Physics

Lens (geology)

Spatial light modulator

Mathematics

Biology

Fourier transform

Spatial frequency

Optics

Laguerre polynomials

Epistemology

Basis (linear algebra)

Decomposition

Gaussian

Philosophy

Property (philosophy)

Ecology

Geometry

Computer science

Quantum mechanics

Nature Communications

Exploiting a particular wave property for a particular application necessitates components capable of discriminating in the basis of that property. While spectral or polarisation decomposition can be straightforward, spatial decomposition is inherently more difficult and few options exist regardless of wave type. Fourier decomposition by a lens is a rare simple example of a spatial decomposition of great practical importance and practical simplicity; a two-dimensional decomposition of a beam into its linear momentum components. Yet this is often not the most appropriate spatial basis. Previously, no device existed capable of a two-dimensional decomposition into orbital angular momentum components, or indeed any discrete basis, despite it being a fundamental property in many wave phenomena. We demonstrate an optical device capable of decomposing a beam into a Cartesian grid of identical Gaussian spots each containing a single Laguerre-Gaussian component, using just a spatial light modulator and mirror.

Laguerre-Gaussian mode sorter