Abstract
Acoustic sensors and acoustic measurements receive much attention in various applications. Because waveguides are commonly used in sensor design, theoretical means to study acoustic propagation and interaction in waveguides are necessary. However, current methods for elastic wave coupling, including the transfer matrix method and coupled mode theory in planar 2D waveguides, are not satisfactory. In this work, a coupled mode analysis for acoustic waves in 3D stress-free elastic waveguides is proposed. Similar to the coupled mode theory in optical waveguides, the analysis is presented by the evolution of modal amplitudes. It can solve various modal conversion and scattering problems in elastic waveguides with small changes of cross sections and stress-free boundaries. To demonstrate the practicability, the coupled mode analysis is used to calculate the reflection spectrum of the newly proposed structure, the acoustic fiber Bragg grating. In a notch-based grating fabricated on a thin cylindrical waveguide, the results from coupled mode analysis are in good agreement with those from the transfer matrix method, which has been already validated experimentally. The coupled mode analysis is a promising method to solve various scattering problems.
Highlights
Sensing with acoustic waves is an important technology
To further determine the accuracy of the method, the results from coupled mode analysis are compared to existing experimentally-validated transfer matrix method in the special case of notch-acoustic fiber Bragg grating (AFBG), where the cross section has periodic step variations [13], [18]
The paper is organized as follows: section II develops constraining equations of fields and mode orthogonality; section III derives the general coupled mode equations; section IV applies the theory to AFBG; section V compares the results of coupled mode theory and of transfer matrix method; section VI summarizes the work
Summary
Sensing with acoustic waves is an important technology. By monitoring temperature [1]–[3], damage [4]–[6] and other parameters, an acoustic sensing system provides feedback controls for optimized operation and sends early warnings for potential failures. Structures in waveguides to enhance sensing ability One such example is the recently proposed acoustic fiber Bragg grating (AFBG) [13], which introduces periodic variations of the cross sections of a waveguide. He et al.: Coupled Mode Analysis for 3D Stress-Free Elastic Acoustic Waveguide in various applications of either continuous or stepwise waveguide perturbations, for example, optical fiber Bragg gratings (OFBGs) [23]. To further determine the accuracy of the method, the results from coupled mode analysis are compared to existing experimentally-validated transfer matrix method in the special case of notch-AFBG, where the cross section has periodic step variations [13], [18]. The paper is organized as follows: section II develops constraining equations of fields and mode orthogonality; section III derives the general coupled mode equations; section IV applies the theory to AFBG; section V compares the results of coupled mode theory and of transfer matrix method; section VI summarizes the work
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