Inverse Design of Photonic Crystal Cavities with Controllable Far-Field Numerical Aperture

Photonic crystal cavities confine light to subwavelength volumes which enables strong light–matter interactions for applications in low-power photonics, optoelectronics, nonlinear optics, and quantum information. Realizing these applications requires cavities that combine high quality factors, low mode volumes, and efficient coupling. Optimizing across all these metrics demands navigating a vast design space, motivating the use of inverse design strategies. Previous efforts largely focused on maximizing quality factor and minimizing mode volume, often at the expense of coupling efficiency or without precise control of the far-field radiation pattern. In this work, we introduce an inverse design framework that simultaneously optimizes cavity quality factor and far-field numerical aperture as explicit design objectives. Using this approach, we design L3 photonic crystal cavities with specified far-field numerical apertures in the visible range and fabricate them in silicon nitride. Photoluminescence measurements verify control of the far-field numerical aperture and demonstrate 28-fold and 3.9-fold improvements in coupling efficiency and quality factor, respectively, compared to the standard L3 cavity. Disorder analysis further confirms that the designs retain robust performance despite nanofabrication imperfections. This work establishes a versatile inverse-design framework for multi-objective optimization of photonic crystal cavities, simultaneously achieving high quality factors and coupling efficiency.