Objective Multimode fiber (MMF) has become one of the important media for short-reach fiber communication because of its high throughput property. However, modal dispersion of the MMF results in the formation of seemly chaotic speckle at the distal end of the MMF, where the input information cannot be directly decoded using simple intensity detection. Information decoding from the speckle output of the MMF requires accurate characterization of the MMF's multiple-input-multiple-output (MIMO) transmission properties. Currently, popular computational imaging methods for retrieving the mapping functions of MIMO systems include the transmission matrix (TM)-based methods and the deep learning-based methods, both of which have their advantages and disadvantages. To solve the problem of precise decoding over an MMF, this study explores the parallel information transmission over a kilometer-scale MMF based on the inverse transmission matrix (ITM) method. The results of this study could provide new insight for the development of short-reach fiber communication, spatial optical communication and secure optical communication.

Methods This article utilizes wavefront shaping to accurately measure the TM of the MMF, where self-interference optical setup is used to measure the complex optical field at the distal end of the MMF. Binary information and 256-level grayscale image with a resolution of 32×32 are used as the phase encoded information of the input wavefront, which are modulated by a digital micromirror device and coupled into the MMF. Then the ITM method is used to retrieve the encoded information from the chaotic speckle patterns. If the TM is not a square matrix, pseudo-inversion of the matrix is performed instead.

Results and Discussions The experimental results are shown (Fig.3(a)). It can be seen that the ITM method can retrieve the phase encoded information over the MMF, providing the TM of the MMF and the complex light field at the output can be precisely measured. The comparisons with the experimental results using the scattering-correlation scattering matrix (SSM) method are also shown (Fig.3(b)), where two methods share the same TM. As can be seen from the retrieval results of uncorrelated random binary information, the highest accuracy of the SSM method and the ITM method are achieved when γ = 121 (γ = 64) are 75.9% (64.3%) and 100% (100%), respectively, where γ is the ratio between the output channel number and the input channel number. The high-fidelity reconstruction of 256-level grayscale images and transmission of high definition full-color video over the MMF using the ITM method are also experimentally demonstrated, respectively, where the results are shown (Fig.4-5). These experimental results verify the effectiveness of the ITM method in unscrambling the modal dispersion in the MMF and achieving computational imaging.

Conclusions As a high-throughput transmission carrier, MMFs have unique advantages in the field of information transmission. This article experimentally verifies the feasibility and advantages of the ITM method in achieving parallel information transmission over the MMF compared with the SSM method. The results show that high fidelity decoding can be achieved for uncorrelated random binary information, 256-level grayscale images, and high definition full-color video. Although precise measurement of the TM of the MMF has been achieved under our experimental conditions, the robustness of the ITM method to time-varying environment may not be better than that of deep learning-based methods, where the TM measured at a certain moment cannot adapt to the long-term dynamic changes of the MMF. Combing the TM-based methods with the deep learning-based methods is an important future perspective. It is anticipated that the results presented in this article could facilitate the development of short-range optical communication, spatially multiplexed optical communication, optically secured and confidential communication, and long-distance optical logic communication. Meanwhile, the verified capability of grayscale image transmission could provide new ideas for practical applications such as holographic imaging, light-field projection, and endoscopic imaging.