We assume that the refractive index
perturbation of the grating is homogeneous and restricted to the fiber core (ncladding =
)
and then the D parameter is given by
|
(C-12) |
where h is the fraction of the
modal power that is contained in the fiber core. From equations (C-7), (C-8)
and (C-12) we see that 2|k| = hkDeac/2ncore,
q = Arg(k) and s = hkDedc/2ncore. The refractive
index change is small and then De = D(n2core) = 2ncoreDn and using (eq.
(C-11) we obtain
|
(C-13) |
Since the index perturbation is small,
equation (C-7) can be written
|
(C-14) |
where Dnac and Dndc
are the "ac" and "dc" index change, respectively. The following approximation
has been used
|
(C-15) |
The modulus of the coupling coefficient
q is proportional to the refractive index modulation amplitude. The coupling
coefficient phase corresponds to the excess optical phase of the grating; the
term q(z) is the spatial grating phase and the integral term gives the
optical modification to the spatial phase due to the dc index change.
The derivative of the coupling
coefficient phase gives the extra spatial frequency of the grating in addition
to 2p/Ld
|
(C-16) |
and then an effective grating period can be
defined for wavelength close to the Bragg grating as
|
(C-17) |
|
