Chirality and helicity of linearly-polarised Laguerre-Gaussian beams of small beam waists

The chirality and helicity of a linearly polarised Laguerre-Gaussian (LG) beam are examined. Such a type of light possesses a large longitudinal field amplitude when it is created with a sufficiently small beam waist and so gives rise to substantial magnitudes of chirality and helicity density distributions. In the simplest case of a doughnut beam of winding number l = 1 and another identical to it but for which l = -1, we obtain different chirality and helicity distributions in the focal plane z = 0. We also show that this chiral behaviour persists and the patterns evolve so that on planes at z < 0 and z > 0 the beam convergence phase contributes differently to the changes in the chirality and helicity distributions.