As a newly-developing direction, integrated optics have played a strong role in promoting astronomy, biosensing, quantum computing, etc. Silicon photonics is very promising since silicon has several metrics, such as transparency in the main communication bands, high refractive index contrast for high density integration, compatibility with Complementary Metal-Oxide-Semiconductor (CMOS) process for volume production and so on. Silicon waveguide bend is one of the important components for silicon photonics. Although the loss of a single silicon waveguide bend is relativelysmall, the accumulative effect in a large-scale integrated optical circuit can enhance the total loss and may lead to a significant deterioration of the device's performance. Usually, increasing the bend radius of silicon waveguide bends can effectively reduce the loss, but this will degrade the integration density of the chip. It is very important to achieve silicon waveguide bends with compact size and low loss simultaneously. Some solutions to achieve this goal for silicon waveguide bends have been proposed, such as introducing deep etching slots or introducing offset on straight optical waveguides, which have small fabrication tolerance and are difficult to fabricate. In contrast, the special curve-based waveguide bend does not require special fabrication processes and has good process compatibility.The Euler curve, as a special curve used in optical waveguide bends, has a gradual change in curvature from 0 to the maximum value. This scheme effectively reduces the mode mismatch loss between a straight optical waveguide and a bent optical waveguide. In addition, the mode evolution within the bent optical waveguide is limited at the same time. Thus, the overall loss of the bent optical waveguide can be optimized well. However, when the curvature of the Euler curve grows to a maximum value, the corresponding radius of curvature reaches a minimum, where a large radiation loss will exist.As known, by widening the width of the waveguide, the confinement of the optical field can be enhanced, which is an effective way to decrease the radiation loss. To achieve a smaller size and a lower loss, two silicon-based single-mode 90° waveguide bend structures based on different inner and outer curves to realize width gradient are proposed in this paper. The waveguide bend Ⅰ consists of a circular inner curve and an Euler-circular outer curve, and the waveguide bend Ⅱ combines an Euler-circular inner curve and an Euler outer curve. On the one hand, according to the variability of the radius of curvature of the inner and outer curves, the curve proportion of the Euler-circular curve can be adjusted by optimizing the design parameters accordingly, making the width inside the waveguide bend changes gradually to effectively reducing the radiation loss. On the other hand, the curvature of an Euler-circular curve or an Euler curve in waveguide bend Ⅰ and Ⅱ increases from zero, which reduces the mode mismatch loss at the connections of the straight optical waveguides and the bent optical waveguides, further decreasing the bending loss. In terms of fabrication, the proposed structure has no special process requirements and is easy to fabricate.The proposed two silicon waveguide bend structures are simulated and optimized by three dimensional finite difference time domain (3D-FDTD) method. The simulation results show that the loss of the waveguide bend I is smaller than those of the circular bend, Euler bend, Euler-circular bend, and Bezier bend when the equivalent bending radius R₀ is in the range of 2 to 5 μm. In particular, when R₀=2 μm, a silicon waveguide bend with bending loss of only 0.005 6 dB/90° is obtained, and low wavelength dependence of the loss is achieved. When R₀=4 μm and 5 μm, the loss of the waveguide bend II is also one order of magnitude lower than the above mentioned waveguide bends. In summary, the proposed silicon waveguide bend Ⅰ and Ⅱ have the advantages of compact size and low loss, which are very promising for future applications in compact and large-scale silicon photonic chips.