Tapered Simplified Modal Method for Analysis of Non-rectangular Gratings

The Simplified Modal Method (SMM) provides a quick and intuitive way to analyze the performance of gratings of rectangular shapes. For non-rectangular shapes, a version of SMM has been developed, but it applies only to the Littrow-mounting incidence case and it neglects reflection. Here, we use the theory of mode-coupling in a tapered waveguide to improve SMM so that it applies to non-rectangular gratings at arbitrary angles of incidence. Moreover, this new 'Tapered Simplified Modal Method' (TSMM) allows us to properly account for reflected light. We present here the analytical development of the theory and numerical simulations, demonstrating the validity of the method.