Coupling light into or out of a photonic integrated circuit is often accomplished by establishing a vertical link between a single mode optical fibre and a resonant waveguide grating, which is then followed by a tapered and a single mode waveguides. For a chip to fibre coupler, the period of the diffraction grating is often apodized to achieve an optimal beam profile at the input of the optical fibre. The tapered waveguide operates as a spot-size converter, expanding laterally the light beam in the single mode waveguide, to match the profile of the fundamental mode of the resonant waveguide grating. In this work, we propose using subwavelength structures to modulate the refractive index of the tapered waveguide for the lateral expansion of the light beam, when operating at the 1550 nm wavelength. The engineered graded index structure is simulated through adequate numerical methods and its performance is analysed in terms of efficiency and mode profile matching. With our proposed inverted taper waveguide, we were able to obtain an adiabatic power transfer and coupling efficiency with the TE fundamental mode of -0.26 dB and -0.92 dB, respectively. This performance has been achieved in a structure 11.1 μm long and 14.27 μm wide. Furthermore, the obtained fields were fed into a resonant waveguide grating to evaluate the coupling efficiency into the fundamental mode of an optical fibre, resulting in an expected performance decrease of 0.1 dB and ∼0.6 dB by comparing respectively with the power transfer and coupling efficiency of the resonant waveguide grating when propagating the calculated TE0 mode.