Optomechanical Analyzer of Azimuthal Quadratures for Structured Light

We demonstrate optomechanical spatial projection of azimuthally structured optical beams. The system is based on an ultra-low loss circular membrane integrated into an interferometric setup, that exploits the spatial analogies between the mechanical modes and the structured optical fields. A weak anisotropy lifts the degeneracy of the membrane modes, producing a spectrally resolved mechanical doublet composed of two orthogonal eigenmodes. Petal-shaped optical intensity distributions, formed by coherent superpositions of orbital-angular-momentum eigenstates with opposite topological charges and generated via a q-plate, are used to probe the membrane in a readout-only regime, where the motion is thermally excited. By rotating the azimuthal orientation of the optical pattern, we observe a controlled redistribution of spectral weight between the two members of the mechanical doublet. The split doublet, therefore, acts as a two-channel mechanical spatial analyzer for azimuthal quadratures, providing a wavelength-independent platform for the projection and processing of structured optical fields. Since the analyzer relies on spatial mode matching rather than optical spectral properties, the platform can interface with a wide range of optical sources and channels, making it an ideal candidate for optical and quantum communication applications.