Decision-driven phase-locked loop for optical homodyne receivers: Performance analysis and laser linewidth requirements

Abstract

Optical homodyne receivers based on decision-driven phase-locked loops are investigated. The performance of these receivers is affected by two phase noises due to the laser transmitter and laser local oscillator, and by two shot noises due to the two detectors employed in the receiver. The impact of these noises is minimized if the loop bandwidth <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</tex> is chosen optimally. The value of B <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</inf> and the corresponding optimum loop performance are evaluated in this paper. It is shown that second-order phase-locked loops require at least 0.8 pW of signal power per every kilohertz of laser linewidth (this number refers to the system with the detector responsivity 1 A/W, dumping factor 0.7, and rms phase error 10°). This signal power is used for phase locking, and is, therefore, lost from the data receiver. Further, the maximum permissible laser linewidth <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Delta\nu</tex> is evaluated and for second order loops with the dumping factor 0.7 found to be <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3.1 \times 10^{-4} \cdot R_{b}</tex> , where R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</inf> (bit/s) is the system bit rate. For <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_{b} = 100</tex> Mbit/s, this leads to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Delta\nu = 31</tex> kHz. For comparison, heterodyne receivers with noncoherent postdetection processing only require <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Delta\nu = 0.72-9</tex> MHz for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_{b} = 100</tex> Mbit/s. Thus, the homodyne systems impose much more stringent requirements on the laser linewidth than the heterodyne systems. However, homodyne systems have several important advantages over heterodyne systems, and the progress of laser technology may make homodyning increasingly attractive. Even today, homodyne reception is feasible with experimental external cavity lasers, which have been demonstrated to have <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Delta\nu</tex> as low as 10 kHz.