A homogeneous FBG has constant values
for Dnac, Dndc and L in the range 0 £ z £ L. In this case, the
coupled mode equations can be solved analytically by differentiating
equations (3-2) and substituting the first derivatives by the
equations (3-2); for example for u(z,d), we have
|
(3-4) |
The same kind of equation is obtained
for v(z,d) [3-2]. Using the appropriate boundary conditions, the
reflection amplitude r(d) and the transmission amplitude t(d) are found to be
|
(3-5) |
where g2 = |q|2 - d2. A meaningful expression of q is obtained for a design period that
corresponds exactly to the physical period L and for an effective
refractive index set to n0+Dndc (and then the integral term in
equation (3-3) vanishes). In this case, the coupling coefficient phase
factor reduces to p/2 and then q = i|q| = i×h×p×Dnac/l.
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