  Modern microelectronic processors have migrated towards parallel computing
architectures with many-core processors. However, such expansion comes with
diminishing returns exacted by the high cost of data movement between
individual processors. The use of optical interconnects has burgeoned as a
promising technology that can address the limits of this data transfer. While
recent pushes to enhance optical communication have focused on developing
wavelength-division multiplexing technology, this approach will eventually
saturate the usable bandwidth, and new dimensions of data transfer will be
paramount to fulfill the ever-growing need for speed. Here we demonstrate an
integrated intra- and inter-chip multi-dimensional communication scheme enabled
by photonic inverse design. Using broad-band inverse-designed mode-division
multiplexers, we combine wavelength- and mode- multiplexing of data at a rate
exceeding terabit-per-second. Crucially, as we take advantage of an orthogonal
optical basis, our approach is inherently scalable to a multiplicative
enhancement over the current state of the art.
