This paper presents a probability density function formula for predicting the polarization dependent loss (PDL) in an optical transmission system composed of passive devices and connecting fibers. A new calculation technique, which enables the probability density function formula to be obtained theoretically, is used instead of the most complicated part of the Muller-matrix or Jones-matrix calculations, which has been thought to be necessary for analyzing PDL. This technique involves calculation of the transmission coefficients of the transmission system and its devices from their PDLs. In the theoretical development, the central limit theorem is used as the sole approximation. A Monte Carlo numerical simulation was done to verify the validity of the analytical theory. Very good agreement between simulation and analytical theory is obtained when the number of devices having PDL is four or more. An experiment also demonstrated the validity of the analytical theory. The theory can also explain some phenomena that occur in systems composed of optical amplifiers,even though it had originally been developed to explain PDL-related phenomena in systems composed of passive devices only.
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