Topological phase structures of conical refraction beams: expanding orbital angular momentum applications...

Topologically structured light carrying orbital angular momentum (OAM) has emerged as a powerful tool for nano-photonics and biomedical optics, yet conventional integer-charge Laguerre-Gaussian (LG) beams suffer from rotational degeneracy that limits diagnostic precision. Here, we demonstrate that conical refraction (CR) beams, specifically the Lloyd, Poggendorff, and Raman families, overcome this fundamental limitation through their inherent generation of fractional OAM states with unambiguous phase signatures. Through systematic interferometric comparison of LG (ℓ = 3, 5) and CR beam propagation in tissues, we show that CR beams achieve superior diagnostic performance: while LG beams exhibit three-fold rotational ambiguity (4.19 rad uncertainty), Poggendorff CR beams provide phase determination with 0.08 rad precision. Both LG and CR beam families display remarkable topological resilience, preserving phase coherence as they traverse tissue samples while attaining refractive index sensitivity at the 10^-6 level, three orders of magnitude beyond conventional refractometry. Most significantly, we present the first experimental evidence that CR beams can discriminate between healthy and cancerous kidney tissues through distinct phase rotations (4.71 vs. 5.04 rad, p < 0.001) and a tenfold amplification in polarisation-induced distortion. The fractional topological charges of CR beams, ranging continuously between integer values, expand the accessible OAM phase space and enable 3.7-fold superior signal-to-noise ratio compared to ${\text{LG}}_0^3$ measurements. These results establish CR-generated fractional OAM as the preferred modality for label-free tissue diagnostics, bridging fundamental nanophotonics with clinical applications in cancer detection and intraoperative margin assessment.