Walsh modes and radial quantum correlations of spatially entangled photons

Orthogonal sets of 2D transverse modes are key to controlling the spatial degree of freedom of light in a classical or quantum context. In contrast to the azimuthal part, which is easily accessible using orbital angular momentum modes, control of the radial part is more difficult. We show here that simple sets of orthogonal binary sequences, the Walsh functions, provide a workable solution for exploration of the radial space with phase-only spatial light modulation. We demonstrate this by measuring "sequency" quantum correlations between different radial Walsh modes of spatially entangled photon pairs and for numerically optimized versions thereof.