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Data centers, the engines of the global Internet, are supported by massive high-speed optical interconnects. In optical fiber communication, the classic direct detection obtains only the intensity of the optical field, while the coherent detection counterpart utilizes both phase and polarization diversities at the expense of beating with a narrow-linewidth and high-stable local oscillator (LO). Herein, we propose and demonstrate a four-dimensional Jones space optical field recovery (4-D JSFR) scheme without LO. The information encoded on the intensity and phase of both polarizations can be captured by the polarization-diversity full-field receiver structure and subsequently extracted through deep neural network-aided field recovery. It achieves similar electrical spectral efficiency as standard intradyne coherent detection. The fully recovered optical field can extend the transmission distance beyond the power fading limitation induced by fiber chromatic dispersion. Furthermore, the LO-free advantage makes 4-D JSFR suitable for monolithic photonic integration, offering a spectrally efficient and cost-effective candidate for large-scale data center applications. Our results could motivate a fundamental paradigm shift in the optical field recovery theory and future optical transceiver design., Comment: 29 pages, 7 figures