A miniature-cavity realization of the cavity ring-down concept, which permits extension of the technique to spectroscopy of surfaces, thin films, liquids, and, potentially, solids, is explored using a wave-optics model. The novel spectrometer design incorporates a monolithic, total-internal-reflection-ring cavity of regular polygonal geometry with at least one convex facet to induce stability. Evanescent waves generated by total-internal reflection probe absorption by matter in the vicinity of the cavity. Optical radiation enters or exits the resonator by photon tunneling, which permits precise control of input and output coupling. The broadband nature of total-internal reflection circumvents the narrow bandwidth restriction imposed by dielectric mirrors in conventional gas-phase cavity ring-down spectroscopy. Following a general discussion of design criteria, calculations are presented for square and octagonal cavity geometries that quantify intrinsic losses and reveal an optimal cavity size for each geometry. Calculated absorption spectra for theNO3radical from 450 to 750 nm in a nitric acid solution are presented to demonstrate bandwidth and sensitivity.