On the pull-in behavior of optical injection phase-lock loop

Abstract

This paper presents a detailed study of the pull-in behavior of an optical injection phase-lock loop (OIPLL) neglecting the noise components of the loop. We provide formulas for pull-in voltage and pull-in range of OIPLL in terms of the loop propagation delay, line-width enhancement factor and other parameters of the loop. In addition, we give a compact expression for the frequency pulling time of OIPLL for low injection and high injection level in presence of loop-delay. The effects of loop-delay and optical injection on the pull-in performance of the OIPLL are studied for non-zero values of line-width enhancement factor. Analytical expression of the maximum allowable loop delay is presented to study the deterministic stability of the loop. From the stochastic stability of the loop, we provide formula for the maximum value of the laser line-width to achieve the desired tracking performance. The simulation results are given in partial support of the conclusions of the analysis.