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Compact and broadband multimode waveguide bend by shape-optimizing with transformation optics

Multimode waveguide bend is one of the key components for realizing high-density mode-division multiplexing systems on chip. However, the reported multimode waveguide bends are either large, bandwidth-limited or fabrication-complicated, which hinders their applications in future high-density multimode photonic circuits. Here we propose a compact multimode waveguide bend supporting four TE modes simply by shape-optimizing with transformation optics. The shape of the waveguide is optimized in the virtual space with gradient distribution of the refractive index, so that the scattering loss and intermode cross talk are well suppressed. After conformal mapping back into the physical space, a compact (effective radius of 17 μm) multimode bending waveguide is obtained. Simulations show that the proposed multimode waveguide bend has little loss (<0.1  dB) and low cross talk (<−20  dB) throughout an ultrabroad wavelength range of 1.16–1.66 μm. We also fabricated the shape-optimized multimode bending waveguide on a silicon-on-insulator wafer. At 1550 nm wavelength, the measured excess losses for the four lowest-order TE modes are less than 0.6 dB, and the intermode cross talks are all below −17  dB. Our study paves the way for realizing high-density and large-scale multimode integrated optical circuits for optical interconnect.