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Sandbox Physics

Optics 089 · Waveguides, structured light, and modern optics

Beam Shift Microscope

An independently initialized three-dimensional apparatus connects Goos–Hänchen shift, Imbert–Fedorov shift, Spin-dependent amplification. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelBeam Shift Microscope
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 Beam Shift Microscope

BackgroundBeam Shift Microscope is one independently initialized apparatus with three linked investigations: Goos–Hänchen shift, Imbert–Fedorov shift, Spin-dependent amplification. Its two controls—Incident angle and Beam waist—feed the governing relation ΔGH≈−∂ϕr∂k∥\Delta_{\mathrm{GH}}\approx-\frac{\partial\phi_r}{\partial k_\parallel}. 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 finite beam width and polarization reveal tiny longitudinal and transverse interface shifts?

Start with the essentials

Focus question
How do finite beam width and polarization reveal tiny longitudinal and transverse interface shifts?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from ΔGH≈−∂ϕr∂k∥\Delta_{\mathrm{GH}}\approx-\frac{\partial\phi_r}{\partial k_\parallel}. 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

ΔGH≈−∂ϕr∂k∥\Delta_{\mathrm{GH}}\approx-\frac{\partial\phi_r}{\partial k_\parallel}

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: Goos–Hänchen shift

    Select Goos–Hänchen shift. Sweep Incident angle, hold Beam waist 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: Imbert–Fedorov shift

    Select Imbert–Fedorov shift. Sweep Incident angle, hold Beam waist 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: Spin-dependent amplification

    Select Spin-dependent amplification. Sweep Incident angle, hold Beam waist 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.