Optical Fourier Surfaces for Integrated Photonics.

Integrated photonics has enabled the miniaturization and development of classical as well as quantum-optical technologies. However, traditional lithographic techniques limit the required optical elements to binary height profiles. By relaxing these constraints, grayscale fabrication methods have the potential to deliver more efficient and compact devices. In contrast to binary profiles, wavy surfaces (also known as optical Fourier surfaces, OFSs) only introduce spatial frequencies that are required for their functionality, yielding more control over the optical response. In this work, we demonstrate photonic integrated circuits with grayscale OFS elements in state-of-the-art material platforms, including silicon-on-insulator and thin-film lithium niobate. Using thermal scanning-probe lithography and dry etching, the OFSs are written and transferred with high fidelity. We employ an intuitive and straightforward design scheme to create a series of devices that exploit the capabilities of wavy height profiles. First, we fabricate sinusoidal single- and multiband Bragg reflectors in silicon waveguides with an extinction ratio of up to 44 dB at 1550 nm. Second, cavities in lithium-niobate waveguides are fabricated with a high quality factor of 1.6 × 10