Aperiodic optical phased array based on number theory

The optical phased array has been developed to realize solid-state optical beam steering following the advent of silicon photonics. Thus far, its feasibility has lacked either steering quality or optical efficiency, and its optimal design still remains unknown. Herein, we propose a scalable and wavelength-independent phased array design methodology that achieves steering quality and optical efficiency. This novel design methodology is based on a special aperiodicity from number theory of a complete residue system that is fundamentally suited for phasor cancellation for the desired array sparsity. A specific design derived based on this methodology was implemented in silicon with 128 phase-controlled antennas in the O band, and it was experimentally verified in a two-dimensional steering demonstration that featured a record-high beam-forming efficiency (>30%) and a high-grating-lobe suppression (>10 dB) over a field-of-view of 40 ⅹ 7.2°. This optical efficiency improved by at least 250% compared with prior art.