The simplifiedmodal method (SMM) [Opt. Quantum Electron. 37, 309 (2005)] provides a quick, intuitive way to analyze the performance of the gratings of rectangular shapes. For non-rectangular shapes, a version of SMM has been developed [Opt. Lett. 33, 1554 (2008)], but it applies only to the Littrow-mounting incidence case and 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 and requires fewer coupled guided modes to compute the correct diffracted field than required plane wave modes in rigorous coupled wave analysis (RCWA). We present here the analytical development of the theory and numerical simulations, demonstrating the validity of the method by comparing it with RCWA and the finite difference time domain method. (C) 2016 Optical Society of America
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