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Sandbox Physics

Optics 083 · Waveguides, structured light, and modern optics

Optical Fiber: Rays to Modes

An independently initialized three-dimensional apparatus connects Acceptance cone and rays, LP mode spectrum, Single-mode cutoff. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelOptical Fiber: Rays to Modes
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 Fiber: Rays to Modes

BackgroundOptical Fiber: Rays to Modes is one independently initialized apparatus with three linked investigations: Acceptance cone and rays, LP mode spectrum, Single-mode cutoff. Its two controls—Core radius and Index difference—feed the governing relation V=2πaλn12−n22V=\frac{2\pi a}{\lambda}\sqrt{n_1^2-n_2^2}. 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 mattersWhen must the total-reflection ray picture be replaced by a guided-mode picture?

Start with the essentials

Focus question
When must the total-reflection ray picture be replaced by a guided-mode picture?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from V=2πaλn12−n22V=\frac{2\pi a}{\lambda}\sqrt{n_1^2-n_2^2}. 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

V=2πaλn12−n22V=\frac{2\pi a}{\lambda}\sqrt{n_1^2-n_2^2}

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: Acceptance cone and rays

    Select Acceptance cone and rays. Sweep Core radius, hold Index difference 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: LP mode spectrum

    Select LP mode spectrum. Sweep Core radius, hold Index difference 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: Single-mode cutoff

    Select Single-mode cutoff. Sweep Core radius, hold Index difference 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.