  The degree of freedom of orbital angular momentum (OAM) is an important
resource in high-dimensional quantum information processing, as the quantum
number of OAM can be infinite. The Dove prism (DP) is a most common tool to
manipulate the OAM light, such as in interferometers. However, the Dove prism
does not preserve the polarization of the photon states and decreases the
sorting fidelity of the interferometer. In this work, we analyze the
polarization-dependent effect of the DP on single-path Sagnac interferometers.
The results are instructive to quantum information processing with OAM light.
We also proposed a modified single-path beam splitter Sagnac interferometer
(BSSI), of which the sorting fidelity is independent on input polarization and
can be 100\% in principle. The single-path BSSI is stable for free running.
These merits are crucial in quantum information processing, such as quantum
cryptography.
