Indistinguishability and collection efficiency of transition metal dichalcogenides single photon emitters embedded in silicon nitride photonic integrated circuits

This work explores the impact of waveguide design in photon collection efficiency and indistinguishability of single photon emitters embedded in photonic integrated circuits. Transition Metal Dichalcogenides (TMDC) materials have been selected as single photon emitters because their prominent properties for single photon emission: their giant oscillator strength promotes a stronger Purcell effect and their short exciton lifetimes enhances the indistinguishability of photons. We have calculated the photon extraction efficiency and the indistinguishability of a TMDC point-source of photons with arbitrary orientation embedded at an arbitrary location within a SiN waveguide. For the calculation we propose an analytical model based in the Green dyadic of the Helmholtz equation for different geometries of the waveguide, position of the source and orientation. Calculations have been numerically evaluated through finite-difference time-domain (FDTD) simulations showing consistent results. We have found a maximum coupling up to 81% to the fundamental mode when the quantum emitter is placed in the centre of the waveguide and a maximum indistinguishability of 81% when the emitter is placed 10 nm away from the edge of the waveguide. The results help for a better understanding of the coupling of quantum emitters to nanophotonic devices and photonic integrated circuits (PICs).