Laguerre-Gaussian mode sorter

Abstract

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.

Fig. 1

Laguerre–Gaussian mode sorter based on multi-plane light conversion. Cartesian grid of Gaussian spots (MFD = 60 μm) at positions (x,y) pass through the MPLC system, consisting of 7 phase plates separated by ~25 mm of free-space propagation, implemented using a spatial light modulator and a mirror. Through these 7 planes each input spot at position x,y is mapped to a corresponding Hermite–Gaussian mode (m,n) (MFD = 400 μm), which is in turn transformed into the Laguerre–Gaussian basis through use of two cylindrical lenses

Fig. 2

Cartesian to Hermite–Gaussian transformation using multi-plane light conversion. a 7 phase planes used to perform the transformation. b Total intensity of the first 210 modes in each plane. c Example of the evolution of the complex amplitude of the HG16,3 mode through the device. The physical width of these 7 masks is 15.344 mm (7 planes × 8 μm pixel pitch × 274 pixels). Although the same design can be scaled to other dimensions as discussed in Supplementary Note 8

Fig. 3

Measured optical fields at 1565 nm. a Measurement apparatus based on off-axis digital holography. b Composite image of the full set of 210 modes. Azimuthal index runs left-to-right, mode-group runs top-to-bottom. c Select modes of various order

Fig. 4

Measured properties of LG mode sorter for 210 azimuthal and radial components (20 groups). a Simulated and measured insertion loss (IL) and mode-dependent loss (MDL). b Simulated and measured information capacity per received photon. c Measured amplitude of transfer matrix at centre wavelength (1565 nm). d Measured loss of LG modes. e Measured total crosstalk of LG modes