  We investigate a theoretical model for a dynamic Moir\'e grating which is
capable of producing slow and stopped light with improved performance when
compared with a static Moir\'e grating. A Moir\'e grating superimposes two
grating periods which creates a narrow slow light resonance between two band
gaps. A Moir\'e grating can be made dynamic by varying its coupling strength in
time. By increasing the coupling strength the reduction in group velocity in
the slow light resonance can be improved by many orders of magnitude while
still maintaining the wide bandwidth of the initial, weak grating. We show that
for a pulse propagating through the grating this is a consequence of altering
the pulse spectrum and therefore the grating can also perform bandwidth
modulation. Finally we present a possible realization of the system via an
electro-optic grating by applying a quasi-static electric field to a poled
$\chi^{(2)}$ nonlinear medium.
