Coupled-mode equations for periodic superstructure Bragg gratings.

Periodic superstructure Bragg gratings are gratings in which the parameters vary periodically. Although one can determine their properties by using the standard coupled-mode equations for the electric field envelopes, it is shown that the analysis is simplified if one considers the super envelopes, i.e., the envelopes of the usual envelope functions. These super envelopes satisfy a set of (super) coupled-mode equations, which are formally identical to the standard coupled-mode equations for a uniform grating. This shows that, within certain frequency ranges, any superstructure Bragg grating acts approximately as a uniform grating.