# How to understand the Orbital angular momentum of a photon that is not an integer？

How to understand the topological charge that is not an integer, how would the signal OAM crosstalk if one were to model its transport in turbulence, for example, if the beam carries a topological charge of 1.1, what is the topological charge that it would crosstalk to, and would it be like jumping to an energy level with a difference of 1 like atomic physics?

• There isn't really any such thing as a topological charge of 1.1. Fractional OAMs have indeed been discussed, but the details depend on the context. Where did you see this being discussed? Aug 22 at 15:04
• Thanks for your reply, I am currently working on the Lommel beam, which is thought to have a continuously variable topological charge, which seems to be realizable as a 1.1 topological charge Aug 22 at 15:13

In many cases light that exhibits integer orbital angular momentum (OAM) has a phase vortex with a phase singularity at its centre where the phase is undefined (see e.g. https://en.wikipedia.org/wiki/Orbital_angular_momentum_of_light). Around this point the phase wraps by $$2 \pi q$$ where $$q$$ is the integer that determines the orbital angular momentum, often written as $$L=\hbar q$$. This singularity has a value that does not exist in the parameter space of the phase of the light - in other words, the parameter space has a "hole" in it and this "hole" determines the topology of this space. The "hole" is associated with the $$2 \pi q$$ phase wrapping and is often referred to as the topological charge with value $$q$$, since its presence affects the entire phase pattern of the vortex. The sign of the charge relates to the direction in which the phase increases (i.e. clockwise or anticlockwise) about the singularity.