Beam Mode

Topological charge ℓ: 2 Radial index p: 0 Beam waist w: 0.35

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OAM / photon2 ℏ

Topological charge ℓ2

Radial index p0

Beam waist w0.35

Phase windings2

Intensity rings1

Laguerre–Gauss LG_p,ℓ beams carry orbital angular momentum ℓℏ per photon. The helical phase exp(iℓφ) forces a dark on-axis singularity, giving a doughnut for ℓ≠0; the radial index p adds concentric rings (p+1 total). Interfere with a spherical wave to count spiral arms, or with a tilted plane wave to count fork prongs — both equal |ℓ|.