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.
Highlights
Wave mode governs energy propagation pattern, and modal interactions by mode conversion have been widely explored in electromagnetics to acoustics1–14 for nonreciprocal propagation1, energy channeling in magnetic fusion6, cloaking9,10 and others
We derived the exact theory for the perfect transmodal Fabry-Perot interferometers (TFPIs), expressed it explicitly with two sets of equations and explained the mechanics occurring at the Perfect mode conversion (PMC) frequencies
The pattern of peak mode-conversion transmissions in the TFPI is similar to that in the single-mode FPI, unique multimodal interactions must be considered in the TFPI
Summary
Wave mode governs energy propagation pattern, and modal interactions by mode conversion have been widely explored in electromagnetics to acoustics for nonreciprocal propagation, energy channeling in magnetic fusion, cloaking and others. The common mode conversion methods use Snell’s critical angle. The common mode conversion methods use Snell’s critical angle17 These methods can hardly produce high mode-converting efficiency due to impedance mismatch. Complete mode conversion might be theoretically possible with double negative metamaterials, their use is very restrictive and no actual realization is attempted. A mode conversion phenomenon through anisotropic slabs has been reported and the observed phenomenon was called the TFPR (transmodal Fabry-Perot resonance). On the assumption that the slabs are weekly-coupled and the background mediums are low-reflective, the pattern of local peaks in the mode conversion transmission was observed. The perfect mode-conversion showing exactly the same interference phenomenon as observed in the classical Fabry-Perot interference phenomenon was not possible
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