An increasing number of integrated photonic solutions find applications in the fields of biomedicine, manufacture, quantum computation and telecommunications. Size mismatch between optical fibers, light sources, photodetectors and photonic waveguides is usually significant, typically with the former having cross-sections on the orders of hundreds of micrometers or more and the latter a few micrometers or hundreds of nanometers. Efficiency in coupling light to and from photonic integrated circuits is an extremely important parameter since it influences device's performance, affecting signal-to-noise ratio. Several approaches exist for light coupling, such as off-plane coupling with the assistance of grating couplers, onplane/edge coupling with or without the assistance of tapers and adiabatic coupling. In this study we focus on grating couplers designed in amorphous silicon-on-insulator (SOI) platforms. Grating couplers are compact, can be tested at waferlevel, and do not require application specific fiber terminations, such as lenses and/or tapers. Two approaches in the optimization of grating couplers were explored, one based on a lithographic mask defined by the superposition of two different grating patterns, with different periods, having an offset to provide a random distribution of grating elements, and a technique based on the quadratic variation of the refractive index of the grating structure along its length. Results were obtained from 2D-FDTD simulations. Coupling efficiencies for the quasi-TE mode over -13 dB and -3 dB were obtained for the random and quadratic variations of the effective refractive index at a wavelength of 1550 nm, without bottom reflectors.