Laguerre-Gaussian beam with orbital angular momentum ℓℏ per photon
Laguerre-Gaussian modes LG_{p,ℓ} carry orbital angular momentum ℓℏ per photon from the helical phase exp(iℓφ). The intensity profile forms a doughnut ring (zero at center due to phase singularity) with p+1 radial rings. The phase winds ℓ times around the singularity. Unlike spin angular momentum (circular polarization), OAM can take any integer value — enabling optical tweezers and quantum information encoding.