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Sandbox Physics

Optics 047 · Interference, coherence, cavities, and metrology

Mach–Zehnder Sensor

An independently initialized three-dimensional apparatus connects Gas-index sensing, Thermal phase object, Balanced which-path detection. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelMach–Zehnder Sensor
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 Mach–Zehnder Sensor

BackgroundMach–Zehnder Sensor is one independently initialized apparatus with three linked investigations: Gas-index sensing, Thermal phase object, Balanced which-path detection. Its two controls—Phase difference and Arm transmission—feed the governing relation I±=I02(1±∣γ∣cos⁡Δϕ)I_{\pm}=\frac{I_0}{2}\left(1\pm|\gamma|\cos\Delta\phi\right). The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersHow do complementary outputs separate phase, absorption, and which-path information?

Start with the essentials

Focus question
How do complementary outputs separate phase, absorption, and which-path information?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from I±=I02(1±∣γ∣cos⁡Δϕ)I_{\pm}=\frac{I_0}{2}\left(1\pm|\gamma|\cos\Delta\phi\right). 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

I±=I02(1±∣γ∣cos⁡Δϕ)I_{\pm}=\frac{I_0}{2}\left(1\pm|\gamma|\cos\Delta\phi\right)

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: Gas-index sensing

    Select Gas-index sensing. Sweep Phase difference, hold Arm transmission 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: Thermal phase object

    Select Thermal phase object. Sweep Phase difference, hold Arm transmission 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: Balanced which-path detection

    Select Balanced which-path detection. Sweep Phase difference, hold Arm transmission 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.