The four-frequency autocorrelation function of polarization mode dispersion and its application to measurements

The four-frequency autocorrelation function (ACF) of the polarization-mode-dispersion (PMD) vector in optical fibers is obtained. The derivation of this function is part of a general effort aimed at understanding the complex behavior of the PMD vector as a stochastic process in frequency. The four-frequency ACF is also used for assessing the possibility of improving measurements of the mean differential group delay (DGD) by processing information regarding the measured correlations between the PMD vector at various frequencies. By manipulating the four-frequency ACF, the ACF of the square modulus of the PMD derivative is obtained and it is rigorously shown that DGD measurements that exploit this quantity are characterized by a 20% improvement in measurement accuracy.