In this paper, we consider the scheduling of SE(switching element)-disjoint multicasting in photonic Banyan-type switching networks constructed with directional couplers. This ensures that at most, one connection holds each SE in a given time thus, neither crosstalk nor blocking will arise in the network. Such multicasting usually takes several routing rounds hence, it is desirable to keep the number of rounds(i.e., scheduling length) to a minimum. We first present the necessary and sufficient condition for connections to pass through a common SE(i.e., make crosstalk) in the photonic Banyan-type networks capable of supporting one-to-many connections. With definition of uniquely splitting a multicast connection into distinct subconnections, the crosstalk relationship of a set of connections is represented by a graph model. In order to analyze the worst case crosstalk we characterize the upper bound on the degree of the graph. The successor paper(Part II)[14] is devoted to the scheduling algorithm and the upper bound on the scheduling length. Comparison with related results is made in detail.