Mode conversion based on dielectric metamaterial in silicon.

We propose, design and analyze a novel mode converter in silicon waveguide based on a graded index co-directional grating coupler. The device has a periodic variation in its refractive index along the propagation direction and a graded index profile along the transverse direction. The graded index profile is realized by the implementation of nanoscale dielectric metamaterial consisting of silicon features that are etched into the waveguide based on the concept of effective medium. Design considerations are discussed and analyzed in details in the framework of the coupled mode theory (CMT) and the effective medium theory (EMT). Using 3D finite difference time domain (FDTD) simulations we show that the mode converter can couple between different symmetric and asymmetric modes which are propagating along a single bus multimode waveguide. Mode purity on the order of 96%, crosstalk with the input mode of better than -23dB, and transmission of more than 96% can be obtained, with device length as short as 20µm, and over ~25nm spectral bandwidth around the design wavelength of 1550nm.