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Orbital angular momentum exchange, both in cavity free stimulated parametric down conversion and in an optical parametric oscillator, is studied. In both cases, the conditions for parametric amplification are discussed in terms of the orbital angular momentum exchange between the interacting fields. It is shown that in cavity free parametric down conversion, parametric amplification is conditioned to conserve orbital angular momentum. However, for parametric oscillation, cavity and anisotropy effects play a crucial role in the orbital angular momentum exchange between the interacting fields.

Twin photons can be entangled in transverse momentum and position, giving rise to the so-called quantum images. The term quantum image has been used for images measured with photon coincidence schemes, also called correlated images. Some kinds of correlated images are prepared by transferring the angular spectrum of the pump beam to the correlated twin beams. In this case, it is possible to show that transverse correlations can violate a classical inequality, leading to spatial photon anti-bunching. We briefly review the use of the transfer of the angular spectrum in the production of these non-classical correlations. In addition, we demonstrate experimentally that the quantum image can be prepared partially through the nonlinear interaction and partially by propagation of signal and idler beams through lenses. Using this kind of preparation it is also possible to use a telescope for transmitting the quantum image, compensating the divergence of signal and idler beams.

We discuss how it is possible to manipulate quantum spatial properties of light beams by using the transfer of the angular spectrum. Twin beams from the parametric down-conversion can be prepared in a state that carries two different quantum images. At the same time, the twin photons can be entangled in polarization. This preparation allows the selection between the detection of each one of the images at a time or a mixture by performing proper projections onto polarization sub-spaces. As another example, we show how to produce a light beam presenting spatial anti-bunching through the control of the entangled angular spectrum and reflections.