An apparatus includes an input receiving a modulated optical data signal having components of at least first and second polarizations, a first optical detector receiving the data signal, the first optical detector being first polarization-selective or first polarization-sensitive, passing components of the data signal having the second polarization, and outputting a first electrical signal, a second optical detector coupled to the first optical detector to receive the components of the data signal having the second polarization, and outputting a second electrical signal, and a processor applying a Kramers-Kronig process to the first and second electrical signals, and outputting the data signal using the Kramers-Kronig processed first and second electrical signals. A combiner is connected between the input and the first optical detector and combines the data signal with an unmodulated optical signal such that the unmodulated optical signal serves as a Kramers-Kronig carrier for the first and second polarizations.