Third-Order Spontaneous Parametric Down Conversion in Dielectric Nonlinear Resonant Metasurfaces

We propose a general scheme to investigate photon triplet generation (PTG) via third-order spontaneous parametric downconversion (TOSPDC) in χ(3) nonlinear structures. Our approach leverages the quantum-classical correspondence between TOSPDC and its reverse classical process, three-wave sum-frequency generation (TSFG), to efficiently estimate the PTG rate. We apply this framework to nonlinear metasurfaces supporting quasi-bound states in the continuum (qBICs) in the optical range. From numerical analysis of noncollinear TSFG with degenerate input waves at qBIC wavelengths, we predict wavelength-tunable three-photon emission with spatio-angular correlations. These findings establish a novel method for modeling TOSPDC and also highlight the potential of nonlinear resonant metasurfaces as compact free-space photon triplet sources with quantum state control.