Optical Fiber Communications 4th Edition by Gerd Keiser

Exercise 11

Consider the 2 × 2 coupler shown in Fig. 10.8, where a and b are the matrices representing the field strengths of the input and output propagating waves, respectively. For a given input a 1 , we impose the condition that there is no power emerging from the second input port; that is, a 2 = 0. Find expressions for the transmissivity T and the reflectivity R in terms of the elements s iJ in the scattering matrix S given in Eq. (10.8).