Theory for Perfect Transmodal Fabry-Perot Interferometer

Abstract

We establish the theory for perfect transmodal Fabry-Perot interferometers that can convert longitudinal modes solely to transverse modes and vice versa, reaching up to 100% efficiency. Two exact conditions are derived for plane mechanical waves: simultaneous constructive interferences of each of two coupled orthogonal modes, and intermodal interference at the entrance and exit sides of the interferometer with specific skew polarizations. Because the multimodal interferences and specific skew motions require unique anisotropic interferometers, they are realized by metamaterials. The observed peak patterns by the transmodal interferometers are similar to those found in the single-mode Fabry-Perot resonance, but multimodality complicates the involved mechanics. We provide their design principle and experimented with a fabricated interferometer. This theory expands the classical Fabry-Perot resonance to the realm of mode-coupled waves, having profound impact on general wave manipulation. The transmodal interferometer could sever as a device to transfer wave energy freely between dissimilar modes.

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Asymmetric full mode-converting transmission of elastic waves

“…Origami metamaterials were also designed to realize efficient mode conversion, by exploring its statically-coupled compression-torsion [33] or the polarization band structure induced by extreme anisotropy [34]. The well-known Fabry-Perot interference [35,36] and quarter-wave impedance matching mechanism [37,38] were extended to deal with inter-mode energy transfer, and a pure-mode [36] and complete conversion were realized respectively [37,38]. With a high mode conversion efficiency, recent applications can be found in non-invasive flow sensing [39] and medical needle insertion [40]; the former utilized the mode conversion between longitudinal and shear waves, while the latter longitudinal and torsional waves.…”

“…Recently, the authors [44] proposed a type of mode-converting metamaterial based on the locally resonance mechanism, which consists of a transmodal component for mode conversion and a fluid-like component for mode selection. Although it can realize a pure-mode asymmetric mode-converting transmission, yet a complete forward mode-converting efficiency is impossible because of its Fabry-Perot working mechanism [35,36]. Besides, because of the local resonance mechanism, it is only applicable in the ultralow frequency range, since it is impossible to fabricate the unit cells in the ultrasonic ranges.…”

“…A giant magnetostrictive patch transducer (MPT) which has a 40-turns figure-of-eight type coiling copper wires was used to generate a plane L wave, and the reflected and transmitted waves were measured by using mode selective receiving MPTs. The nickel patch for the giant MPT has a dimension of 400 mm × 27 mm, while the patches for the receiving MPTs are of 54 mm × 41 mm and 31 mm × 41 mm, respectively for L and T modes [35,36,38]. Because the incident wave passes through a reflection receiver before arrives at the metamaterial, we use relatively thin nickel patches (0.15 mm thickness) to mitigate unnecessary reflections.…”