Multi-height Identification of Sausage and Fluting Eigenmodes in a Solar Pore

Magnetic pores are compact, strongly magnetised waveguides in the lower solar atmosphere and therefore provide favourable conditions for identifying magnetohydrodynamic (MHD) wave modes. Earlier seeing-free observations revealed concurrent sausage, kink, and fluting modes in photospheric pores, but only at a single sampled layer. In this Letter, we exploit the dense spectral sampling of the near-ultraviolet 327-329 nm window observed by the Sunrise-III UV Spectropolarimeter and Imager (SUSI) to investigate how pore wave modes behave across multiple photospheric and low-chromospheric heights spanning roughly 500 km. We analyse ~75 min of a Sunrise-III/SUSI time series containing a small solar pore. From eight selected spectral lines sampling different estimated formation heights, we identify the pore boundary at each line and time step and apply proper orthogonal decomposition (POD) to the boundary oscillations. In all eight lines, the first POD mode is consistently identified as an axisymmetric sausage mode, with dominant power at ~1-2 mHz, and carries the dominant normalised eigenvalue fraction, typically about 66-86%, while the second mode is a fluting mode with azimuthal wave number m = 2, dominant at ~2-3.5 mHz, and contributes about 4-10%. Cross-line wavelet phase analysis of the temporal coefficients shows that the sausage mode remains close to zero phase difference across the sampled heights, consistent with standing or near-standing behaviour, whereas the fluting mode displays a modest but systematic increase in phase with height, reaching about 50 degrees, indicative of an upward-propagating component. These observations provide the first multi-height identification and phase characterisation of sausage and fluting modes inferred from pore-boundary oscillations.