Optical full-field recovery makes it possible to compensate fiber impairments such as chromatic dispersion and polarization mode dispersion (PMD) in the digital signal processing. Coherent detection dominates over the long-haul transmission system due to its high spectral efficiency and tolerance against optical impairments. For cost-sensitive short-reach optical networks, some advanced single-polarization (SP) optical field recovery schemes are recently proposed to avoid chromatic dispersion-induced power fading effect, and improve the spectral efficiency for larger potential capacity. Polarization division multiplexing (PDM) can further double both the spectral efficiency and the system capacity of these SP carrier-assisted direct detection (DD) schemes. However, the so-called polarization fading phenomenon induced by random polarization rotation is a fundamental obstacle to exploit the polarization diversity for carrier-assisted DD systems. In this paper, we propose a receiver of Jones-space field recovery (JSFR) to realize polarization diversity with SP carrier-assisted DD schemes in the Jones space. There different receiver structures of proposed JSFR and the simplification for JSFR are explored theoretically. The proposed JSFR pushes the SP DD schemes towards PDM without no extra optical signal-to-noise ratio (OSNR) penalty. In addition, the JSFR shows good tolerance to PMD since the optical field recovery is conducted before polarization recovery. In the concept-of-proof experiment, we demonstrate 448-Gb/s reception over 80-km single-mode fiber using the proposed JSFR based on 2×2 couplers. Qualitatively, we compare the optical field recovery in the Jones space and Stokes space from the perspective of the modulation dimension.

Phase-retrieval (PR) schemes based on the modified Gerchberg-Saxton (GS) algorithm capture the full-field employing a dispersive element and intensity-only measurements to eliminate the use of a local oscillator. In this work, we propose two carrier-assisted PR schemes, namely central carrier-assisted PR (CCA-PR) and edge carrier-assisted PR (ECA-PR), to improve the comprehensive performance of PR receiver in terms of convergence speed, redundancy, and computational complexity. The proposed CCA-PR recovers the electrical field employing a reference carrier at 0 GHz with several iterations between two projection planes. It avoids pilot symbols and digital backpropagation to the transmitter and offers a flexible electrical bandwidth requirement compared with conventional PR schemes. To lower the carrier-to-signal power ratio (CSPR) requirement and enable faster convergence for the carrier-assisted PR schemes, the ECA-PR is proposed to obtain the initial phase for the GS algorithm. We numerically characterize the performance of the two schemes and experimentally demonstrate them for 30 GBaud 16-quadrature amplitude modulation (16-QAM) transmission over 80 km single-mode fiber with a bit error rate (BER) below the threshold of 7% hard-decision forward error correction (HD-FEC). Several critical parameters are analyzed, including the applied dispersion value, CSPR, and electrical bandwidth. Moreover, we compare the hardware complexity and optical signal-to-noise ratio (OSNR) sensitivity of proposed PR schemes with mainstream field recovery schemes.