Theoretical basis of polarization mode dispersion equalization up to the second order

We introduce a theoretical basis of polarization mode dispersion (PMD) equalizers based on the operator representation of PMD using Taylor's expansion. The two types of configuration of PMD equalizers are derived as the inverse of diagonalization operators and delay time difference compensation. One is a type using physical rotation of quarter wave phase plates. The other is a type using variable phase shifters suitable for PLC integration. Waveform comparison algorithm was simulated to show the existence of multiple equivalent optimum points due to the symmetry and periodicity of optical circuits. The second order PMD equalization is discussed briefly on the case of cascading the first and the second PMD equalizing circuits with two different polarization state converters.