Exceptional points (EPs) in non-Hermitian systems can produce nonlinear responses to weak perturbations, but maintaining these responses at a stable operating frequency remains challenging. Here, we develop a hyperbolic photonic metacrystal that combines dispersion and loss engineering. By exploiting the opposite angular dispersions of the hyperbolic and dielectric layers, we achieve first-order phase compensation that suppresses angular variations in the accumulated optical phase and keeps the localized resonances nearly unchanged with incident angle. We first consider a parity-time (PT)-symmetric system with balanced effective gain and loss, where a Hamiltonian EP coincides with a scattering-matrix (S-matrix) EP. Although this operating point exhibits square-root scattering-eigenvalue splitting, refractive-index perturbations also shift the Hamiltonian eigenfrequencies, limiting the stability of the operating frequency. By breaking the effective gain-loss balance, we obtain a PT-asymmetric state in which the squared coupling strength equals the product of effective gain and loss. Under this condition, a bound-state-in-the-continuum (BIC)-associated real-frequency solution emerges, and the S-matrix remains at an EP while the effective Hamiltonian no longer exhibits an EP. The scattering eigenvalue splitting therefore retains its square-root dependence on refractive-index perturbations, while the resonance-frequency drift is substantially reduced. Together with hyperbolic phase compensation, this response is maintained over incident angles from 0° to 60°, offering a route to EP-based sensing that combines angular robustness with spectral stability without sacrificing the square-root scattering response.

We discover that a standard Fourier transformation intrinsically imparts a parity-dependent phase shift to optical vortices, yielding a phase difference of π between modes carrying odd and even topological charges. This phase shift, however, is not directly observable from the intensity profile of the transformed beam. To render it measurable, we develop a spin-selective Fourier transformer by co-designing propagation-induced dynamic phase and Pancharatnam-Berry geometric phase in a pair of hybrid-lenses. This device converts the parity-dependent phase shift into orthogonal polarization states via spin-orbit interaction, enabling non-destructive separation of both individual and superimposed orbital angular momentum (OAM) modes without the need for an interferometer. Our work establishes Fourier transformation as a new mechanism for parity-resolved vortex manipulation, offering an integrable platform for high-dimensional photonic applications.