Design of grating-assisted codirectional couplers with discrete inverse-scattering algorithms

We present a flexible and accurate approach for the design of grating-assisted codirectional couplers. The design method is based on a discrete coupling model. The two spectral responses of the coupler are chosen according to certain physical constraints. We prove necessary and sufficient conditions for realizability and demonstrate how they can be applied for determining an optimal coupler response. The ambiguity when designing a coupler with a specified cross-coupling response is also discussed in detail. Once the realizable responses have been found, they can be applied as input to a layer-peeling inverse-scattering method which computes the required coupler structure. The layer-peeling algorithm is implemented in the time domain for increased efficiency and clarity. Since the algorithm is tailored to the special case of codirectional coupling, divergence problems for strong coupling is avoided. Numerical design examples are shown in order to illustrate the performance of the method. Various realizations of square passband filters with high power transfer and a long-period fiber grating filter for EDFA gain flattening within the entire C-band have been designed.