Page 26 - Fiber Bragg Gratings

1.3 Origins of the refractive index of glass 7

0.4079426 (0.7182), and 0.8974794 (0.8542) [33,34], where the data in
parentheses refers to GeO 2. The group index N is defined as

which determines the velocity at which a pulse travels in a fiber. These
quantities are plotted in Fig. 1.2, calculated from Eqs. (1.1.2) and (1.1.3).
We note that the refractive index of pure silica at 244 nm at 20°C is
1.51086. The data for germania-doped silica may be found by interpolation
of the data for the molar concentration of both materials. Although this
applies to the equilibrium state in bulk samples, they may be modified
by the fiber fabrication process.
The change in the refractive index of the fiber at a wavelength A may
be calculated from the observed changes in the absorption spectrum in
the ultraviolet using the Kramers-Kronig relationship [32,35],

where the summation is over discrete wavelength intervals around each
of the i changes in measured absorption, a t. Therefore, a source of photoin-
duced change in the absorption at A l < A' < A 2 will change the refractive
index at wavelength A.

Figure 1.2: Refractive index n and the group index, N of pure silica at 20°C.