Laguerre-Gaussian Beams and Orbital Angular Momentum

As dicussed previously, our lasers have a Gaussian intensity profile. However after interacting with the spatial light modulator, they are actually become Laguerre-Gaussian beams, a higher order mode of the standard Gaussian beam.

Orbital Angular Momentum of Light

Within the equation, two main parameters govern our beam design, the topological charge m and the order of the Laguerre polynomial n.

The topological charge, m, characterizes the helical waveform and corresponding optical vortex of the beam. It describes the number of times that the light rotates about the axis in one wavelength; therefore, the higher the topological charge, the faster the light is rotating, and the greater OAM it carries. When presented as a cross-section of the intensity, the orbital vortex will appear as a dark “hole” in the center of the light, due to the light at the axis interfering in a destructive manner. As the topological charge increases, the radius of the orbital vortex increases.

The order of the Laguerre polynomial, n, adds additional rings of light to the base Gaussian form. This is the result of sharp phase changes created by the Laguerre polynomial (L). This is important, because the rings allow us to diversify our beam alphabet and make it easier for the Machine Learning Network to more accurately decode the transmitted message.

The effect of increasing topological charge, m: vortex radius increases

The effect of increasing the order of the Laguerre Polynomial, n:

Laguerre-Gaussian beams can be combined to form incredibly unique intensity patterns!