The preprint proposes a mathematical bridge between spin- and angle-resolved photoemission (SARPES) and its inverse, spin- and angle-resolved inverse photoemission (SARIPES). Its central object is a response tensor, which records how photon polarization and electron-spin polarization are coupled. In the reciprocal treatment used by the authors, the two processes have equal transition probabilities when momentum and spin are reversed. The transfer is defined for the corresponding time-reversed version of the same setup.
A compact bridge between light and spin
In SARPES, the source term in the tensor is photon polarization; in SARIPES, it is electron-spin polarization. The light is represented through Stokes components—quantities used here to describe photon polarization—paired with spin-polarization components.
Mirror symmetry sharply narrows the possibilities. For the stated mirror-plane geometry, even Stokes components pair with even spin components and odd with odd; all other tensor elements vanish.
Testing the construction
To test the construction, the authors combined density-functional calculations with a one-step photoemission model and spin-polarized relativistic layer-KKR calculations, using a Dirac single-site scattering treatment that includes spin-orbit coupling. The W(110) tensor was calibrated at a polar angle of 45° and an azimuth of 0° with 9.5 eV photons, while the H̄Γ̄H̄ scans covered energies from EF to EF + 4 eV.
A proposed polarization-tomography procedure—a reconstruction step—uses six equal-amplitude photon-polarization states to calibrate the tensor from SARPES intensities. The computed tensor obeyed the required symmetry, reproduced the input and output SARPES data with relative error better than 10⁻⁶, and passed positivity checks.
Spin changes the predicted emission
The inverse calculation produced both s- and p-polarized radiation from a fully y-polarized incident electron beam, Py = +1. The maximum p-polarized emission was approximately one-sixth of the maximum s-polarized emission, with intensities reported in arbitrary units.
When Py was reversed from +1 to −1, the simulated W2 flat-band maximum moved from negative kx to positive kx. The authors treated that shift as evidence of spin-dependent changes in SARIPES intensity.
The modeled SARIPES intensity difference also showed what the paper calls a convincing correlation with the topmost layer’s y-spin spectral-density difference. The correspondence was strongest at W2 and was also present near W1, although it was not exact because SARIPES includes contributions from deeper layers and matrix elements.
What the calculation cannot yet establish
In a separate in-plane-spin calculation, reversing the spin left the emitted elliptically polarized intensity unchanged but reversed its helicity, or handedness. For x- and z-polarized beams, helicity resembled spectral density only partially or less. The authors say circular polarization was governed predominantly by photoemission matrix elements, making that geometry less suitable for spin retrieval.
Taken together, the result is a fixed-setup transfer, not a universal conversion. The tensor depends on crystal orientation, emission and incidence directions, and photon energy; a tensor calibrated with SARPES predicts reciprocal SARIPES only for the corresponding time-reversed arrangement.
The modeled case is a nonmagnetic W(110) mirror-plane geometry, and the authors leave magnetic systems for future work, noting that broken time-reversal symmetry may add spin-dependent tensor terms. The document is an arXiv version 1 preprint dated 20 Aug 2026.
Paper data and sources
Original title: A Unified Theoretical Framework for Photoemission and Its Inverse: Reciprocity, Spin, and Photon Polarization
Authors: Frank O. Schumann, Jürgen Henk
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text