In the intricate world of light, a journey through inhomogeneous media often leads to distortions in space, time, spectrum, and polarization. These distortions, detrimental to applications like optical manipulation, imaging, and communication, have long posed a challenge. Enter the art of wavefront shaping (WS) – a potent tool for correcting these wave maladies in linear optics. But that's not all. Nonlinearity adds a twist, finding purpose in fields from biological sensing to phototherapy. Now, picture combining these forces – nonlinearity and WS – opening doors to unprecedented control.

Yet, most existing setups rely on iterative feedback loops, guzzling computational resources and time. There's a smarter way. Meet the scattering matrix (SM) method, capable of sculpting light output with minimal optimization time. As a bonus, SM offers insights into the scattering medium's mesoscopic traits, unveiling memory effects and transmission eigenchannels.

Figure: Reconfigurable focusing of nonlinear signals via wavefront shaping method based on SM. (a) Measured SM which connects the input modes (horizontal axis) and output nonlinear modes (vertical axis). Hue and brightness represent phase and amplitude, respectively. Calculated phase patterns (b) and the corresponding focal spots (c) located on different positions of ROI. (d) Intensity cross-section of the nonlinear focal spots located on different sub-regions of ROI.

Our group has developed this method and taken the concept further. We have cracked the code to determine the SM of a scattering medium embedded with quadratic nonlinearity. The method, using a 256x256 SM dimension, emerges from four-phase interferometry. We have proved its validity by coaxing nonlinear signals into refocused single and double spots, employing optical phase conjugation.

Imagine, a carefully orchestrated dance of light – where a matrix row's phase pattern triggers precise nonlinear focus. The result? Sum-frequency generation dances in multiple spots across the region of interest, each with comparable intensity and a remarkable peak-to-background ratio of about 25.

But that's just the beginning. The SM method wields unparalleled nonlinear scattered light control. We showcase point-by-point scans along predefined paths, adjusting the phase pattern switch speed to fine-tune scanning pace. This breakthrough offers a doorway to high-resolution scanning microscopy and particle trapping through dense, scattering media.

In essence, this work reimagines nonlinear scattering. Its implications span nonlinear signal recovery, microscopic imaging, and tracking through scattering media, even delving into the intricate realm of quantum information processing within complex environments. The future of light manipulation looks astonishingly bright.

This research is published in “Fengchao Ni, Haigang Liu, Yuanlin Zheng and Xianfeng Chen, Nonlinear harmonic wave manipulation in nonlinear scattering medium via scattering-matrix method, Advanced Photonics, 5(4), 046010 (2023)”.

Link: https://www.researching.cn/Articles/OJa42b953eea5bbc67