Page 355 - Fiber Bragg Gratings

332 Chapter 7 Chirped Fiber Bragg Gratings

Figure 7.16: The transmission spectra of four cosine apodized gratings (L g
5
= 100 mm, An = 7.5 X 10~ , AA cfeirp = 0.75 nm) as a function of random variation
in the refractive index modulation. A has <5An = 0; B, C and D have a maximum
5
random variation <5A/i = le X 10~ over length scales of 50,100, and 200 microns,
respectively, as in Fig. 7.15.

amounts to —10 pm at a wavelength of 1550 nm for an index change of
5
1 X 10~ . The same change in the wavelength occurs for a random varia-
tion in the Bragg wavelength period 8A g of ~ 3.42pm.

7.3 Super-step-chirped gratings

Chapter 3 introduces the fabrication of ultralong gratings. One of the
methods of generating ultralong gratings is by stitching together a set of
short chirped gratings, to form the super-step-chirped grating (SSCG)
[46]. The structure is schematically shown in Fig. 5.18, Chapter 5. Here
we consider the influence of an imperfect stitch between two sections of
the SSCG. Figure 7.17 shows three step-chirped gratings with gaps in
between. The first SCG (LHS) begins at A l and finishes at A 2, in AT sections,
each with an integral number of periods. The number of periods is adjusted
so that each section is nominally the same length within the length of a
period. The second SCG begins with a period A 2 + <5A and ends at a period
A 2 + (N — 1) 5A. The two gratings are written sequentially, ideally with
zero gap in between. In a perfect grating, the periods would simply follow