A reciprocity-aware GUM assessment of mode-selective back-reflection suppression in mid-infrared laser power measurement using a bulk-Dirac-semimetal photonic spin Hall multilayer

Abstract

A reciprocity-aware theoretical assessment is presented for using a bulk-Dirac-semimetal (BDS) photonic spin Hall effect (PSHE) multilayer in a mid-infrared laser-power measurement chain. The revision does not treat the passive asymmetric multilayer as a strict two-port optical isolator. Instead, the device is analysed as one element of a mode-selective return-light rejection architecture that also contains relay optics, a centred spatial-mode collector and a rejected-light dump. The distinction is essential: a horizontally polarised beam is decomposed into left- and right-circular components that acquire opposite transverse shifts, while the total beam centroid remains unchanged in the equal-weight model. Lorentz reciprocity further requires zero isolation for a specular time-reversed field in the matched input–output mode. Conditional suppression is therefore evaluated only for mode-converted return fields that populate a different spatial or polarisation state.

Using the published shift bounds ${\delta }_{\mathrm{low}}\le 1.20\lambda$ and ${\delta }_{\mathrm{high}}=14.36\lambda$ at $\lambda =8.9\mu m$, an illustrative $6\times$ relay and a Gaussian collector radius of 200 $\mu$m yield a conditional mode-rejection ratio of 63 dB under ideal alignment. The ratio remains 50 dB at a lateral collector offset of $\pm 0.10\mathrm{mm}$. A common angular mismatch of $\pm 0.20°$ reduces desired-mode coupling by 0.71 dB but does not change the ratio in the symmetric Gaussian-overlap model. Monte Carlo vibration analysis gives a 95% lower rejection bound of 62 dB for 10 $\mu$m rms lateral jitter and 0.02° rms pointing jitter. The Cd${}_3$As${}_2$ conductivity case at $E_F=11.1$ meV is explicitly classified as cryogenic; room-temperature operation requires a finite-temperature conductivity model and experimental re-optimisation.

A parametric GUM model replaces the unsupported assumption that back-reflection is universally 2%–5% of incident power. For a baseline standard uncertainty of 1.5%, a bounded coherent perturbation exceeding approximately 2.3% makes an expanded-uncertainty design target of 4% unattainable at $k=2$. The results define testable conditions and limitations for a future experiment rather than claiming an experimentally certified isolator.