Mosaic-based waveguide lenses designed by the adjoint method based on the finite-element scheme.

Waveguide lenses based on mosaic structure are proposed and experimentally demonstrated. The devices are designed by an adjoint method based on the finite-element method (AM-FEM). In AM-FEM, it is easy to calculate the gradient of the objective function with respect to the refractive index distribution, and it is especially useful for multi-port and multi-mode problems. First, to demonstrate the effectiveness of the AM-FEM, simple 1 × 2 power splitters are designed, and the importance of the initial structure is demonstrated together with experimental results. And then, the design of single-mode waveguide lenses is demonstrated. After passing through the mosaic lens, the wavefront of the light is aligned, and the light can traverse a slab region, which has no confinement mechanism in the transverse direction. Also, multimode waveguide lenses are presented for the first time, showing low-loss and almost wavelength-independent characteristics. The designed devices are fabricated, and the measured results are in good agreement with the theory. These devices can be useful for various wavefront controlling devices.