Page 204 - Fiber Bragg Gratings

4.8 Grating simulation 181

in which the field amplitudes on the RHS are the same as the those
expressed in Eq. (4.8.1).
Replacing the N multiplied 2x 2 matrices in Eq. (4.8.5) by a single
2x 2 matrix, we get the transfer function of the whole grating,

where the matrix T is

Now the transmissivity rof the whole grating follows from Eqs. (4.8.3)
and (4.8.4),

and reflectivity p,

From the solution to the coupled-mode equations (4.3.9) and (4.3.10),
the transfer matrix elements for the y'th section are

A schematic of the sectioned gratings with the relevant parameters
is shown in Fig. 4.31.