title: Modal characterization using principal component analysis: application to Bessel, higher-order Gaussian beams and their superposition.
abstract: The modal characterization of various families of beams is a topic of current interest. We recently reported a new method for the simultaneous determination of both the azimuthal and radial mode indices for light fields possessing orbital angular momentum. The method is based upon probing the far-field diffraction pattern from a random aperture and using the recorded data as a 'training set'. We then transform the observed data into uncorrelated variables using the principal component analysis (PCA) algorithm. Here, we show the generic nature of this approach for the simultaneous determination of the modal parameters of Hermite-Gaussian and Bessel beams. This reinforces the widespread applicability of this method for applications including information processing, spectroscopy and manipulation. Additionally, preliminary results demonstrate reliable decomposition of superpositions of Laguerre-Gaussians, yielding the intensities and relative phases of each constituent mode. Thus, this approach represents a powerful method for characterizing the optical multi-dimensional Hilbert space.
authors.affiliation: SUPA, School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews KY16 9SS, UK.
authors.forename: A
authors.initials: A
authors.lastname: Mourka
authors.forename: M
authors.initials: M
authors.lastname: Mazilu
authors.forename: E M
authors.initials: EM
authors.lastname: Wright
authors.forename: K
authors.initials: K
authors.lastname: Dholakia