Slow and Stopped Light in Dynamic Moir\'e Gratings

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.