“…Adjoint-based sensitivities trace their roots to control theory [29][30][31][32], and have since been used for rapid, efficient optimization in circuit theory [33], aerodynamics [34], mechanics and elasticity [35], quantum dynamics [36,37], and deep learning [38][39][40], where it is known as "backpropagation." More recently it has emerged as a promising design tool for nanophotonics [18,19,41] for applications including waveguide demultiplexers [17,42,43], beam deflectors [44,45], photonic bandgaps [46], solar cells [47], and many others. Preliminary studies have applied inverse design to metasurfaces [13,20,45,48], including large-area metasurfaces [15,49], albeit thus far limited to isolated frequencies or metrics other than lens focusing (beam deflection, polarizers, etc.…”