Many-mode grating couplers by avoiding undesired couplings

Abstract

To couple many independent modes from free space to on chip, the key challenge is not enhancing the many necessary coupling rates (scattering-matrix elements) between targeted mode pairs. Instead, the key is to avoid additional cross-couplings to undesired modes, due to the presence of multiple simultaneously satisfied phase-matching conditions. With this principle, we identify scaling laws for the maximum number of high-efficiency multi-mode couplings that may be achievable for a given refractive index and design region, which are strongly supported by extensive numerical inverse-design experiments in 2D (one-dimensional coupler patterns, scattering in 2D). For such couplers, typical mode counts of 5--10 appear achievable. Three-dimensional couplers (patterned across two dimensions) can be markedly better, with tens of Fourier components in a single-layer device offering the possibility of high-efficiency coupling of hundreds to thousands of modes in relatively compact form factors. Numerical simulations of such a device, without any parameter optimization, predict efficiencies on the order of 5\% for 100 modes -- a collective order-of-magnitude improvement over previous designs.

8 pages, 7 figures, plus Supporting Information