Consider a compact Riemannian manifold of dimension ≥ 3 with strictly convex boundary, such that the manifold admits a strictly convex function. We show that the attenuated ray transform in the presence of an arbitrary connection and Higgs field is injective modulo the natural obstruction for functions and one-forms. We also show that the connection and the Higgs field are uniquely determined by the scattering relation modulo gauge transformations. The proofs involve a reduction to a local result showing that the geodesic X-ray transform with a matrix weight can be inverted locally near a point of strict convexity at the boundary, and a detailed analysis of layer stripping arguments based on strictly convex exhaustion functions. As a somewhat striking corollary, we show that these integral geometry problems can be solved on strictly convex manifolds of dimension ≥ 3 having non-negative sectional curvature (similar results were known earlier in negative sectional curvature). We also apply our methods to solve some inverse problems in quantum state tomography and polarization tomography.

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We systematically explore the performance of ultrathin amorphous silicon solar cells integrated on plasmonic substrates of several different morphologies. Angle-resolved reflectance, external quantum efficiency measurements, and finite-difference time-domain simulations highlight the importance of the spacer layer in determining the mode profiles to which light can couple. Coupling mechanisms are found to strongly differ between periodic silver nanovoid arrays and randomly textured silver substrates. Tailoring the spacer thickness leads to 50% higher quantum efficiencies and short-circuit current densities by tuning the coupling between the near-field and trapped modes with enhanced optical path lengths. The balance of absorption for the plasmonic near field at the metal/semiconductor interface is analytically derived for a broad range of leading photovoltaic materials. This yields key design principles for plasmonic thin-film solar cells, predicting strong near-field enhancement only for CdTe, CuInGaSe 2 , and organic polymer devices.