Multimode fibers (MMFs) are a promising solution for high-throughput signal transmission in the time domain. However, crosstalk among different optical modes within the MMF scrambles input information and creates seemingly random speckle patterns at the output. To characterize this process, a transmission matrix (TM) can be used to relate input and output fields. Recent innovations use TMs to manipulate the output field by shaping the input wavefront for exciting advances in deep-brain imaging, neuron stimulation, quantum networks, and analog operators. However, these approaches consider input/output segments as independent, limiting their use for separate signal processing, such as logic operations. Our proposed method, which makes input/output segments as interdependent, adjusts the phase of corresponding output fields using phase bias maps superimposed on input segments. Coherent superposition enables signal logic operations through a 15-m-long MMF. In experiments, a single optical logic gate containing three basic logic functions and cascading multiple logic gates to handle binary operands is demonstrated. Bitwise operations are performed for multi-bit logic operations, and multiple optical logic gates are reconstructed simultaneously in a single logic gate with polarization multiplexing. The proposed method may open new avenues for long-range logic signal processing and transmission via MMFs.

Information retrieval from visually random optical speckle patterns is desired in many scenarios yet considered challenging. It requires accurate understanding or mapping of the multiple scattering process, or reliable capability to reverse or compensate for the scattering-induced phase distortions. In whatever situation, effective resolving and digitization of speckle patterns are necessary. Nevertheless, on some occasions, to increase the acquisition speed and/or signal-to-noise ratio (SNR), speckles captured by cameras are inevitably sampled in the sub-Nyquist domain via pixel binning (one camera pixel contains multiple speckle grains) due to finite size or limited bandwidth of photosensors. Such a down-sampling process is irreversible; it undermines the fine structures of speckle grains and hence the encoded information, preventing successful information extraction. To retrace the lost information, super-resolution interpolation for such sub-Nyquist sampled speckles is needed. In this work, a deep neural network, namely SpkSRNet, is proposed to effectively up sample speckles that are sampled below 1/10 of the Nyquist criterion to well-resolved ones that not only resemble the comprehensive morphology of original speckles (decompose multiple speckle grains from one camera pixel) but also recover the lost complex information (human face in this study) with high fidelity under normal- and low-light conditions, which is impossible with classic interpolation methods. These successful speckle super-resolution interpolation demonstrations are essentially enabled by the strong implicit correlation among speckle grains, which is non-quantifiable but could be discovered by the well-trained network. With further engineering, the proposed learning platform may benefit many scenarios that are physically inaccessible, enabling fast acquisition of speckles with sufficient SNR and opening up new avenues for seeing big and seeing clearly simultaneously in complex scenarios.

Optical imaging through or inside scattering media, such as multimode fiber and biological tissues, has a significant impact in biomedicine yet is considered challenging due to the strong scattering nature of light. In the past decade, promising progress has been made in the field, largely benefiting from the invention of iterative optical wavefront shaping, with which deep-tissue high-resolution optical focusing and hence imaging becomes possible. Most of the reported iterative algorithms can overcome small perturbations on the noise level but fail to effectively adapt beyond the noise level, e.g., sudden strong perturbations. Reoptimizations are usually needed for significant decorrelation to the medium since these algorithms heavily rely on the optimization performance in the previous iterations. Such ineffectiveness is probably due to the absence of a metric that can gauge the deviation of the instant wavefront from the optimum compensation based on the concurrently measured optical focusing. In this study, a square rule of binary-amplitude modulation, directly relating the measured focusing performance with the error in the optimized wavefront, is theoretically proved and experimentally validated. With this simple rule, it is feasible to quantify how many pixels on the spatial light modulator incorrectly modulate the wavefront for the instant status of the medium or the whole system. As an example of application, we propose a novel algorithm, the dynamic mutation algorithm, which has high adaptability against perturbations by probing how far the optimization has gone toward the theoretically optimal performance. The diminished focus of scattered light can be effectively recovered when perturbations to the medium cause a significant drop in the focusing performance, which no existing algorithms can achieve due to their inherent strong dependence on previous optimizations. With further improvement, the square rule and the new algorithm may boost or inspire many applications, such as high-resolution optical imaging and stimulation, in instable or dynamic scattering environments.