Envelope statistics for filtered optical signals corrupted by phase noise

Consideration is given to the case of an optical pulse containing phase noise which is passed through either an optical filter or (following heterodyne lightwave detection) an electrical filter. Because of the phase noise, the envelope of the filter output at any instant is a random variable. An analytical method is developed for estimating the probability density function (pdf) of this envelope for different kinds of filter responses and for realistic combinations of phase noise severity and filter bandwidth. Obvious applications are to detection analyses of coherent lightwave systems, wherein finite laser linewidths constitute an important source of impairment. For each of the several types of filters considered, the envelope PDF can be accurately fitted by an exponential function approximation, where the decay constant is related in a simple way to known system parameters