  Single photons with orbital angular momentum (OAM) have attracted substantial
attention from researchers. A single photon can carry infinite OAM values
theoretically. Thus, OAM photon states have been widely used in quantum
information and fundamental quantum mechanics. Although there have been many
methods for sorting quantum states with different OAM values, the
nondestructive and efficient sorter of high-dimensional OAM remains a
fundamental challenge. Here, we propose a scalable OAM sorter which can
categorize different OAM states simultaneously, meanwhile, preserving both OAM
and spin angular momentum. Fundamental elements of the sorter are composed of
symmetric multiport beam splitters (BSs) and Dove prisms with cascading
structure, which in principle can be flexibly and effectively combined to sort
arbitrarily high-dimensional OAM photons. The scalable structures proposed here
greatly reduce the number of BSs required for sorting high-dimensional
OAMstates. In view of the nondestructive and extensible features, the sorters
can be used as fundamental devices not only for high-dimensional quantum
information processing, but also for traditional optics.
