Simultaneous determination of the constituent azimuthal and radial mode indices for light fields possessing orbital angular momentum

Abstract

A wide array of diffractive structures such as arrays of pinholes, triangular apertures, slits, and holograms have all recently been used to measure the azimuthal index of individual Laguerre-Gaussian beams. Here, we demonstrate a powerful approach to simultaneously measure both the radial and azimuthal indices of pure Laguerre-Gaussian light fields using the method of principal component analysis. We find that the shape of the diffracting element used to measure the mode indices is in fact of little importance and the crucial step is training any diffracting optical system and transforming the observed pattern into uncorrelated variables. The method is generic and may be extended to other families of light fields such as Bessel or Hermite-Gaussian beams.

Measuring the orbital angular momentum of partially coherent optical vortices through singularities in their cross-spectral density functions

“…Other methods for measuring the topological charge of an optical vortex have included the diffraction intensity pattern after an axicon [18] or an annular triangle aperture [19]. Very recent studies have shown the use of multivariate statistical analysis for the diffraction pattern from any arbitrary aperture and shown that by training the system one may deduce the index m of the vortex from the diffraction pattern of any aperture [20]. While some of above methods may deal with vortices generated with temporally incoherent light, it is noteworthy that all of these methods have assumed that the optical field is fully spatially coherent.…”

Orbital angular momentum filter of photon based on spin-orbital angular momentum coupling

“…The second one is diffraction-based schemes [26][27][28][29][30][31][32][33][34] in which the diffraction pattern of the photons through an obstacle is observed. The magnitude of can be decided according to the patterns.…”

Random super-prism wavelength meter

“…This property can be used, for example, to simultaneously measure the azimuthal and radial modes of Laguerre-Gaussian beams [5,6]. It is interesting to consider the possibility of using this very same approach in random media to measure other key properties of the light field such as polarization state or wavelength.…”

“…This algorithm is similar to the one that we used for the detection of the azimuthal and radial mode indices of higher-order Laguerre Gaussian beams [5]. The procedure consists of two parts.…”

“…In effect, the SMF acts as the input slit in a monochromator, ensuring that at the output of the monochromator only variations in wavelength generate an intensity variation. However, replacing the SMF by a multimode fiber or pinhole would add to the wavelength variability of the speckle pattern the variations due to the beam shape [5,6]. An interesting issue arises when multiple parameters vary at the same time.…”