Bent waveguides are fundamental to compact the on-chip photonic integrated circuits (PICs), however, the bending-induced loss has become one of the significant challenges on achieving high integration density. Here we propose an optimized waveguide design based on the Euler-circular bend geometry, implementing two key methods: embedding the bent waveguide within an air layer and introducing an offset at the transition between straight and curved sections. For the small bending radius of 1 μm, where the current reported designs typically experience significant bending loss, the improvement achieves remarkable loss reduction from 0.9059 dB to 0.0181 dB at 1550 nm wavelength. Accordingly, a high-density structure is designed to accommodate ten signal channels within a compact 7×7 μm2 footprint. By applying our optimized waveguide, the structure exbibits low loss for one or dual signals and maintains excellent signal independency even under simultaneous transmission of all ten channels. This advancement offers a promising pathway for next-generation PICs with greater functional complexity and smaller device footprints.