Title: Circular photonic crystal grating design for charge-tunable quantum light sources in the telecom C-band

Abstract: Efficient generation of entangled photon pairs at telecom wavelengths is a key ingredient for long-range quantum networks. While embedding semiconductor quantum dots into hybrid circular Bragg gratings has proven effective, it conflicts with $p$-$i$-$n$ diode heterostructures which offer superior coherence. We propose and analyze hybrid circular photonic crystal gratings, incorporating air holes to facilitate charge carrier transport without compromising optical properties. Through numerical simulations, a broad cavity mode with a Purcell factor of 23 enhancing both exciton and biexciton transitions, and exceptional collection efficiency of 92.4% into an objective with numerical aperture of 0.7 are achieved. Furthermore, our design demonstrates direct coupling efficiency over 90% into a single-mode fiber over the entire telecom C-band. The hybrid circular photonic crystal grating thereby emerges as a promising solution for the efficient generation of highly coherent, polarization-entangled photon pairs.