  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.
