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 two-photon interference. This paper develops a unified theory-numerics framework to compute angle-resolved far-field two-photon correlations from arbitrary lossless dielectric scatterers. We describe the input-output relation using a multi-channel scattering formulation that maps two populated incident channels to two selected far-field detection modes, yielding a compact two-channel transfer relation for second-order correlation function and time-domain coincidence counts. The required transfer coefficients are extracted from classical far-field complex amplitudes computed by an fast Fourier transform-accelerated volume integral equation solver, avoiding perfectly matched layers and near-to-far-field post-processing. The method is validated against analytical results for dielectric spheres and demonstrated on a polarization-converting Pancharatnam-Berry-phase metasurface, revealing strong angular dependence of quantum interference and its direct impact on HOM-dip visibility. The framework provides an efficient and physically transparent tool for structure-dependent quantum-correlation analysis, with potential applications in scatterers-enabled quantum state engineering and quantum inverse design.