The performance of optical phase-locked loops in the presence of nonnegligible loop propagation delay

The optical phase-locked loop is analyzed taking into account shot noise, phase noise, and loop propagation delay. The degradation of loop phase error due to propagation delay is evaluated in terms of the delay bandwidth product <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_{n} \cdot \tau_{D}</tex> . This product was found to have a maximum value of 0.736 for absolute loop stability. The resulting effect on a Costas loop system optimized for zero time delay is discussed. It is found that in order to maintain a 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-9</sup> BER system performance with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\xi = 1/2^{0.5}, R = 0.85</tex> A/W, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P_{DATA} = -59.2</tex> dBm, and a 1-MHz beat linewidth, the delay time must be kept below 1.8 ns. If the beat linewidth increases to 15 MHz this figure drops to 0.12 ns.