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Sandbox Physics

Optics 096 · Waveguides, structured light, and modern optics

Superoscillation Designer

An independently initialized three-dimensional apparatus connects Binary-ring optimization, Subdiffraction hotspot, Sidelobe energy audit. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelSuperoscillation Designer
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 Superoscillation Designer

BackgroundSuperoscillation Designer is one independently initialized apparatus with three linked investigations: Binary-ring optimization, Subdiffraction hotspot, Sidelobe energy audit. Its two controls—Local frequency factor and Band order—feed the governing relation U(x)=∑∣km∣≤k0ameikmxU(x)=\sum_{|k_m|\le k_0}a_m e^{ik_mx}. 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 a band-limited field make a tiny hotspot while paying in sidelobes, efficiency, and field of view?

Start with the essentials

Focus question
How can a band-limited field make a tiny hotspot while paying in sidelobes, efficiency, and field of view?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from U(x)=∑∣km∣≤k0ameikmxU(x)=\sum_{|k_m|\le k_0}a_m e^{ik_mx}. 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

U(x)=∑∣km∣≤k0ameikmxU(x)=\sum_{|k_m|\le k_0}a_m e^{ik_mx}

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: Binary-ring optimization

    Select Binary-ring optimization. Sweep Local frequency factor, hold Band order 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: Subdiffraction hotspot

    Select Subdiffraction hotspot. Sweep Local frequency factor, hold Band order 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: Sidelobe energy audit

    Select Sidelobe energy audit. Sweep Local frequency factor, hold Band order 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.