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We propose a new scheme for optical quantum simulation of topologicalsystems: by using optical systems to simulate the variation of eigenstates oftopological systems in momentum space, we can obtain the information oftopological numbers. In this paper the scheme is applied to the one-dimensional(1D) Su-Schrieffer-Heeger (SSH) model and the two-dimensional (2D)Bernevig-Hughes-Zhang (BHZ) model. In addition, in order to apply our scheme to2D topological systems, we design a method of calculating topological numbersby line integral. Furthermore, we propose a more effective optical simulationscheme for the 2D topological system: we do the optical simulation arounddiscontinuity points to obtain the vorticity of every discontinuity points andthe topological number is just the sum of the vorticity of all discontinuitypoints.

Using Optical Systems to Simulate Topological Systems in Momentum Space and Measure Their Topological Numbers