  We investigate the gradual emergence of the disorder-related phenomena in
intermediate regimes between a deterministic periodic Bragg grating and a fully
random grating and highlight two critical properties of partially disordered
Bragg gratings. First, the integral of the logarithm of the transmittance over
the reciprocal wavevector space is a conserved quantity. Therefore, adding
disorder merely redistributes the transmittance over the reciprocal space.
Second, for any amount of disorder, the average transmittance decays
exponentially with the number of grating layers in the simple form of
$\exp(-\eta N)$ for sufficiently large $N$, where $\eta$ is a constant and $N$
is the number of layers. Conversely, the simple exponential decay form does not
hold for small $N$ except for a highly disordered system. Implications of these
findings are demonstrated.
