Impact of flicker noise and random-walk noise on a phase-locked loop with finite propagation delay

Approximate expressions for the phase-error variance due to the nonwhite frequency noise of optical sources are derived to analyze the performance of optical phase-locked loops (PLL´s). The approximation incorporates the loop propagation delay, which is inevitable in actual systems. The obtained expressions are in simple form and yield only 3% maximum error. Using the obtained expressions, the influence of the flicker frequency noise and the random-walk frequency noise on the laser linewidth requirements are discussed. By examining semiconductor lasers that have been reported, it is found, quantitatively, that the flicker frequency noise does not affect the linewidth requirements, even in the presence of finite loop propagation delay. The obtained approximate expressions are used to examine low-white-frequency-noise optical sources, such as solid-state lasers, and to yield the allowable values of flicker frequency noise and random-walk frequency noise