The ability to generate any arbitrarily chosen optical field in a three-dimensional (3D) space, in the absence of any sources, without modifying the index of refraction, remains an elusive but much-desired capability with applications in various fields such as optical micromanipulation, imaging, and data communications, to name a few. In this work, we show analytically that it is possible to generate any desired scalar optical field with predefined amplitude and phase in 3D space, where the generated field is an exact duplicate of the desired field in case it is a solution of Helmholtz wave equation, or if the existence of such field is strictly forbidden, the generated field is the closest possible rendition of the desired field in amplitude and phase. The developed analytical approach is further supported via experimental demonstration of optical beams with exotic trajectories and can have a significant impact on the aforementioned application areas.
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.
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