  Light's spatial properties represent an infinite state space, making it
attractive for applications requiring high dimensionality, such as quantum
mechanics and classical telecommunications, but also inherently spatial
applications such as imaging and sensing. However, there is no demultiplexing
device in the spatial domain comparable to a grating or calcite for the
wavelength and polarisation domains respectively. Specifically, a simple device
capable of splitting a finite beam into a large number of discrete spatially
separated spots each containing a single orthogonal spatial component. We
demonstrate a device capable of decomposing a beam into a Cartesian grid of
identical Gaussian spots each containing a single Laguerre-Gaussian component.
This is the first device capable of decomposing the azimuthal and radial
components simultaneously, and is based on a single spatial light modulator and
mirror. We demonstrate over 210 spatial components, meaning it is also the
highest dimensionality mode multiplexer of any kind.
