Delayed-fibre linewidth measurement

Two delayed copies of the same laser field probe its first-order optical coherence. With equal detected intensities and matched polarizations, the interferometric visibility is $V=|g^{(1)}(\tau )|$. A Lorentzian line shape of frequency full width at half maximum $\Delta \nu$ gives $V=e^{-\pi \Delta \nu |\tau |}$. For a fibre length difference $\Delta l$, the delay is $\tau =n_g\Delta l/c$, where $n_g$ is the group index. Hence $\Delta \nu =-\log V/(\pi |\tau |)$. Replacing $n_g$ by the effective phase index requires negligible dispersion. Polarization mismatch, unequal intensities and uncontrolled phase drift can reduce visibility independently of linewidth.