  We present a quantum mechanical analysis of the orbital angular momentum of a
class of recently discovered elliptically-symmetric stable light fields --- the
so-called Ince-Gauss modes. We study, in a fully quantum formalism, how the
orbital angular momentum of these beams varies with their ellipticity and
discover several compelling features, including: non-monotonic behavior, stable
beams with real continuous (non-integer) orbital angular momenta, and
orthogonal modes with the same orbital angular momenta. We explore, and explain
in detail, the reasons for this behavior. These features may have application
to quantum key distribution, atom trapping, and quantum informatics in general
--- as the ellipticity opens up a new way of navigating the photonic Hilbert
space.
