The problems associated with the frequency response of an uniform FBG, like the high side lobe can be overcome by apodizing the refractive index profile of the FBG. Also by using the complex refractive index profile the frequency response can be tailored to meet the desired requirements
For a non-uniform grating, the spatial refractive profile can be written as
Here is called the visibility of the FBG and its value lies between 0 and 1, is the spatial chirp of the FBG, and is a slowly varying function of z.
The DC coupling coefficient becomes
And the AC coupling coefficient becomes
Both DC and AC coupling coefficients are function of z in this case.
By varying, the three parameters , various types of gratings can be realized.
Figure shows refractive index variation for various types of apodized gratings used in practice.
is called the visibility of the FBG and its value lies between 0 and 1, 
is the spatial chirp of the FBG, and 
is a slowly varying function of z. 
, various types of gratings can be realized. 
