Spontaneous parametric down-conversion in one-dimensional photonic structures with boundaries

Abstract

Emission of photon pairs has been numerically investigated in both the volume and at the boundaries of layered Gallium-Nitride/Aluminium-Nitride (GaN/AlN) structures that occurs in the process of spontaneous parametric down conversion (SPDC). The developed model of SPDC is one dimensional and exploits the quantization of momentum of an electromagnetic field (EM field). Nonlinear boundary conditions for the quantized EM field between the linear (AlN) and nonlinear (GaN) layers are treated by the transfer-matrix formalism. The developed theory describes both the volume and interface emissions of photon pairs and it also allows for their separation. The emission of photon pairs from interfaces contributes by 9.7 % of total number of emitted photon pairs. In the spectral regions with low volume emission, the spectral joint photon number density for interface emitted photon pairs reaches up to 40 % of the quantity characterizing the photon pairs emitted in the volume.