Silicon nitride waveguide devices based on gradient-index lenses implemented by subwavelength silicon grating metamaterials.

The rapid development of photonic integrated circuits demands the design of efficient and compact waveguide devices such as waveguide tapers and crossings. Some components in the silicon nitride (SiN) waveguide platform are superior to their counterparts in the silicon waveguide platform. Designing a compact SiN waveguide taper and crossing is crucial to reduce the size of SiN photonic components. In this paper, we utilize the focusing property of the Luneburg lens to design an SiN taper connecting a 10-µm-wide waveguide to a 1-µm-wide waveguide. Three-dimensional full-wave simulations indicate that the designed 13-µm-long taper has an average transmission efficiency of 92% in the wavelength range of 1500-1600 nm. We also present an in-plane SiN waveguide crossing based on the imaging property of the square Maxwell's fisheye lens designed with quasi-conformal transformation optics. The designed waveguide crossing occupies a compact footprint of 5.65µ×5.65µ, while its average insertion loss is 0.46 dB in the bandwidth of 1500-1600 nm. To the best our knowledge, the designed SiN waveguide taper and crossing have the smallest footprints to date.