Geometry-controlled exceptional points in helicoidal orbital-angular-momentum photonics

Exceptional points (EPs) are non-Hermitian spectral singularities at which eigenvalues and eigenvectors coalesce. We study an orbital-angular-momentum (OAM) photonic system in which helicoidal twist controls the real detuning between opposite-OAM modes, while openness, gain, loss, leakage, or channel coupling provides the non-Hermiticity. The EP is reached when the geometric detuning compensates a residual mode splitting and the linewidth contrast satisfies the non-Hermitian balance condition. We derive the OAM splitting for a confined quantum problem and for a helically twisted paraxial guide, then embed the selected doublet in a multimode OAM model to test its isolation from spectator modes. The EP is identified through eigenvalue coalescence, phase-rigidity collapse, linear tracking of its position with residual detuning, and branch exchange under geometric encircling. We also formulate OAM-resolved input–output observables and compare the reduced theory with device-level paraxial simulations of reciprocal and asymmetric-coupling platforms. In both cases, the calibrated twist tunes the real detuning of an already-open system through the defective degeneracy.