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Sandbox Physics

Optics 041 · Interference, coherence, cavities, and metrology

Coherent Wave Composer

An independently initialized three-dimensional apparatus connects Two-wave phasors, Many-wave synthesis, Beat and coherence loss. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelCoherent Wave Composer
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 Coherent Wave Composer

BackgroundCoherent Wave Composer is one independently initialized apparatus with three linked investigations: Two-wave phasors, Many-wave synthesis, Beat and coherence loss. Its two controls—Phase difference and Frequency detuning—feed the governing relation E=∑jAjei(kj⋅r−ωjt+ϕj)E=\sum_j A_j e^{i(\mathbf k_j\cdot\mathbf r-\omega_j t+\phi_j)}. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersHow do phasors, wavefronts, and detector intensity tell the same superposition story?

Start with the essentials

Focus question
How do phasors, wavefronts, and detector intensity tell the same superposition story?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from E=∑jAjei(kj⋅r−ωjt+ϕj)E=\sum_j A_j e^{i(\mathbf k_j\cdot\mathbf r-\omega_j t+\phi_j)}. 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

E=∑jAjei(kj⋅r−ωjt+ϕj)E=\sum_j A_j e^{i(\mathbf k_j\cdot\mathbf r-\omega_j t+\phi_j)}

The implementation evaluates this relation with dimensional inputs and an executable analytic or numerical benchmark. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

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: Two-wave phasors

    Select Two-wave phasors. Sweep Phase difference, hold Frequency detuning 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: Many-wave synthesis

    Select Many-wave synthesis. Sweep Phase difference, hold Frequency detuning 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: Beat and coherence loss

    Select Beat and coherence loss. Sweep Phase difference, hold Frequency detuning 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.