Simulations of waveguide Bragg grating filters based on subwavelength grating waveguide

Subwavelength grating waveguides represent a flexible and perspective alternative to standard silicon-on-insulator nanophotonic waveguides. In such structures, waves propagate in the form of Bloch modes, in contrast to standard longitudinally uniform waveguides. Tunability of parameters of subwavelength grating structures possesses a great advantage of a broad variability of the (effective) refractive index and its dispersion, without significantly increasing fabrication complexity. A subwavelength grating structure is based on a (quasi)-periodic arrangement of two different materials, i.e. rectangular nanoblocks of silicon, embedded into a lower-index superstrate, with a period (much) smaller than the operational wavelength of the optical radiation. Clearly, by changing the filling factor, i.e., the duty-cycle of the subwavelength grating structure, its effective refractive index can be varied essentially between that of the superstrate and that of silicon. Our contribution is devoted to a detailed numerical analysis of Bloch modes in subwavelength grating waveguides and Bragg gratings based on subwavelength grating waveguides. Two independent versions of 3D Fourier modal methods developed within last years in our laboratories are used as our standard numerical tools. By comparison with results obtained with a 2D FDTD commercially available method we show that for reliable design of subwavelength grating waveguide devices of this kind, full-vector 3D methods have to be used. It is especially the case of Bragg gratings based on subwavelength grating waveguides, as analyzed in this paper. We discuss two options of a subwavelength grating modulation - designed by changing the subwavelength grating duty cycle, and by misplacement of Si blocks, and compare their properties from the point of view of fabrication feasibility.