Page 166 - Fiber Bragg Gratings

4.3 Coupling of counterpropagating guided modes 143

By choosing the appropriate ft value for identical modes (/u, = u) but
with opposite propagation directions in Eq. (4.3.1) and dividing both sides
by exp[j(w£ + fi^z)],

which leads to the following simple coupled-mode equations by choosing
the appropriate synchronous terms,

with

and the dc coupling constant,

while the ac coupling constant K ac includes the overlap integral,

if /u = v. The change in the amplitude of the driving mode may also be
derived from Eq. (4.2.21) as

Eqs. (4.3.3) and (4.3.7) are the coupled-mode equations from which the
transfer characteristics of the Bragg grating can be calculated.