Reshaping compact waveguide bend for mode transmission and conversion.

Compact waveguide bends with functionalities of mode manipulation, including certain mode transmission, multimode transmission, and mode conversion, are highly desirable in photonic integrated circuits. In this paper, an inverse design scheme for reshaped waveguide bend is presented, in which mode manipulation is achieved without additional nanoscale structures. We adopt quasi-3D models in finite element method to simulate the optical field, Bernstein polynomials to describe the deformation of two Si/air boundaries, and a gradient-based algorithm to efficiently determine the optimal design from a strict circular arc with a radius of 3.5 µm. 3D FDTD simulations with SOI configuration are implemented to measure the performance of the proposed designs. Three designs for certain mode transmission (individual TE0, TE1 and TE2) are first demonstrated as a validation of the method. For multimode transmission, the simultaneous TE0, TE1 and TE2 mode transmission in the bend requires a multi-target optimization and the design is achieved after 26 iterations. The output mode purities are 0.996, 0.971 and 0.989 at the center wavelength of 1550 nm, respectively. Furthermore, designs for TE0-to-TE1, TE0-to-TE2 and TE1-to-TE2 mode conversions in 90° bends are realized within 30 iterations. The output mode purities reach 0.985, 0.981 and 0.965, respectively. The performances of all designs remain acceptable within an operational bandwidth of 60 nm.