Optical Vortex Beam — 2D Laguerre–Gauss Cross-Section

Beam Mode

Topological charge ℓ: 2 Radial index p: 0 Beam waist w₀: 0.35

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Animate propagation

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OAM / photon2 ℏ

Ring radius0.00

Topological charge ℓ2

Radial index p0

Rings (p+1)1

Cross-section of a Laguerre–Gauss LG_p,ℓ beam. Amplitude ∝ (r√2/w₀)^|ℓ| · L_p^|ℓ|(2r²/w₀²) · e^{−r²/w₀²}, phase = ℓθ. The helical phase forces zero amplitude on-axis, giving the doughnut; p adds p concentric extra rings. "Animate propagation" spins the helical phase front, as it would along the beam's optical axis.