaging.
• Approximations in existing models limit their accuracy for strongly focused or quasi-collimated beams.

Discussion:

• This study introduces exact, non-approximated solutions for scalar Helmholtz beams in spherical coordinates.
• The complex source point method is employed to derive generalized solutions for arbitrary beam orders and degrees.
• These solutions encompass a range of beam types, including pseudo-Gaussian vortex, intermediate vortex, hollow, and trigonometric beams.

Key Insights:

• The derived solutions offer efficient and fast computational modeling of wave-fronts.
• Beam characteristics, such as focusing and collimation, are controllable via the dimensionless waist parameter (kw0).
• Numerical simulations validate the solutions, visualizing pressure wave fields for various beam types and focusing conditions.

Outlook:

• Potential applications include beam-forming design, high-resolution imaging, and particle manipulation in acoustical tweezers.
• Further research can explore these exact solutions for phenomena like scattering, radiation force, and torque.
• The generalized solutions provide a robust framework for designing and analyzing advanced acoustic and optical beam systems.