Page 211 - Fiber Bragg Gratings

188 Chapter ^ Theory of Fiber Bragg Gratings

As before for the matrix method, combining Eqs. (4.9.3M4.9.7) leads
to

Equation (4.9.8) may be simplified as for the T-matrix method as,

from which the matrix elements follow as

Applying the boundary condition in the region n 3, which is infinite,
leads to S 3 = 0 as applied to Eq. (4.8.2). The simple complex reflectivity
for the layer n 2 follows

and the transmission coefficient r 2 is given by

Replacing the second section by a single interface as shown in Fig.
4.34b and adding another layer with fields R± and S 4 above section 3, the
composite reflectivity p follows from