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

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A four-element array design for the implementation of the third-order super-cardioid beam pattern.

Qiumu Wang¹, Yu Lan², Jun Fan¹

¹State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China.

The Journal of the Acoustical Society of America

|November 1, 2022

Summary

A novel four-element array design practically achieves a third-order super-cardioid beam pattern (SCBP) using the array product theorem. This acoustic source utilizes flextensional transducers for effective low-frequency underwater applications.

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Area of Science:

Acoustics
Array Signal Processing
Underwater Transducer Technology

Background:

Super-cardioid beam patterns (SCBP) are crucial for directional acoustic sensing and source localization.
Implementing higher-order SCBP often requires complex array configurations.
Flextensional transducers offer efficient low-frequency underwater acoustic transduction.

Purpose of the Study:

To present a practical acoustic source capable of generating a third-order super-cardioid beam pattern (SCBP).
To demonstrate the application of the array product theorem for designing higher-order beam patterns.
To validate the proposed array design using finite element analysis and experimental testing.

Main Methods:

Utilized the array product theorem to derive the third-order dipole beam pattern from first and second-order patterns.
Designed a four-element array configuration based on the derived beamforming principles.
Employed single-sided radiation flextensional transducers as array elements.
Conducted finite element method (FEM) analysis for transducer characterization.
Fabricated and tested a prototype four-element array.

Main Results:

Successfully implemented a third-order super-cardioid beam pattern (SCBP) with the designed four-element array.
Demonstrated that the same four-element array can also achieve a second-order dipole beam pattern.
FEM analysis provided insights into the performance of the flextensional transducer elements.
Experimental validation confirmed the practical feasibility of the proposed acoustic source.

Conclusions:

The combination of the array product theorem and a specialized four-element array offers a practical method for achieving third-order SCBP.
Flextensional transducers are suitable elements for constructing such directional acoustic arrays.
The developed acoustic source has potential applications in low-frequency underwater acoustics.