Stability analysis of optical phase-locked loop in the presence of non-negligible loop propagation delay

The impact of loop-delay on the phase margin of first- and second-order optical phase-locked loop is analyzed. Analytical expressions of the phase margin for first- and second-order optical phase-locked loop with two different loop filter configurations are presented. It is found that to achieve practical phase margin on the order of 30 - 60° with damping factor ξ = 1, the normalized loop propagation delay ωnτ (where, ωn is the loop natural frequency and τ is the loop propagation delay) must be kept with in the range 0.37 - 0.15 and 0.25 - 0.10 for active low-pass and modified first-order loop filter, respectively. Also, the relative stability of modified optical phase-locked loop having an additional arrangement of phase modulation is analyzed and the effect of external phase control on the phase margin is reported in the presence of non-negligible loop propagation delay.