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Sandbox Physics

Optics 101 · How lasers are generated and controlled

Absorption, Spontaneous & Stimulated Emission

An independently initialized three-dimensional apparatus connects Absorption events, Spontaneous emission, Stimulated coherent copies. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelAbsorption, Spontaneous & Stimulated Emission
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 Absorption, Spontaneous & Stimulated Emission

BackgroundAbsorption, Spontaneous & Stimulated Emission is one independently initialized apparatus with three linked investigations: Absorption events, Spontaneous emission, Stimulated coherent copies. Its two controls—Radiation density and Spontaneous rate—feed the governing relation dN2dt=B12ρN1−(A21+B21ρ)N2\frac{\mathrm dN_2}{\mathrm dt}=B_{12}\rho N_1-\left(A_{21}+B_{21}\rho\right)N_2. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersWhen does resonant light cause net absorption, random emission, or coherent amplification?

Start with the essentials

Focus question
When does resonant light cause net absorption, random emission, or coherent amplification?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from dN2dt=B12ρN1−(A21+B21ρ)N2\frac{\mathrm dN_2}{\mathrm dt}=B_{12}\rho N_1-\left(A_{21}+B_{21}\rho\right)N_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

dN2dt=B12ρN1−(A21+B21ρ)N2\frac{\mathrm dN_2}{\mathrm dt}=B_{12}\rho N_1-\left(A_{21}+B_{21}\rho\right)N_2

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: Absorption events

    Select Absorption events. Sweep Radiation density, hold Spontaneous rate 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: Spontaneous emission

    Select Spontaneous emission. Sweep Radiation density, hold Spontaneous rate 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: Stimulated coherent copies

    Select Stimulated coherent copies. Sweep Radiation density, hold Spontaneous rate 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.