Graded-index materials offer virtually complete control over light propagation in integrated photonic chips but can be challenging to implement. Here, an anisotropic graded-index metamaterial, synthesized with fully etched silicon subwavelength structures, is proposed. Based on this material, a spot size converter that expands the transverse electric (TE) mode field profile from a 0.5 µm wide silicon wire waveguide to a 15 µm wide waveguide within a length of only 14 µm is designed. Measured insertion losses are below 1 dB in an unprecedented 130 nm bandwidth, limited by the measurement setup, with full 3D finite-difference time-domain (FDTD) simulations predicting a bandwidth in excess of 300 nm. Furthermore, the device is well suited to feed fiber-to-chip grating couplers, while requiring a footprint ten times smaller than conventional adiabatic tapers.