Ta2O5-SiO2 quasi-rugate filters with a reasonable optimization of rugate notch filter design were prepared by ion-beam sputtering. The optical properties and laser-induced damage threshold are studied. Compared with the spectrum of HL-stacks, the spectrum of quasi-rugate filters have weaker second harmonic peaks and narrower stopbands. According to the effect of functionally graded layers (FGLs), 1-on-1 and S-on-1 Laser induced damage threshold (LIDT) of quasi-rugate filters are about 22% and 50% higher than those of HL stacks, respectively. Through the analysis of the damage morphologies, laser-induced damage of films under nanosecond multi-pulse are dominated by a combination of thermal shock stress and thermomechanical instability due to nodules. Compared with catastrophic damages, the damage sits of quasi-rugate filters are developed in a moderate way. The damage growth behavior of defect-induced damage sites have been effectively restrained by the structure of FGLs. Generally, FGLs are used to reduce thermal stress by the similar thermal-expansion coefficients of neighboring layers and solve the problems such as instability and cracking raised by the interface discontinuity of nodular boundaries, respectively. (C) 2018 Elsevier B.V. All rights reserved.