Optimized design of a Silica encapsulated photonic crystal nanobeam cavity for integrated Silicon-based nonlinear and quantum photonics

Abstract: Photonic resonators allowing to confine the electromagnetic field in ultra-small volumes and with long decay times are crucial to a number of applications requiring enhanced nonlinear effects. For applications to integrated photonic devices on chip, compactness and optimized in-plane transmission become relevant figures of merit as well. Here we optimize an encapsulated Si/SiO$_2$ photonic crystal nanobeam cavity at telecom wavelengths by means of a global optimization procedure, where only the first few holes surrounding the cavity are varied to decrease its radiative losses. This strategy allows to achieve close to 10 million intrinsic quality factor, sub-diffraction limited mode volumes, and in-plane transmission above 65\%, in a structure with a record small footprint of around $8~\mu$m$^2$. We address and quantitatively assess the dependence of the main figures of merit on the nanobeam length and fabrication disorder. Finally, we theoretically give a realistic estimate of the single-photon nonlinearity in such a device, which holds promise for prospective experiments in low-power nonlinear and quantum photonics.