We propose a measurement method based on the time-domain cross-correlation technique,
combined with the cut-back method, enabling the measurement of group
refractive indices (n
g
) in few-mode fibers (FMF). A
Mach–Zehnder interferometric system, equipped with high-precision and
extensive range delay devices, is established. The system records
off-axis holograms of spatial reference light at various delays
interfering with the emitted light from the fiber under test. The
interference energy is extracted from these holograms, and a
time-domain mode energy curve is developed utilizing the principle of
cross correlation. Optimal holograms at each of the curve peaks are
used to reconstruct the modal field distribution, effectively
separating and accurately identifying each mode within the FMF. By
integrating the cut-back method, the n
g
corresponding to each mode is
calculated based on the changes in group delay before and after fiber
cutting. The n
g
of modes in the two-mode fibers was
measured and the differential group delay calculated from the
measurement agrees with the manufacturer’s specifications. The
measured n
g
of a standard single-mode fiber
aligns with the manufacturer’s specifications. Furthermore, the n
g
of the higher-order modes in
four-mode fibers were measured by exciting them at different angles
and validating the wave optics theory that the n
g
of the fiber modes is independent of
the excitation angle. This method can simultaneously measure the n
g
of several modes in a fiber,
providing support for the development and application of FMFs.