Introduction

Helical phase fronts are commonly associated with Laguerre-Gaussian (LG) beams and optical vortices. These beams are characterized by an input field normally expressed as exp(−ilϕ), where l is an integer called the topological charge, which describes the magnitude and handedness of the helical phase profile. In quantum theory, the topological charge relates to a quantized orbital angular momentum (OAM) of lℏ per photon [1–2]. When projected in the far field, the azimuthal components of the phase create destructive interference giving rise to a dark centre surrounded by a high-intensity ring of light via constructive interference. As the topological charge is increased, the steeper phase gradients deflect light farther off-axis, thereby enlarging the light ring surrounding the dark centre.

When focused using a lens, the propagation of an LG beam along the optical axis follows a conical ray until it reaches a minimum ring radius at the focus and then conically increases after the focus. A high concentration of photons is maintained at the outskirts of the conical beam forming a ring at the transverse plane. Increasing the topological charge (and consequently the OAM) disperses the distribution of photons around a larger ring. Aside from circularly symmetric beams, higher-order LG beams bring about unique laser transverse modes, which display unique three-dimensional (3D) light patterns. Hence, the interplay of helical phase fronts results in far field beam profiles that can be uniquely utilized in optical tweezers [3–7] or as means of engineering the point spread function in laser microscopy [8].