Bragg grating waveguide is a photonic device, contained of arrays of partially overlapped refractive index voxels \cite{devices}.  These refractive index voxels form a one-dimensional photonic bandgap, which only allows a narrow spectrum of a broadband signal to be reflected and propagated through the waveguide . Figure 1 shows the schematic cross-section of the waveguide. The core of the waveguide is silica (SiO2)