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The efficiency of thin film silicon solar cells critically depends on the optical absorption. In this work, we numerically investigate the light trapping effect in the weak absorption regime for 1.5 μm thick crystalline silicon at normal incidence. Using electromagnetic simulations, we study the impact of different textures on the light absorption enhancement in two-dimensional (2D) device configuration. We discover that the light trapping effect of commercially used textures from Asahi glass is close to the 2D Lambertian result (F = πn), while optimized periodic gratings show better performances, and both rectangular and triangular gratings are capable to exceed the Lambertian result. To further explore the optimal light trapping structures, we develop a simulation method combining finite-difference time-domain (FDTD) calculations and the optimization algorithm (Nlopt-COBYLA). Over a 900-1100 nm wavelength range, our optimized surface texture in two dimensions (2D) enhances absorption by a factor of 2.7πn, considerably larger than the original πn Lambertian result and exceeding by almost 50% a recent generalization of Lambertian model for periodic structures in finite spectral range. However, our structure still obeys the conventional πn Lambertian limit when averaged over all the angles.