Full-Tensor Magic Angle Pair Spectroscopy

Linear dichroism (LD) optical absorption spectroscopy historically has found substantial yet still limited application in broad areas of science. In particular, full-dipole-tensor reconstruction has been onerous, usually requiring tedious and difficult measurements on single crystals at many orientations using a four-circle goniometer. As a consequence, it is very seldom done. Here, we propose, and test by numerical simulation, a simpler, faster, novel method of determining the full dipole optical absorption tensor of homogeneous planar films in real time as a function of energy (or wavelength), while requiring only minimal additional time and instrumentation. The goal of this paper is to explain the theory and to demonstrate the effectiveness and stability of the procedure using synthetic data sets. Experimental implementation and testing is deferred to future work and publications. The full-tensor spectrum, after construction from the experimental data, allows one to instantly calculate the absorption for any selected polarization direction, even those that are physically inaccessible to experimental measurement. Although our specific application in this paper is X-ray Absorption Fine Structure (XAFS) Spectroscopy, the method should be applicable to UV–Vis, IR, THz, microwave, and other wavelengths. A strength of this measurement modality is that full-tensor data can be acquired using essentially the same sort of scanning geometry that is normally used for XAFS, with only a discrete shift in the spin axis orientation between groups of scans. The additional instrumentation needed to determine the five Fourier components of the signal at each energy is minimal; two angles gives ten parameters, while six are strictly needed. Robust inversion from data to tensor elements is demonstrated, implemented via simple matrix multiplication. Outside of XAFS, FTMAPS is also expected to be applicable to diverse scientific and technological areas such as oriented bio-molecular films, semiconductor and materials physics, and process control of thin-film photovoltaics and semiconductors.