In the current landscape of scientific research and technological innovation, fiber optic communication technology, as the cornerstone of the information society, is facing unprecedented opportunities and challenges. With the rapid development of technologies such as big data, cloud computing, and the Internet of Things, there is an increasing demand for communication networks that are high-speed, high-capacity, and low-latency. Against this backdrop, multi-mode fibers (MMFs) have become one of the key technologies for enhancing the capacity of fiber optic communication systems due to their ability to support a large number of modes. However, MMFs face issues in practical applications, such as mode cross-coupling and speckle effects, which can lead to signal distortion and reduced transmission efficiency. Since 2007, the introduction of wavefront shaping techniques has significantly expanded the application scenarios of multi-mode fibers (MMFs). By applying different phase patterns on spatial light modulators (SLMs) and iteratively optimizing the input wavefront to arbitrarily modulate the output optical field of MMFs, exciting applications based on a single MMF have been developed, such as deep-brain imaging, 3D holographic optical tweezers, single neuron stimulation, spectrometers, and nonlinear modulation. In these applications, all input patterns on the SLM serve as a single unit for a specific output target, suitable only for single-channel signal processing tasks.

This study proposes a transmission matrix (TM)-based wavefront shaping method that achieves long-distance all-optical logic operations by adjusting the phase distribution of the input optical field in multi-mode fibers. This method is not only capable of performing basic logic gate operations, such as AND, OR, and NOT, but also able to handle more complex signal processing tasks by cascading multiple logic gates. Furthermore, by employing polarization multiplexing techniques, researchers can simultaneously reconstruct multiple optical logic gates within a single logic gate, offering new avenues for enhancing system integration and security. Relevant research results were recently published in Photonics Research, Volume 12, No. 3, 2024. [ Zhipeng Yu, Tianting Zhong, Huanhao Li, Haoran Li, Chi Man Woo, Shengfu Cheng, Shuming Jiao, Honglin Liu, Chao Lu, Puxiang Lai. Long distance all-optical logic operations through a single multimode fiber empowered by wavefront shaping[J]. Photonics Research, 2024, 12(3): 587 ]

Figure 1. (A) presents a schematic flowchart illustrating the implementation of long-distance all-optical logic operations through a single multimode fiber using optical wavefront shaping technology; (B) demonstrates the verification of basic logic gate operations; (C) shows the implementation of cascaded logic gates; (D) exhibits the demonstration of multi-bit logic operations; (E) illustrates the realization of polarization multiplexing technology.

As depicted in Fig. 1A, researchers have devised a method for implementing optical logic operations in a MMF through wavefront shaping technology. This method involves selecting and marking three sub-areas of different colors on the input layer (digital micromirror device, DMD), with each sub-area carrying the expected wavefront patterns representing the logic operation combination "0+1". The light transmitted through the MMF forms the corresponding optical field on the output layer (digital camera), where two circular areas are pre-designated to represent the logic states "0" and "1". By using computer-generated off-axis holography, researchers measured the transmission matrix (TM) of the MMF, which involves scanning with a two-dimensional focal spot array on the near end face of the fiber and determining the MMF's TM (T_i) based on the output light field that results from each input light field (E_i). The logic computation result (Q) of the output optical field is determined by comparing the light intensity in the regions representing "1" and "0". To ensure the efficiency of all logic operations, researchers adjusted the light beam patterns projected onto the DMD and the coupling efficiency of the MMF. By introducing a common reference area on the DMD, researchers ensured the predominance of the reference light in all TM measurements of the sub-areas, which is crucial for logic operations based on phase. The achievements and innovations of this study mainly include the following four aspects:

1. Verification of Basic Logic Gate Operations: In the experiment, we successfully implemented AND, OR, and NOT logic gate operations in a single MMF by precisely controlling the wavefront patterns on the DMD (Fig. 1B). These operations were completed through specific subregions defined on the DMD, each corresponding to binary inputs ("0" and "1") and logic types. By measuring the TMs of the MMF and calculating the corresponding input wavefronts, the experimental results showed high-contrast light foci matching the expected logic output, verifying the correctness and reliability of the basic logic gates.
2. Implementation of Cascaded Logic Gates: We explored the method of cascading multiple logic gates to perform complex logic operations (Fig. 1C). By selecting and activating corresponding subregions on the DMD and loading precalculated wavefront patterns, the experiment successfully demonstrated the cascading operation of two logic gates. For example, by connecting the output of an AND gate to the output of an OR gate, more complex logic functions were achieved. This approach provides the possibility for constructing more complex optical logic circuits and signal processing systems.
3. Demonstration of Multi-bit Logic Operations: The experiment was not limited to single-bit logic operations; we extended the method to multi-bit logic operations (Fig. 1D). Researchers successfully executed 6-bit "bitwise AND" and "bitwise OR" operations by assigning different logic types to each bit position and loading corresponding wavefront patterns on the DMD. The output results of these operations were consistent with the expected logic outcomes, proving the effectiveness of this method in handling multi-bit logic operations.
4. Implementation of Polarization Multiplexing Technology: To enhance the system's integration and security, we also explored the use of polarization multiplexing technology to simultaneously implement multiple logic operations within the same logic gate (Fig. 1E). By displaying different wavefront patterns on the DMD and controlling the polarization state of light at the output end with a linear polarizer, the experiment successfully achieved OR and AND operations in different polarization channels. This method not only improves the integration of the system but also strengthens the security of information transmission.

In the future, the technology of all-optical logic operations based on multimode fibers is expected to make significant leaps forward. With further advancements in spatial light modulators (SLMs) and wavefront shaping, we can anticipate substantial improvements in system speed and processing capabilities, enabling more complex logic operations and multi-bit manipulations. Additionally, by integrating advanced multiplexing technologies such as polarization, wavelength, and time division multiplexing, the integration and information security of systems will be enhanced, laying foundations for the construction of high-density, high-security photonic systems. In terms of practical applications, this technology is poised to drive upgrades in fiber optic communication networks and foster innovation in fields such as quantum information processing. Moreover, its inherent eavesdropping resistance offers new avenues for the development of next-generation secure communication systems. As these technologies mature and become practical, they are set to bring revolutionary changes to photonics and related fields, propelling the evolution of high-speed, high-capacity, and high-security optical communication and photonic computing technologies.