Page 210 - Fiber Bragg Gratings
P. 210
4.9 Multilayer analysis 187
Figure 4.34: (a) Two layers on a substrate. The refractive index of each layer
is also indicated. The left-hand figure is transformed into the problem shown in
(b), with a complex reflectivity p^ at the interface with the substrate, replacing
the layer n 2.
Equations (4.9.2) and (4.9.3) can be expressed by algebraic manipula-
tion in the following matrix form:
The reflectivity r l at the substrate interface is
and the transmission coefficient, t l}
Once again applying continuity at the second interface from the bot-
tom, the reflected and transmitted fields are described as
The phase <PJ = fySlj = ^TTUjSLjlX.
