  In quantum mechanics the position and momentum operators are related to each
other via the Fourier transform. In the same way, here we show that the
so-called Pegg-Barnett phase operator can be obtained by the application of the
discrete Fourier transform to the number operator defined in a
finite-dimensional Hilbert space. Furthermore, we show that the structure of
the London-Susskind-Glogower phase operator, whose natural logarithm give rise
the Pegg-Barnett phase operator, is contained into the Hamiltonian of circular
waveguide arrays. Our results may find applications in the development of new
finite-dimensional photonic systems with interesting phase-dependent
properties.
