Abstract: Optical beam splitter ( BS) is one of the basic linear elements in quantum optics，which is widely

used in the preparation of quantum states.Based on the matrix transformation relation of BS，we derive the natural

representation of BS operator in the coherent state representation.Then，its normally form can be concisely deduced

by virtue of the technique of integration within ordered product ( IWOP) .Furthermore，as an application of coherent

state representation of BS operator，we conveniently derive the output state of multiphoton catalysis with coherent

state input.Compared with other methods，this method is easier and neater.

Key words: Optical beam splitter operator, coherent state representation, normal ordering product, quantum catalysis