Calculator
Choose a model, enter parameters, then calculate.
Formula used
Thermal equilibrium (two-level)
The population ratio follows the Boltzmann distribution:
N₂/N₁ = (g₂/g₁)·exp(−ΔE/(kᵦT))
With total population N, we use N₂ = N·r/(1+r) and N₁ = N/(1+r), where r = N₂/N₁.
Pumped steady-state (rate estimate)
A simple steady-state estimate with pump rate Wₚ and upper-state lifetime τ₂:
N₂ = N·(Wₚτ₂)/(1+Wₚτ₂)
We test inversion per sublevel using (N₂/g₂) − (N₁/g₁). Inversion is achieved when this value is positive.
How to use this calculator
- Select a model: thermal equilibrium or pumped steady state.
- Enter degeneracies g₁ and g₂, plus total population N.
- Thermal mode: enter temperature and an energy gap input.
- Pumped mode: enter pump rate Wₚ and lifetime τ₂.
- Click Calculate. Results appear above the form.
- Use CSV for spreadsheets and PDF for reports.
Example data table
| Model | Key inputs | Typical outcome |
|---|---|---|
| Thermal | T = 300 K, ΔE = 1.2 eV, g₁=g₂=1, N=1×10²⁰ | N₂ ≪ N₁; inversion not achieved. |
| Pumped | Wₚ = 2000 s⁻¹, τ₂ = 0.001 s, g₁=g₂=1, N=1×10²⁰ | Wₚτ₂ = 2; inversion achieved. |
| Pumped | Wₚ = 200 s⁻¹, τ₂ = 0.001 s, g₁=g₂=1, N=1×10²⁰ | Wₚτ₂ = 0.2; no inversion. |