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Sandbox Physics

Optics 091 · Waveguides, structured light, and modern optics

Self-Healing Beam Arena

An independently initialized three-dimensional apparatus connects Bessel obstacle test, Airy acceleration, Finite-energy sideband budget. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelSelf-Healing Beam Arena
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 Self-Healing Beam Arena

BackgroundSelf-Healing Beam Arena is one independently initialized apparatus with three linked investigations: Bessel obstacle test, Airy acceleration, Finite-energy sideband budget. Its two controls—Obstacle radius and Cone angle—feed the governing relation UB(r,z)∝J0(krr)eikzzU_{\mathrm B}(r,z)\propto J_0(k_r r)e^{ik_z z}. 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 can Bessel and Airy beams reconstruct after an obstacle, and what energy trade-off pays for it?

Start with the essentials

Focus question
How can Bessel and Airy beams reconstruct after an obstacle, and what energy trade-off pays for it?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from UB(r,z)∝J0(krr)eikzzU_{\mathrm B}(r,z)\propto J_0(k_r r)e^{ik_z z}. 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

UB(r,z)∝J0(krr)eikzzU_{\mathrm B}(r,z)\propto J_0(k_r r)e^{ik_z z}

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: Bessel obstacle test

    Select Bessel obstacle test. Sweep Obstacle radius, hold Cone angle 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: Airy acceleration

    Select Airy acceleration. Sweep Obstacle radius, hold Cone angle 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: Finite-energy sideband budget

    Select Finite-energy sideband budget. Sweep Obstacle radius, hold Cone angle 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.