Interference phenomenon on the complex degree of coherence

A two-beam interferometer (TBI) with a two-mode fiber (TMF) as a dispersive medium in one arm and air in the other provides evidence of interference related to the complex degree of coherence \(\gamma \). A TMF with a low differential group delay (DGD) is used to measure the interference effect, since the overlapping of each individual mode at the output of a TMF is easily and artificially created in the vicinity of the zero DGD wavelength. When \(\gamma _{01}\) and \(\gamma _{11}\), respectively, are the complex degrees of coherence for the interferences between the \(\hbox {LP}_{01}\) and \(\hbox {LP}_{11}\) modes propagating through a TMF and a wave traversing air-path, the interference effect can be verified using the relationship \(|\gamma |^2=|\gamma _{01}+\gamma _{11}|^2\). The experiments are carried out using a low coherence source and three kinds of TMFs with zero DGD wavelengths around 1550 nm. It is clearly observed that \(|\gamma |^2\)-response waveforms have oscillatory structures due to the interference between \(\gamma _{01}\) and \(\gamma _{11}\). A \(|\gamma |^2\)-response measurement employing the TBI reveals that the theoretically obtained \(|\gamma |^2\)-curves well reflect \(|\gamma |^2\)-curve obtained experimentally for a temporally overlapped wave composed of the two modes. To the best of our knowledge, this is the first experimental demonstration of the interference between complex degrees of coherence.