Page 208 - Fiber Bragg Gratings

4.9 Multilayer analysis 185

Figure 4.33: The effect of too many sections on the simulation of a 6-nm
chirped 2-mm-long grating with 3729 (1 period/section) and 100 (37
periods/section) sections. The 100-section grating accurately models the grating,
while the assumptions for the simulation are violated for too many sections.

Third, adequate care must also be taken to smooth any spatial varia-
tion in the refractive index modulation. Sections of constant K ac but differ-
ent from adjacent ones inevitably form a superstructure [60, 61].
Superstructure can be responsible for replicas of the main Bragg reflection
peak at far-removed wavelengths, causing spurious cross-channel inter-
ference in filters. The smaller the section, the wider the wavelength band
over which the superstructure replicas may appear. Thus, there is a lower
limit to the number of grating sections that must be used to reduce this
detrimental effect. However, superstructure gratings, when carefully de-
signed, can be used to perform useful functions [62] and are covered in
Chapters 6 and 7.
Fourth, when simulating long chirped gratings, care must be taken
to allow adequate spectral resolution in order to calculate the group delay
accurately.

4.9 Multilayer analysis

4.9.1 Rouard's method
Simulation using this method relies on sectioning the grating into
multilayers and replacing the layer by an interface with a complex reflecti-
vity, which includes the phase change through the layer. To accurately