An apodized fiber Bragg grating, and a phase mask, method and system for making such a grating are disclosed. The refractive index profile of the grating has a periodic apodization phase component which is designed so that the grating fringes reflecting light in a spectral region of interest are apodized, by generating spurious reflection features outside of this spectral region of interest. Apodization is therefore provided through a phase variation of the grating as opposed to an amplitude variation. The phase component is added to the profile of the phase mask grating corrugations to obtain the phase-apodized grating.