Designing optical fields in inhomogeneous media

Designing optical fields with predetermined properties in source-free inhomogeneous media has been a long-sought goal due to its potential utilization in many applications, such as optical trapping, micromachining, imaging, and data communications. Using ideas from the calculus of variations, we provide a general framework based on the Helmholtz equation to design optical fields with prechosen amplitude and phase inside an inhomogeneous medium. The generated field is guaranteed to be the closest physically possible rendition of the desired field. The developed analytical approach is then verified via different techniques, where the approach's validity is demonstrated by generating the desired optical fields in different inhomogeneous media.