Chirality-controlled conjugate complex-gradient differentiation at a reciprocal photonic Weyl interface

We investigate chirality-controlled complex-gradient differentiation at a reciprocal chiral photonic Weyl interface using Maxwell boundary conditions and angular-spectrum theory. Reversing the enantiomeric parameter χ = ±1 leaves co-polarized reflection unchanged while reversing cross-polarized amplitudes. For p-polarized incidence, a chirality-matched elliptical analyzer suppresses the zeroth-order specular field and isolates a first-order dark-port response. At the balanced operating point, the normalized transfer function approaches H^¯ _χ ≃k _x /k₀-iχk _y /k₀, where k _x and k _y are transverse spectral components and k₀ is the vacuum wavenumber. The two enantiomers therefore exhibit nearly identical magnitude responses but opposite phase winding. Fourier-optics calculations confirm annular Gaussian-beam responses and nearly chirality-invariant two-dimensional edge intensities with reversed phase circulation. Material chirality thus controls the handedness of the complex differential operator.