“…G RATINGS in waveguides and cavities play an important role in many active and passive integrated optical devices, such as distributed Bragg reflectors (DBRs) and distributed feedback (DFB) lasers [1], optical grating couplers [2], single wavelength microring mirrors [3], and single wavelength ring lasers [4], [5]. For the design and analysis of these periodic devices, the coupled mode theory (CMT) is known to be a fast and relatively accurate method.…”