Long-distance pattern projection through an unfixed multimode fiber with natural evolution strategy-based wavefront shaping.

Focusing light into an arbitrary pattern through complex media is desired in energy delivery-related scenarios and has been demonstrated feasible with the assistance of wavefront shaping. However, it still encounters challenges in terms of pattern fidelity and focusing contrast, especially in a noisy and perturbed environment. In this work, we show that the strategy relying on natural gradient ascent-based parameter optimization can help to resist noise and disturbance, enabling rapid wavefront optimization towards high-quality pattern projection through complex media. It is revealed that faster convergence and better robustness can be achieved compared with existing phase control algorithms. Meanwhile, a new fitness function based on cosine similarity is adopted for the algorithm, leading to higher focusing contrast without sacrificing similarity to the target pattern. As a result, long-distance projection of an arbitrary pattern can be accomplished with considerably enhanced performance through a 15-meter multimode fiber that is not fixed and susceptible to perturbation. With further engineering, the approach may find special interests for many biomedical applications, such as deep-tissue photon therapy and optogenetics, where free-space localized optical delivery encounters challenges.