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Sandbox Physics

Optics 085 · Waveguides, structured light, and modern optics

Evanescent Directional Coupler

An independently initialized three-dimensional apparatus connects Separated guides, Power beating, Fifty-fifty coupler design. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelEvanescent Directional Coupler
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 Evanescent Directional Coupler

BackgroundEvanescent Directional Coupler is one independently initialized apparatus with three linked investigations: Separated guides, Power beating, Fifty-fifty coupler design. Its two controls—Waveguide gap and Coupling length—feed the governing relation P2(z)=P0sin⁡2(κz)P_2(z)=P_0\sin^2(\kappa 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 do gap and interaction length transfer power between neighboring waveguides?

Start with the essentials

Focus question
How do gap and interaction length transfer power between neighboring waveguides?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from P2(z)=P0sin⁡2(κz)P_2(z)=P_0\sin^2(\kappa 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

P2(z)=P0sin⁡2(κz)P_2(z)=P_0\sin^2(\kappa 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: Separated guides

    Select Separated guides. Sweep Waveguide gap, hold Coupling length 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: Power beating

    Select Power beating. Sweep Waveguide gap, hold Coupling length 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: Fifty-fifty coupler design

    Select Fifty-fifty coupler design. Sweep Waveguide gap, hold Coupling length 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.