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Updated: Aug 11, 2025

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

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Published on: August 12, 2013

A steerable non-paraxial Gaussian beam expansion for a steerable parametric array loudspeaker.

Tao Zhuang¹, Jiaxin Zhong², Feng Niu³

¹Key Laboratory of Modern Acoustics and Institute of Acoustics, Nanjing University, Nanjing 210093, China.

The Journal of the Acoustical Society of America

|February 2, 2023

Summary

A new non-paraxial Gaussian beam expansion (GBE) method accurately models steerable parametric array loudspeakers (PALs), overcoming limitations of conventional GBE at large steering angles. This advancement significantly reduces prediction errors without increasing computational cost.

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Area of Science:

Acoustics
Signal Processing
Computational Physics

Background:

Steerable parametric array loudspeakers (PALs) enable directional audio beam steering without mechanical rotation.
The Gaussian beam expansion (GBE) method is computationally efficient for modeling PALs but relies on paraxial approximations.
Paraxial approximations in conventional GBE lead to significant inaccuracies, especially at large steering angles.

Purpose of the Study:

To propose a steerable non-paraxial Gaussian beam expansion (GBE) method for accurate modeling of PALs.
To address the limitations of conventional GBE concerning inaccuracies at large steering angles.
To improve the accuracy of audio beam steering predictions in PALs.

Main Methods:

Developed a steerable non-paraxial GBE by rotating the coordinate system to include the mainlobe of the steered ultrasonic beam.
Employed a non-paraxial approximation during the integration of virtual audio sources for enhanced accuracy.
Compared numerical results with conventional GBE and an exact solution.

Main Results:

The proposed non-paraxial GBE method reduces prediction errors to less than 1 dB at large angles, compared to over 30 dB for conventional GBE.
The improvement is most pronounced at large steering angles, low audio frequencies, and outside the paraxial region.
Achieved enhanced accuracy with computational costs comparable to the conventional GBE.

Conclusions:

The steerable non-paraxial GBE method offers a significant improvement in accuracy for modeling PALs, particularly in non-paraxial conditions.
This method provides a more reliable tool for designing and analyzing steerable audio beam systems.
The computational efficiency is maintained, making it a practical advancement for acoustic research and development.