Modeling of Far-Field Quantum Coherence by Dielectric Bodies Based on the Volume Integral Equation Method

Abstract: The Hong-Ou-Mandel (HOM) effect is a hallmark of nonclassical photon interference. Accurate modeling of angle-resolved two-photon correlations in complex dielectric structures remains challenging because no efficient numerical framework directly links classical electromagnetic quantities to quantum correlation functions. We present a unified theoretical and computational framework for evaluating far-field HOM interference from arbitrary dielectric bodies. By quantizing plane-wave scattering modes and computing their far-field responses with a volume integral equation (VIE) solver, we determine the second-order normalized correlation function without near-to-far-field transformations or perfectly matched layers. This enables efficient evaluation of frequency-domain correlations and time-domain coincidence counts for photon wave packets. The approach is validated against analytical results for dielectric spheres and applied to a polarization-converting Pancharatnam-Berry-phase metasurface, revealing strong angular dependence of quantum interference that correlates with the characteristics of the HOM dip. The framework offers a computationally efficient and physically transparent tool for exploring structure-dependent quantum correlations, with applications to quantum antennas, metasurface-based quantum state engineering, and quantum inverse design.