Techniques to sort Bessel beams

In this work we will present two techniques for the measurement of superimposed higher-order Bessel beams. In the first technique we will outline a simple approach using only a spatial light modulator and a Fourier transforming lens to decompose the OAM spectrum of an optical field. We test this approach on symmetric and non-symmetric superpositions of non-diffracting higher-order Bessel beams. Our second procedure consists of two refractive optical elements which perform a Cartesian to log-polar coordinate transformation, translating helically phased beams into a transverse phase gradient. By introducing two cylindrical lenses we can focus each of the azimuthal modes associated with each Bessel beam to a different lateral position in the Fourier plane, while separating the radial wave-vectors in the image-plane.