Conventional optical coherent receivers capture the full electrical field, including amplitude and phase, of a signal waveform by measuring its interference against a stable continuous-wave local oscillator (LO). In optical coherent communications, powerful digital signal processing (DSP) techniques operating on the full electrical field can effectively undo transmission impairments such as chromatic dispersion (CD), and polarization mode dispersion (PMD). Simpler direct detection techniques do not have access to the full electrical field and therefore lack the ability to compensate for these impairments. We present a full-field measurement technique using only direct detection that does not require any beating with a strong carrier LO. Rather, phase retrieval algorithms based on alternating projections that makes use of dispersive elements are discussed, allowing to recover the optical phase from intensity-only measurements. In this demonstration, the phase retrieval algorithm is a modified Gerchberg Saxton (GS) algorithm that achieves a simulated optical signal-to-noise ratio (OSNR) penalty of less than 4dB compared to theory at a bit-error rate of 2 times 10-2. Based on the proposed phase retrieval scheme, we experimentally demonstrate signal detection and subsequent standard 2x2 multiple-input-multiple-output (MIMO) equalization of a polarization-multiplexed 30-Gbaud QPSK transmitted over a 520-km standard single-mode fiber (SMF) span.
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