Optical speckles, generated through interference of scattered light, have been widely used in optical imaging and sensing applications, as well as providing disordered optical potentials for localization of cold atoms, colloidal particles and active media. While fully-developed speckles typically satisfy Rayleigh statistics, recent studies have shown that fully-developed speckles can be customized to possess non-Rayleigh statistics in a single plane. However, upon axial propagation, those customized statistics erode away. Whether it is possible to create axially-varying speckles with tailored statistics has remained an open question. The major obstacle comes from the fact that the field profiles at different axial planes are related—the field profile at one axial plane determines the fields at all planes after it.

To resolve this challenge, we propose and experimentally demonstrate a method to customize the intensity statistics of 3D-speckles. Specifically, we control the intensity probability density functions of speckle patterns on multiple axial planes. This is accomplished by appropriately manipulating the phase front of a laser beam, with a spatial light modulator. We can tailor the far-field speckles to maintain a desired intensity PDF, while propagating axially and evolving into distinct patterns. We can also create speckles with different intensity PDFs on multiple planes, demonstrating that distinct statistics can be independently encoded at varying axial locations.

Our method to design 3D speckle statistics opens many possibilities in both fundamental studies and applied research, such as three-dimensional imaging and sensing, optical trapping and manipulation. Moreover, the optical potentials created by 3D customized speckles can provide an effective platform for studying 3D transport and localization of cold atoms in disordered potentials.