Nonlinear optical (NLO) responses of topological materials are under active research in recent years. Yet by far most studies focused on the bulk properties, whereas the surface effects and the difference between surface and bulk responses have not been systematically studied. In this work, we develop a generic Greens function framework to investigate the surface NLO properties of topological materials. The Greens function framework can naturally incorporate many body effects and can be easily extended to high order NLO responses. Using $rm T_d WTe_2$ as an example, we reveal that the surface can behave disparately from the bulk under light illumination. Remarkably, the shift and circular current on the surface can flow in opposite directions to that in the bulk. Moreover, the light induced spin current on the surface can be orders of magnitude stronger than that in the bulk. We also study the responses under inhomogeneous field and higher order NLO effect, which are all distinct on the surface. These anomalous surface NLO responses suggest that light can be a valuable tool for probing the surface states of topological materials, while on the other hand, the surface effects shall be prudently considered when investigating the optical properties of topological materials.
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