Page 34 - Fiber Bragg Gratings

2.1. Photorefractivity and photosensitivity 15

and

(1) (2)
where e r = 1 + ^ is the linear permittivity, ^ is the first term of the
nonlinear susceptibility (which can be nonzero in crystalline media), and
(3)
^ is the third-order nonlinearity (nonzero in all materials).
Using Equations (2.1.2) and (2.1.3), the perturbed permittivity under
the influence of an applied electric field is

and since the refractive index n is related to the permittivity as

from which immediately follows

2)
In photorefractive materials with an active ^ , an internal charge
can build up due to trapped carriers released from defects. These give
rise to an internal field, which modulates the refractive index locally via
the first term in Eq. (2.1.7). The induced index changes result directly
(2)
from the linear electro-optic effect (^ ) and are in general quite large,
4 (2)
~10~ . However, with ^ being zero in glass, the induced refractive
index with an applied field can only result from the nonzero third-order
(3)
susceptibility, x - Even if an internal field could develop, the refractive
7
index change is small, ~10~ ; however, as will be seen, if an internal field
is possible in glass, it results in a modest nonlinearity [2]. We now assume
the existence of an internal field E dc and apply an external field E app[ied.
The induced index change is as follows: