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Sandbox Physics

Optics 093 · Waveguides, structured light, and modern optics

Optical Vortex & OAM

An independently initialized three-dimensional apparatus connects Vortex phase and donut, Fork interferogram, OAM sorting. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelOptical Vortex & OAM
Primary prediction P1\mathcal P_10.500.50
Physical scale P2\mathcal P_250%50\%
Limit check V\mathcal V0.00π0.00\pi
Model regimevalid model regime\text{valid model regime}

Physics tutorial

How to investigate Optical Vortex & OAM

BackgroundOptical Vortex & OAM is one independently initialized apparatus with three linked investigations: Vortex phase and donut, Fork interferogram, OAM sorting. Its two controls—Topological charge and Beam radius—feed the governing relation Uℓ(r,ϕ)∝A(r)eiℓϕU_\ell(r,\phi)\propto A(r)e^{i\ell\phi}. The page uses the stated modal, coupled-mode, effective-medium, or envelope approximation and marks its breakdown instead of presenting it as a full-wave result.

Why it mattersHow does a phase singularity create a dark core, helical wavefront, and measurable orbital angular momentum?

Start with the essentials

Focus question
How does a phase singularity create a dark core, helical wavefront, and measurable orbital angular momentum?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from Uℓ(r,ϕ)∝A(r)eiℓϕU_\ell(r,\phi)\propto A(r)e^{i\ell\phi}. Geometry and glow are presentation encodings; the equation, units, conservation or limit check, and validity indicator are the quantitative evidence.

Core mathematical model

Governing relation

Uℓ(r,ϕ)∝A(r)eiℓϕU_\ell(r,\phi)\propto A(r)e^{i\ell\phi}

The implementation evaluates this relation with dimensional inputs and an executable analytic or numerical benchmark. The page uses the stated modal, coupled-mode, effective-medium, or envelope approximation and marks its breakdown instead of presenting it as a full-wave result.

Common difficulties

Mistaking glow for measured power

Typical misconceptionA brighter cinematic trail must represent proportionally more optical power.

Better mental modelUse the detector and normalized readouts for comparison. Glow is deliberately nonlinear so weak structure stays visible.

Run the experiment

  1. 01

    Scene 1: Vortex phase and donut

    Select Vortex phase and donut. Sweep Topological charge, hold Beam radius fixed, and then reverse the roles. Drag the stage probe to repeat the first sweep directly.

    What to observe: Read the primary prediction, physical scale, limit check, and validity indicator together. Record where the approximation boundary changes.
  2. 02

    Scene 2: Fork interferogram

    Select Fork interferogram. Sweep Topological charge, hold Beam radius fixed, and then reverse the roles. Drag the stage probe to repeat the first sweep directly.

    What to observe: Read the primary prediction, physical scale, limit check, and validity indicator together. Record where the approximation boundary changes.
  3. 03

    Scene 3: OAM sorting

    Select OAM sorting. Sweep Topological charge, hold Beam radius fixed, and then reverse the roles. Drag the stage probe to repeat the first sweep directly.

    What to observe: Read the primary prediction, physical scale, limit check, and validity indicator together. Record where the approximation boundary changes.