Back-propagation-assisted inverse design of structured light fields for given profiles of optical force.

Designing a monochromatic spatially-structured light field that recovers the pre-specified profile of optical force (OF) exerted on a particle is an inverse problem. It usually requires high dimensional optimization and involves lengthy calculations, thus remaining little studied despite decades of research on OF. We report here the first attempt to attack this inverse design problem. The modus operandi relies on the back-propagation algorithm, which is facilitated by the currently available machine learning framework, and, in particular, by an exact and efficient expression of OF that shows only polynomial and trigonometric functional dependence on the engineered parameters governing the structured light field. Two illustrative examples are presented in which the inversely designed structured light fields reproduce, respectively, a predefined spatial pattern of OF and a negative longitudinal OF in a transversely trapping area.