A theoretical study has been made on adapting 2×2 optical transfer matrices for use in investigating the acoustical properties of multilayer structures, including superlattices. First, the acoustical transfer matrix for a single layer is obtained by analogy to the optical transfer matrix. Subsequently, various multilayer systems are considered and the results compared with those in the literature. The wavelength-dependent effective moduli for isotropic symmetric multilayers are obtained for the first time. These moduli reduce to known results in the long wavelength limit. It is concluded that the use of the acoustical analog of optical transfer matrices greatly simplifies investigation of the acoustical properties of multilayer media, including superlattices. In addition, it would enable one to adapt to acoustics, in a straightforward way, much of the vast literature on the optics of thin films.
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Acoustic Wave Phenomena Research
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FuenteThe Journal of the Acoustical Society of America