Thin-film polymer-on-silicon modulators are efficient devices which have shown potential for integration scalability due to chromophore-based electro-optic constant engineering. Assembling them into hybrid silicon-photonics integrated circuits poses an interesting challenge in terms of bandwidth and footprint. Accordingly, we propose the first, to the best of our knowledge, sub-wavelength silicon tapered structures to couple light vertically from a polymer film platform to a silicon-on-insulator chip. By designing horizontally tapered and longitudinally segmented waveguides in the subwavelength regime to couple light vertically, we can overcome the bandwidth limitations of grating couplers while still have considerable footprint reduction when compared to continuous linearly tapered evanescent vertical coupling. Our simulation results show that silicon-on-insulator-compatible linearly tapered segmented waveguides offer losses bellow 0.5 dB in the C and L bands with four times smaller coupling length than their continuous counterpart. Preliminary studies show that there is good horizontal misalignment tolerance up to 1.5 micrometers.