A monolithically integrated asymmetric graded index (GRIN) or step-index (GRIN) mode converters for microphotonic waveguides are proposed and described. The design parameters and tolerances are calculated for amorphous silicon (a-Si) couplers integrated with silicon-on-insulator waveguides. The GRIN and step-index couplers operate over a wide wavelength range with low polarization dependence, and the lithographic resolution needed is only ±1 μm. Finally, experimental results are presented for a single layer 3 μm thick step-index a-Si coupler integrated on a 0.8 μm thick SOI waveguide. The measured variation of coupling efficiency with coupler length is in agreement with theory, with an optimal coupling length of 15 μm for this device.