Monolithic Silicon-Based Nanobeam Cavities for Integrated Nonlinear and Quantum Photonics

Photonic resonators that allow an electromagnetic field to be confined in an ultrasmall volume with a long decay time 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 $\mathrm{Si}/{\mathrm{Si}\mathrm{O}}_{2}$ 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 us to theoretically achieve intrinsic quality factors close to 10 million, sub-diffraction-limited mode volumes, and in-plane transmission above 65%, in a structure with a very small footprint of about $8\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}{\mathrm{m}}^{2}$. We address and quantitatively assess the dependence of the main figures of merit on the nanobeam length and on fabrication disorder. Finally, we study a system of two optimized and laterally coupled nanobeam cavities with the goal of demonstrating an unconventional photon blockade at room temperature in a monolithic passive device. We estimate the single-photon nonlinearity of this device and discuss the relevant figures of merit, which lead to sub-Poissonian photon statistics of the transmitted signal. Our results hold promise for prospective experiments in low-power nonlinear and quantum photonics.