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Programmable photonic integrated waveguide mesh (PPIWM) is similar to field programmable gate array (FPGA) in electronics, which can be programmed to form a variety of topologies to provide different functions flexibly. In mesh structure, the calculation of transmission characteristics between arbitrary input and output ports is the premise to realize its application. With the continuous development of PPIWM in scale and structure, it is particularly important to automatically and efficiently calculate the transmission characteristics between input and output ports by programming. At present, the existing calculation method is complicated, which is not conducive to programming and has the prominent problems of low computational efficiency. In this paper, the mesh structure is mapped to a graph network represented by dual node, which is easy to be calculated programmatically. On this basis, a calculation method for solving the transfer function between arbitrary input and output ports required by the mesh is proposed by successively simplifying the nodes. This method can greatly reduce the time of solving the transfer function in the large and complex mesh structure, and has the advantages of easy programming and high efficiency. A specific example of the mesh is given to verify the effectiveness of the algorithm.
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