In recent years, great effort was spent by the nano-photonic community in the research on integrated slow light devices. Delay of light pulses directly on chip, allowing for all-optical memory and buffer operation, will be a key building block in the realization of a fully optical communication networks. Slow-light devices are also promising for reducing the footprint of components like optical modulators. In this context, one-dimensional grating waveguides are one of the possible solutions. They exhibit a slow-light band near the edge of photonic band gap, where the group index can in theory be arbitrarily high and is only limited by loss and backscattering induced by fabrication disorder [1,2]. Also, such waveguides are compatible with the standard Silicon-On-Insulator (SOI) platform. Their simple geometry makes them much easier to fabricate compared to systems proposed for slow-light implementation, like photonics crystal waveguides and coupled ring resonators. In this work, by using an exact approach to the solution of Maxwell equations through the Aperiodic-Fourier Modal Method (A-FMM) , we systematically study band dispersion in one-dimensional grating waveguides in SOI as a function of geometrical parameters. We show that by proper optimization of the geometry it is possible to increase band-edge slow-light propagation over previously reported values. The A-FMM is also well suited to study transmission and reflection spectra through a finite length of slow-light waveguide, allowing for the design of tapered structures with optimal coupling to standard silicon wires.
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 C. Scancalepore et al, Proc. SPIE Vol. 9372 93720G-1 (2015), DOI: 10.1117/12.2075334
 J.P. Hugonin et al., Opt. Quantum Electron. 37, 107 (2005)