In this paper, a new all-optical phase-locked loop (OPLL) in a TDM system is proposed and analyzed. The scheme relies on using fiber optical parametric amplifier (FOPA) device models and theories. In the proposed OPLL, the local clock pulse stream and the received data signal pulses are fed into the FOPA as its pump and amplified signals, respectively. The power of the resulting, relatively, strong idler signal depends on the phase difference between the local clock and the received data signal pulses, and it is used to reveal the OPLL's error signal. We characterize the mathematical structure of the proposed OPLL and identify its three intrinsic sources of phase noises namely, randomness of received data pulses, detector's shot noise, and the FOPA noises such as amplified spontaneous emission (ASE). The ASE noise is reflected in the FOPA's noise figure parametrically. However, the effects of the other two noise sources on the proposed OPLL performance are investigated, using the power spectral densities (PSDs) of the signals involved in the OPLL. Finally, the PSDs are used to obtain a mathematical expression for the OPLL's timing jitter. From the analytical results, our proposed OPLL benefits from the FOPA's inherent large bandwidth and exhibits a very low timing jitter, which is in the order of femtosecond, for an OTDM system with 80 Gbps data rate.
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