Comparison of 2D and 3D Fourier modal methods for modeling subwavelength-structured silicon waveguides

Frequency-domain Fourier modal methods have recently evolved into efficient tools for rigorous numerical modeling of a wide class of photonic and plasmonic structures and devices. In this contribution we describe the application of our 2D and 3D in-house tools, namely aperiodic rigorous coupled wave analysis (aRCWA) and bi-directional mode expansion propagation method using harmonic expansion (BEXX), on a recently described novel type of subwavelength grating (SWG) waveguides. They are created by means of periodically interlacing silicon segments with a superstrate material with a lower refractive index. It has been shown recently, both theoretically and experimentally, that for a suitable choice of SWG parameters such as grating period and duty cycle, the structure can support low-loss guided (Bloch) mode. Its effective index, mode profile and dispersion characteristics can thus be tailored to specific needs without the necessity of changing material composition. In our methods, either complex coordinate transformation or uniaxial anisotropic perfectly matched layers have been applied as efficient absorption boundary conditions. In order to reduce the number of expansion terms needed to reach required accuracy, the adaptive spatial resolution technique has been implemented. Structural symmetries of the devices can be fully utilized to this aim, too. Propagation constants of Bloch modes are also compared with those obtained with a full-vector film mode matching (FiMM) mode solver using the very simple effective medium theory (EMT).